Editing Chassis and suspension design

Formula One chassis and suspension design defines the vehicle’s mechanical grip envelope, vertical load control, and its interaction with aerodynamic structures. The system is not merely structural; it governs pitch, ride, and roll behaviour under aerodynamic and tyre-dominated force regimes at frequencies up to 20 Hz. 

Advanced design must account for:

* Torsional and bending stiffness of the monocoque
* Multibody suspension kinematics and compliance
* Ride height–aerodynamic coupling in ground-effect flows
* Inerter-tuned heave response
* Tyre load sensitivity and contact patch stability

== Torsional Rigidity and Structural Dynamics ==

Torsional stiffness is critical for preserving kinematic integrity. Twist under cross-axle torque alters suspension angles and misaligns aerodynamic reference planes.

<math>
k_t = \frac{T}{\theta}
</math>

Where:
* <math>T</math> = applied torque (Nm)  
* <math>\theta</math> = angular displacement (rad)  

Benchmark targets:
- F1 monocoque: ≥ 35,000 Nm/deg  
- Deviations under load: < 0.1° at 3.5 kNm  
- GP2 monocoques: ~18,000–22,000 Nm/deg  

Typical FIA torsional test uses a load fixture with two lateral beams at front and rear bulkheads. Displacement is measured with ±0.01 mm tolerances.

== Suspension Kinematics and Load Vector Decomposition ==

All teams use double wishbone suspension at each corner. Rod orientation, pivot height, and triangle length define instantaneous centres and vertical load reaction geometry.

=== Anti-Dive Model ===

During braking, the front suspension compresses due to weight transfer. Anti-dive resists this using suspension geometry.

<math>
\%_{\text{Anti-Dive}} = \left( \frac{Z_{\text{IC}}}{h_{\text{CG}}} \right) \cdot \frac{a_{\text{long}}}{g} \cdot 100
</math>

Where:
* <math>Z_{\text{IC}}</math> = vertical distance from ground to Instantaneous Centre (typically 120–150 mm)
* <math>h_{\text{CG}}</math> = CG height (~310 mm for 2024 cars)
* <math>a_{\text{long}}</math> = longitudinal deceleration (1.7–2.0 g)

Effective range: 30–45%  
Higher values reduce pitch but can reduce front load feel and exacerbate tyre flat-spotting under longitudinal lock.

=== Anti-Squat ===

Applied at the rear to limit squat under traction. Geometry is defined similarly, with slightly reduced height leverage.

Typical value range: 20–30%  
Measured via pitch rate differential at 80% throttle, 3rd gear, with DRS closed.

== Ride Height Sensitivity and Platform Control ==

2022–2025 F1 cars exploit floor-generated downforce via venturi tunnels. Platform control is critical for diffuser efficiency and vortex sealing.

Static targets:
* Front ride height: 25–30 mm  
* Rear ride height: 45–55 mm  
* Rake: 1.5° (Red Bull), <1.0° (Mercedes)

Aero model output (CFD correlation):

{| class="wikitable"
! Change !! Aero Impact
|-
| +1 mm front ride height || –0.8% downforce, +1.4% balance rearward
|-
| +1° pitch forward || –2.2% aero balance forward, +3% yaw sensitivity
|-
| +2 mm heave stroke mid-corner || diffuser stall risk ↑ 18%
|}

Teams simulate with pitch-sweep and heave oscillation modes under fuel load variation and rear wing DRS closure. 1 mm pitch instability can cause >0.1s/lap penalty on aero-sensitive tracks (e.g., Silverstone).

== Inerter Systems and Heave Mode Response ==

Inerters ("J-dampers") generate force as a function of vertical acceleration:

<math>
F = b \cdot \ddot{x}
</math>

Where:
* <math>b</math>= inertance (kg), usually 3.5–6.5 kg  
* <math>\ddot{x}</math> = suspension vertical acceleration

Heave resonance tuning targets:
* Frequency: 9–13 Hz (above floor oscillation frequency)  
* RMS displacement: <2.5 mm at max velocity (60 mm/s)  
* Damping ratio (ζ): 0.65–0.75 for vertical critical damping

Disallowed if hydraulically linked across axles under 2016–2021 FIA interpretations.

== Tyre Load Sensitivity and Vertical Compliance ==

Suspension compliance affects contact patch consistency. Tyre grip scales with vertical load until saturation, but lateral grip is highly load-sensitive.

<math>
F_y = \mu \cdot F_z \cdot (1 - S \cdot \Delta F_z)
</math>

Where:
* <math>S</math> = load sensitivity coefficient (0.07–0.12)
* <math>\Delta F_z</math> = load variation

Target load variation over a lap:

- High-load corner (e.g., Copse): ΔFz < 8% peak-to-peak

- Kerb strike (e.g., Monza T1): 3–5 mm damper compression, 20–25 g peak shock

== Suspension Compliance and K&C Mapping ==

K&C rigs measure hardpoint movement under applied loads.

{| class="wikitable"
! Parameter
! Target Value
! Comments
|-
| Toe compliance
| < 0.08°/kN lateral
| Controls oversteer/understeer behaviour during cornering loads
|-
| Bump steer gradient
| ~0.12° per 10 mm bump
| Affects stability and steering response at high slip angles
|-
| Roll centre migration
| < 2 mm/° roll
| Maintains aero platform and balance during lateral loading
|-
| Camber gain
| ~0.2° per 25 mm compression
| Preserves tyre contact patch under heave and roll
|-
| Compliance steer
| < 0.05°/kN lateral
| Ensures predictable handling at 3–5 g lateral acceleration
|-
| Scrub radius
| 10–15 mm
| Influences steering feedback and kickback under braking
|-
| Caster trail
| 18–22 mm
| Governs self-aligning torque and yaw sensitivity
|}

== Simulation and Rig Validation Process ==

Development cycle:

* Geometry defined in CAD → kinematic hardpoint solver
* Simpack/Dymola model for transient lap input simulation
* K&C test rig used to validate:
  - Vertical displacement vs load
  - Bump steer & toe curve
  - Roll gradient under 2g cornering
* 7-post rig simulation:
  - Damper settings for energy control
  - Ride energy profile from full lap replay

Track correlation:
* Laser ride height sensors at all corners
* Linear poten
tiometers on dampers
* Infrared tyre surface sensors

== Further Reading ==
* [[Kinematic Instantaneous Centre Modelling]]
* [[Inerter Systems in Formula Race Vehicles]]
* [[Load Transfer and Cross-Axle Migration]]
* [[CFD-Ride Height Coupling in Ground Effect Vehicles]]
* [[FIA 2022–2026 Suspension Regulatory Interpretations]]

== References ==

* [https://www.fia.com/regulation/category/110 FIA Regulations Hub]
* [https://www.fia.com/sites/default/files/fia_2025_formula_1_technical_regulations_-_issue_01_-_2024-12-11_1.pdf 2025 FIA Technical Regulations (Issue 01)]
* [https://api.fia.com/system/files/documents/fia_2025_formula_1_sporting_regulations_-_issue_4_-_2025-02-26.pdf 2025 FIA Sporting Regulations (Issue 4)]
* [https://www.fia.com/sites/default/files/fia_2026_formula_1_technical_regulations_issue_8_-_2024-06-24.pdf 2026 FIA Technical Regulations (Issue 8)]
* [https://www-control.eng.cam.ac.uk/foswiki/pub/Main/MalcolmSmith/cued_control_859.pdf Smith (2002): “Synthesis of Mechanical Networks: The Inerter” — IEEE (author PDF)]
* [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]
* [https://ep.liu.se/ecp/124/004/ecp16124004.pdf Sundström (2016): “Virtual Vehicle Kinematics & Compliance Test Rig” — Modelica Conference PDF]
* [https://publications.lib.chalmers.se/records/fulltext/219391/219391.pdf Danielsson (2014): “Influence of Body Stiffness on Vehicle Dynamics” — Chalmers PDF]
* [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]
* [https://search.worldcat.org/title/Race-car-vehicle-dynamics/oclc/31288484 Milliken & Milliken (1995): ''Race Car Vehicle Dynamics'' — WorldCat record]

[[Category:Chassis Design]]
[[Category:Suspension Systems]]
[[Category:Vehicle Dynamics]]
[[Category:Formula One Engineering]]