How this calculator works
The vehicle centre of mass follows a point-particle trajectory. Optional drag uses a constant frontal area equal to width times body height and is integrated with a fourth-order Runge-Kutta method. Pitch is torque-free in flight: either enter release angular speed or estimate it from constant rear-contact torque over a wheelbase/speed exit interval. That exit approximation holds the gravity lever arm fixed and ignores suspension, tyre forces and aerodynamic torque. Box inertia assumes uniform mass; measured inertia is preferable. Heights are centre-of-mass elevations, and reaching the plane does not establish wheel or body clearance.
Formula
ax=-(rho Cd A/(2m)) |v| vx; ay=-g-(rho Cd A/(2m)) |v| vy. I_box=m(length^2+height^2)/12. Exit estimate: alpha=-mg(xc cos(theta)-zc sin(theta))/(I_cm+m(xc^2+zc^2)); omega0=alpha wheelbase/v; pitch(t)=pitch_release+omega0 t.
Worked example
With no drag, a horizontal 10 m/s launch from 20 m above the landing elevation at g=10 m/s2 lasts 2 s and travels 20 m. A level-to-level launch with components 8 and 6 m/s travels 9.6 m in 1.2 s.
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Frequently asked questions
Does reaching the landing elevation mean the car clears a ramp?
No. This model follows the centre of mass. Vehicle corners, wheels, ramp edges and suspension can collide earlier.
How reliable is the pitch estimate?
A measured release rate is the clearer input. The exit-impulse option is a small-motion approximation, not a detailed ramp-contact simulation.
Does pitching change drag area?
No. Frontal area and drag coefficient remain fixed, and drag acts through the centre of mass. The model omits aerodynamic pitch torque.