Understanding the car jump distance calculator — concept and principle
Film stunts, video games and physics classes all ask the same question: how far will a car fly off a ramp? This calculator treats the car as a projectile without air drag and finds the jump distance, flight time, peak height and the speed needed to clear a gap.
How it is calculated
- Horizontal speed vx = v cos θ stays constant; vertical position y = v sin θ × t − ½gt².
- Landing time at height h: t = (v sin θ + √(v² sin²θ − 2gh)) ÷ g.
- Jump distance = vx × t; peak height above the lip = (v sin θ)² ÷ (2g).
- Speed to clear a gap D at height h: v = √(gD² ÷ (2cos²θ (D tan θ − h))).
The principle
Once the wheels leave the ramp, only gravity acts (ignoring air), so horizontal motion is uniform and vertical motion is uniformly accelerated. Combining the two gives a parabola. For landing at the take-off height, the range is v² sin 2θ ÷ g, greatest at 45°. Distance grows with the square of speed, so a small increase in speed adds a lot of distance.
Worked example
Default inputs: 60 km/h, ramp angle 15°, landing at the same height, gap 12 m, g = 9.80665 m/s².
- v = 60 ÷ 3.6 = 16.67 m/s.
- Flight time = 2 × 16.67 × sin 15° ÷ 9.80665 ≈ 0.88 s.
- Jump distance = 16.67² × sin 30° ÷ 9.80665 ≈ 14.16 m; margin over the 12 m gap = 2.16 m.
- Highest point above the lip = (16.67 × sin 15°)² ÷ (2 × 9.80665) ≈ 0.95 m.
- Minimum speed for 12 m = √(9.80665 × 12 ÷ sin 30°) ≈ 15.34 m/s ≈ 55.2 km/h; landing speed = 60 km/h.
| Take-off speed (km/h) | Jump distance, horizontal (m) |
|---|---|
| 15 | 0.89 |
| 30 | 3.54 |
| 45 | 7.97 |
| 60 | 14.16 |
| 75 | 22.13 |
| 90 | 31.87 |
| 120 | 56.65 |
How to read the result
The margin tells you how sensitive the jump is: here a speed only about 8% lower would just reach the gap. Real cars lose speed to drag, pitch nose-down or nose-up and need a downward landing ramp to survive, so this ideal estimate is optimistic and only suitable for films, games and classroom problems.
Common mistakes
- Using km/h in formulas that need m/s.
- Ignoring the landing height difference.
- Expecting 45° to be practical for a car.
- Forgetting that air drag shortens real jumps.
Frequently asked questions
How far can a car jump at 60 km/h?
In this idealised model off a 15° ramp, about 14 m on level landing.
What ramp angle gives the longest jump?
45° for equal take-off and landing heights, ignoring drag, but steep ramps are impractical for cars.
Why does speed matter so much?
Range grows with the square of speed.
Sources: Halliday, Resnick & Walker, Fundamentals of Physics (projectile motion) · OpenStax, University Physics Volume 1, Section 4.3 Projectile Motion