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: $T_{\text{race}}\;=\;\sum _{i=1}^{N_{\text{laps}}}{\Big [}T_{0}(c_{i})\;+\;\Delta t_{\text{deg}}(c_{i},a_{i})\;+\;\Delta t_{\text{fuel}}(m_{i})\;+\;\Delta t_{\text{traffic}}(g_{i})\;+\;\Delta t_{\text{conditions}}(w_{i}){\Big ]}\;+\;\sum _{p=1}^{N_{\text{stops}}}L_{\text{pit}}^{(p)}$

Where:

• $c_{i}$ = tyre compound on lap $i$ (C1…C5 / Intermediate / Wet)
• $a_{i}$ = tyre age (laps since last stop)
• $m_{i}$ = fuel mass carried on lap $i$
• $g_{i}$ = traffic gap / overtake state
• $w_{i}$ = weather + flag state (green / VSC / SC / wet)
• $L_{\text{pit}}^{(p)}$ = pit lane loss for stop $p$

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).

Tyre degradation model

Degradation is parameterised per compound by a convex lap-age curve (thermal + wear): $\Delta t_{\text{deg}}(c,a)\;=\;\alpha _{c}\,a\;+\;\beta _{c}\,a^{2}\;+\;\gamma _{c}\,\max(0,\,T_{\text{tyre}}-T_{c}^{*})$

• $\alpha _{c},\beta _{c}$ (s/lap, s/lap²) capture linear and quadratic deg.
• $T_{\text{tyre}}$ is carcass/bulk estimate; $T_{c}^{*}$ the compound’s nominal window.

Illustrative parameterisation (to be calibrated):

Compound	\alpha_c (s/lap)	\beta_c (s/lap²)	Typical stint (laps)
C1 (hard)	0.015	0.00018	25–35
C2	0.020	0.00025	20–30
C3	0.025	0.00035	16–24
C4	0.030	0.00050	12–20
C5 (soft)	0.035	0.00070	8–15

Note: Real values are circuit-specific (asphalt μ, track temp, energy distribution).

Fuel mass effect

Lap-time sensitivity to fuel is approximated by: $\Delta t_{\text{fuel}}(m)\;=\;k_{f}\,m$ with $k_{f}\approx 0.030{\text{–}}0.040\;{\text{s/kg/lap}}$ for 2022+ cars. Fuel burn per lap ${\dot {m}}_{\text{lap}}$ updates $m_{i}$.

Pit lane loss and flag discounts

Pit loss splits into entry, stop, and exit components:

$L_{\mathrm {pit} }={\big (}t_{\mathrm {entry} }+t_{\mathrm {exit} }-t_{\mathrm {bypass} }{\big )}+t_{\mathrm {stop} }$

Under reduced-speed conditions, an effective discount factor $\phi$ applies:

• Green: $\phi =1.00$
• VSC: $\phi \approx 0.60{\text{–}}0.70$
• SC: $\phi \approx 0.30{\text{–}}0.45$

So the expected pit loss is $L_{\text{pit}}^{\text{flag}}=\phi \,L_{\text{pit}}$.

Typical pit lane losses (illustrative priors; replace with your telemetry):

Circuit	Green pit loss (s)	VSC multiplier \phi	SC multiplier \phi
Monza	18–20	0.65	0.40
Silverstone	23–25	0.65	0.40
Monaco	18–20	0.70	0.45
Spa-Francorchamps	21–23	0.60	0.35
Suzuka	22–24	0.65	0.40

Traffic and overtaking penalty

Let $d_{i}$ be the gap to the car ahead at corner entry. A simple penalty model: $\Delta t_{\mathrm {traffic} }(g_{i})=\lambda \,u_{i}\;-\;\eta \,z_{i}$

$u_{i}={\begin{cases}1,&d_{i}<d^{\ast }\\[2pt]0,&{\text{otherwise}}\end{cases}}\qquad z_{i}={\begin{cases}1,&{\text{DRS active}}\\[2pt]0,&{\text{otherwise}}\end{cases}}$ with $\lambda \in [0.15,0.60]\;{\text{s/lap}}$, $\eta \in [0.10,0.30]\;{\text{s/lap}}$. More detailed models map dirty-air loss by sector.

Safety Car / VSC stochastic model

Use a discrete-time hazard model with lap-dependent probability $h_{i}$ (accidents, failures, debris): $\Pr({\text{caution on lap }}i\mid {\text{no caution before}})\;=\;h_{i}$

Calibrate $h_{i}$ 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 $\phi$.

Optimisation methods

Dynamic Programming (DP)

State $s_{i}=(c,a,m,{\text{flag}})$; actions ${\mathcal {A}}=\{{\text{stay}},{\text{box to }}c'\}$. Bellman recursion: $V_{i}(s)=\min _{a\in {\mathcal {A}}}\;\mathbb {E} {\big [}\;\Delta t_{i}(s,a)\;+\;V_{i+1}(s')\;{\big ]}$ Transitions $s\!\to \!s'$ include tyre-age reset, fuel update, and stochastic flags.

Monte Carlo with look-ahead

At each lap, simulate $K$ futures with candidate actions; select the action minimising expected race time (or a risk-adjusted objective).

MPC (receding horizon)

Optimise over a shorter horizon $H$ with frequent re-plans, robust to forecast drift.

Rule constraints (FIA)

• Dry race: at least two dry compounds must be used (unless red-flag classified per regs).
• Refuelling prohibited; full-distance fuel must be started with (subject to max flow/usage rules).
• Tyre allocation per event and parc fermé constraints govern available sets and starting compound.
• Pit Delta & minimum times: governed by pit-lane speed limit and article-specific procedures.

(See FIA Technical/Sporting Regulations below.)

Worked example (one- vs two-stop)

Given priors:

• Baseline pace: $T_{0}({\text{C3}})=90.000\,{\text{s}}$
• Deg: $\alpha _{\text{C3}}=0.025$, $\beta _{\text{C3}}=3.5\!\times \!10^{-4}$
• Fuel sens.: $k_{f}=0.035\,{\text{s/kg/lap}}$, fuel burn 1.6 kg/lap
• Green pit loss 23.5 s; VSC multiplier 0.65 (probability 0.25 in laps 15–35)

Simulate two plans:

1. One-stop: C3→C2 around lap 28
2. Two-stop: C3→C4 (lap 18) → C3 (lap 38)

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.

Data inputs & calibration

• Sector-level base pace per compound (FP/qualy trimming).
• Deg coefficients per compound & temperature (long runs).
• Pit lane timing traces (entry/exit deltas, stationaries).
• Safety Car/VSC hazards per circuit & weather class.
• Traffic modelling (dirty-air loss vs gap; DRS usage).
• Tyre set availability & heat cycles.

Validation

• Back-test on prior season races at the same circuit (same tyre nomination).
• Check out-lap/undercut deltas against tyre warm-up model.
• Sensitivity: tornado plots for $\alpha ,\beta ,k_{f},\phi ,h_{i}$.
• Live: cross-check with real-time standoff (gap to pit-window car).

See also

• Tyre degradation modelling
• Data and telemetry
• Aerodynamics in Formula One
• Chassis and suspension design in Formula One

References

• FIA Regulations Hub
• 2025 FIA Formula 1 Technical Regulations (Issue 01)
• 2025 FIA Formula 1 Sporting Regulations (Issue 4)
• 2026 FIA Formula 1 Technical Regulations (Issue 8)
• 2026 FIA F1 Power Unit Technical Regulations (Issue 7)
• Smith (2002) “Synthesis of Mechanical Networks: The Inerter” — author PDF
• Papageorgiou & Smith (2009) “Experimental Testing and Analysis of Inerter Devices” — ASME PDF
• Sundström (2016) “Virtual Vehicle Kinematics & Compliance Test Rig” — Modelica Conf. PDF
• Danielsson (2014) “Influence of Body Stiffness on Vehicle Dynamics” — Chalmers PDF
• Park et al. (2003) “Kinematic Suspension Model Applicable to Dynamic Full Vehicle Simulation” — SAE landing
• Multimatic DSSV (motorsport applications)
• Morse Measurements — K&C testing case study
• HORIBA MIRA SPMM (K&C) test case study — AB Dynamics PDF
• Pirelli F1 tyres: compounds & technical data