Mahindra Thar ramp launch at 60 km/h

Inputs & what-if

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Vehicle Ramp Launch (projectile motion)

Vehicle dynamics / Classical mechanics

The scenario involves a body leaving a ramp and travelling through the air under gravity, so a ballistic trajectory with optional aerodynamic drag is the appropriate model.

Equations

• v₀ₓ = v₀·cos(θ), v₀ᵧ = v₀·sin(θ)
• a = −g ŷ − (½ρ·CdA/m)·|v|·v
• x(t+Δt) = x(t) + vₓΔt (Δt = 2 ms, semi-implicit Euler)
• E_k = ½mv², p = mv

Validity range

Speeds 5–200 km/h, angles 0–60°, sub-transonic, near-sea-level air density.

Limitations

• This is a simplified physics model, not a full multi-body vehicle dynamics simulation.
• Pitch rotation is illustrative only; real rotation depends on suspension rebound and CG position.
• Landing damage, rollover and chassis loads are not computed.

Sensitivity

Effect of a +10% change on Air time

Timeline

• 0.00 sTakeoff — object leaves the ramp
• 0.97 sApex reached at 5.84 m
• 2.07 sLanding at 27.97 m from takeoff

External data & sources

• Kerb massreported · medium

  ≈1,850 kg

  Mahindra Thar published specifications · retrieved 1970-01-01

  View source
• Frontal drag area (Cd·A)estimated · low

  ≈1.6 m²

  Estimated from boxy SUV geometry (Cd ≈ 0.6, A ≈ 2.7 m²) · retrieved 1970-01-01

Assumptions

• Ramp exit height assumed 1.2 m
• Level landing surface
• No traction loss on the ramp
• Vehicle treated as a point mass at its centre of gravity.
• Ramp exit velocity equals approach speed (no traction/rolling losses on the ramp).
• Flat, level landing surface at ramp-exit height reference.
• No suspension travel, tyre deformation or aerodynamic lift.

Results

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Scientific integrity

Results are computed by an explicit, deterministic model integrated in SI units. Values are labelled as user input, external data, assumption, estimate or calculated result. Simplified models are educational approximations, not engineering-grade predictions.