A short and incomplete list of equations and calculators useful for trails.
Math (elsewhere) On This Site
- Jumps and rollers/drains with calculator
- Turns with calculator
- Rigging (diagram) (Excel spreadsheet)
- Dragging diagram
- Levers (rock bars) (diagram)
- Walls (diagram) (Excel: Lateral-Earth-Pressure)
- Stairs (trail-step-calculatorv2)
note: Forest Service Trail Accessibility Guidelines (FSTAG) 220.127.116.11 “The cross slope [out slope] shall not exceed 1:20 (5 percent). Where the surface is paved or is elevated above the natural ground, the cross slope shall not be steeper than 1:48 (2 percent).”
A rough estimate of the trail length for a segment based on elevation gain or loss (typically the average grade should be less than 10%):
180° Turn Grade? Rise/Run @ Diameter vs. Rise/Run @ Circumference:
More on the complicated machinations of turning on a bike:
- Turning Radius calculation
- Geometry and Kinematics
- Bikes Don’t Turn by Leaning
- Counter-Steering Made Easy-Peasy
- Why does a cyclist bend or lean during a turn?
- Bicycle and motorcycle dynamics
- Bicycle Physics
- The bicycle problem that nearly broke mathematics
I hope to publish some nomograms in the future for some of the above math applications on this and other pages.