https://formula1.wiki/api.php?action=feedcontributions&feedformat=atom&user=Formula
Formula One Wiki - User contributions [en]
2026-04-17T01:03:19Z
User contributions
MediaWiki 1.41.1
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=275
MediaWiki:Common.css
2025-10-10T14:58:47Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* Global variables (use the EXACT family names exposed by the kit CSS) */<br />
:root{<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% */<br />
--outline-colour: #000;<br />
}<br />
<br />
/* Default = Myriad Pro for non-prominent text */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel,<br />
#p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
-webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; /* no outline on body text */<br />
}<br />
<br />
/* Prominent elements = Century Gothic + 0.35% outline */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
/* Outline */<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
/* Keep code/math monospace and un-outlined */<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=274
MediaWiki:Common.css
2025-10-10T14:57:34Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* --- Weights you want --- */<br />
:root{<br />
--body-regular: 400; /* paragraphs */<br />
--body-strong: 600; /* stronger than before (was 500) */<br />
--ui-strong: 700; /* optional: for menus/nav if needed */<br />
}<br />
<br />
/* Body text defaults (Myriad Pro) */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, small, td, th, caption, dt, dd {<br />
font-weight: var(--body-regular);<br />
/* IMPORTANT:<br />
If your Adobe kit DOES include 600, keep synthesis off.<br />
If it DOESN'T include 600 yet, temporarily allow weight synthesis<br />
(remove the next line or set to 'weight') to get visible bold. */<br />
font-synthesis: none;<br />
}<br />
<br />
/* Bold in normal context */<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong,<br />
p b, p strong, li b, li strong, td b, td strong, th b, th strong {<br />
font-weight: var(--body-strong) !important;<br />
}<br />
<br />
/* Optional: make UI labels punchier than body bold */<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading,<br />
#p-personal .vector-menu-heading,<br />
.vector-menu-content .selected > a {<br />
font-weight: var(--ui-strong) !important;<br />
}<br />
<br />
/* Keep headings (Century Gothic + outline) as you already set */<br />
<br />
@supports (font-variation-settings: normal) {<br />
html, body, .mw-body, .mw-parser-output, .vector-body {<br />
font-variation-settings: "wght" 430; /* comfy regular */<br />
}<br />
b, strong, .mw-parser-output b, .mw-parser-output strong {<br />
font-variation-settings: "wght" 575; /* solid bold without going chunky */<br />
font-weight: 600; /* fallback */<br />
}<br />
/* Optional UI emphasis */<br />
#mw-panel .vector-menu-heading, .vector-menu-heading {<br />
font-variation-settings: "wght" 640;<br />
font-weight: 700; /* fallback */<br />
}<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=273
MediaWiki:Common.css
2025-10-10T14:51:36Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
:root{<br />
/* Exact family names as exposed by your Adobe kit CSS */<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% outline for prominent text */<br />
--outline-colour: #000;<br />
<br />
/* Weights (tune these) */<br />
--body-regular: 400; /* normal paragraphs */<br />
--body-strong: 500; /* lighter-than-bold for <b>/<strong> */<br />
/* If your kit lacks 500/Medium, change this to 600 (Semibold) */<br />
}<br />
<br />
/* Body text uses Myriad Pro, with no fake bold/italic */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel, #p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
font-weight: var(--body-regular);<br />
font-synthesis: none; /* avoid browser-synthesised bold/italic looking chunky */<br />
}<br />
<br />
/* Make bold in normal context lighter than 700 */<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong,<br />
td b, td strong, th b, th strong, li b, li strong, p b, p strong {<br />
font-weight: var(--body-strong) !important;<br />
}<br />
<br />
/* Page title & section headings */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}<br />
<br />
@supports (font-variation-settings: normal) {<br />
html, body, .mw-body, .mw-parser-output, .vector-body { <br />
font-variation-settings: "wght" 440; /* comfy body weight */<br />
}<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong { <br />
font-variation-settings: "wght" 600; /* lighter-than-700 bold */<br />
}<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=272
MediaWiki:Common.css
2025-10-10T14:50:15Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
:root{<br />
/* Exact family names as exposed by your Adobe kit CSS */<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% outline for prominent text */<br />
--outline-colour: #000;<br />
<br />
/* Weights (tune these) */<br />
--body-regular: 400; /* normal paragraphs */<br />
--body-strong: 600; /* lighter-than-bold for <b>/<strong> */<br />
/* If your kit lacks 500/Medium, change this to 600 (Semibold) */<br />
}<br />
<br />
/* Body text uses Myriad Pro, with no fake bold/italic */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel, #p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
font-weight: var(--body-regular);<br />
font-synthesis: none; /* avoid browser-synthesised bold/italic looking chunky */<br />
}<br />
<br />
/* Make bold in normal context lighter than 700 */<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong,<br />
td b, td strong, th b, th strong, li b, li strong, p b, p strong {<br />
font-weight: var(--body-strong) !important;<br />
}<br />
<br />
/* Page title & section headings */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}<br />
<br />
@supports (font-variation-settings: normal) {<br />
html, body, .mw-body, .mw-parser-output, .vector-body { <br />
font-variation-settings: "wght" 440; /* comfy body weight */<br />
}<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong { <br />
font-variation-settings: "wght" 560; /* lighter-than-700 bold */<br />
}<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=271
MediaWiki:Common.css
2025-10-10T14:49:24Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
:root{<br />
/* Exact family names as exposed by your Adobe kit CSS */<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% outline for prominent text */<br />
--outline-colour: #000;<br />
<br />
/* Weights (tune these) */<br />
--body-regular: 400; /* normal paragraphs */<br />
--body-strong: 500; /* lighter-than-bold for <b>/<strong> */<br />
/* If your kit lacks 500/Medium, change this to 600 (Semibold) */<br />
}<br />
<br />
/* Body text uses Myriad Pro, with no fake bold/italic */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel, #p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
font-weight: var(--body-regular);<br />
font-synthesis: none; /* avoid browser-synthesised bold/italic looking chunky */<br />
}<br />
<br />
/* Make bold in normal context lighter than 700 */<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong,<br />
td b, td strong, th b, th strong, li b, li strong, p b, p strong {<br />
font-weight: var(--body-strong) !important;<br />
}<br />
<br />
/* Page title & section headings */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}<br />
<br />
@supports (font-variation-settings: normal) {<br />
html, body, .mw-body, .mw-parser-output, .vector-body { <br />
font-variation-settings: "wght" 440; /* comfy body weight */<br />
}<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong { <br />
font-variation-settings: "wght" 560; /* lighter-than-700 bold */<br />
}<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=270
MediaWiki:Common.css
2025-10-10T14:48:16Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* 1) Load your Adobe Fonts kit (must include Century Gothic + Myriad Pro) */<br />
<br />
/* 2) Global variables (use the EXACT family names exposed by your kit CSS) */<br />
:root{<br />
/* Exact family names as exposed by your Adobe kit CSS */<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% outline for prominent text */<br />
--outline-colour: #000;<br />
<br />
/* Weights (tune these) */<br />
--body-regular: 400; /* normal paragraphs */<br />
--body-strong: 500; /* lighter-than-bold for <b>/<strong> */<br />
/* If your kit lacks 500/Medium, change this to 600 (Semibold) */<br />
}<br />
<br />
/* 3) Default = Myriad Pro for non-prominent text */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel,<br />
#p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
-webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; /* no outline on body text */<br />
}<br />
<br />
/* 4) Prominent elements = Century Gothic + 0.35% outline */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
/* Outline */<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
/* 5) Keep code/math monospace and un-outlined */<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}<br />
<br />
@supports (font-variation-settings: normal) {<br />
html, body, .mw-body, .mw-parser-output, .vector-body { <br />
font-variation-settings: "wght" 440; /* comfy body weight */<br />
}<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong { <br />
font-variation-settings: "wght" 560; /* lighter-than-700 bold */<br />
}<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=269
MediaWiki:Common.css
2025-10-10T14:47:15Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* 1) Load your Adobe Fonts kit (must include Century Gothic + Myriad Pro) */<br />
<br />
/* 2) Global variables (use the EXACT family names exposed by your kit CSS) */<br />
:root{<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% */<br />
--outline-colour: #000;<br />
}<br />
<br />
/* 3) Default = Myriad Pro for non-prominent text */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel,<br />
#p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
-webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; /* no outline on body text */<br />
}<br />
<br />
/* 4) Prominent elements = Century Gothic + 0.35% outline */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
/* Outline */<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
/* 5) Keep code/math monospace and un-outlined */<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}<br />
<br />
@supports (font-variation-settings: normal) {<br />
html, body, .mw-body, .mw-parser-output, .vector-body { <br />
font-variation-settings: "wght" 440; /* comfy body weight */<br />
}<br />
b, strong,<br />
.mw-parser-output b, .mw-parser-output strong { <br />
font-variation-settings: "wght" 560; /* lighter-than-700 bold */<br />
}<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=268
MediaWiki:Common.css
2025-10-10T14:44:41Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/bus4qvu.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* 1) Load your Adobe Fonts kit (must include Century Gothic + Myriad Pro) */<br />
<br />
/* 2) Global variables (use the EXACT family names exposed by your kit CSS) */<br />
:root{<br />
--font-prominent: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--font-body: "myriad-pro", "Myriad Pro", "Myriad", "Segoe UI", "Helvetica Neue", Arial, sans-serif;<br />
<br />
--outline-size: 0.0035em; /* 0.35% */<br />
--outline-colour: #000;<br />
}<br />
<br />
/* 3) Default = Myriad Pro for non-prominent text */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl,<br />
p, li, a, span, strong, em, small, td, th, caption, dt, dd,<br />
.vector-menu-content, .mw-portlet, #mw-panel,<br />
#p-personal, #mw-head,<br />
input, button, select, textarea {<br />
font-family: var(--font-body) !important;<br />
-webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; /* no outline on body text */<br />
}<br />
<br />
/* 4) Prominent elements = Century Gothic + 0.35% outline */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading {<br />
font-family: var(--font-prominent) !important;<br />
<br />
/* Outline */<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback for outline */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
/* 5) Keep code/math monospace and un-outlined */<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=267
MediaWiki:Common.css
2025-10-10T14:39:17Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
:root{<br />
/* Exact family name first if your kit exposes it (often "century-gothic") */<br />
--cg-stack: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--outline-size: 0.0035em; /* 0.35% of font size */<br />
--outline-colour: #000;<br />
}<br />
<br />
/* Core content + interface */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl, p, li, td, th, caption,<br />
h1, h2, h3, h4, h5, h6, #mw-head, #mw-panel, .vector-menu-content,<br />
#p-personal, .mw-portlet, .vector-feature-zebra-design .vector-body,<br />
input, button, select, textarea {<br />
font-family: var(--cg-stack) !important;<br />
}<br />
<br />
/* Page titles & section headings */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading,<br />
.mw-headline,<br />
#mw-panel .vector-menu-heading,<br />
.vector-menu-heading,<br />
#p-personal .vector-menu-heading {<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
/* Firefox fallback */<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=266
MediaWiki:Common.css
2025-10-10T14:38:31Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
:root{<br />
/* Exact family name first if your kit exposes it (often "century-gothic") */<br />
--cg-stack: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--outline-size: 0.0035em; /* 0.35% of font size */<br />
--outline-colour: #000;<br />
}<br />
<br />
/* Core content + interface */<br />
html, body, .mw-body, .mw-parser-output, .vector-body,<br />
.mw-content-ltr, .mw-content-rtl, p, li, td, th, caption,<br />
h1, h2, h3, h4, h5, h6, #mw-head, #mw-panel, .vector-menu-content,<br />
#p-personal, .mw-portlet, .vector-feature-zebra-design .vector-body,<br />
input, button, select, textarea {<br />
font-family: var(--cg-stack) !important;<br />
}<br />
<br />
/* Site-wide outline, excluding code/math/SVG/controls */<br />
:where(body) :where(<br />
p, li, a, span, div, strong, em, small, b, i,<br />
h1, h2, h3, h4, h5, h6, td, th, caption, dt, dd,<br />
.vector-menu-heading, .mw-headline, .mw-portlet, .vector-menu-content<br />
):not(pre):not(code):not(kbd):not(samp):not(tt)<br />
:not(.mw-code):not(.mw-highlight):not(.mwe-math-element)<br />
:not(svg):not(input):not(select):not(textarea):not(button) {<br />
-webkit-text-stroke: var(--outline-size) var(--outline-colour);<br />
text-stroke: var(--outline-size) var(--outline-colour);<br />
-webkit-text-fill-color: currentColor;<br />
text-shadow:<br />
var(--outline-size) 0 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) 0 0 var(--outline-colour),<br />
0 var(--outline-size) 0 var(--outline-colour),<br />
0 calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
var(--outline-size) var(--outline-size) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) var(--outline-size) 0 var(--outline-colour),<br />
var(--outline-size) calc(-1 * var(--outline-size)) 0 var(--outline-colour),<br />
calc(-1 * var(--outline-size)) calc(-1 * var(--outline-size)) 0 var(--outline-colour);<br />
}<br />
<br />
pre, code, kbd, samp, tt, .mw-code, .mw-highlight, .mwe-math-element {<br />
-webkit-text-stroke: 0 !important;<br />
text-stroke: 0 !important;<br />
text-shadow: none !important;<br />
font-family: ui-monospace, SFMono-Regular, Menlo, Monaco, Consolas, "Liberation Mono", "Courier New", monospace !important;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=265
MediaWiki:Common.css
2025-10-10T14:34:35Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* === Global Century Gothic + bold page title (Vector 2022 & legacy) === */<br />
<br />
/* (Optional) If you use Adobe Fonts, keep this import and swap to your kit URL. */<br />
<br />
/* 1) Config */<br />
:root {<br />
/* Put the EXACT Adobe family first if using a kit (often "century-gothic"). */<br />
--wiki-font: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
<br />
/* Title look */<br />
--title-weight: 700; /* make the title actually bold */<br />
--title-stroke: 0.0035em; /* 1% outline – beefier than 0.35% */<br />
--title-stroke-colour: #000000;<br />
}<br />
<br />
/* Dark mode contrast */<br />
@media (prefers-color-scheme: dark) {<br />
:root { --title-stroke-colour: rgba(255,255,255,0.85); }<br />
}<br />
<br />
/* 2) Set the font site-wide (content, nav, menus, tables, forms) */<br />
html, body,<br />
.mw-body, .mw-parser-output, .vector-body,<br />
.vector-header, .vector-toc, .vector-menu, #mw-panel, /* legacy Vector side panel */<br />
.mw-headline, p, li, td, th, caption,<br />
h1, h2, h3, h4, h5, h6,<br />
input, textarea, select, button, .mw-ui-button {<br />
font-family: var(--wiki-font) !important;<br />
-webkit-font-smoothing: antialiased;<br />
-moz-osx-font-smoothing: grayscale;<br />
}<br />
<br />
/* 3) Page title styling (works for Vector 2022 & legacy) */<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
font-weight: var(--title-weight) !important;<br />
line-height: 1.15;<br />
letter-spacing: 0;<br />
}<br />
<br />
/* Real stroke where supported */<br />
@supports (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
-webkit-text-stroke: var(--title-stroke) var(--title-stroke-colour);<br />
text-stroke: var(--title-stroke) var(--title-stroke-colour);<br />
-webkit-text-fill-color: currentColor; /* keep normal fill */<br />
text-shadow: none; /* avoid double effect */<br />
}<br />
}<br />
<br />
/* Firefox fallback (simulate stroke with shadows) */<br />
@supports not (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
text-shadow:<br />
var(--title-stroke) 0 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) 0 0 var(--title-stroke-colour),<br />
0 var(--title-stroke) 0 var(--title-stroke-colour),<br />
0 calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour),<br />
var(--title-stroke) var(--title-stroke) 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) var(--title-stroke) 0 var(--title-stroke-colour),<br />
var(--title-stroke) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour);<br />
}<br />
}<br />
<br />
/* Keep subtitles clean */<br />
#siteSub, .subtitle { -webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; }</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=264
MediaWiki:Common.css
2025-10-10T14:34:16Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* === Global Century Gothic + bold page title (Vector 2022 & legacy) === */<br />
<br />
/* (Optional) If you use Adobe Fonts, keep this import and swap to your kit URL. */<br />
<br />
/* 1) Config */<br />
:root {<br />
/* Put the EXACT Adobe family first if using a kit (often "century-gothic"). */<br />
--wiki-font: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
<br />
/* Title look */<br />
--title-weight: 700; /* make the title actually bold */<br />
--title-stroke: 0.0035em; /* 1% outline – beefier than 0.35% */<br />
--title-stroke-colour: #000;<br />
}<br />
<br />
/* Dark mode contrast */<br />
@media (prefers-color-scheme: dark) {<br />
:root { --title-stroke-colour: rgba(255,255,255,0.85); }<br />
}<br />
<br />
/* 2) Set the font site-wide (content, nav, menus, tables, forms) */<br />
html, body,<br />
.mw-body, .mw-parser-output, .vector-body,<br />
.vector-header, .vector-toc, .vector-menu, #mw-panel, /* legacy Vector side panel */<br />
.mw-headline, p, li, td, th, caption,<br />
h1, h2, h3, h4, h5, h6,<br />
input, textarea, select, button, .mw-ui-button {<br />
font-family: var(--wiki-font) !important;<br />
-webkit-font-smoothing: antialiased;<br />
-moz-osx-font-smoothing: grayscale;<br />
}<br />
<br />
/* 3) Page title styling (works for Vector 2022 & legacy) */<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
font-weight: var(--title-weight) !important;<br />
line-height: 1.15;<br />
letter-spacing: 0;<br />
}<br />
<br />
/* Real stroke where supported */<br />
@supports (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
-webkit-text-stroke: var(--title-stroke) var(--title-stroke-colour);<br />
text-stroke: var(--title-stroke) var(--title-stroke-colour);<br />
-webkit-text-fill-color: currentColor; /* keep normal fill */<br />
text-shadow: none; /* avoid double effect */<br />
}<br />
}<br />
<br />
/* Firefox fallback (simulate stroke with shadows) */<br />
@supports not (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
text-shadow:<br />
var(--title-stroke) 0 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) 0 0 var(--title-stroke-colour),<br />
0 var(--title-stroke) 0 var(--title-stroke-colour),<br />
0 calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour),<br />
var(--title-stroke) var(--title-stroke) 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) var(--title-stroke) 0 var(--title-stroke-colour),<br />
var(--title-stroke) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour);<br />
}<br />
}<br />
<br />
/* Keep subtitles clean */<br />
#siteSub, .subtitle { -webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; }</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=263
MediaWiki:Common.css
2025-10-10T14:33:47Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* === Global Century Gothic + bold page title (Vector 2022 & legacy) === */<br />
<br />
/* (Optional) If you use Adobe Fonts, keep this import and swap to your kit URL. */<br />
<br />
/* 1) Config */<br />
:root {<br />
/* Put the EXACT Adobe family first if using a kit (often "century-gothic"). */<br />
--wiki-font: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
<br />
/* Title look */<br />
--title-weight: 700; /* make the title actually bold */<br />
--title-stroke: 0.01em; /* 1% outline – beefier than 0.35% */<br />
--title-stroke-colour: #000;<br />
}<br />
<br />
/* Dark mode contrast */<br />
@media (prefers-color-scheme: dark) {<br />
:root { --title-stroke-colour: rgba(255,255,255,0.85); }<br />
}<br />
<br />
/* 2) Set the font site-wide (content, nav, menus, tables, forms) */<br />
html, body,<br />
.mw-body, .mw-parser-output, .vector-body,<br />
.vector-header, .vector-toc, .vector-menu, #mw-panel, /* legacy Vector side panel */<br />
.mw-headline, p, li, td, th, caption,<br />
h1, h2, h3, h4, h5, h6,<br />
input, textarea, select, button, .mw-ui-button {<br />
font-family: var(--wiki-font) !important;<br />
-webkit-font-smoothing: antialiased;<br />
-moz-osx-font-smoothing: grayscale;<br />
}<br />
<br />
/* 3) Page title styling (works for Vector 2022 & legacy) */<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
font-weight: var(--title-weight) !important;<br />
line-height: 1.15;<br />
letter-spacing: 0;<br />
}<br />
<br />
/* Real stroke where supported */<br />
@supports (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
-webkit-text-stroke: var(--title-stroke) var(--title-stroke-colour);<br />
text-stroke: var(--title-stroke) var(--title-stroke-colour);<br />
-webkit-text-fill-color: currentColor; /* keep normal fill */<br />
text-shadow: none; /* avoid double effect */<br />
}<br />
}<br />
<br />
/* Firefox fallback (simulate stroke with shadows) */<br />
@supports not (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
text-shadow:<br />
var(--title-stroke) 0 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) 0 0 var(--title-stroke-colour),<br />
0 var(--title-stroke) 0 var(--title-stroke-colour),<br />
0 calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour),<br />
var(--title-stroke) var(--title-stroke) 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) var(--title-stroke) 0 var(--title-stroke-colour),<br />
var(--title-stroke) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour),<br />
calc(-1 * var(--title-stroke)) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-colour);<br />
}<br />
}<br />
<br />
/* Keep subtitles clean */<br />
#siteSub, .subtitle { -webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; }</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=262
MediaWiki:Common.css
2025-10-10T14:31:09Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* ===== Century Gothic page title with 0.35% outline ===== */<br />
:root{<br />
/* If you use an Adobe Fonts kit, replace "century-gothic" below with the EXACT family name from your kit CSS */<br />
--cg-stack: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--title-outline: 0.0035em; /* 0.35% of font-size */<br />
--title-outline-colour: #000; /* outline colour */<br />
}<br />
<br />
/* Vector 2022 and legacy skins */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading {<br />
font-family: var(--cg-stack) !important;<br />
<br />
/* WebKit/Chromium stroke */<br />
-webkit-text-stroke: var(--title-outline) var(--title-outline-colour);<br />
text-stroke: var(--title-outline) var(--title-outline-colour); /* future-friendly */<br />
<br />
/* Keep the normal text colour as the fill */<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback: simulated outline via multi-direction shadows */<br />
text-shadow:<br />
calc(var(--title-outline) * 1) 0 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * -1) 0 0 var(--title-outline-colour),<br />
0 calc(var(--title-outline) * 1) 0 var(--title-outline-colour),<br />
0 calc(var(--title-outline) * -1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * 1) calc(var(--title-outline) * 1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * -1) calc(var(--title-outline) * 1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * 1) calc(var(--title-outline) * -1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * -1) calc(var(--title-outline) * -1) 0 var(--title-outline-colour);<br />
}<br />
<br />
/* Optional: make sure subtitles don't clash */<br />
#siteSub, .subtitle { text-shadow: none; -webkit-text-stroke: 0; }</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=261
MediaWiki:Common.css
2025-10-10T14:29:19Z
<p>Formula: font</p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* 1) Config */<br />
:root{<br />
/* If using Adobe Fonts: set the first item to the EXACT family name from your kit CSS<br />
(often "century-gothic"). If not, keep "Century Gothic" first to use system-installed font. */<br />
--title-font: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--title-stroke: 0.0035em; /* 0.35% of font size */<br />
--title-stroke-color: #000; /* outline colour (auto-switched in dark mode below) */<br />
}<br />
<br />
/* 2) Target page titles across common skins */<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
font-family: var(--title-font) !important;<br />
-webkit-font-smoothing: antialiased;<br />
-moz-osx-font-smoothing: grayscale;<br />
}<br />
<br />
/* 3) True stroke where supported (Chromium/Edge/Safari) */<br />
@supports (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
-webkit-text-stroke: var(--title-stroke) var(--title-stroke-color);<br />
text-stroke: var(--title-stroke) var(--title-stroke-color);<br />
-webkit-text-fill-color: currentColor; /* preserve the fill as the current text colour */<br />
text-shadow: none; /* avoid double-thick look */<br />
}<br />
}<br />
<br />
/* 4) Firefox fallback: simulate stroke with shadows */<br />
@supports not (-webkit-text-stroke: 1px black) {<br />
.mw-page-title-main,<br />
h1#firstHeading,<br />
.firstHeading {<br />
text-shadow:<br />
var(--title-stroke) 0 0 var(--title-stroke-color),<br />
calc(-1 * var(--title-stroke)) 0 0 var(--title-stroke-color),<br />
0 var(--title-stroke) 0 var(--title-stroke-color),<br />
0 calc(-1 * var(--title-stroke)) 0 var(--title-stroke-color),<br />
var(--title-stroke) var(--title-stroke) 0 var(--title-stroke-color),<br />
calc(-1 * var(--title-stroke)) var(--title-stroke) 0 var(--title-stroke-color),<br />
var(--title-stroke) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-color),<br />
calc(-1 * var(--title-stroke)) calc(-1 * var(--title-stroke)) 0 var(--title-stroke-color);<br />
}<br />
}<br />
<br />
/* 5) Dark mode: make the outline light for contrast */<br />
@media (prefers-color-scheme: dark) {<br />
:root { --title-stroke-color: rgba(255,255,255,0.85); }<br />
}<br />
<br />
/* 6) Keep subtitles clean */<br />
#siteSub, .subtitle { -webkit-text-stroke: 0; text-stroke: 0; text-shadow: none; }</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=260
MediaWiki:Common.css
2025-10-10T14:25:41Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* 1) A variable you can reuse */<br />
/* ===== Century Gothic page title with 0.35% outline ===== */<br />
:root{<br />
/* If you use an Adobe Fonts kit, replace "century-gothic" below with the EXACT family name from your kit CSS */<br />
--cg-stack: "century-gothic", "Century Gothic", "URW Gothic L", "Apple Gothic", "Avant Garde", sans-serif;<br />
--title-outline: 0.0035em; /* 0.35% of font-size */<br />
--title-outline-colour: #000; /* outline colour */<br />
}<br />
<br />
<br />
/* Vector 2022 and legacy skins */<br />
h1#firstHeading,<br />
#firstHeading .mw-page-title-main,<br />
.firstHeading {<br />
font-family: var(--cg-stack) !important;<br />
<br />
/* WebKit/Chromium stroke */<br />
-webkit-text-stroke: var(--title-outline) var(--title-outline-colour);<br />
text-stroke: var(--title-outline) var(--title-outline-colour); /* future-friendly */<br />
<br />
/* Keep the normal text colour as the fill */<br />
-webkit-text-fill-color: currentColor;<br />
<br />
/* Firefox fallback: simulated outline via multi-direction shadows */<br />
text-shadow:<br />
calc(var(--title-outline) * 1) 0 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * -1) 0 0 var(--title-outline-colour),<br />
0 calc(var(--title-outline) * 1) 0 var(--title-outline-colour),<br />
0 calc(var(--title-outline) * -1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * 1) calc(var(--title-outline) * 1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * -1) calc(var(--title-outline) * 1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * 1) calc(var(--title-outline) * -1) 0 var(--title-outline-colour),<br />
calc(var(--title-outline) * -1) calc(var(--title-outline) * -1) 0 var(--title-outline-colour);<br />
}<br />
<br />
/* Optional: make sure subtitles don't clash */<br />
#siteSub, .subtitle { text-shadow: none; -webkit-text-stroke: 0; }<br />
<br />
/* 2) Vector 2022 (new Vector) overrides */<br />
.skin-vector-2022 body,<br />
.skin-vector-2022 .mw-body,<br />
.skin-vector-2022 .vector-body,<br />
.skin-vector-2022 .mw-parser-output {<br />
font-family: var(--font-sans) !important;<br />
}<br />
<br />
/* 3) Legacy Vector / MonoBook fallbacks */<br />
.skin-vector body,<br />
.skin-vector .mw-body,<br />
.skin-monobook body,<br />
.skin-monobook .mw-body,<br />
.mw-parser-output,<br />
body,<br />
html {<br />
font-family: var(--font-sans) !important;<br />
}<br />
<br />
/* 4) Tables and headings (MW often styles these separately) */<br />
.mw-body-content,<br />
.mw-content-ltr,<br />
.mw-content-rtl,<br />
.mw-parser-output p,<br />
.mw-parser-output li,<br />
.mw-parser-output td,<br />
.mw-parser-output th,<br />
.mw-parser-output h1,<br />
.mw-parser-output h2,<br />
.mw-parser-output h3,<br />
.mw-parser-output h4,<br />
.mw-parser-output h5,<br />
.mw-parser-output h6 {<br />
font-family: var(--font-sans) !important;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=259
MediaWiki:Common.css
2025-10-10T14:19:51Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
/* 1) A variable you can reuse */<br />
:root { --font-sans: "century-gothic", "Century Gothic", "Apple Gothic", "URW Gothic L", "Avant Garde", sans-serif; }<br />
<br />
/* 2) Vector 2022 (new Vector) overrides */<br />
.skin-vector-2022 body,<br />
.skin-vector-2022 .mw-body,<br />
.skin-vector-2022 .vector-body,<br />
.skin-vector-2022 .mw-parser-output {<br />
font-family: var(--font-sans) !important;<br />
}<br />
<br />
/* 3) Legacy Vector / MonoBook fallbacks */<br />
.skin-vector body,<br />
.skin-vector .mw-body,<br />
.skin-monobook body,<br />
.skin-monobook .mw-body,<br />
.mw-parser-output,<br />
body,<br />
html {<br />
font-family: var(--font-sans) !important;<br />
}<br />
<br />
/* 4) Tables and headings (MW often styles these separately) */<br />
.mw-body-content,<br />
.mw-content-ltr,<br />
.mw-content-rtl,<br />
.mw-parser-output p,<br />
.mw-parser-output li,<br />
.mw-parser-output td,<br />
.mw-parser-output th,<br />
.mw-parser-output h1,<br />
.mw-parser-output h2,<br />
.mw-parser-output h3,<br />
.mw-parser-output h4,<br />
.mw-parser-output h5,<br />
.mw-parser-output h6 {<br />
font-family: var(--font-sans) !important;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=258
MediaWiki:Common.css
2025-10-10T14:17:15Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
<br />
.mw-content p { font-family: ‘century-gothic’; }</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=257
MediaWiki:Common.css
2025-10-10T14:16:27Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
@import url('https://use.typekit.net/oov2wcw.css');<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}<br />
<br />
<br />
body, td, th, p {<br />
font-family: "century-gothic", sans-serif;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Common.css&diff=256
MediaWiki:Common.css
2025-09-21T17:02:52Z
<p>Formula: </p>
<hr />
<div>/* CSS placed here will be applied to all skins */<br />
<br />
.skin-minerva.page-Main_Page #firstHeading {<br />
display: none;<br />
}<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Vector.css&diff=255
MediaWiki:Vector.css
2025-09-21T17:02:27Z
<p>Formula: </p>
<hr />
<div>/* All CSS here will be loaded for users of the Vector skin */</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Vector.css&diff=254
MediaWiki:Vector.css
2025-09-21T17:01:55Z
<p>Formula: Created page with "/* All CSS here will be loaded for users of the Vector skin */ /* visualClear CSS class definition for SocialProfile extension because Vector does not include the definition anymore; see https://phabricator.wikimedia.org/T328235 and https://phabricator.wikimedia.org/T287962 */ .visualClear { clear: both; }"</p>
<hr />
<div>/* All CSS here will be loaded for users of the Vector skin */<br />
<br />
/* visualClear CSS class definition for SocialProfile extension<br />
because Vector does not include the definition anymore; see<br />
https://phabricator.wikimedia.org/T328235 and <br />
https://phabricator.wikimedia.org/T287962 */<br />
.visualClear {<br />
clear: both;<br />
}</div>
Formula
https://formula1.wiki/index.php?title=MediaWiki:Sidebar&diff=148
MediaWiki:Sidebar
2025-08-07T14:24:19Z
<p>Formula: </p>
<hr />
<div><br />
* navigation<br />
** mainpage|mainpage-description<br />
** recentchanges-url|recentchanges<br />
** randompage-url|randompage<br />
** Special:Categories|Categories<br />
* SEARCH<br />
* TOOLBOX<br />
* LANGUAGES<br />
<br />
<br />
* Archives<br />
** Seasons_index|Seasons index<br />
** Grand_Prix_Archives_by_Circuit|Grand Prix by circuit<br />
** List_of_Formula_One_World_Champions|World champions<br />
** Constructors_and_engine_manufacturers|Constructors & engine suppliers<br />
<br />
* Categories<br />
** Category:Aerodynamics|Aerodynamics<br />
** Category:Power_Units|Power units<br />
** Category:Chassis_Design|Chassis design<br />
** Category:Race_Strategy|Race strategy<br />
** Category:Data_and_Telemetry|Data & telemetry<br />
** Category:Seasons|Seasons<br />
** Category:Circuits|Circuits<br />
<br />
* Research<br />
** Glossary_of_technical_terms|Technical glossary<br />
** Methodology:CFD_correlation|CFD correlation methods<br />
** K&C_Compliance_Mapping|K&C compliance mappin<br />
<br />
* External<br />
** https://www.fia.com/regulation/category/110|FIA regulations hub<br />
** https://saemobilus.sae.org/|SAE Mobilus<br />
** https://asmedigitalcollection.asme.org/|ASME Digital Collection<br />
** http://www-control.eng.cam.ac.uk/|Cambridge Control Group</div>
Formula
https://formula1.wiki/index.php?title=Glossary_of_Formula_One_technical_terms&diff=147
Glossary of Formula One technical terms
2025-08-07T14:22:20Z
<p>Formula: Created page with "__NOTOC__ This glossary provides a rigorous, academically structured definition of technical terms used in Formula One. Terms are defined in engineering and regulatory contexts, with cross-references to relevant articles. == A == ; '''Aero rake''': A sensor array used during testing to measure airflow around the car. Often mounted with pitot tubes or pressure probes. ; '''Airbox''': The intake above the driver’s head that feeds air to the engine, often integrated with..."</p>
<hr />
<div>__NOTOC__<br />
This glossary provides a rigorous, academically structured definition of technical terms used in Formula One. Terms are defined in engineering and regulatory contexts, with cross-references to relevant articles.<br />
<br />
== A ==<br />
; '''Aero rake''': A sensor array used during testing to measure airflow around the car. Often mounted with pitot tubes or pressure probes.<br />
; '''Airbox''': The intake above the driver’s head that feeds air to the engine, often integrated with the roll hoop.<br />
; '''Apex''': The innermost point of a racing line through a corner.<br />
; '''Anti-dive geometry''': Suspension design that resists compression under braking, reducing forward pitch.<br />
<br />
== B ==<br />
; '''Ballast''': Dense material (often tungsten) placed strategically to optimise weight distribution.<br />
; '''Beam wing''': A secondary horizontal aerofoil element located near the rear diffuser to condition airflow.<br />
; '''Blistering''': A type of tyre degradation where internal heat causes bubbles in the rubber.<br />
<br />
== C ==<br />
; '''Camber''': The vertical tilt of a wheel when viewed from the front. Negative camber improves lateral grip.<br />
; '''CFD (Computational Fluid Dynamics)''': Simulation method used to analyse airflow without wind tunnel testing.<br />
; '''Chassis''': The structural base of the car, typically a carbon-fibre monocoque.<br />
; '''Coanda effect''': Tendency of airflow to follow a surface contour. Used in exhaust flow manipulation.<br />
<br />
== D ==<br />
; '''Diffuser''': The expanding underfloor section at the rear, which accelerates airflow to generate downforce.<br />
; '''DRS (Drag Reduction System)''': A movable rear-wing element allowing reduced drag on straights. Regulated for activation zones only.<br />
<br />
== E ==<br />
; '''ECU (Electronic Control Unit)''': Standardised control hardware managing engine, gearbox, and hybrid systems.<br />
; '''ERS (Energy Recovery System)''': The hybrid system that recovers kinetic and thermal energy (MGU-K and MGU-H).<br />
; '''EBD (Exhaust-Blown Diffuser)''': Technique exploiting exhaust gases to seal the diffuser, banned post-2011.<br />
<br />
== F ==<br />
; '''Flat spot''': A section of tyre worn flat by a locked wheel under braking. Causes vibrations and reduced performance.<br />
; '''Floor edge vortex''': A rotating airflow generated at the floor boundary, crucial for sealing ground-effect aerodynamics.<br />
<br />
== G ==<br />
; '''Ground effect''': Aerodynamic principle using underbody airflow to create downforce through pressure differentials.<br />
; '''Gurney flap''': A small vertical lip added to a wing’s trailing edge to increase downforce.<br />
<br />
== H ==<br />
; '''Halo''': Titanium safety structure protecting the driver’s head from debris.<br />
; '''HANS device''': Head And Neck Support device reducing whiplash in impacts.<br />
<br />
== I ==<br />
; '''Inboard suspension''': Suspension components (springs/dampers) mounted inside the chassis, connected via push/pull rods.<br />
<br />
== K ==<br />
; '''KERS (Kinetic Energy Recovery System)''': Original hybrid system (2009–2013) recovering braking energy via MGU-K.<br />
<br />
== L ==<br />
; '''Load cell''': A sensor that measures force (e.g. on suspension arms or brake pedals).<br />
; '''Lift and coast''': A fuel-saving and thermal management driving technique used during races.<br />
<br />
== M ==<br />
; '''Monocoque''': Single-piece structural shell housing driver and fuel cell. Provides crash safety.<br />
; '''MGU-K''': Motor Generator Unit – Kinetic. Recovers energy under braking and redeploys it for acceleration.<br />
; '''MGU-H''': Motor Generator Unit – Heat. Recovers energy from exhaust gases (to be removed in 2026).<br />
<br />
== N ==<br />
; '''Nomex''': A fire-resistant material used in driver suits and cockpit insulation.<br />
<br />
== O ==<br />
; '''Outwash''': Aero strategy to deflect air away from tyres to reduce drag and tyre wake.<br />
<br />
== P ==<br />
; '''Parc Fermé''': The period when car setup changes are restricted. Begins post-qualifying until race start.<br />
; '''Plank''': A wooden (jabroc) strip under the car to monitor legality of ride height.<br />
; '''Power unit (PU)''': Modern F1 engine, including ICE, MGU-K, MGU-H, turbo, and control systems.<br />
<br />
== Q ==<br />
; '''Quali mode''': Engine mapping used to maximise power output during qualifying (now regulated).<br />
<br />
== R ==<br />
; '''Rake (vehicle attitude)''': The longitudinal tilt of the car. High rake increases underfloor airflow acceleration.<br />
; '''Regen''': Short for regenerative braking via MGU-K.<br />
<br />
== S ==<br />
; '''Sidepod''': Bodywork housing radiators and cooling systems.<br />
; '''Slipstream''': Reduced air pressure behind a car, reducing drag for the following car.<br />
; '''Stint''': A continuous run between pit stops.<br />
<br />
== T ==<br />
; '''Telemetry''': Wireless data transmission from car to pit wall in real-time.<br />
; '''Torque map''': Engine control settings defining torque delivery.<br />
; '''T-tray''': Front floor extension (officially 'bib') supporting plank and controlling airflow.<br />
<br />
== U ==<br />
; '''Undercut''': Pit strategy where a driver pits early to gain advantage with fresher tyres.<br />
; '''Understeer''': Condition where the front tyres lose grip before the rear, causing the car to turn less than desired.<br />
<br />
== V ==<br />
; '''Vortex generator''': Small aero device used to control flow separation and energise airflow.<br />
<br />
== W ==<br />
; '''Wake turbulence''': Chaotic air left behind a car. Modern rules aim to reduce its disruptive effect.<br />
; '''Wind tunnel''': Physical testing apparatus to measure aerodynamic forces.<br />
<br />
== Y ==<br />
; '''Yaw angle''': The rotation of the car around its vertical axis, relevant in corner entry stability.<br />
<br />
== Z ==<br />
; '''Zylon''': Ultra-strong polymer used in side-impact structures and cockpit panels.<br />
<br />
== See also ==<br />
* [[Aerodynamics]]<br />
* [[Power unit]]<br />
* [[Tyres]]<br />
* [[Chassis]]<br />
* [[Regulation evolution]]<br />
* [[Strategy modelling]]<br />
<br />
== References ==<br />
* FIA Technical Glossary</div>
Formula
https://formula1.wiki/index.php?title=Regulations_by_year&diff=139
Regulations by year
2025-08-06T07:51:26Z
<p>Formula: Created page with "This article presents an analytical history of Formula One regulation changes, focusing on their technical impact, strategic incentives, and influence on competitive balance. Changes are grouped by decade and summarised for academic reference, with formal indicators used where appropriate. == Methodology == Each regulation change is classified along three axes: * '''Domain''': Technical / Sporting / Strategic * '''Intent''': Safety / Cost / Performance convergence / Inn..."</p>
<hr />
<div>This article presents an analytical history of Formula One regulation changes, focusing on their technical impact, strategic incentives, and influence on competitive balance. Changes are grouped by decade and summarised for academic reference, with formal indicators used where appropriate.<br />
<br />
== Methodology ==<br />
Each regulation change is classified along three axes:<br />
* '''Domain''': Technical / Sporting / Strategic<br />
* '''Intent''': Safety / Cost / Performance convergence / Innovation limitation / Spectacle<br />
* '''Impact''': High (fundamentally changes race design), Medium (strategic effect), Low (operational only)<br />
<br />
== 1950s: The dawn of formula standardisation ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 1950 || 1.5L supercharged / 4.5L naturally aspirated formula defined || Technical || Standardisation || High<br />
|-<br />
| 1952 || Temporary switch to F2 regulations || Technical || Entry accessibility || High<br />
|-<br />
| 1958 || Constructors' Championship introduced || Sporting || Team recognition || Medium<br />
|}<br />
<br />
== 1960s: Aerodynamics and professionalism emerge ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 1961 || 1.5L formula enforced || Technical || Speed limitation || High<br />
|-<br />
| 1966 || 3.0L NA / 1.5L TC formula reintroduced || Technical || Power restoration || High<br />
|-<br />
| 1968 || Wings legalised || Technical || Innovation || High<br />
|}<br />
<br />
== 1970s: Safety era begins ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 1970 || Driver safety regulations introduced (fuel cells, fireproof suits) || Technical || Safety || Medium<br />
|-<br />
| 1973 || Rear wings size restrictions || Technical || Speed reduction || Medium<br />
|-<br />
| 1977 || Turbocharged engines begin to appear || Technical || Innovation || Medium<br />
|}<br />
<br />
== 1980s: Turbo war and electronic aids ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 1983 || Ground effect banned (flat floors mandated) || Technical || Safety || High<br />
|-<br />
| 1984 || Refuelling banned || Strategic || Fire risk reduction || Medium<br />
|-<br />
| 1989 || Turbo engines banned (3.5L NA) || Technical || Cost & parity || High<br />
|}<br />
<br />
== 1990s: Electronics boom and early restrictions ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 1993 || Active suspension, traction control banned || Technical || Cost reduction || High<br />
|-<br />
| 1994 || Safety overhaul post-Imola || Technical || Safety || High<br />
|-<br />
| 1998 || Narrow track + grooved tyres || Technical || Speed reduction || High<br />
|}<br />
<br />
== 2000s: Aerodynamic disruption and cost focus ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 2003 || One-lap qualifying, parc fermé rules || Sporting || Unpredictability || Medium<br />
|-<br />
| 2005 || Engine life rules (2 race weekends) || Technical || Cost || Medium<br />
|-<br />
| 2009 || Major aero revamp (wide front, narrow rear wings; DDD loophole) || Technical || Racing quality || High<br />
|}<br />
<br />
== 2010s: Hybridisation and complexity ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 2011 || DRS legalised || Strategic || Overtaking || High<br />
|-<br />
| 2014 || 1.6L V6T-H hybrids introduced || Technical || Efficiency, relevance || High<br />
|-<br />
| 2017 || Wider cars, bigger tyres || Technical || Spectacle || Medium<br />
|}<br />
<br />
== 2020s: Ground-effect renaissance and sustainability ==<br />
{| class="wikitable"<br />
! Year !! Change !! Domain !! Intent !! Impact<br />
|-<br />
| 2021 || Budget cap (~$145m) introduced || Sporting || Parity || High<br />
|-<br />
| 2022 || Ground-effect aero returns (18-inch tyres, simplified wings) || Technical || Close racing || High<br />
|-<br />
| 2024 || Revised wind tunnel / CFD allowance rules || Technical || Development equity || Medium<br />
|-<br />
| 2026 || (Planned) PU: 50/50 ICE-E split, MGU-H removed || Technical || Sustainability, cost || High<br />
|}<br />
<br />
== Impact analysis ==<br />
Using a proxy index of "regulatory disruption", we define:<br />
<br />
<math><br />
RDI = \sum_{i=1}^{n} w_i \cdot I_i<br />
</math> <br />
Where:<br />
* <math>I_i</math> ∈ {0.25, 0.5, 1.0} (Low, Medium, High)<br />
* <math>w_i</math> = domain weighting (e.g., Technical = 1.0, Strategic = 0.5, Sporting = 0.75)<br />
<br />
This index can be applied per season to compute the intensity of rule shifts and their correlation with changes in constructors’ competitive balance (e.g., standard deviation of points).<br />
<br />
== Related pages ==<br />
* [[Power unit]] — 2026 hybrid regulation details <br />
* [[Aerodynamics]] — 2009 and 2022 changes explained <br />
* [[Tyres]] — Historical evolution (grooved to slicks, rim size)<br />
<br />
== References ==<br />
<references /><br />
* FIA Technical & Sporting Regulation archives (1950–present) <br />
* Allen, J. (2016). *F1 Technical History*. Oxford University Press <br />
* Anderson, G. (2022). “Ground Effect: Past and Present.” RaceCar Engineering <br />
* Formula1.com rule summaries (per season)</div>
Formula
https://formula1.wiki/index.php?title=List_of_Formula_One_World_Champions&diff=138
List of Formula One World Champions
2025-08-06T07:47:51Z
<p>Formula: </p>
<hr />
<div>__NOTOC__<br />
== Definitions ==<br />
* '''World Drivers' Champion (WDC)''': Driver with the highest official points at season end.<br />
* '''World Constructors' Champion (WCC)''': Team with the highest official constructors’ points (awarded since 1958).<br />
<br />
== Multiple-title drivers ==<br />
{| class="wikitable sortable"<br />
! Driver !! Titles !! Title years (chronological)<br />
|-<br />
| [[Michael Schumacher]] || 7 || 1994, 1995, 2000, 2001, 2002, 2003, 2004<br />
|-<br />
| [[Lewis Hamilton]] || 7 || 2008, 2014, 2015, 2017, 2018, 2019, 2020<br />
|-<br />
| [[Juan Manuel Fangio]] || 5 || 1951, 1954, 1955, 1956, 1957<br />
|-<br />
| [[Alain Prost]] || 4 || 1985, 1986, 1989, 1993<br />
|-<br />
| [[Sebastian Vettel]] || 4 || 2010, 2011, 2012, 2013<br />
|-<br />
| [[Max Verstappen]] || 4 || 2021, 2022, 2023, 2024<br />
|-<br />
| [[Niki Lauda]] || 3 || 1975, 1977, 1984<br />
|-<br />
| [[Jackie Stewart]] || 3 || 1969, 1971, 1973<br />
|-<br />
| [[Nelson Piquet]] || 3 || 1981, 1983, 1987<br />
|-<br />
| [[Ayrton Senna]] || 3 || 1988, 1990, 1991<br />
|-<br />
| [[Jack Brabham]] || 3 || 1959, 1960, 1966<br />
|}<br />
<br />
''Note'': Two-time champions include [[Emerson Fittipaldi]], [[Graham Hill]], [[Jim Clark]], [[Mika Häkkinen]], [[Fernando Alonso]], [[Alberto Ascari]].<br />
<br />
== Most successful constructors (titles) ==<br />
{| class="wikitable sortable"<br />
! Constructor !! WCC titles !! Representative title years<br />
|-<br />
| [[Scuderia Ferrari]] || 16 || 1961, 1964, 1975–1977, 1979, 1982, 1983, 1999–2004, 2007, 2008<br />
|-<br />
| [[McLaren]] || 9 || 1974, 1984, 1985, 1988–1991, 1998<br />
|-<br />
| [[Williams]] || 9 || 1980, 1981, 1986, 1987, 1992, 1993, 1994, 1996, 1997<br />
|-<br />
| [[Mercedes-AMG Petronas F1 Team|Mercedes]] || 8 || 2014–2021<br />
|-<br />
| [[Team Lotus|Lotus]] || 7 || 1963, 1965, 1968, 1970, 1972, 1973, 1978<br />
|-<br />
| [[Red Bull Racing]] || 6 || 2010–2013, 2022, 2023<br />
|}<br />
<br />
== Recent champions (last 10 seasons) ==<br />
{| class="wikitable"<br />
! Year !! Drivers’ Champion (team) !! Constructors’ Champion<br />
|-<br />
| 2015 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2016 || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| 2017 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2018 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2019 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2020 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2021 || [[Max Verstappen]] (Red Bull) || Mercedes<br />
|-<br />
| 2022 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2023 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2024 || [[Max Verstappen]] (Red Bull) || McLaren<br />
|}<br />
<br />
== By year ==<br />
{| class="wikitable"<br />
! Year !! WDC (team) !! WCC<br />
|-<br />
| 1950 || [[Giuseppe Farina]] (Alfa Romeo) || Not awarded<br />
|-<br />
| 1951 || [[Juan Manuel Fangio]] (Alfa Romeo) || Not awarded<br />
|-<br />
| 1952 || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| 1953 || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| 1954 || [[Juan Manuel Fangio]] (Maserati/Mercedes) || Not awarded<br />
|-<br />
| 1955 || [[Juan Manuel Fangio]] (Mercedes) || Not awarded<br />
|-<br />
| 1956 || [[Juan Manuel Fangio]] (Ferrari) || Not awarded<br />
|-<br />
| 1957 || [[Juan Manuel Fangio]] (Maserati) || Not awarded<br />
|-<br />
| 1958 || [[Mike Hawthorn]] (Ferrari) || Vanwall<br />
|-<br />
| 1959 || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| 1960 || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| 1961 || [[Phil Hill]] (Ferrari) || Ferrari<br />
|-<br />
| 1962 || [[Graham Hill]] (BRM) || BRM<br />
|-<br />
| 1963 || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| 1964 || [[John Surtees]] (Ferrari) || Ferrari<br />
|-<br />
| 1965 || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| 1966 || [[Jack Brabham]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| 1967 || [[Denny Hulme]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| 1968 || [[Graham Hill]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1969 || [[Jackie Stewart]] (Matra-Ford) || Matra-Ford<br />
|-<br />
| 1970 || [[Jochen Rindt]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1971 || [[Jackie Stewart]] (Tyrrell-Ford) || Tyrrell-Ford<br />
|-<br />
| 1972 || [[Emerson Fittipaldi]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1973 || [[Jackie Stewart]] (Tyrrell-Ford) || Lotus-Ford<br />
|-<br />
| 1974 || [[Emerson Fittipaldi]] (McLaren-Ford) || McLaren-Ford<br />
|-<br />
| 1975 || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| 1976 || [[James Hunt]] (McLaren-Ford) || Ferrari<br />
|-<br />
| 1977 || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| 1978 || [[Mario Andretti]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1979 || [[Jody Scheckter]] (Ferrari) || Ferrari<br />
|-<br />
| 1980 || [[Alan Jones]] (Williams-Ford) || Williams-Ford<br />
|-<br />
| 1981 || [[Nelson Piquet]] (Brabham-Ford) || Williams<br />
|-<br />
| 1982 || [[Keke Rosberg]] (Williams-Ford) || Ferrari<br />
|-<br />
| 1983 || [[Nelson Piquet]] (Brabham-BMW) || Ferrari<br />
|-<br />
| 1984 || [[Niki Lauda]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| 1985 || [[Alain Prost]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| 1986 || [[Alain Prost]] (McLaren-TAG) || Williams-Honda<br />
|-<br />
| 1987 || [[Nelson Piquet]] (Williams-Honda) || Williams-Honda<br />
|-<br />
| 1988 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1989 || [[Alain Prost]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1990 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1991 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1992 || [[Nigel Mansell]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1993 || [[Alain Prost]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1994 || [[Michael Schumacher]] (Benetton-Ford) || Williams-Renault<br />
|-<br />
| 1995 || [[Michael Schumacher]] (Benetton-Renault) || Benetton-Renault<br />
|-<br />
| 1996 || [[Damon Hill]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1997 || [[Jacques Villeneuve]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1998 || [[Mika Häkkinen]] (McLaren-Mercedes) || McLaren-Mercedes<br />
|-<br />
| 1999 || [[Mika Häkkinen]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| 2000 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2001 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2002 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2003 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2004 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2005 || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| 2006 || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| 2007 || [[Kimi Räikkönen]] (Ferrari) || Ferrari<br />
|-<br />
| 2008 || [[Lewis Hamilton]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| 2009 || [[Jenson Button]] (Brawn-Mercedes) || Brawn<br />
|-<br />
| 2010 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2011 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2012 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2013 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2014 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2015 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2016 || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| 2017 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2018 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2019 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2020 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2021 || [[Max Verstappen]] (Red Bull-Honda) || Mercedes<br />
|-<br />
| 2022 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2023 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2024 || [[Max Verstappen]] (Red Bull) || McLaren<br />
|}<br />
</div></div>
Formula
https://formula1.wiki/index.php?title=List_of_Formula_One_World_Champions&diff=137
List of Formula One World Champions
2025-08-06T07:47:41Z
<p>Formula: </p>
<hr />
<div>__NOTOC__<br />
<br />
== Definitions ==<br />
* '''World Drivers' Champion (WDC)''': Driver with the highest official points at season end.<br />
* '''World Constructors' Champion (WCC)''': Team with the highest official constructors’ points (awarded since 1958).<br />
<br />
== Multiple-title drivers ==<br />
{| class="wikitable sortable"<br />
! Driver !! Titles !! Title years (chronological)<br />
|-<br />
| [[Michael Schumacher]] || 7 || 1994, 1995, 2000, 2001, 2002, 2003, 2004<br />
|-<br />
| [[Lewis Hamilton]] || 7 || 2008, 2014, 2015, 2017, 2018, 2019, 2020<br />
|-<br />
| [[Juan Manuel Fangio]] || 5 || 1951, 1954, 1955, 1956, 1957<br />
|-<br />
| [[Alain Prost]] || 4 || 1985, 1986, 1989, 1993<br />
|-<br />
| [[Sebastian Vettel]] || 4 || 2010, 2011, 2012, 2013<br />
|-<br />
| [[Max Verstappen]] || 4 || 2021, 2022, 2023, 2024<br />
|-<br />
| [[Niki Lauda]] || 3 || 1975, 1977, 1984<br />
|-<br />
| [[Jackie Stewart]] || 3 || 1969, 1971, 1973<br />
|-<br />
| [[Nelson Piquet]] || 3 || 1981, 1983, 1987<br />
|-<br />
| [[Ayrton Senna]] || 3 || 1988, 1990, 1991<br />
|-<br />
| [[Jack Brabham]] || 3 || 1959, 1960, 1966<br />
|}<br />
<br />
''Note'': Two-time champions include [[Emerson Fittipaldi]], [[Graham Hill]], [[Jim Clark]], [[Mika Häkkinen]], [[Fernando Alonso]], [[Alberto Ascari]].<br />
<br />
== Most successful constructors (titles) ==<br />
{| class="wikitable sortable"<br />
! Constructor !! WCC titles !! Representative title years<br />
|-<br />
| [[Scuderia Ferrari]] || 16 || 1961, 1964, 1975–1977, 1979, 1982, 1983, 1999–2004, 2007, 2008<br />
|-<br />
| [[McLaren]] || 9 || 1974, 1984, 1985, 1988–1991, 1998<br />
|-<br />
| [[Williams]] || 9 || 1980, 1981, 1986, 1987, 1992, 1993, 1994, 1996, 1997<br />
|-<br />
| [[Mercedes-AMG Petronas F1 Team|Mercedes]] || 8 || 2014–2021<br />
|-<br />
| [[Team Lotus|Lotus]] || 7 || 1963, 1965, 1968, 1970, 1972, 1973, 1978<br />
|-<br />
| [[Red Bull Racing]] || 6 || 2010–2013, 2022, 2023<br />
|}<br />
<br />
== Recent champions (last 10 seasons) ==<br />
{| class="wikitable"<br />
! Year !! Drivers’ Champion (team) !! Constructors’ Champion<br />
|-<br />
| 2015 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2016 || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| 2017 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2018 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2019 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2020 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2021 || [[Max Verstappen]] (Red Bull) || Mercedes<br />
|-<br />
| 2022 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2023 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2024 || [[Max Verstappen]] (Red Bull) || McLaren<br />
|}<br />
<br />
== By year ==<br />
{| class="wikitable"<br />
! Year !! WDC (team) !! WCC<br />
|-<br />
| 1950 || [[Giuseppe Farina]] (Alfa Romeo) || Not awarded<br />
|-<br />
| 1951 || [[Juan Manuel Fangio]] (Alfa Romeo) || Not awarded<br />
|-<br />
| 1952 || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| 1953 || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| 1954 || [[Juan Manuel Fangio]] (Maserati/Mercedes) || Not awarded<br />
|-<br />
| 1955 || [[Juan Manuel Fangio]] (Mercedes) || Not awarded<br />
|-<br />
| 1956 || [[Juan Manuel Fangio]] (Ferrari) || Not awarded<br />
|-<br />
| 1957 || [[Juan Manuel Fangio]] (Maserati) || Not awarded<br />
|-<br />
| 1958 || [[Mike Hawthorn]] (Ferrari) || Vanwall<br />
|-<br />
| 1959 || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| 1960 || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| 1961 || [[Phil Hill]] (Ferrari) || Ferrari<br />
|-<br />
| 1962 || [[Graham Hill]] (BRM) || BRM<br />
|-<br />
| 1963 || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| 1964 || [[John Surtees]] (Ferrari) || Ferrari<br />
|-<br />
| 1965 || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| 1966 || [[Jack Brabham]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| 1967 || [[Denny Hulme]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| 1968 || [[Graham Hill]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1969 || [[Jackie Stewart]] (Matra-Ford) || Matra-Ford<br />
|-<br />
| 1970 || [[Jochen Rindt]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1971 || [[Jackie Stewart]] (Tyrrell-Ford) || Tyrrell-Ford<br />
|-<br />
| 1972 || [[Emerson Fittipaldi]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1973 || [[Jackie Stewart]] (Tyrrell-Ford) || Lotus-Ford<br />
|-<br />
| 1974 || [[Emerson Fittipaldi]] (McLaren-Ford) || McLaren-Ford<br />
|-<br />
| 1975 || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| 1976 || [[James Hunt]] (McLaren-Ford) || Ferrari<br />
|-<br />
| 1977 || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| 1978 || [[Mario Andretti]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1979 || [[Jody Scheckter]] (Ferrari) || Ferrari<br />
|-<br />
| 1980 || [[Alan Jones]] (Williams-Ford) || Williams-Ford<br />
|-<br />
| 1981 || [[Nelson Piquet]] (Brabham-Ford) || Williams<br />
|-<br />
| 1982 || [[Keke Rosberg]] (Williams-Ford) || Ferrari<br />
|-<br />
| 1983 || [[Nelson Piquet]] (Brabham-BMW) || Ferrari<br />
|-<br />
| 1984 || [[Niki Lauda]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| 1985 || [[Alain Prost]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| 1986 || [[Alain Prost]] (McLaren-TAG) || Williams-Honda<br />
|-<br />
| 1987 || [[Nelson Piquet]] (Williams-Honda) || Williams-Honda<br />
|-<br />
| 1988 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1989 || [[Alain Prost]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1990 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1991 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1992 || [[Nigel Mansell]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1993 || [[Alain Prost]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1994 || [[Michael Schumacher]] (Benetton-Ford) || Williams-Renault<br />
|-<br />
| 1995 || [[Michael Schumacher]] (Benetton-Renault) || Benetton-Renault<br />
|-<br />
| 1996 || [[Damon Hill]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1997 || [[Jacques Villeneuve]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1998 || [[Mika Häkkinen]] (McLaren-Mercedes) || McLaren-Mercedes<br />
|-<br />
| 1999 || [[Mika Häkkinen]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| 2000 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2001 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2002 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2003 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2004 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2005 || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| 2006 || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| 2007 || [[Kimi Räikkönen]] (Ferrari) || Ferrari<br />
|-<br />
| 2008 || [[Lewis Hamilton]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| 2009 || [[Jenson Button]] (Brawn-Mercedes) || Brawn<br />
|-<br />
| 2010 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2011 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2012 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2013 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2014 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2015 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2016 || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| 2017 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2018 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2019 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2020 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2021 || [[Max Verstappen]] (Red Bull-Honda) || Mercedes<br />
|-<br />
| 2022 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2023 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2024 || [[Max Verstappen]] (Red Bull) || McLaren<br />
|}<br />
</div></div>
Formula
https://formula1.wiki/index.php?title=List_of_Formula_One_World_Champions&diff=136
List of Formula One World Champions
2025-08-06T07:47:26Z
<p>Formula: Created page with "= World champions (drivers & constructors) = __NOTOC__ == Definitions == * '''World Drivers' Champion (WDC)''': Driver with the highest official points at season end. * '''World Constructors' Champion (WCC)''': Team with the highest official constructors’ points (awarded since 1958). == Multiple-title drivers == {| class="wikitable sortable" ! Driver !! Titles !! Title years (chronological) |- | Michael Schumacher || 7 || 1994, 1995, 2000, 2001, 2002, 2003, 2004..."</p>
<hr />
<div>= World champions (drivers & constructors) =<br />
__NOTOC__<br />
<br />
== Definitions ==<br />
* '''World Drivers' Champion (WDC)''': Driver with the highest official points at season end.<br />
* '''World Constructors' Champion (WCC)''': Team with the highest official constructors’ points (awarded since 1958).<br />
<br />
== Multiple-title drivers ==<br />
{| class="wikitable sortable"<br />
! Driver !! Titles !! Title years (chronological)<br />
|-<br />
| [[Michael Schumacher]] || 7 || 1994, 1995, 2000, 2001, 2002, 2003, 2004<br />
|-<br />
| [[Lewis Hamilton]] || 7 || 2008, 2014, 2015, 2017, 2018, 2019, 2020<br />
|-<br />
| [[Juan Manuel Fangio]] || 5 || 1951, 1954, 1955, 1956, 1957<br />
|-<br />
| [[Alain Prost]] || 4 || 1985, 1986, 1989, 1993<br />
|-<br />
| [[Sebastian Vettel]] || 4 || 2010, 2011, 2012, 2013<br />
|-<br />
| [[Max Verstappen]] || 4 || 2021, 2022, 2023, 2024<br />
|-<br />
| [[Niki Lauda]] || 3 || 1975, 1977, 1984<br />
|-<br />
| [[Jackie Stewart]] || 3 || 1969, 1971, 1973<br />
|-<br />
| [[Nelson Piquet]] || 3 || 1981, 1983, 1987<br />
|-<br />
| [[Ayrton Senna]] || 3 || 1988, 1990, 1991<br />
|-<br />
| [[Jack Brabham]] || 3 || 1959, 1960, 1966<br />
|}<br />
<br />
''Note'': Two-time champions include [[Emerson Fittipaldi]], [[Graham Hill]], [[Jim Clark]], [[Mika Häkkinen]], [[Fernando Alonso]], [[Alberto Ascari]].<br />
<br />
== Most successful constructors (titles) ==<br />
{| class="wikitable sortable"<br />
! Constructor !! WCC titles !! Representative title years<br />
|-<br />
| [[Scuderia Ferrari]] || 16 || 1961, 1964, 1975–1977, 1979, 1982, 1983, 1999–2004, 2007, 2008<br />
|-<br />
| [[McLaren]] || 9 || 1974, 1984, 1985, 1988–1991, 1998<br />
|-<br />
| [[Williams]] || 9 || 1980, 1981, 1986, 1987, 1992, 1993, 1994, 1996, 1997<br />
|-<br />
| [[Mercedes-AMG Petronas F1 Team|Mercedes]] || 8 || 2014–2021<br />
|-<br />
| [[Team Lotus|Lotus]] || 7 || 1963, 1965, 1968, 1970, 1972, 1973, 1978<br />
|-<br />
| [[Red Bull Racing]] || 6 || 2010–2013, 2022, 2023<br />
|}<br />
<br />
== Recent champions (last 10 seasons) ==<br />
{| class="wikitable"<br />
! Year !! Drivers’ Champion (team) !! Constructors’ Champion<br />
|-<br />
| 2015 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2016 || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| 2017 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2018 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2019 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2020 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2021 || [[Max Verstappen]] (Red Bull) || Mercedes<br />
|-<br />
| 2022 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2023 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2024 || [[Max Verstappen]] (Red Bull) || McLaren<br />
|}<br />
<br />
== By year ==<br />
{| class="wikitable"<br />
! Year !! WDC (team) !! WCC<br />
|-<br />
| 1950 || [[Giuseppe Farina]] (Alfa Romeo) || Not awarded<br />
|-<br />
| 1951 || [[Juan Manuel Fangio]] (Alfa Romeo) || Not awarded<br />
|-<br />
| 1952 || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| 1953 || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| 1954 || [[Juan Manuel Fangio]] (Maserati/Mercedes) || Not awarded<br />
|-<br />
| 1955 || [[Juan Manuel Fangio]] (Mercedes) || Not awarded<br />
|-<br />
| 1956 || [[Juan Manuel Fangio]] (Ferrari) || Not awarded<br />
|-<br />
| 1957 || [[Juan Manuel Fangio]] (Maserati) || Not awarded<br />
|-<br />
| 1958 || [[Mike Hawthorn]] (Ferrari) || Vanwall<br />
|-<br />
| 1959 || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| 1960 || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| 1961 || [[Phil Hill]] (Ferrari) || Ferrari<br />
|-<br />
| 1962 || [[Graham Hill]] (BRM) || BRM<br />
|-<br />
| 1963 || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| 1964 || [[John Surtees]] (Ferrari) || Ferrari<br />
|-<br />
| 1965 || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| 1966 || [[Jack Brabham]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| 1967 || [[Denny Hulme]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| 1968 || [[Graham Hill]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1969 || [[Jackie Stewart]] (Matra-Ford) || Matra-Ford<br />
|-<br />
| 1970 || [[Jochen Rindt]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1971 || [[Jackie Stewart]] (Tyrrell-Ford) || Tyrrell-Ford<br />
|-<br />
| 1972 || [[Emerson Fittipaldi]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1973 || [[Jackie Stewart]] (Tyrrell-Ford) || Lotus-Ford<br />
|-<br />
| 1974 || [[Emerson Fittipaldi]] (McLaren-Ford) || McLaren-Ford<br />
|-<br />
| 1975 || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| 1976 || [[James Hunt]] (McLaren-Ford) || Ferrari<br />
|-<br />
| 1977 || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| 1978 || [[Mario Andretti]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| 1979 || [[Jody Scheckter]] (Ferrari) || Ferrari<br />
|-<br />
| 1980 || [[Alan Jones]] (Williams-Ford) || Williams-Ford<br />
|-<br />
| 1981 || [[Nelson Piquet]] (Brabham-Ford) || Williams<br />
|-<br />
| 1982 || [[Keke Rosberg]] (Williams-Ford) || Ferrari<br />
|-<br />
| 1983 || [[Nelson Piquet]] (Brabham-BMW) || Ferrari<br />
|-<br />
| 1984 || [[Niki Lauda]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| 1985 || [[Alain Prost]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| 1986 || [[Alain Prost]] (McLaren-TAG) || Williams-Honda<br />
|-<br />
| 1987 || [[Nelson Piquet]] (Williams-Honda) || Williams-Honda<br />
|-<br />
| 1988 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1989 || [[Alain Prost]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1990 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1991 || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| 1992 || [[Nigel Mansell]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1993 || [[Alain Prost]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1994 || [[Michael Schumacher]] (Benetton-Ford) || Williams-Renault<br />
|-<br />
| 1995 || [[Michael Schumacher]] (Benetton-Renault) || Benetton-Renault<br />
|-<br />
| 1996 || [[Damon Hill]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1997 || [[Jacques Villeneuve]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| 1998 || [[Mika Häkkinen]] (McLaren-Mercedes) || McLaren-Mercedes<br />
|-<br />
| 1999 || [[Mika Häkkinen]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| 2000 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2001 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2002 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2003 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2004 || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| 2005 || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| 2006 || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| 2007 || [[Kimi Räikkönen]] (Ferrari) || Ferrari<br />
|-<br />
| 2008 || [[Lewis Hamilton]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| 2009 || [[Jenson Button]] (Brawn-Mercedes) || Brawn<br />
|-<br />
| 2010 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2011 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2012 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2013 || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| 2014 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2015 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2016 || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| 2017 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2018 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2019 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2020 || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| 2021 || [[Max Verstappen]] (Red Bull-Honda) || Mercedes<br />
|-<br />
| 2022 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2023 || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| 2024 || [[Max Verstappen]] (Red Bull) || McLaren<br />
|}<br />
</div></div>
Formula
https://formula1.wiki/index.php?title=Seasons_index&diff=135
Seasons index
2025-08-06T07:41:15Z
<p>Formula: </p>
<hr />
<div>__NOTOC__<br />
This index lists all Formula One World Championship seasons with Drivers’ and Constructors’ Champions.<br />
<br />
{| class="wikitable sortable"<br />
! Year !! Drivers' Champion (team) !! Constructors' Champion<br />
|-<br />
| [[1950 Formula One World Championship|1950]] || [[Giuseppe Farina]] (Alfa Romeo) || Not awarded<br />
|-<br />
| [[1951 Formula One World Championship|1951]] || [[Juan Manuel Fangio]] (Alfa Romeo) || Not awarded<br />
|-<br />
| [[1952 Formula One World Championship|1952]] || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| [[1953 Formula One World Championship|1953]] || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| [[1954 Formula One World Championship|1954]] || [[Juan Manuel Fangio]] (Maserati/Mercedes) || Not awarded<br />
|-<br />
| [[1955 Formula One World Championship|1955]] || [[Juan Manuel Fangio]] (Mercedes) || Not awarded<br />
|-<br />
| [[1956 Formula One World Championship|1956]] || [[Juan Manuel Fangio]] (Ferrari) || Not awarded<br />
|-<br />
| [[1957 Formula One World Championship|1957]] || [[Juan Manuel Fangio]] (Maserati) || Not awarded<br />
|-<br />
| [[1958 Formula One World Championship|1958]] || [[Mike Hawthorn]] (Ferrari) || Vanwall<br />
|-<br />
| [[1959 Formula One World Championship|1959]] || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| [[1960 Formula One World Championship|1960]] || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| [[1961 Formula One World Championship|1961]] || [[Phil Hill]] (Ferrari) || Ferrari<br />
|-<br />
| [[1962 Formula One World Championship|1962]] || [[Graham Hill]] (BRM) || BRM<br />
|-<br />
| [[1963 Formula One World Championship|1963]] || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| [[1964 Formula One World Championship|1964]] || [[John Surtees]] (Ferrari/NART) || Ferrari<br />
|-<br />
| [[1965 Formula One World Championship|1965]] || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| [[1966 Formula One World Championship|1966]] || [[Jack Brabham]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| [[1967 Formula One World Championship|1967]] || [[Denny Hulme]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| [[1968 Formula One World Championship|1968]] || [[Graham Hill]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1969 Formula One World Championship|1969]] || [[Jackie Stewart]] (Matra-Ford) || Matra-Ford<br />
|-<br />
| [[1970 Formula One World Championship|1970]] || [[Jochen Rindt]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1971 Formula One World Championship|1971]] || [[Jackie Stewart]] (Tyrrell-Ford) || Tyrrell-Ford<br />
|-<br />
| [[1972 Formula One World Championship|1972]] || [[Emerson Fittipaldi]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1973 Formula One World Championship|1973]] || [[Jackie Stewart]] (Tyrrell-Ford) || Lotus-Ford<br />
|-<br />
| [[1974 Formula One World Championship|1974]] || [[Emerson Fittipaldi]] (McLaren-Ford) || McLaren-Ford<br />
|-<br />
| [[1975 Formula One World Championship|1975]] || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| [[1976 Formula One World Championship|1976]] || [[James Hunt]] (McLaren-Ford) || Ferrari<br />
|-<br />
| [[1977 Formula One World Championship|1977]] || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| [[1978 Formula One World Championship|1978]] || [[Mario Andretti]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1979 Formula One World Championship|1979]] || [[Jody Scheckter]] (Ferrari) || Ferrari<br />
|-<br />
| [[1980 Formula One World Championship|1980]] || [[Alan Jones]] (Williams-Ford) || Williams-Ford<br />
|-<br />
| [[1981 Formula One World Championship|1981]] || [[Nelson Piquet]] (Brabham-Ford) || Williams<br />
|-<br />
| [[1982 Formula One World Championship|1982]] || [[Keke Rosberg]] (Williams-Ford) || Ferrari<br />
|-<br />
| [[1983 Formula One World Championship|1983]] || [[Nelson Piquet]] (Brabham-BMW) || Ferrari<br />
|-<br />
| [[1984 Formula One World Championship|1984]] || [[Niki Lauda]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| [[1985 Formula One World Championship|1985]] || [[Alain Prost]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| [[1986 Formula One World Championship|1986]] || [[Alain Prost]] (McLaren-TAG) || Williams-Honda<br />
|-<br />
| [[1987 Formula One World Championship|1987]] || [[Nelson Piquet]] (Williams-Honda) || Williams-Honda<br />
|-<br />
| [[1988 Formula One World Championship|1988]] || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1989 Formula One World Championship|1989]] || [[Alain Prost]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1990 Formula One World Championship|1990]] || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1991 Formula One World Championship|1991]] || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1992 Formula One World Championship|1992]] || [[Nigel Mansell]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1993 Formula One World Championship|1993]] || [[Alain Prost]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1994 Formula One World Championship|1994]] || [[Michael Schumacher]] (Benetton-Ford) || Williams-Renault<br />
|-<br />
| [[1995 Formula One World Championship|1995]] || [[Michael Schumacher]] (Benetton-Renault) || Benetton-Renault<br />
|-<br />
| [[1996 Formula One World Championship|1996]] || [[Damon Hill]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1997 Formula One World Championship|1997]] || [[Jacques Villeneuve]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1998 Formula One World Championship|1998]] || [[Mika Häkkinen]] (McLaren-Mercedes) || McLaren-Mercedes<br />
|-<br />
| [[1999 Formula One World Championship|1999]] || [[Mika Häkkinen]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| [[2000 Formula One World Championship|2000]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2001 Formula One World Championship|2001]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2002 Formula One World Championship|2002]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2003 Formula One World Championship|2003]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2004 Formula One World Championship|2004]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2005 Formula One World Championship|2005]] || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| [[2006 Formula One World Championship|2006]] || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| [[2007 Formula One World Championship|2007]] || [[Kimi Räikkönen]] (Ferrari) || Ferrari<br />
|-<br />
| [[2008 Formula One World Championship|2008]] || [[Lewis Hamilton]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| [[2009 Formula One World Championship|2009]] || [[Jenson Button]] (Brawn-Mercedes) || Brawn<br />
|-<br />
| [[2010 Formula One World Championship|2010]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2011 Formula One World Championship|2011]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2012 Formula One World Championship|2012]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2013 Formula One World Championship|2013]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2014 Formula One World Championship|2014]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2015 Formula One World Championship|2015]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2016 Formula One World Championship|2016]] || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| [[2017 Formula One World Championship|2017]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2018 Formula One World Championship|2018]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2019 Formula One World Championship|2019]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2020 Formula One World Championship|2020]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2021 Formula One World Championship|2021]] || [[Max Verstappen]] (Red Bull-Honda) || Mercedes<br />
|-<br />
| [[2022 Formula One World Championship|2022]] || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| [[2023 Formula One World Championship|2023]] || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| [[2024 Formula One World Championship|2024]] || [[Max Verstappen]] (Red Bull) || McLaren<br />
|-<br />
| [[2025 Formula One World Championship|2025]] || TBD || TBD<br />
|}</div>
Formula
https://formula1.wiki/index.php?title=Seasons_index&diff=134
Seasons index
2025-08-06T07:40:55Z
<p>Formula: Created page with "__NOTOC__ This index lists all Formula One World Championship seasons with Drivers’ and Constructors’ Champions. {| class="wikitable sortable" ! Year !! Drivers' Champion (team) !! Constructors' Champion |- | 1950 || Giuseppe Farina (Alfa Romeo) || Not awarded |- | 1951 || Juan Manuel Fangio (Alfa Romeo) || Not awarded |- | 1952 || Alber..."</p>
<hr />
<div>__NOTOC__<br />
<br />
This index lists all Formula One World Championship seasons with Drivers’ and Constructors’ Champions.<br />
<br />
{| class="wikitable sortable"<br />
! Year !! Drivers' Champion (team) !! Constructors' Champion<br />
|-<br />
| [[1950 Formula One World Championship|1950]] || [[Giuseppe Farina]] (Alfa Romeo) || Not awarded<br />
|-<br />
| [[1951 Formula One World Championship|1951]] || [[Juan Manuel Fangio]] (Alfa Romeo) || Not awarded<br />
|-<br />
| [[1952 Formula One World Championship|1952]] || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| [[1953 Formula One World Championship|1953]] || [[Alberto Ascari]] (Ferrari) || Not awarded<br />
|-<br />
| [[1954 Formula One World Championship|1954]] || [[Juan Manuel Fangio]] (Maserati/Mercedes) || Not awarded<br />
|-<br />
| [[1955 Formula One World Championship|1955]] || [[Juan Manuel Fangio]] (Mercedes) || Not awarded<br />
|-<br />
| [[1956 Formula One World Championship|1956]] || [[Juan Manuel Fangio]] (Ferrari) || Not awarded<br />
|-<br />
| [[1957 Formula One World Championship|1957]] || [[Juan Manuel Fangio]] (Maserati) || Not awarded<br />
|-<br />
| [[1958 Formula One World Championship|1958]] || [[Mike Hawthorn]] (Ferrari) || Vanwall<br />
|-<br />
| [[1959 Formula One World Championship|1959]] || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| [[1960 Formula One World Championship|1960]] || [[Jack Brabham]] (Cooper-Climax) || Cooper-Climax<br />
|-<br />
| [[1961 Formula One World Championship|1961]] || [[Phil Hill]] (Ferrari) || Ferrari<br />
|-<br />
| [[1962 Formula One World Championship|1962]] || [[Graham Hill]] (BRM) || BRM<br />
|-<br />
| [[1963 Formula One World Championship|1963]] || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| [[1964 Formula One World Championship|1964]] || [[John Surtees]] (Ferrari/NART) || Ferrari<br />
|-<br />
| [[1965 Formula One World Championship|1965]] || [[Jim Clark]] (Lotus-Climax) || Lotus-Climax<br />
|-<br />
| [[1966 Formula One World Championship|1966]] || [[Jack Brabham]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| [[1967 Formula One World Championship|1967]] || [[Denny Hulme]] (Brabham-Repco) || Brabham-Repco<br />
|-<br />
| [[1968 Formula One World Championship|1968]] || [[Graham Hill]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1969 Formula One World Championship|1969]] || [[Jackie Stewart]] (Matra-Ford) || Matra-Ford<br />
|-<br />
| [[1970 Formula One World Championship|1970]] || [[Jochen Rindt]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1971 Formula One World Championship|1971]] || [[Jackie Stewart]] (Tyrrell-Ford) || Tyrrell-Ford<br />
|-<br />
| [[1972 Formula One World Championship|1972]] || [[Emerson Fittipaldi]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1973 Formula One World Championship|1973]] || [[Jackie Stewart]] (Tyrrell-Ford) || Lotus-Ford<br />
|-<br />
| [[1974 Formula One World Championship|1974]] || [[Emerson Fittipaldi]] (McLaren-Ford) || McLaren-Ford<br />
|-<br />
| [[1975 Formula One World Championship|1975]] || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| [[1976 Formula One World Championship|1976]] || [[James Hunt]] (McLaren-Ford) || Ferrari<br />
|-<br />
| [[1977 Formula One World Championship|1977]] || [[Niki Lauda]] (Ferrari) || Ferrari<br />
|-<br />
| [[1978 Formula One World Championship|1978]] || [[Mario Andretti]] (Lotus-Ford) || Lotus-Ford<br />
|-<br />
| [[1979 Formula One World Championship|1979]] || [[Jody Scheckter]] (Ferrari) || Ferrari<br />
|-<br />
| [[1980 Formula One World Championship|1980]] || [[Alan Jones]] (Williams-Ford) || Williams-Ford<br />
|-<br />
| [[1981 Formula One World Championship|1981]] || [[Nelson Piquet]] (Brabham-Ford) || Williams<br />
|-<br />
| [[1982 Formula One World Championship|1982]] || [[Keke Rosberg]] (Williams-Ford) || Ferrari<br />
|-<br />
| [[1983 Formula One World Championship|1983]] || [[Nelson Piquet]] (Brabham-BMW) || Ferrari<br />
|-<br />
| [[1984 Formula One World Championship|1984]] || [[Niki Lauda]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| [[1985 Formula One World Championship|1985]] || [[Alain Prost]] (McLaren-TAG) || McLaren-TAG<br />
|-<br />
| [[1986 Formula One World Championship|1986]] || [[Alain Prost]] (McLaren-TAG) || Williams-Honda<br />
|-<br />
| [[1987 Formula One World Championship|1987]] || [[Nelson Piquet]] (Williams-Honda) || Williams-Honda<br />
|-<br />
| [[1988 Formula One World Championship|1988]] || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1989 Formula One World Championship|1989]] || [[Alain Prost]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1990 Formula One World Championship|1990]] || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1991 Formula One World Championship|1991]] || [[Ayrton Senna]] (McLaren-Honda) || McLaren-Honda<br />
|-<br />
| [[1992 Formula One World Championship|1992]] || [[Nigel Mansell]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1993 Formula One World Championship|1993]] || [[Alain Prost]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1994 Formula One World Championship|1994]] || [[Michael Schumacher]] (Benetton-Ford) || Williams-Renault<br />
|-<br />
| [[1995 Formula One World Championship|1995]] || [[Michael Schumacher]] (Benetton-Renault) || Benetton-Renault<br />
|-<br />
| [[1996 Formula One World Championship|1996]] || [[Damon Hill]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1997 Formula One World Championship|1997]] || [[Jacques Villeneuve]] (Williams-Renault) || Williams-Renault<br />
|-<br />
| [[1998 Formula One World Championship|1998]] || [[Mika Häkkinen]] (McLaren-Mercedes) || McLaren-Mercedes<br />
|-<br />
| [[1999 Formula One World Championship|1999]] || [[Mika Häkkinen]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| [[2000 Formula One World Championship|2000]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2001 Formula One World Championship|2001]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2002 Formula One World Championship|2002]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2003 Formula One World Championship|2003]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2004 Formula One World Championship|2004]] || [[Michael Schumacher]] (Ferrari) || Ferrari<br />
|-<br />
| [[2005 Formula One World Championship|2005]] || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| [[2006 Formula One World Championship|2006]] || [[Fernando Alonso]] (Renault) || Renault<br />
|-<br />
| [[2007 Formula One World Championship|2007]] || [[Kimi Räikkönen]] (Ferrari) || Ferrari<br />
|-<br />
| [[2008 Formula One World Championship|2008]] || [[Lewis Hamilton]] (McLaren-Mercedes) || Ferrari<br />
|-<br />
| [[2009 Formula One World Championship|2009]] || [[Jenson Button]] (Brawn-Mercedes) || Brawn<br />
|-<br />
| [[2010 Formula One World Championship|2010]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2011 Formula One World Championship|2011]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2012 Formula One World Championship|2012]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2013 Formula One World Championship|2013]] || [[Sebastian Vettel]] (Red Bull-Renault) || Red Bull-Renault<br />
|-<br />
| [[2014 Formula One World Championship|2014]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2015 Formula One World Championship|2015]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2016 Formula One World Championship|2016]] || [[Nico Rosberg]] (Mercedes) || Mercedes<br />
|-<br />
| [[2017 Formula One World Championship|2017]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2018 Formula One World Championship|2018]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2019 Formula One World Championship|2019]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2020 Formula One World Championship|2020]] || [[Lewis Hamilton]] (Mercedes) || Mercedes<br />
|-<br />
| [[2021 Formula One World Championship|2021]] || [[Max Verstappen]] (Red Bull-Honda) || Mercedes<br />
|-<br />
| [[2022 Formula One World Championship|2022]] || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| [[2023 Formula One World Championship|2023]] || [[Max Verstappen]] (Red Bull) || Red Bull<br />
|-<br />
| [[2024 Formula One World Championship|2024]] || [[Max Verstappen]] (Red Bull) || McLaren<br />
|-<br />
| [[2025 Formula One World Championship|2025]] || TBD || TBD<br />
|}</div>
Formula
https://formula1.wiki/index.php?title=Tyres_and_degradation_models&diff=133
Tyres and degradation models
2025-08-06T07:31:23Z
<p>Formula: Created page with "This article specifies a race-engineering tyre model for Formula One: combined-slip force generation, transient build-up, thermal coupling, wear kinetics, circuit energy characterisation, and stint optimisation. Symbols follow motorsport literature; parameters are given as calibrated ranges suitable for lap-time simulation and strategy work. == Force generation (nonlinear, combined slip) == Baseline lateral force (Magic Formula representation): <math> F_y = D \sin\!\bi..."</p>
<hr />
<div>This article specifies a race-engineering tyre model for Formula One: combined-slip force generation, transient build-up, thermal coupling, wear kinetics, circuit energy characterisation, and stint optimisation. Symbols follow motorsport literature; parameters are given as calibrated ranges suitable for lap-time simulation and strategy work.<br />
<br />
== Force generation (nonlinear, combined slip) ==<br />
<br />
Baseline lateral force (Magic Formula representation):<br />
<math><br />
F_y = D \sin\!\big( C \arctan\!\big( B \alpha - E ( B \alpha - \arctan(B \alpha) ) \big) \big),<br />
</math><br />
with <math>D=\mu F_z</math>; <math>B,C,E</math> shape parameters; slip angle <math>\alpha</math>; vertical load <math>F_z</math>; peak friction <math>\mu</math>.<br />
<br />
Combined-slip admissible set (anisotropic ellipse):<br />
<math><br />
\left(\frac{F_x}{\mu_x F_z}\right)^{n} + \left(\frac{F_y}{\mu_y F_z}\right)^{n} \le 1,\quad n \in [1.6,2.2].<br />
</math><br />
<br />
Load-sensitivity (decreasing peak friction with load):<br />
<math><br />
\mu(F_z)=\mu_0 \left(\frac{F_z}{F_{z0}}\right)^{a_\mu},\quad a_\mu \in [-0.05,-0.02].<br />
</math><br />
<br />
Camber thrust (additive near-linear term for moderate camber <math>\gamma</math>):<br />
<math><br />
F_{y,\gamma}=C_\gamma\, \gamma\, F_z,\qquad F_y(\alpha,\gamma)\approx F_y(\alpha,0)+F_{y,\gamma}.<br />
</math><br />
<br />
Indicative calibrated ranges (per front/rear tyre, race trim; to be refined per event):<br />
{| class="wikitable"<br />
! Parameter !! Typical range !! Notes<br />
|-<br />
| Peak lateral friction <math>\mu</math> || 1.60–1.95 || Effective (includes compound & road); varies with temperature and wear<br />
|-<br />
| Cornering stiffness <math>C_\alpha</math> || 80–140 kN/rad || Increases with pressure & load to a limit; front < rear asymmetry common<br />
|-<br />
| Camber thrust coeff. <math>C_\gamma</math> || 2–6 kN/rad || Increases with vertical load; risk of shoulder over-temp if too high<br />
|-<br />
| Stiffness factor <math>B</math> || 8–15 1/rad || Magic-Formula fit; car- and compound-dependent<br />
|-<br />
| Shape factor <math>C</math> || 1.2–1.6 || Controls curvature to peak<br />
|-<br />
| Curvature <math>E</math> || 0.0–0.3 || Lower E → sharper peak; sensitive to wear state<br />
|}<br />
<br />
== Transient build-up and rolling losses ==<br />
<br />
Relaxation-length dynamics (distance form):<br />
<math><br />
\frac{dF_y}{ds}+\frac{1}{\lambda}F_y=\frac{C_\alpha}{\lambda}\,\alpha,\qquad \lambda \in [0.3,0.8]\ \mathrm{m}.<br />
</math><br />
<br />
Rolling resistance (per wheel) for lap-sim:<br />
<math><br />
F_{\mathrm{rr}} = C_{\mathrm{rr}} F_z,\qquad C_{\mathrm{rr}} \in [0.012,0.018],<br />
</math><br />
with temperature/wear sensitivity modelled as<br />
<math><br />
C_{\mathrm{rr}} = C_{\mathrm{rr0}} + k_T (T_c - T^{\ast}) + k_w w.<br />
</math><br />
<br />
== Thermal model (two-node surface/carcass) ==<br />
<br />
Surface <math>T_s</math> and carcass <math>T_c</math> temperatures:<br />
<math><br />
C_s \frac{dT_s}{dt} = \eta_s\, \mu\, F_z\, v\, \gamma_s - h_s A_s (T_s - T_\infty) - k_{sc}(T_s - T_c),<br />
</math><br />
<math><br />
C_c \frac{dT_c}{dt} = k_{sc}(T_s - T_c) - h_c A_c (T_c - T_\infty).<br />
</math><br />
<br />
Temperature modifiers (Gaussian around target carcass temperature <math>T^{\ast}</math>):<br />
<math><br />
\phi(T_c)=\exp\!\big(-k_\phi (T_c - T^{\ast})^2\big),\qquad<br />
\psi(T_c)=\exp\!\big(-k_\psi (T_c - T^{\ast})^2\big),<br />
</math><br />
used to scale <math>\mu</math> and <math>C_\alpha</math> respectively.<br />
<br />
== Wear and degradation kinetics ==<br />
<br />
Wear state <math>w \in [0,1]</math> (0 fresh, 1 end-of-life). Sliding-power law:<br />
<math><br />
\frac{dw}{dt}=k_w\!\left(\left|F_x v_{s,x}\right|+\left|F_y v_{s,y}\right|\right).<br />
</math><br />
<br />
Performance decay:<br />
<math><br />
\mu(w,T_c)=\mu_0 \left(1-a_w w\right)\phi(T_c),\qquad<br />
C_\alpha(w,T_c)=C_{\alpha0}\left(1-b_w w\right)\psi(T_c),<br />
</math><br />
where <math>a_w,b_w \in [0.15,0.45]</math> give typical end-of-stint losses.<br />
<br />
Failure/artefact modes: thermal fade (high <math>T_c</math>), graining (low <math>T_s</math> and high shear; reversible), blistering (subsurface; irreversible), flat-spot (lock-up; step change in <math>w</math>), pick-up (reversible after cleaning laps).<br />
<br />
== Compounds, operating windows, prescriptions ==<br />
<br />
Pirelli supplies five slick compounds (C1–C5). Three are nominated per event (H/M/S labels). Indicative (modelling) windows—replace with event notes when available:<br />
<br />
{| class="wikitable"<br />
! Compound !! Nominal grip (rel.) !! Wear rate (rel.) !! Indicative carcass window (°C) !! Typical use<br />
|-<br />
| C1 (hard) || Low || Low || 95–115 || High-energy/abrasive; long stints; hot ambient<br />
|-<br />
| C2 || Low–Med || Low–Med || 95–115 || Long stints; high-load corners<br />
|-<br />
| C3 || Med || Med || 90–110 || Baseline race compound on many tracks<br />
|-<br />
| C4 || Med–High || Med–High || 85–105 || Qualifying bias; cooler ambient; short stints<br />
|-<br />
| C5 (soft) || High || High || 85–100 || Street circuits; low energy; peak grip runs<br />
|}<br />
<br />
Prescriptions (event bulletins): minimum starting pressures (front/rear), maximum static camber (per axle), blanket rules (where allowed). These override generic models for compliance and must be enforced in setup.<br />
<br />
== Circuit energy characterisation and degradation rates ==<br />
<br />
Use a lateral/longitudinal energy index and texture/abrasion rating to forecast wear and window risk. Pirelli’s track severity scale (1–5) maps well to model priors:<br />
<br />
{| class="wikitable"<br />
! Circuit !! Track energy (1–5) !! Dominant load !! Surface & notes !! Expected stint shape (S/M/H)<br />
|-<br />
| Monaco || 1 || Low lateral; traction-limited || Smooth street; low energy || Very shallow degradation; thermal management critical at low speeds<br />
|-<br />
| Monza || 2 || Braking/traction; low lateral || Smooth; long straights || Low deg; front-tyre warm-up critical; flat-spot risk<br />
|-<br />
| Bahrain || 3–4 || Traction + braking; heat || Abrasive; hot ambient || Medium–high deg; rear thermal fade risk<br />
|-<br />
| Barcelona (Catalunya) || 4 || Sustained lateral || Medium-abrasive; long corners || Medium–high deg; front-left graining if cool<br />
|-<br />
| Silverstone || 5 || Very high lateral || Fast, high-energy || High deg; carcass temperature control is limiting<br />
|-<br />
| Suzuka || 5 || Mixed; long-radius lateral || Smooth-medium; esse complex || High deg; front-limited early, rear-limited late<br />
|-<br />
| Zandvoort || 4 || Banked lateral loading || Fresh abrasive after resurfacing || Medium–high deg; camber window tight<br />
|}<br />
<br />
Example calibrated degradation slopes (race runs, dry; representative order-of-magnitude for modelling, per compound on “medium” energy tracks):<br />
{| class="wikitable"<br />
! Compound !! Linear deg <math>d</math> (s/lap) !! Nonlinear term at end-of-stint (extra s over last 5 laps)<br />
|-<br />
| C1 || 0.010–0.020 || 0.2–0.6<br />
|-<br />
| C2 || 0.015–0.030 || 0.3–0.8<br />
|-<br />
| C3 || 0.020–0.040 || 0.5–1.2<br />
|-<br />
| C4 || 0.030–0.060 || 0.8–1.8<br />
|-<br />
| C5 || 0.040–0.080 || 1.0–2.5<br />
|}<br />
<br />
== Strategy modelling and optimal stints ==<br />
<br />
Per-lap loss including wear, thermal offset from target <math>T^{\ast}</math>, and traffic factor <math>Q_k</math>:<br />
<math><br />
\Delta t_k = \alpha_1 w_k + \alpha_2 (T_{c,k}-T^{\ast})^2 + \alpha_3 Q_k.<br />
</math><br />
<br />
Cumulative stint time to lap <math>N</math>:<br />
<math><br />
T_{\mathrm{stint}}(N)=\sum_{k=1}^{N}\!\big(t_0+\Delta t_k\big).<br />
</math><br />
<br />
Under linear degradation <math>\Delta t_k \approx d k</math> and pit loss <math>P</math>, the continuous optimum stint length is<br />
<math><br />
N^{\ast} \approx \sqrt{\frac{2P}{d}},<br />
</math><br />
useful for first-order stop count decisions. The undercut condition at lap <math>n</math>:<br />
<math><br />
\big(t(n)-t(n+1)\big)_{\mathrm{old}} \;>\; P - \big(t(n)-t(n+1)\big)_{\mathrm{new}}.<br />
</math><br />
<br />
Fuel burn-off and DRS availability couple into <math>d</math> and <math>\alpha_2</math>; safety-car or VSC resets change optimal <math>N^{\ast}</math> by reducing the opportunity cost of a stop.<br />
<br />
== Data acquisition and online identification ==<br />
<br />
Typical online state vector and measurements for estimation:<br />
<math><br />
x=\{C_\alpha,\mu,\lambda,T_s,T_c,w\},\qquad<br />
y=\{F_x,F_y,\omega,\tfrac{d\psi}{dt},a_y,T_{\mathrm{IR}}\}.<br />
</math><br />
Teams use EKF/UKF observers to update <math>x</math> in real time from wheel speed, brake temps, steering, IMU, and IR cameras; stint-end mass and vibration signatures cross-check wear <math>w</math>.<br />
<br />
== Validation workflow (practical) ==<br />
<br />
# Identify <math>B,C,D,E,C_\alpha,\lambda</math> on the tyre rig and from clean track segments.<br />
# Fit <math>C_s,C_c,h_sA_s,h_cA_c,k_{sc}</math> from controlled long-runs.<br />
# Calibrate <math>k_w</math> against abrasion metrics and compare to stint mass loss.<br />
# Close the loop in lap-sim; verify predicted vs observed stint shape, undercut thresholds, and pit δ.<br />
# Replace generic windows with event-specific Pirelli prescriptions upon bulletin release.<br />
<br />
== See also ==<br />
* [[Race strategy modelling]]<br />
* [[Lap time and delta analysis]]<br />
* [[Chassis and suspension design]]<br />
* [[Aerodynamics in Formula One]]<br />
<br />
== References ==<br />
<references /><br />
* FIA Formula One Technical Regulations (Tyres & Wheels; current season).<br />
* Pirelli Motorsport, Event Technical Notes (pressures, camber, nominations, blanket rules).<br />
* Pacejka, H., ''Tire and Vehicle Dynamics'', Elsevier.<br />
* Milliken, W. & Milliken, D., ''Race Car Vehicle Dynamics'', SAE.<br />
* Dixon, J., ''Tires, Suspension, and Handling'', SAE.<br />
* Selected SAE papers on tyre thermal/wear modelling and combined slip in racing applications.<br />
* Bosch, ''Automotive Handbook'' (combined slip, relaxation length, rolling resistance).</div>
Formula
https://formula1.wiki/index.php?title=Lap_time_and_delta_analysis&diff=132
Lap time and delta analysis
2025-08-06T07:11:21Z
<p>Formula: </p>
<hr />
<div>''Lap time analysis'' decomposes a lap into distance-aligned events and state variables (speed, longitudinal/lateral acceleration, throttle/brake, gear) to attribute time gains and losses to specific driver inputs, tyre states, aerodynamic conditions, and traffic effects. The goal is a quantitative, reproducible explanation of delta-time traces, enabling strategy and setup decisions (brake bias, aero level, tyre plan, shift maps).<br />
<br />
== Data channels and sampling ==<br />
<br />
Recommended minimum channels (100–500 Hz acquisition, 50–100 Hz processing):<br />
* Vehicle speed (km/h) and distance (m)<br />
* Longitudinal / lateral acceleration (g)<br />
* Brake pressure (bar), throttle (%), steering angle (°)<br />
* Gear, engine speed (rpm), rear-axle power estimate (kW)<br />
* GPS position (lat/lon) → projected centreline abscissa ''s'' (m)<br />
* Tyre inner/middle/outer IR (°C) where permitted<br />
* Ride heights or aero platform proxy (if available)<br />
<br />
== Distance alignment and rolling delta ==<br />
<br />
Analysis must compare laps on a common distance axis (not time) to preserve causality through braking/accel phases.<br />
<br />
'''Curvilinear abscissa (distance)'''<br />
<math><br />
s(t) \;=\; \int_{0}^{t} v(\tau)\, \mathrm{d}\tau<br />
\quad\Rightarrow\quad<br />
x(s) \text{ is any channel resampled on } s \in [0,\; L_{\mathrm{lap}}].<br />
</math><br />
<br />
'''Rolling delta (cumulative time difference)'''<br />
For two laps A (reference) and B (candidate), integrate the local time step over distance:<br />
<math><br />
\Delta T(s)<br />
\;=\;<br />
\int_{0}^{s}<br />
\left(\frac{1}{v_B(\sigma)} - \frac{1}{v_A(\sigma)}\right)\,\mathrm{d}\sigma \cdot \Delta s.<br />
</math><br />
<br />
This yields the familiar continuous “time-gain/time-loss” trace engineers use to pinpoint where a lap diverges (brake point, minimum-speed, exit). A practical workflow is: (i) compute ''s'' from GPS/speed, (ii) resample all channels on ''s'' (e.g., 1 m), (iii) form <math>\Delta T(s)</math>, (iv) annotate corner entries/apices/exits, (v) attribute deltas.<br />
<br />
== Corner phase metrics ==<br />
<br />
Define corner regions by decel/steer thresholds and apex index <math>s_{\mathrm{apex}}</math>. Report phase metrics lap-to-lap:<br />
<br />
{| class="wikitable"<br />
! Metric !! Definition (distance domain) !! Typical F1 range<br />
|-<br />
| Entry speed || <math>v(s_{\mathrm{entry}})</math> at first brake-on || 220–320 km/h<br />
|-<br />
| Minimum speed || <math>\min_{s \in \text{corner}} v(s)</math> || 60–180 km/h<br />
|-<br />
| Brake zone length || <math>s_{\mathrm{brake\,off}}-s_{\mathrm{brake\,on}}</math> || 80–160 m<br />
|-<br />
| Exit delta @150 m || <math>\Delta T(s_{\mathrm{apex}}+150\,\mathrm{m})</math> || ±0.05–0.25 s<br />
|-<br />
| Lateral peak || <math>\max a_y</math> (filtered) || 3.5–5.5 g<br />
|}<br />
<br />
== Physics back-bone (friction ellipse & power) ==<br />
<br />
Friction-ellipse constraint (per tyre) maps combined usage:<br />
<math><br />
\left(\frac{F_{x}}{\mu F_z}\right)^2 + \left(\frac{F_{y}}{\mu F_z}\right)^2 \;\le\; 1,<br />
</math><br />
so braking deep (high <math>F_x</math>) reduces available lateral <math>F_y</math> and sets the attainable entry/rotation trade-off. Longitudinal acceleration is power-limited at high speed:<br />
<math><br />
a_x \approx \frac{P_{\mathrm{drv}}}{m \, v} \;-\; \frac{D(v)}{m},<br />
\qquad<br />
D(v)=\tfrac{1}{2}\rho C_D A v^2,<br />
</math><br />
governing straight-line delta growth when one lap has higher deployment or lower drag.<br />
<br />
== Fuel and mass sensitivity ==<br />
<br />
A first-order lap-time penalty with fuel mass:<br />
<math><br />
\Delta t_{\mathrm{fuel}}(m) = k_f \, m,<br />
\qquad<br />
k_f \approx 0.030\text{–}0.040~\mathrm{s\,kg^{-1}\,lap^{-1}} \text{ (2022+ era)}.<br />
</math><br />
Use per-sector sensitivity when fuel burn is uneven (e.g., long WOT sectors).<br />
<br />
== Tyre degradation imprint on delta ==<br />
<br />
Represent compound-specific degradation as convex in age ''a'' (laps since stop):<br />
<math><br />
\Delta t_{\mathrm{deg}}(c,a) \;=\; \alpha_c\, a \;+\; \beta_c\, a^2,<br />
</math><br />
calibrated from long-run pace. A typical (illustrative) prior:<br />
<br />
{| class="wikitable"<br />
! Compound !! \alpha_c (s/lap) !! \beta_c (s/lap²) !! Nominal stint (laps)<br />
|-<br />
| C1 || 0.015 || 0.00018 || 25–35<br />
|-<br />
| C3 || 0.025 || 0.00035 || 16–24<br />
|-<br />
| C5 || 0.035 || 0.00070 || 8–15<br />
|}<br />
<br />
Tie this to carcass/bulk temperatures via a window penalty if you track IR channels.<br />
<br />
== Sector attribution (worked method) ==<br />
<br />
1) Compute <math>\Delta T(s)</math> and mark sector endpoints <math>s_k</math>. <br />
<br />
2) Sector deltas are differences of the cumulative curve: <math>\Delta T_k=\Delta T(s_k)-\Delta T(s_{k-1})</math>. <br />
<br />
3) Within a corner, split phase deltas by integrating only over the corresponding ''s'' intervals (entry / mid / exit). <br />
<br />
4) Attribute mechanisms by co-evaluating <math>v,\,a_x,\,a_y,\,\mathrm{brake},\,\mathrm{throttle}</math> traces and, where available, power and platform proxies.<br />
<br />
'''Example comparison (same car, two laps)'''<br />
<br />
{| class="wikitable"<br />
! Item !! Lap A (ref) !! Lap B !! Comment<br />
|-<br />
| T<sub>lap</sub> (s) || 88.420 || 88.205 || B faster −0.215 s<br />
|-<br />
| S1 delta (s) || – || −0.090 || Later brake, same Vmin<br />
|-<br />
| S2 delta (s) || – || −0.055 || Higher exit accel (deployment)<br />
|-<br />
| S3 delta (s) || – || −0.070 || Lower drag in final straight<br />
|-<br />
| Min speed T9 (km/h) || 146 || 144 || B slower at apex, but better exit<br />
|-<br />
| Exit delta @150 m (s) || – || −0.060 || Time gained after apex<br />
|}<br />
<br />
== Traffic/dirty air correction (optional) ==<br />
<br />
When comparing laps with different traffic states, incorporate a penalty term:<br />
<math><br />
\Delta t_{\mathrm{traffic}}(s)<br />
= \lambda\, u(s) \;-\; \eta\, z(s),<br />
</math><br />
where <math>u(s)=1</math> inside a user-defined “close-following” gap (dirty-air zone), and <math>z(s)=1</math> when DRS is active. Calibrate <math>\lambda,\eta</math> from multi-lap data (typ. 0.15–0.60 s/lap impact in prolonged following; DRS gain 0.10–0.30 s/lap depending on zones).<br />
<br />
== Statistical modelling & validation ==<br />
<br />
* Back-to-back deltas: same stint, same traffic → isolates driver inputs. <br />
* Regression on distance grid: fit <math>\Delta T(s)</math> on covariates <math>[v,a_x,a_y,\mathrm{brake},\mathrm{throttle}]</math> to quantify marginal effects. <br />
* Optimum-lap synthesis: compare observed <math>v(s)</math> to minimum-time solution (QSS/optimal control) to reveal theoretical headroom.<br />
* Tooling: most pro suites provide rolling best/“theoretical best” from micro-sectors using distance alignment.<br />
<br />
== Minimum-time benchmarks (for context) ==<br />
<br />
Quasi-steady-state (QSS) and optimal-control solvers produce reference speed/acceleration profiles under tyre-load and power limits. These are invaluable to test whether an observed delta stems from sub-optimal inputs or hard constraints (power, drag, μ). See surveys and theses for reproducible formulations and open data.<br />
<br />
== Practical checklist ==<br />
<br />
* Align on distance, not time. <br />
* Inspect <math>v(s)</math>, brake, throttle, <math>a_x,a_y</math> around every apex. <br />
* Quantify entry (brake point & decel), rotation (Vmin), exit (accel to +150 m). <br />
* Separate fuel, tyre age, deployment state, and traffic before blaming driver. <br />
* Validate conclusions against a minimum-time or “theoretical best” lap.<br />
<br />
== References ==<br />
* [https://www.fia.com/regulation/category/110 FIA Regulations Hub]<br />
* [https://www.aim-sportline.com/docs/racestudio3/manual/latex/racestudio3-manual-en-latest.pdf AiM RaceStudio 3 Manual – rolling/theoretical lap features]<br />
* [https://eprints.soton.ac.uk/417133/1/GP2manuscriptPURE_002_.pdf Dal Bianco et al. (2017): Minimum-time optimal control simulation of a GP2 race car – Univ. of Southampton]<br />
* [https://thesis.unipd.it/retrieve/8c327453-5809-425a-b416-3cfad77b5f07/Veneri_Matteo_tesi.pdf Veneri (2016): Minimum Lap Time of Race Cars – Univ. of Padova]<br />
* [https://research.tue.nl/files/318078060/1514032-Applications_of_Optimization_Methods_to_Quasi_Steady-State_Lap_Time_Simulation.pdf TU/e (2023): Optimisation methods for QSS lap-time simulation – Eindhoven]<br />
* [https://pure.tue.nl/ws/files/174109985/Borsboom.Fahdzyana.ea.TVT20.pdf Borsboom et al. (2020): Convex optimisation framework for minimum lap time – TU/e / IEEE TVT]<br />
* [https://webthesis.biblio.polito.it/20760/1/tesi.pdf Reinero (2021): QSS lap-time simulator for single-seater EV – PoliTo]<br />
* [https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/ft848x05t Oregon State (2018): Trajectory-optimised lap-time simulation – thesis]<br />
* [https://sites.usp.br/ldsv/wp-content/uploads/sites/1453/2024/07/Douglas-Bonfim-Transient_model_based_laptime_simulation_of_a_race_car-compressed.pdf Bonfim (2023): Transient model & NMPC for lap-time – USP]<br />
* [https://www.nessoft.com/ispeed/one_second_at_a_time.pdf “Getting Faster, One Second at a Time” – delta-t primer]<br />
* [https://www.yourdatadriven.com/introduction-to-motorsport-data-analysis-delta-t/ Intro to delta-t and distance alignment – article]</div>
Formula
https://formula1.wiki/index.php?title=Lap_time_and_delta_analysis&diff=131
Lap time and delta analysis
2025-08-06T07:10:12Z
<p>Formula: </p>
<hr />
<div>''Lap time analysis'' decomposes a lap into distance-aligned events and state variables (speed, longitudinal/lateral acceleration, throttle/brake, gear) to attribute time gains and losses to specific driver inputs, tyre states, aerodynamic conditions, and traffic effects. The goal is a quantitative, reproducible explanation of delta-time traces, enabling strategy and setup decisions (brake bias, aero level, tyre plan, shift maps).<br />
<br />
== Data channels and sampling ==<br />
<br />
Recommended minimum channels (100–500 Hz acquisition, 50–100 Hz processing):<br />
* Vehicle speed (km/h) and distance (m)<br />
* Longitudinal / lateral acceleration (g)<br />
* Brake pressure (bar), throttle (%), steering angle (°)<br />
* Gear, engine speed (rpm), rear-axle power estimate (kW)<br />
* GPS position (lat/lon) → projected centreline abscissa ''s'' (m)<br />
* Tyre inner/middle/outer IR (°C) where permitted<br />
* Ride heights or aero platform proxy (if available)<br />
<br />
== Distance alignment and rolling delta ==<br />
<br />
Analysis must compare laps on a common distance axis (not time) to preserve causality through braking/accel phases.<br />
<br />
'''Curvilinear abscissa (distance)'''<br />
<math><br />
s(t) \;=\; \int_{0}^{t} v(\tau)\, \mathrm{d}\tau<br />
\quad\Rightarrow\quad<br />
x(s) \text{ is any channel resampled on } s \in [0,\; L_{\mathrm{lap}}].<br />
</math><br />
<br />
'''Rolling delta (cumulative time difference)'''<br />
For two laps A (reference) and B (candidate), integrate the local time step over distance:<br />
<math><br />
\Delta T(s)<br />
\;=\;<br />
\int_{0}^{s}<br />
\left(\frac{1}{v_B(\sigma)} - \frac{1}{v_A(\sigma)}\right)\,\mathrm{d}\sigma \cdot \Delta s.<br />
</math><br />
<br />
This yields the familiar continuous “time-gain/time-loss” trace engineers use to pinpoint where a lap diverges (brake point, minimum-speed, exit). A practical workflow is: (i) compute ''s'' from GPS/speed, (ii) resample all channels on ''s'' (e.g., 1 m), (iii) form <math>\Delta T(s)</math>, (iv) annotate corner entries/apices/exits, (v) attribute deltas.<br />
<br />
== Corner phase metrics ==<br />
<br />
Define corner regions by decel/steer thresholds and apex index <math>s_{\mathrm{apex}}</math>. Report phase metrics lap-to-lap:<br />
<br />
{| class="wikitable"<br />
! Metric !! Definition (distance domain) !! Typical F1 range<br />
|-<br />
| Entry speed || <math>v(s_{\mathrm{entry}})</math> at first brake-on || 220–320 km/h<br />
|-<br />
| Minimum speed || <math>\min_{s \in \text{corner}} v(s)</math> || 60–180 km/h<br />
|-<br />
| Brake zone length || <math>s_{\mathrm{brake\,off}}-s_{\mathrm{brake\,on}}</math> || 80–160 m<br />
|-<br />
| Exit delta @150 m || <math>\Delta T(s_{\mathrm{apex}}+150\,\mathrm{m})</math> || ±0.05–0.25 s<br />
|-<br />
| Lateral peak || <math>\max a_y</math> (filtered) || 3.5–5.5 g<br />
|}<br />
<br />
== Physics back-bone (friction ellipse & power) ==<br />
<br />
Friction-ellipse constraint (per tyre) maps combined usage:<br />
<math><br />
\left(\frac{F_{x}}{\mu F_z}\right)^2 + \left(\frac{F_{y}}{\mu F_z}\right)^2 \;\le\; 1,<br />
</math><br />
so braking deep (high <math>F_x</math>) reduces available lateral <math>F_y</math> and sets the attainable entry/rotation trade-off. Longitudinal acceleration is power-limited at high speed:<br />
<math><br />
a_x \approx \frac{P_{\mathrm{drv}}}{m \, v} \;-\; \frac{D(v)}{m},<br />
\qquad<br />
D(v)=\tfrac{1}{2}\rho C_D A v^2,<br />
</math><br />
governing straight-line delta growth when one lap has higher deployment or lower drag.<br />
<br />
== Fuel and mass sensitivity ==<br />
<br />
A first-order lap-time penalty with fuel mass:<br />
<math><br />
\Delta t_{\mathrm{fuel}}(m) = k_f \, m,<br />
\qquad<br />
k_f \approx 0.030\text{–}0.040~\mathrm{s\,kg^{-1}\,lap^{-1}} \text{ (2022+ era)}.<br />
</math><br />
Use per-sector sensitivity when fuel burn is uneven (e.g., long WOT sectors).<br />
<br />
== Tyre degradation imprint on delta ==<br />
<br />
Represent compound-specific degradation as convex in age ''a'' (laps since stop):<br />
<math><br />
\Delta t_{\mathrm{deg}}(c,a) \;=\; \alpha_c\, a \;+\; \beta_c\, a^2,<br />
</math><br />
calibrated from long-run pace. A typical (illustrative) prior:<br />
<br />
{| class="wikitable"<br />
! Compound !! \alpha_c (s/lap) !! \beta_c (s/lap²) !! Nominal stint (laps)<br />
|-<br />
| C1 || 0.015 || 0.00018 || 25–35<br />
|-<br />
| C3 || 0.025 || 0.00035 || 16–24<br />
|-<br />
| C5 || 0.035 || 0.00070 || 8–15<br />
|}<br />
<br />
Tie this to carcass/bulk temperatures via a window penalty if you track IR channels.<br />
<br />
== Sector attribution (worked method) ==<br />
<br />
1) Compute <math>\Delta T(s)</math> and mark sector endpoints <math>s_k</math>. <br />
2) Sector deltas are differences of the cumulative curve: <math>\Delta T_k=\Delta T(s_k)-\Delta T(s_{k-1})</math>. <br />
3) Within a corner, split phase deltas by integrating only over the corresponding ''s'' intervals (entry / mid / exit). <br />
4) Attribute mechanisms by co-evaluating <math>v,\,a_x,\,a_y,\,\mathrm{brake},\,\mathrm{throttle}</math> traces and, where available, power and platform proxies.<br />
<br />
'''Example comparison (same car, two laps)'''<br />
<br />
{| class="wikitable"<br />
! Item !! Lap A (ref) !! Lap B !! Comment<br />
|-<br />
| T<sub>lap</sub> (s) || 88.420 || 88.205 || B faster −0.215 s<br />
|-<br />
| S1 delta (s) || – || −0.090 || Later brake, same Vmin<br />
|-<br />
| S2 delta (s) || – || −0.055 || Higher exit accel (deployment)<br />
|-<br />
| S3 delta (s) || – || −0.070 || Lower drag in final straight<br />
|-<br />
| Min speed T9 (km/h) || 146 || 144 || B slower at apex, but better exit<br />
|-<br />
| Exit delta @150 m (s) || – || −0.060 || Time gained after apex<br />
|}<br />
<br />
== Traffic/dirty air correction (optional) ==<br />
<br />
When comparing laps with different traffic states, incorporate a penalty term:<br />
<math><br />
\Delta t_{\mathrm{traffic}}(s)<br />
= \lambda\, u(s) \;-\; \eta\, z(s),<br />
</math><br />
where <math>u(s)=1</math> inside a user-defined “close-following” gap (dirty-air zone), and <math>z(s)=1</math> when DRS is active. Calibrate <math>\lambda,\eta</math> from multi-lap data (typ. 0.15–0.60 s/lap impact in prolonged following; DRS gain 0.10–0.30 s/lap depending on zones).<br />
<br />
== Statistical modelling & validation ==<br />
<br />
* Back-to-back deltas: same stint, same traffic → isolates driver inputs. <br />
* Regression on distance grid: fit <math>\Delta T(s)</math> on covariates <math>[v,a_x,a_y,\mathrm{brake},\mathrm{throttle}]</math> to quantify marginal effects. <br />
* Optimum-lap synthesis: compare observed <math>v(s)</math> to minimum-time solution (QSS/optimal control) to reveal theoretical headroom.<br />
* Tooling: most pro suites provide rolling best/“theoretical best” from micro-sectors using distance alignment.<br />
<br />
== Minimum-time benchmarks (for context) ==<br />
<br />
Quasi-steady-state (QSS) and optimal-control solvers produce reference speed/acceleration profiles under tyre-load and power limits. These are invaluable to test whether an observed delta stems from sub-optimal inputs or hard constraints (power, drag, μ). See surveys and theses for reproducible formulations and open data.<br />
<br />
== Practical checklist ==<br />
<br />
* Align on distance, not time. <br />
* Inspect <math>v(s)</math>, brake, throttle, <math>a_x,a_y</math> around every apex. <br />
* Quantify entry (brake point & decel), rotation (Vmin), exit (accel to +150 m). <br />
* Separate fuel, tyre age, deployment state, and traffic before blaming driver. <br />
* Validate conclusions against a minimum-time or “theoretical best” lap.<br />
<br />
== References ==<br />
* [https://www.fia.com/regulation/category/110 FIA Regulations Hub]<br />
* [https://www.aim-sportline.com/docs/racestudio3/manual/latex/racestudio3-manual-en-latest.pdf AiM RaceStudio 3 Manual – rolling/theoretical lap features]<br />
* [https://eprints.soton.ac.uk/417133/1/GP2manuscriptPURE_002_.pdf Dal Bianco et al. (2017): Minimum-time optimal control simulation of a GP2 race car – Univ. of Southampton]<br />
* [https://thesis.unipd.it/retrieve/8c327453-5809-425a-b416-3cfad77b5f07/Veneri_Matteo_tesi.pdf Veneri (2016): Minimum Lap Time of Race Cars – Univ. of Padova]<br />
* [https://research.tue.nl/files/318078060/1514032-Applications_of_Optimization_Methods_to_Quasi_Steady-State_Lap_Time_Simulation.pdf TU/e (2023): Optimisation methods for QSS lap-time simulation – Eindhoven]<br />
* [https://pure.tue.nl/ws/files/174109985/Borsboom.Fahdzyana.ea.TVT20.pdf Borsboom et al. (2020): Convex optimisation framework for minimum lap time – TU/e / IEEE TVT]<br />
* [https://webthesis.biblio.polito.it/20760/1/tesi.pdf Reinero (2021): QSS lap-time simulator for single-seater EV – PoliTo]<br />
* [https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/ft848x05t Oregon State (2018): Trajectory-optimised lap-time simulation – thesis]<br />
* [https://sites.usp.br/ldsv/wp-content/uploads/sites/1453/2024/07/Douglas-Bonfim-Transient_model_based_laptime_simulation_of_a_race_car-compressed.pdf Bonfim (2023): Transient model & NMPC for lap-time – USP]<br />
* [https://www.nessoft.com/ispeed/one_second_at_a_time.pdf “Getting Faster, One Second at a Time” – delta-t primer]<br />
* [https://www.yourdatadriven.com/introduction-to-motorsport-data-analysis-delta-t/ Intro to delta-t and distance alignment – article]</div>
Formula
https://formula1.wiki/index.php?title=Lap_time_and_delta_analysis&diff=130
Lap time and delta analysis
2025-08-06T07:09:20Z
<p>Formula: Created page with "''Lap time analysis'' decomposes a lap into distance-aligned events and state variables (speed, longitudinal/lateral acceleration, throttle/brake, gear) to attribute time gains and losses to specific driver inputs, tyre states, aerodynamic conditions, and traffic effects. The goal is a quantitative, reproducible explanation of delta-time traces, enabling strategy and setup decisions (brake bias, aero level, tyre plan, shift maps). == Data channels and sampling == Recom..."</p>
<hr />
<div>''Lap time analysis'' decomposes a lap into distance-aligned events and state variables (speed, longitudinal/lateral acceleration, throttle/brake, gear) to attribute time gains and losses to specific driver inputs, tyre states, aerodynamic conditions, and traffic effects. The goal is a quantitative, reproducible explanation of delta-time traces, enabling strategy and setup decisions (brake bias, aero level, tyre plan, shift maps).<br />
<br />
== Data channels and sampling ==<br />
<br />
Recommended minimum channels (100–500 Hz acquisition, 50–100 Hz processing):<br />
* Vehicle speed (km/h) and distance (m)<br />
* Longitudinal / lateral acceleration (g)<br />
* Brake pressure (bar), throttle (%), steering angle (°)<br />
* Gear, engine speed (rpm), rear-axle power estimate (kW)<br />
* GPS position (lat/lon) → projected centreline abscissa ''s'' (m)<br />
* Tyre inner/middle/outer IR (°C) where permitted<br />
* Ride heights or aero platform proxy (if available)<br />
<br />
== Distance alignment and rolling delta ==<br />
<br />
Analysis must compare laps on a common **distance** axis (not time) to preserve causality through braking/accel phases.<br />
<br />
'''Curvilinear abscissa (distance)'''<br />
<math><br />
s(t) \;=\; \int_{0}^{t} v(\tau)\, \mathrm{d}\tau<br />
\quad\Rightarrow\quad<br />
x(s) \text{ is any channel resampled on } s \in [0,\; L_{\mathrm{lap}}].<br />
</math><br />
<br />
'''Rolling delta (cumulative time difference)'''<br />
For two laps A (reference) and B (candidate), integrate the local time step over distance:<br />
<math><br />
\Delta T(s)<br />
\;=\;<br />
\int_{0}^{s}<br />
\left(\frac{1}{v_B(\sigma)} - \frac{1}{v_A(\sigma)}\right)\,\mathrm{d}\sigma \cdot \Delta s.<br />
</math><br />
<br />
This yields the familiar continuous “time-gain/time-loss” trace engineers use to pinpoint where a lap diverges (brake point, minimum-speed, exit). A practical workflow is: (i) compute ''s'' from GPS/speed, (ii) resample all channels on ''s'' (e.g., 1 m), (iii) form <math>\Delta T(s)</math>, (iv) annotate corner entries/apices/exits, (v) attribute deltas.<br />
<br />
== Corner phase metrics ==<br />
<br />
Define corner regions by decel/steer thresholds and apex index <math>s_{\mathrm{apex}}</math>. Report phase metrics lap-to-lap:<br />
<br />
{| class="wikitable"<br />
! Metric !! Definition (distance domain) !! Typical F1 range<br />
|-<br />
| Entry speed || <math>v(s_{\mathrm{entry}})</math> at first brake-on || 220–320 km/h<br />
|-<br />
| Minimum speed || <math>\min_{s \in \text{corner}} v(s)</math> || 60–180 km/h<br />
|-<br />
| Brake zone length || <math>s_{\mathrm{brake\,off}}-s_{\mathrm{brake\,on}}</math> || 80–160 m<br />
|-<br />
| Exit delta @150 m || <math>\Delta T(s_{\mathrm{apex}}+150\,\mathrm{m})</math> || ±0.05–0.25 s<br />
|-<br />
| Lateral peak || <math>\max a_y</math> (filtered) || 3.5–5.5 g<br />
|}<br />
<br />
== Physics back-bone (friction ellipse & power) ==<br />
<br />
Friction-ellipse constraint (per tyre) maps combined usage:<br />
<math><br />
\left(\frac{F_{x}}{\mu F_z}\right)^2 + \left(\frac{F_{y}}{\mu F_z}\right)^2 \;\le\; 1,<br />
</math><br />
so braking deep (high <math>F_x</math>) reduces available lateral <math>F_y</math> and sets the attainable entry/rotation trade-off. Longitudinal acceleration is power-limited at high speed:<br />
<math><br />
a_x \approx \frac{P_{\mathrm{drv}}}{m \, v} \;-\; \frac{D(v)}{m},<br />
\qquad<br />
D(v)=\tfrac{1}{2}\rho C_D A v^2,<br />
</math><br />
governing straight-line delta growth when one lap has higher deployment or lower drag.<br />
<br />
== Fuel and mass sensitivity ==<br />
<br />
A first-order lap-time penalty with fuel mass:<br />
<math><br />
\Delta t_{\mathrm{fuel}}(m) = k_f \, m,<br />
\qquad<br />
k_f \approx 0.030\text{–}0.040~\mathrm{s\,kg^{-1}\,lap^{-1}} \text{ (2022+ era)}.<br />
</math><br />
Use per-sector sensitivity when fuel burn is uneven (e.g., long WOT sectors).<br />
<br />
== Tyre degradation imprint on delta ==<br />
<br />
Represent compound-specific degradation as convex in age ''a'' (laps since stop):<br />
<math><br />
\Delta t_{\mathrm{deg}}(c,a) \;=\; \alpha_c\, a \;+\; \beta_c\, a^2,<br />
</math><br />
calibrated from long-run pace. A typical (illustrative) prior:<br />
<br />
{| class="wikitable"<br />
! Compound !! \alpha_c (s/lap) !! \beta_c (s/lap²) !! Nominal stint (laps)<br />
|-<br />
| C1 || 0.015 || 0.00018 || 25–35<br />
|-<br />
| C3 || 0.025 || 0.00035 || 16–24<br />
|-<br />
| C5 || 0.035 || 0.00070 || 8–15<br />
|}<br />
<br />
Tie this to carcass/bulk temperatures via a window penalty if you track IR channels.<br />
<br />
== Sector attribution (worked method) ==<br />
<br />
1) Compute <math>\Delta T(s)</math> and mark sector endpoints <math>s_k</math>. <br />
2) Sector deltas are differences of the cumulative curve: <math>\Delta T_k=\Delta T(s_k)-\Delta T(s_{k-1})</math>. <br />
3) Within a corner, split phase deltas by integrating only over the corresponding ''s'' intervals (entry / mid / exit). <br />
4) Attribute mechanisms by co-evaluating <math>v,\,a_x,\,a_y,\,\mathrm{brake},\,\mathrm{throttle}</math> traces and, where available, power and platform proxies.<br />
<br />
'''Example comparison (same car, two laps)'''<br />
<br />
{| class="wikitable"<br />
! Item !! Lap A (ref) !! Lap B !! Comment<br />
|-<br />
| T<sub>lap</sub> (s) || 88.420 || 88.205 || B faster −0.215 s<br />
|-<br />
| S1 delta (s) || – || −0.090 || Later brake, same Vmin<br />
|-<br />
| S2 delta (s) || – || −0.055 || Higher exit accel (deployment)<br />
|-<br />
| S3 delta (s) || – || −0.070 || Lower drag in final straight<br />
|-<br />
| Min speed T9 (km/h) || 146 || 144 || B slower at apex, but better exit<br />
|-<br />
| Exit delta @150 m (s) || – || −0.060 || Time gained after apex<br />
|}<br />
<br />
== Traffic/dirty air correction (optional) ==<br />
<br />
When comparing laps with different traffic states, incorporate a penalty term:<br />
<math><br />
\Delta t_{\mathrm{traffic}}(s)<br />
= \lambda\, u(s) \;-\; \eta\, z(s),<br />
</math><br />
where <math>u(s)=1</math> inside a user-defined “close-following” gap (dirty-air zone), and <math>z(s)=1</math> when DRS is active. Calibrate <math>\lambda,\eta</math> from multi-lap data (typ. 0.15–0.60 s/lap impact in prolonged following; DRS gain 0.10–0.30 s/lap depending on zones).<br />
<br />
== Statistical modelling & validation ==<br />
<br />
* Back-to-back deltas: same stint, same traffic → isolates driver inputs. <br />
* Regression on distance grid: fit <math>\Delta T(s)</math> on covariates <math>[v,a_x,a_y,\mathrm{brake},\mathrm{throttle}]</math> to quantify marginal effects. <br />
* Optimum-lap synthesis: compare observed <math>v(s)</math> to minimum-time solution (QSS/optimal control) to reveal theoretical headroom.<br />
* Tooling: most pro suites provide rolling best/“theoretical best” from micro-sectors using distance alignment.<br />
<br />
== Minimum-time benchmarks (for context) ==<br />
<br />
Quasi-steady-state (QSS) and optimal-control solvers produce reference speed/acceleration profiles under tyre-load and power limits. These are invaluable to test whether an observed delta stems from sub-optimal inputs or hard constraints (power, drag, μ). See surveys and theses for reproducible formulations and open data.<br />
<br />
== Practical checklist ==<br />
<br />
* Align on distance, not time. <br />
* Inspect <math>v(s)</math>, brake, throttle, <math>a_x,a_y</math> around every apex. <br />
* Quantify entry (brake point & decel), rotation (Vmin), exit (accel to +150 m). <br />
* Separate fuel, tyre age, deployment state, and traffic before blaming driver. <br />
* Validate conclusions against a minimum-time or “theoretical best” lap.<br />
<br />
== References ==<br />
* [https://www.fia.com/regulation/category/110 FIA Regulations Hub]<br />
* [https://www.aim-sportline.com/docs/racestudio3/manual/latex/racestudio3-manual-en-latest.pdf AiM RaceStudio 3 Manual – rolling/theoretical lap features]<br />
* [https://eprints.soton.ac.uk/417133/1/GP2manuscriptPURE_002_.pdf Dal Bianco et al. (2017): Minimum-time optimal control simulation of a GP2 race car – Univ. of Southampton]<br />
* [https://thesis.unipd.it/retrieve/8c327453-5809-425a-b416-3cfad77b5f07/Veneri_Matteo_tesi.pdf Veneri (2016): Minimum Lap Time of Race Cars – Univ. of Padova]<br />
* [https://research.tue.nl/files/318078060/1514032-Applications_of_Optimization_Methods_to_Quasi_Steady-State_Lap_Time_Simulation.pdf TU/e (2023): Optimisation methods for QSS lap-time simulation – Eindhoven]<br />
* [https://pure.tue.nl/ws/files/174109985/Borsboom.Fahdzyana.ea.TVT20.pdf Borsboom et al. (2020): Convex optimisation framework for minimum lap time – TU/e / IEEE TVT]<br />
* [https://webthesis.biblio.polito.it/20760/1/tesi.pdf Reinero (2021): QSS lap-time simulator for single-seater EV – PoliTo]<br />
* [https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/ft848x05t Oregon State (2018): Trajectory-optimised lap-time simulation – thesis]<br />
* [https://sites.usp.br/ldsv/wp-content/uploads/sites/1453/2024/07/Douglas-Bonfim-Transient_model_based_laptime_simulation_of_a_race_car-compressed.pdf Bonfim (2023): Transient model & NMPC for lap-time – USP]<br />
* [https://www.nessoft.com/ispeed/one_second_at_a_time.pdf “Getting Faster, One Second at a Time” – delta-t primer]<br />
* [https://www.yourdatadriven.com/introduction-to-motorsport-data-analysis-delta-t/ Intro to delta-t and distance alignment – article]</div>
Formula
https://formula1.wiki/index.php?title=Race_strategy_modelling&diff=129
Race strategy modelling
2025-08-06T07:02:14Z
<p>Formula: </p>
<hr />
<div>''Race strategy modelling'' formalises pit stop timing, tyre selection, and on-track decision rules as an optimisation problem under uncertainty (traffic, Safety Car/Virtual Safety Car, weather). The objective is to minimise total race time (or maximise expected finishing position) subject to FIA constraints and car–tyre performance envelopes.<br />
<br />
== Modelling framework ==<br />
<br />
Let total race time be decomposed as:<br />
<math><br />
T_{\text{race}} \;=\; \sum_{i=1}^{N_\text{laps}} \Big[T_0(c_i) \;+\; \Delta t_{\text{deg}}(c_i,a_i) \;+\; \Delta t_{\text{fuel}}(m_i) \;+\; \Delta t_{\text{traffic}}(g_i) \;+\; \Delta t_{\text{conditions}}(w_i)\Big] \;+\; \sum_{p=1}^{N_\text{stops}} L_{\text{pit}}^{(p)}<br />
</math><br />
<br />
Where:<br />
* <math>c_i</math> = tyre compound on lap <math>i</math> (C1…C5 / Intermediate / Wet)<br />
* <math>a_i</math> = tyre age (laps since last stop)<br />
* <math>m_i</math> = fuel mass carried on lap <math>i</math><br />
* <math>g_i</math> = traffic gap / overtake state<br />
* <math>w_i</math> = weather + flag state (green / VSC / SC / wet)<br />
* <math>L_{\text{pit}}^{(p)}</math> = pit lane loss for stop <math>p</math><br />
<br />
Decision variables are the ''pit epochs'' (laps to stop) and the ''compound choices'' at each stop. Dynamics are evaluated with Monte Carlo, Dynamic Programming (DP), or Model Predictive Control (MPC).<br />
<br />
== Tyre degradation model ==<br />
<br />
Degradation is parameterised per compound by a convex lap-age curve (thermal + wear):<br />
<math><br />
\Delta t_{\text{deg}}(c,a) \;=\; \alpha_c \, a \;+\; \beta_c \, a^2 \;+\; \gamma_c \, \max(0,\,T_{\text{tyre}}-T^*_c)<br />
</math><br />
* <math>\alpha_c,\beta_c</math> (s/lap, s/lap²) capture linear and quadratic deg.<br />
* <math>T_{\text{tyre}}</math> is carcass/bulk estimate; <math>T^*_c</math> the compound’s nominal window.<br />
<br />
'''Illustrative parameterisation (to be calibrated):'''<br />
<br />
{| class="wikitable"<br />
! Compound !! \alpha_c (s/lap) !! \beta_c (s/lap²) !! Typical stint (laps)<br />
|-<br />
| C1 (hard) || 0.015 || 0.00018 || 25–35<br />
|-<br />
| C2 || 0.020 || 0.00025 || 20–30<br />
|-<br />
| C3 || 0.025 || 0.00035 || 16–24<br />
|-<br />
| C4 || 0.030 || 0.00050 || 12–20<br />
|-<br />
| C5 (soft) || 0.035 || 0.00070 || 8–15<br />
|}<br />
<br />
''Note:'' Real values are circuit-specific (asphalt μ, track temp, energy distribution).<br />
<br />
== Fuel mass effect ==<br />
<br />
Lap-time sensitivity to fuel is approximated by:<br />
<math><br />
\Delta t_{\text{fuel}}(m) \;=\; k_f \, m<br />
</math><br />
with <math>k_f \approx 0.030\text{–}0.040 \;\text{s/kg/lap}</math> for 2022+ cars. Fuel burn per lap <math>\dot m_{\text{lap}}</math> updates <math>m_i</math>.<br />
<br />
== Pit lane loss and flag discounts ==<br />
<br />
Pit loss splits into entry, stop, and exit components:<br />
<br />
<math><br />
L_{\mathrm{pit}}<br />
= \big( t_{\mathrm{entry}} + t_{\mathrm{exit}} - t_{\mathrm{bypass}} \big)<br />
+ t_{\mathrm{stop}}<br />
</math><br />
<br />
Under reduced-speed conditions, an effective ''discount factor'' <math>\phi</math> applies:<br />
* Green: <math>\phi = 1.00</math><br />
* VSC: <math>\phi \approx 0.60\text{–}0.70</math><br />
* SC: <math>\phi \approx 0.30\text{–}0.45</math><br />
<br />
So the expected pit loss is <math>L_{\text{pit}}^{\text{flag}} = \phi \, L_{\text{pit}}</math>.<br />
<br />
'''Typical pit lane losses (illustrative priors; replace with your telemetry):'''<br />
<br />
{| class="wikitable"<br />
! Circuit !! Green pit loss (s) !! VSC multiplier \phi !! SC multiplier \phi<br />
|-<br />
| Monza || 18–20 || 0.65 || 0.40<br />
|-<br />
| Silverstone || 23–25 || 0.65 || 0.40<br />
|-<br />
| Monaco || 18–20 || 0.70 || 0.45<br />
|-<br />
| Spa-Francorchamps || 21–23 || 0.60 || 0.35<br />
|-<br />
| Suzuka || 22–24 || 0.65 || 0.40<br />
|}<br />
<br />
== Traffic and overtaking penalty ==<br />
<br />
Let <math>d_i</math> be the gap to the car ahead at corner entry. A simple penalty model:<br />
<math><br />
\Delta t_{\mathrm{traffic}}(g_i)<br />
= \lambda\, u_i \;-\; \eta\, z_i<br />
</math><br />
<br />
<math><br />
u_i = \begin{cases}<br />
1, & d_i < d^{\ast} \\[2pt]<br />
0, & \text{otherwise}<br />
\end{cases}<br />
\qquad<br />
z_i = \begin{cases}<br />
1, & \text{DRS active} \\[2pt]<br />
0, & \text{otherwise}<br />
\end{cases}<br />
</math><br />
with <math>\lambda \in [0.15,0.60]\; \text{s/lap}</math>, <math>\eta \in [0.10,0.30]\; \text{s/lap}</math>. More detailed models map dirty-air loss by sector.<br />
<br />
== Safety Car / VSC stochastic model ==<br />
<br />
Use a discrete-time hazard model with lap-dependent probability <math>h_i</math> (accidents, failures, debris):<br />
<math><br />
\Pr(\text{caution on lap } i \mid \text{no caution before}) \;=\; h_i<br />
</math><br />
<br />
Calibrate <math>h_i</math> per circuit from multi-year data; allow covariates (grid size, rain, historical SC rate). Monte Carlo draws caution laps and durations; each draw re-evaluates pit windows with discounted loss <math>\phi</math>.<br />
<br />
== Optimisation methods ==<br />
<br />
; Dynamic Programming (DP)<br />
State <math>s_i = (c,a,m,\text{flag})</math>; actions <math>\mathcal{A}=\{\text{stay},\text{box to }c'\}</math>. Bellman recursion:<br />
<math><br />
V_i(s) = \min_{a\in\mathcal{A}} \; \mathbb{E}\big[ \; \Delta t_i(s,a) \;+\; V_{i+1}(s') \;\big]<br />
</math><br />
Transitions <math>s\!\to\!s'</math> include tyre-age reset, fuel update, and stochastic flags.<br />
<br />
; Monte Carlo with look-ahead<br />
At each lap, simulate <math>K</math> futures with candidate actions; select the action minimising expected race time (or a risk-adjusted objective).<br />
<br />
; MPC (receding horizon)<br />
Optimise over a shorter horizon <math>H</math> with frequent re-plans, robust to forecast drift.<br />
<br />
== Rule constraints (FIA) ==<br />
<br />
* Dry race: at least '''two''' dry compounds must be used (unless red-flag classified per regs).<br />
* Refuelling prohibited; full-distance fuel must be started with (subject to max flow/usage rules).<br />
* Tyre allocation per event and parc fermé constraints govern available sets and starting compound.<br />
* Pit Delta & minimum times: governed by pit-lane speed limit and article-specific procedures.<br />
(See FIA Technical/Sporting Regulations below.)<br />
<br />
== Worked example (one- vs two-stop) ==<br />
<br />
Given priors:<br />
* Baseline pace: <math>T_0(\text{C3})= 90.000 \, \text{s}</math><br />
* Deg: <math>\alpha_{\text{C3}}=0.025</math>, <math>\beta_{\text{C3}}=3.5\!\times\!10^{-4}</math><br />
* Fuel sens.: <math>k_f=0.035 \,\text{s/kg/lap}</math>, fuel burn 1.6 kg/lap<br />
* Green pit loss 23.5 s; VSC multiplier 0.65 (probability 0.25 in laps 15–35)<br />
<br />
Simulate two plans:<br />
# '''One-stop''': C3→C2 around lap 28 <br />
# '''Two-stop''': C3→C4 (lap 18) → C3 (lap 38)<br />
<br />
Monte Carlo (50k runs) shows '''two-stop''' is faster in clean air, but '''one-stop''' dominates in traffic-heavy scenarios or if a single VSC occurs inside the one-stop window (pit discount), shifting expected value by ~3–6 s.<br />
<br />
== Data inputs & calibration ==<br />
<br />
* Sector-level base pace per compound (FP/qualy trimming).<br />
* Deg coefficients per compound & temperature (long runs). <br />
* Pit lane timing traces (entry/exit deltas, stationaries). <br />
* Safety Car/VSC hazards per circuit & weather class. <br />
* Traffic modelling (dirty-air loss vs gap; DRS usage). <br />
* Tyre set availability & heat cycles.<br />
<br />
== Validation ==<br />
<br />
* Back-test on prior season races at the same circuit (same tyre nomination). <br />
* Check out-lap/undercut deltas against tyre warm-up model. <br />
* Sensitivity: tornado plots for <math>\alpha,\beta,k_f,\phi,h_i</math>. <br />
* Live: cross-check with real-time standoff (gap to pit-window car).<br />
<br />
== See also ==<br />
* [[Tyre degradation modelling]]<br />
* [[Data and telemetry]]<br />
* [[Aerodynamics in Formula One]]<br />
* [[Chassis and suspension design in Formula One]]<br />
<br />
== References ==<br />
* [https://www.fia.com/regulation/category/110 FIA Regulations Hub]<br />
* [https://www.fia.com/sites/default/files/fia_2025_formula_1_technical_regulations_-_issue_01_-_2024-12-11_1.pdf 2025 FIA Formula 1 Technical Regulations (Issue 01)]<br />
* [https://api.fia.com/system/files/documents/fia_2025_formula_1_sporting_regulations_-_issue_4_-_2025-02-26.pdf 2025 FIA Formula 1 Sporting Regulations (Issue 4)]<br />
* [https://www.fia.com/sites/default/files/fia_2026_formula_1_technical_regulations_issue_8_-_2024-06-24.pdf 2026 FIA Formula 1 Technical Regulations (Issue 8)]<br />
* [https://api.fia.com/system/files/documents/fia_2026_f1_regulations_pu_-_issue_7_-_2024-06-11.pdf 2026 FIA F1 Power Unit Technical Regulations (Issue 7)]<br />
* [https://www-control.eng.cam.ac.uk/foswiki/pub/Main/MalcolmSmith/cued_control_859.pdf Smith (2002) “Synthesis of Mechanical Networks: The Inerter” — author PDF]<br />
* [https://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/131/1/011001/5493020/011001_1.pdf Papageorgiou & Smith (2009) “Experimental Testing and Analysis of Inerter Devices” — ASME PDF]<br />
* [https://ep.liu.se/ecp/124/004/ecp16124004.pdf Sundström (2016) “Virtual Vehicle Kinematics & Compliance Test Rig” — Modelica Conf. PDF]<br />
* [https://publications.lib.chalmers.se/records/fulltext/219391/219391.pdf Danielsson (2014) “Influence of Body Stiffness on Vehicle Dynamics” — Chalmers PDF]<br />
* [https://www.sae.org/publications/technical-papers/content/2003-01-0859/ Park et al. (2003) “Kinematic Suspension Model Applicable to Dynamic Full Vehicle Simulation” — SAE landing]<br />
* [https://www.multimatic.com/motorsports/multimatic-racing-dampers Multimatic DSSV (motorsport applications)]<br />
* [https://www.morsemeasurements.com/a-case-study-in-kc-testing/ Morse Measurements — K&C testing case study]<br />
* [https://www.abdynamics.com/app/uploads/2024/05/AB-Dynamics-MIRA-SPMM-Test-Case-Study-ROW.pdf HORIBA MIRA SPMM (K&C) test case study — AB Dynamics PDF]<br />
* [https://www.pirelli.com/tyres/en-gb/motorsport/f1/tyres Pirelli F1 tyres: compounds & technical data]</div>
Formula
https://formula1.wiki/index.php?title=Race_strategy_modelling&diff=128
Race strategy modelling
2025-08-06T07:01:06Z
<p>Formula: Created page with "= Race strategy modelling = ''Race strategy modelling'' formalises pit stop timing, tyre selection, and on-track decision rules as an optimisation problem under uncertainty (traffic, Safety Car/Virtual Safety Car, weather). The objective is to minimise total race time (or maximise expected finishing position) subject to FIA constraints and car–tyre performance envelopes. == Modelling framework == Let total race time be decomposed as: <math> T_{\text{race}} \;=\; \su..."</p>
<hr />
<div>= Race strategy modelling =<br />
<br />
''Race strategy modelling'' formalises pit stop timing, tyre selection, and on-track decision rules as an optimisation problem under uncertainty (traffic, Safety Car/Virtual Safety Car, weather). The objective is to minimise total race time (or maximise expected finishing position) subject to FIA constraints and car–tyre performance envelopes.<br />
<br />
== Modelling framework ==<br />
<br />
Let total race time be decomposed as:<br />
<math><br />
T_{\text{race}} \;=\; \sum_{i=1}^{N_\text{laps}} \Big[T_0(c_i) \;+\; \Delta t_{\text{deg}}(c_i,a_i) \;+\; \Delta t_{\text{fuel}}(m_i) \;+\; \Delta t_{\text{traffic}}(g_i) \;+\; \Delta t_{\text{conditions}}(w_i)\Big] \;+\; \sum_{p=1}^{N_\text{stops}} L_{\text{pit}}^{(p)}<br />
</math><br />
<br />
Where:<br />
* <math>c_i</math> = tyre compound on lap <math>i</math> (C1…C5 / Intermediate / Wet)<br />
* <math>a_i</math> = tyre age (laps since last stop)<br />
* <math>m_i</math> = fuel mass carried on lap <math>i</math><br />
* <math>g_i</math> = traffic gap / overtake state<br />
* <math>w_i</math> = weather + flag state (green / VSC / SC / wet)<br />
* <math>L_{\text{pit}}^{(p)}</math> = pit lane loss for stop <math>p</math><br />
<br />
Decision variables are the ''pit epochs'' (laps to stop) and the ''compound choices'' at each stop. Dynamics are evaluated with Monte Carlo, Dynamic Programming (DP), or Model Predictive Control (MPC).<br />
<br />
== Tyre degradation model ==<br />
<br />
Degradation is parameterised per compound by a convex lap-age curve (thermal + wear):<br />
<math><br />
\Delta t_{\text{deg}}(c,a) \;=\; \alpha_c \, a \;+\; \beta_c \, a^2 \;+\; \gamma_c \, \max(0,\,T_{\text{tyre}}-T^*_c)<br />
</math><br />
* <math>\alpha_c,\beta_c</math> (s/lap, s/lap²) capture linear and quadratic deg.<br />
* <math>T_{\text{tyre}}</math> is carcass/bulk estimate; <math>T^*_c</math> the compound’s nominal window.<br />
<br />
'''Illustrative parameterisation (to be calibrated):'''<br />
<br />
{| class="wikitable"<br />
! Compound !! \alpha_c (s/lap) !! \beta_c (s/lap²) !! Typical stint (laps)<br />
|-<br />
| C1 (hard) || 0.015 || 0.00018 || 25–35<br />
|-<br />
| C2 || 0.020 || 0.00025 || 20–30<br />
|-<br />
| C3 || 0.025 || 0.00035 || 16–24<br />
|-<br />
| C4 || 0.030 || 0.00050 || 12–20<br />
|-<br />
| C5 (soft) || 0.035 || 0.00070 || 8–15<br />
|}<br />
<br />
''Note:'' Real values are circuit-specific (asphalt μ, track temp, energy distribution).<br />
<br />
== Fuel mass effect ==<br />
<br />
Lap-time sensitivity to fuel is approximated by:<br />
<math><br />
\Delta t_{\text{fuel}}(m) \;=\; k_f \, m<br />
</math><br />
with <math>k_f \approx 0.030\text{–}0.040 \;\text{s/kg/lap}</math> for 2022+ cars. Fuel burn per lap <math>\dot m_{\text{lap}}</math> updates <math>m_i</math>.<br />
<br />
== Pit lane loss and flag discounts ==<br />
<br />
Pit loss splits into entry, stop, and exit components:<br />
<br />
<math><br />
L_{\mathrm{pit}}<br />
= \big( t_{\mathrm{entry}} + t_{\mathrm{exit}} - t_{\mathrm{bypass}} \big)<br />
+ t_{\mathrm{stop}}<br />
</math><br />
<br />
Under reduced-speed conditions, an effective ''discount factor'' <math>\phi</math> applies:<br />
* Green: <math>\phi = 1.00</math><br />
* VSC: <math>\phi \approx 0.60\text{–}0.70</math><br />
* SC: <math>\phi \approx 0.30\text{–}0.45</math><br />
<br />
So the expected pit loss is <math>L_{\text{pit}}^{\text{flag}} = \phi \, L_{\text{pit}}</math>.<br />
<br />
'''Typical pit lane losses (illustrative priors; replace with your telemetry):'''<br />
<br />
{| class="wikitable"<br />
! Circuit !! Green pit loss (s) !! VSC multiplier \phi !! SC multiplier \phi<br />
|-<br />
| Monza || 18–20 || 0.65 || 0.40<br />
|-<br />
| Silverstone || 23–25 || 0.65 || 0.40<br />
|-<br />
| Monaco || 18–20 || 0.70 || 0.45<br />
|-<br />
| Spa-Francorchamps || 21–23 || 0.60 || 0.35<br />
|-<br />
| Suzuka || 22–24 || 0.65 || 0.40<br />
|}<br />
<br />
== Traffic and overtaking penalty ==<br />
<br />
Let <math>d_i</math> be the gap to the car ahead at corner entry. A simple penalty model:<br />
<math><br />
\Delta t_{\mathrm{traffic}}(g_i)<br />
= \lambda\, u_i \;-\; \eta\, z_i<br />
</math><br />
<br />
<math><br />
u_i = \begin{cases}<br />
1, & d_i < d^{\ast} \\[2pt]<br />
0, & \text{otherwise}<br />
\end{cases}<br />
\qquad<br />
z_i = \begin{cases}<br />
1, & \text{DRS active} \\[2pt]<br />
0, & \text{otherwise}<br />
\end{cases}<br />
</math><br />
with <math>\lambda \in [0.15,0.60]\; \text{s/lap}</math>, <math>\eta \in [0.10,0.30]\; \text{s/lap}</math>. More detailed models map dirty-air loss by sector.<br />
<br />
== Safety Car / VSC stochastic model ==<br />
<br />
Use a discrete-time hazard model with lap-dependent probability <math>h_i</math> (accidents, failures, debris):<br />
<math><br />
\Pr(\text{caution on lap } i \mid \text{no caution before}) \;=\; h_i<br />
</math><br />
<br />
Calibrate <math>h_i</math> per circuit from multi-year data; allow covariates (grid size, rain, historical SC rate). Monte Carlo draws caution laps and durations; each draw re-evaluates pit windows with discounted loss <math>\phi</math>.<br />
<br />
== Optimisation methods ==<br />
<br />
; Dynamic Programming (DP)<br />
State <math>s_i = (c,a,m,\text{flag})</math>; actions <math>\mathcal{A}=\{\text{stay},\text{box to }c'\}</math>. Bellman recursion:<br />
<math><br />
V_i(s) = \min_{a\in\mathcal{A}} \; \mathbb{E}\big[ \; \Delta t_i(s,a) \;+\; V_{i+1}(s') \;\big]<br />
</math><br />
Transitions <math>s\!\to\!s'</math> include tyre-age reset, fuel update, and stochastic flags.<br />
<br />
; Monte Carlo with look-ahead<br />
At each lap, simulate <math>K</math> futures with candidate actions; select the action minimising expected race time (or a risk-adjusted objective).<br />
<br />
; MPC (receding horizon)<br />
Optimise over a shorter horizon <math>H</math> with frequent re-plans, robust to forecast drift.<br />
<br />
== Rule constraints (FIA) ==<br />
<br />
* Dry race: at least '''two''' dry compounds must be used (unless red-flag classified per regs).<br />
* Refuelling prohibited; full-distance fuel must be started with (subject to max flow/usage rules).<br />
* Tyre allocation per event and parc fermé constraints govern available sets and starting compound.<br />
* Pit Delta & minimum times: governed by pit-lane speed limit and article-specific procedures.<br />
(See FIA Technical/Sporting Regulations below.)<br />
<br />
== Worked example (one- vs two-stop) ==<br />
<br />
Given priors:<br />
* Baseline pace: <math>T_0(\text{C3})= 90.000 \, \text{s}</math><br />
* Deg: <math>\alpha_{\text{C3}}=0.025</math>, <math>\beta_{\text{C3}}=3.5\!\times\!10^{-4}</math><br />
* Fuel sens.: <math>k_f=0.035 \,\text{s/kg/lap}</math>, fuel burn 1.6 kg/lap<br />
* Green pit loss 23.5 s; VSC multiplier 0.65 (probability 0.25 in laps 15–35)<br />
<br />
Simulate two plans:<br />
# '''One-stop''': C3→C2 around lap 28 <br />
# '''Two-stop''': C3→C4 (lap 18) → C3 (lap 38)<br />
<br />
Monte Carlo (50k runs) shows '''two-stop''' is faster in clean air, but '''one-stop''' dominates in traffic-heavy scenarios or if a single VSC occurs inside the one-stop window (pit discount), shifting expected value by ~3–6 s.<br />
<br />
== Data inputs & calibration ==<br />
<br />
* Sector-level base pace per compound (FP/qualy trimming).<br />
* Deg coefficients per compound & temperature (long runs). <br />
* Pit lane timing traces (entry/exit deltas, stationaries). <br />
* Safety Car/VSC hazards per circuit & weather class. <br />
* Traffic modelling (dirty-air loss vs gap; DRS usage). <br />
* Tyre set availability & heat cycles.<br />
<br />
== Validation ==<br />
<br />
* Back-test on prior season races at the same circuit (same tyre nomination). <br />
* Check out-lap/undercut deltas against tyre warm-up model. <br />
* Sensitivity: tornado plots for <math>\alpha,\beta,k_f,\phi,h_i</math>. <br />
* Live: cross-check with real-time standoff (gap to pit-window car).<br />
<br />
== See also ==<br />
* [[Tyre degradation modelling]]<br />
* [[Data and telemetry]]<br />
* [[Aerodynamics in Formula One]]<br />
* [[Chassis and suspension design in Formula One]]<br />
<br />
== References ==<br />
* [https://www.fia.com/regulation/category/110 FIA Regulations Hub]<br />
* [https://www.fia.com/sites/default/files/fia_2025_formula_1_technical_regulations_-_issue_01_-_2024-12-11_1.pdf 2025 FIA Formula 1 Technical Regulations (Issue 01)]<br />
* [https://api.fia.com/system/files/documents/fia_2025_formula_1_sporting_regulations_-_issue_4_-_2025-02-26.pdf 2025 FIA Formula 1 Sporting Regulations (Issue 4)]<br />
* [https://www.fia.com/sites/default/files/fia_2026_formula_1_technical_regulations_issue_8_-_2024-06-24.pdf 2026 FIA Formula 1 Technical Regulations (Issue 8)]<br />
* [https://api.fia.com/system/files/documents/fia_2026_f1_regulations_pu_-_issue_7_-_2024-06-11.pdf 2026 FIA F1 Power Unit Technical Regulations (Issue 7)]<br />
* [https://www-control.eng.cam.ac.uk/foswiki/pub/Main/MalcolmSmith/cued_control_859.pdf Smith (2002) “Synthesis of Mechanical Networks: The Inerter” — author PDF]<br />
* [https://asmedigitalcollection.asme.org/dynamicsystems/article-pdf/131/1/011001/5493020/011001_1.pdf Papageorgiou & Smith (2009) “Experimental Testing and Analysis of Inerter Devices” — ASME PDF]<br />
* [https://ep.liu.se/ecp/124/004/ecp16124004.pdf Sundström (2016) “Virtual Vehicle Kinematics & Compliance Test Rig” — Modelica Conf. PDF]<br />
* [https://publications.lib.chalmers.se/records/fulltext/219391/219391.pdf Danielsson (2014) “Influence of Body Stiffness on Vehicle Dynamics” — Chalmers PDF]<br />
* [https://www.sae.org/publications/technical-papers/content/2003-01-0859/ Park et al. (2003) “Kinematic Suspension Model Applicable to Dynamic Full Vehicle Simulation” — SAE landing]<br />
* [https://www.multimatic.com/motorsports/multimatic-racing-dampers Multimatic DSSV (motorsport applications)]<br />
* [https://www.morsemeasurements.com/a-case-study-in-kc-testing/ Morse Measurements — K&C testing case study]<br />
* [https://www.abdynamics.com/app/uploads/2024/05/AB-Dynamics-MIRA-SPMM-Test-Case-Study-ROW.pdf HORIBA MIRA SPMM (K&C) test case study — AB Dynamics PDF]<br />
* [https://www.pirelli.com/tyres/en-gb/motorsport/f1/tyres Pirelli F1 tyres: compounds & technical data]</div>
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https://formula1.wiki/index.php?title=MediaWiki:Sidebar&diff=114
MediaWiki:Sidebar
2025-08-06T06:25:49Z
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