Toy Car Ramp Speed Calculator
Calculate the speed of a toy car at the bottom of a ramp.
Enter ramp length, angle, and surface friction to get exit velocity in cm/s, m/s, and km/h.
A toy car rolling down a ramp converts gravitational potential energy into kinetic energy. The exit speed depends on ramp length, angle, and the friction between wheels and surface.
The formula for a rolling object on an inclined plane:
v = sqrt(2 x g x L x (sin(theta) - mu x cos(theta)))
Where g = 9.81 m/s squared, L = ramp length in meters, theta = ramp angle in degrees, and mu = coefficient of kinetic friction.
Friction coefficients by surface:
- Smooth wood (sanded, finished): mu = 0.05
- Carpet or felt surface: mu = 0.20
- Rough wood (unfinished): mu = 0.35
What this means in practice: A 1-meter ramp at 30 degrees on smooth wood gives about 2.4 m/s (8.6 km/h). The same ramp at 15 degrees gives about 1.5 m/s. Halving the angle cuts more than a third off the speed.
For toy design: If you want a car to reliably trigger a loop or hit a target, you need predictable ramp speed. Too steep and the car flies off track. Too shallow and it stalls. The sweet spot for wooden track toys is usually 20-35 degrees.
Note: This formula assumes the car rolls without slipping. If wheels skid rather than roll, effective friction is much higher and the car will be slower.