Sledding is an inclined plane experiment you can do every winter. The steeper the hill and the slicker the runners, the faster you go – but friction and air drag keep real speeds below these ideal values.
How to use the Sled Ride Calculator
- Type of sled
- Hill angle
- I know the hill…
- Hill length
- Hill height
- Gravitational acceleration g
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose your sled (each has a typical friction coefficient on snow), the hill angle and either its length along the slope or its height.
Inputs explained
| Field | What to enter |
|---|---|
| Type of sled | Choose one: Steel runners on ice, Plastic sled on packed snow, Inflatable snow tube, Wooden toboggan on snow … |
| Hill angle | Units: °, rad, arcmin, arcsec, mrad |
| I know the hill… | Choose one: Length (along the slope), Height |
| Hill length | Units: m, cm, mm, km, in, ft … |
| Hill height | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
What each result means
- Acceleration = max(0, [Gravitational acceleration g]×(sin(rad([Hill angle])) – [Type of sled]×cos(rad([Hill angle]))))
- Speed at the bottom = sqrt(2×[Acceleration]×[L])
- Hill length = [L]
Example values
How the main result changes when Hill angle changes and everything else stays at the example values above:
| Hill angle (°) | Speed at the bottom (km/h) |
|---|---|
| 7.5 | 32.08 |
| 11.25 | 43.08 |
| 15 | 51.73 |
| 18.75 | 59.02 |
| 22.5 | 65.4 |
| 30 | 76.19 |
Formula
a = g(sin θ − μ cos θ), v = √(2aL), t = √(2L/a)
Worked example
Inputs — Type of sled: Plastic sled on packed snow; Hill angle: 15 °; I know the hill…: Length (along the slope); Hill length: 50 m; Gravitational acceleration g: 9.80665 m/s².
Results — Acceleration = 2.0645 m/s²; Speed at the bottom = 51.73 km/h; Ride time = 6.96 s; Hill length = 50 m.
Key terms
- Kinetic friction
- Friction between surfaces sliding past each other.
Frequently asked questions
Why do I go faster on ice?
The friction coefficient of runners on ice is very low.
Does a heavier rider go faster?
Without air drag, no; with drag, heavier riders reach slightly higher speeds.
What is a safe sledding slope?
Gentle slopes (under about 15°) with a long flat run-out.
Why is my real speed lower?
Air resistance and uneven snow slow you down.