Racing Line Lab

Cornering Physics

How radius, grip and speed decide whether a steady turn is possible.

Constant-radius corner · top viewR = 60 m
20 m40 m60 m80 m100 m120 m
velocity v (tangent)lateral acceleration alat (toward centre)
Experiment controls
60m
1.00
50mph
Results
Max cornering speed
54.3mph
Grip utilizationFraction of the total available tyre force currently in use: √(a_lat² + a_long²) / μg. 100% means the tyres are at their simplified limit.
85%
Required alat
0.85g
Available (grip limit)
1.00g
2 g
Friction circleCombined-grip model: braking/accelerating and cornering share one budget, a_long² + a_lat² ≤ (μg)². Cornering at the limit leaves no grip for braking or accelerating.: the solid ring is the grip limit μg, the dot is the lateral demand v²/R. Pure cornering, so all demand is sideways.
✓Within the grip limit with 4.3 mph of theoretical margin.
Theoretical maximum speed vs corner radius · v_max = √(μgR)
02040608010020406080100120selected 50 mph54.3 mph Corner radius (m) v_max (mph)

Physical principle

To follow a curve, the car must accelerate toward the centre. Only tyre friction can provide that force, and a simple Coulomb model caps it at μ times the car's weight. Speed at which demand equals supply is the steady-state cornering limit.

Equations

a_lat = v² / Ra_lat,max = μ gv_max = √(μ g R)
v
speed (m/s; shown in mph)
R
corner radius (m)
μ
effective tyre–road friction
g
9.81 m/s²

Your results

At R = 60 m and μ = 1.00, the tyres can supply 1.00 g, so v_max = 54.3 mph. At 50 mph the corner needs 0.85 g — 85% of the grip.

Doubling the radius to 120 m would raise v_max by 41% to 76.8 mph — not 100%, because v_max grows with √R. Meanwhile doubling speed would quadruple the lateral demand.

Try this

  • Increase the corner radius while keeping μ constant. Watch the marker climb the √R curve — each extra metre is worth less speed.
  • Find the speed where utilization is exactly 100%, then add 10% to the speed. Utilization jumps by ≈ 21%, because a_lat ∝ v².
  • Drop μ from 1.0 to 0.5 (a wet road). How much radius do you need to keep the same v_max?

Model limits: flat, unbanked road; constant μ; point-mass car; no aerodynamic downforce; steady state only. A real car at the limit transfers load, its tyres slip progressively and its handling depends on suspension and driver input — none of which this experiment simulates.