Saved runs (history)
| Time | Units | Run | Slope | Sled | Snow | Posture | μ | Wind | Crosswind | Start | Ride time | Final | Max | Stop dist |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| No runs saved yet. Calculate to add entries. | ||||||||||||||
Example data table
| Scenario | Run length | Slope | Snow | Posture | Wind | Crosswind | Estimated max speed |
|---|---|---|---|---|---|---|---|
| Packed snow, calm | 220 m | 12° | Packed | Normal | 0 m/s | 0 m/s | ~18–24 m/s |
| Headwind plus crosswind | 200 m | 10° | Packed | Upright | -4 m/s | 6 m/s | ~10–16 m/s |
| Steeper hill, tucked posture | 260 m | 15° | Icy | Tucked | +3 m/s | 0 m/s | ~24–32 m/s |
Formula used
This calculator models motion along a straight constant slope with aerodynamic drag and kinetic friction.
- Fg = m g sin(θ) (gravity along the slope)
- Ff = μ m g cos(θ) (friction opposing motion)
- vrel = √((v − walong)² + wcross²) (relative wind speed)
- Fdrag,along = -½ ρ Cd A (v − walong) · vrel
- a = ((Fg − Ff)·eff + Fdrag,along) / m
The ride is simulated with small time steps (dt) using numerical integration to estimate speed, time, and distance.
How to use this calculator
- Select units and enter run length with angle or drop.
- Pick sled, snow, and posture presets for quick estimates.
- Adjust Cd, area, and μ if you want custom tuning.
- Add wind along the slope plus crosswind if needed.
- Enable auto air density using altitude and temperature.
- Calculate, review results, then export your history.
Sled ride performance guide
1) Slope and distance inputs
Run length is measured along the hill, not horizontally. A 250 m run at 13° produces about 56 m of vertical drop (250·sin13°). Enter angle directly or use the drop mode when you know start and finish elevations. Longer runs also increase drag time, so speed does not always scale linearly.
2) Snow friction and surface feel
The friction coefficient μ controls how quickly the sled loses energy to the snow. Icy tracks often sit near 0.03–0.04, packed snow around 0.05–0.08, powder near 0.08–0.12, and wet snow can exceed 0.10. If your ride stops early, reduce μ or increase angle, or add a starting push.
3) Aerodynamic profile and posture
Air drag scales with Cd·A and with relative wind speed squared. Selecting a sled preset fills typical Cd and frontal area values, then posture multiplies them. Going from Upright to Tucked can cut effective Cd·A by roughly 20–35%. At 20 m/s, that reduction can save hundreds of joules over a few hundred meters.
4) Wind and crosswind effects
Along‑slope wind changes vrel = v − walong, while crosswind raises vrel even without headwind. Example: at v=18 m/s, walong=0, wcross=6 m/s gives vrel≈19.0 m/s, increasing drag about 11% compared with calm air. A headwind (negative walong) can reduce peak speed dramatically on gentle hills.
5) Air density from altitude and temperature
Dense cold air increases drag. With auto density enabled, sea‑level 0°C is near 1.29 kg/m³, while 800 m and −4°C is roughly 1.16 kg/m³. Lower density slightly boosts speed for the same hill. If you prefer manual control, keep ρ near 1.225 kg/m³ as a starting value.
6) Energy and stopping distance
The calculator estimates potential energy mgh, friction and drag losses, and kinetic energy at the finish. Track efficiency reduces the usable downhill force to mimic bumps, turns, and steering losses. Stopping distance uses d = v²/(2·abrake). If abrake=3.0 m/s² and finish speed is 16 m/s, stopping distance is about 42.7 m.
7) Using history and charts
Save multiple runs to compare setups, then export CSV or PDF for records. The speed chart is sampled from the simulation loop, so smaller dt and lower sampling intervals produce smoother curves and accurate peak timing. Use history to test “what‑ifs” such as higher crosswind, lower μ, or a tucked posture.
FAQs
Q1. Why does my sled stop before the full run length?
Friction and drag can overpower gravity on gentle slopes. Increase the slope angle or drop, lower μ, reduce Cd or area, or add a starting push speed. Also check that run length and drop values are consistent.
Q2. Do presets override my custom Cd, area, and μ?
Yes. Sled, posture, and snow presets update Cd, frontal area, and μ before the calculation. Choose “Custom” to keep your own values, or select a preset first and then fine‑tune the fields.
Q3. How is crosswind handled in the model?
Crosswind increases the relative wind speed vrel, which increases drag. The along‑slope drag still depends on (v − walong), but the magnitude is scaled by vrel = √((v − walong)² + wcross²).
Q4. What does track efficiency change?
Efficiency scales the downhill net force to represent bumps, steering, and energy losses on turns. Lower values reduce acceleration and peak speed, and can increase ride time. Use 0.85–1.00 for smoother tracks and lower for rough runs.
Q5. Why is auto air density useful?
Air density changes with altitude and temperature. Using auto density gives more realistic drag, especially in cold weather or high elevations. You can still set ρ manually if you already know a measured value.
Q6. How should I choose dt and chart sampling?
Smaller dt improves numerical accuracy but can slow calculation. A dt near 0.02 s works well for most runs. Chart sampling controls how many points are plotted; lower values make smoother curves but may render slower.