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.
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This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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