Bicycles, The Earth & Basic Trigonometry
- The first bikes and the fixie folks
- How fast can my bike go?
- Vertical speed = radius x angular speed (rpm)
- Gear Inches
- Development: How far you go with one rotation
- Climbing & Passing Gears
- How many revolutions do you make on your ride home?
- How fast are you going with a fixed cadence?
- Why does it feel like the passing gear is taller?
- How big is the equator? (in miles)
- What angle does the US subtend?
In the first bikes, speed depended only on wheel size (60 inches!) What is a 26 inch Mountain Bike Wheel? First, let's just think about the rim.
% 26 inches in diameter, diameter26 = 26; circumference26 = pi*26 % Road bikes & 29er's diameter29 = 29; diameter700c = 27; circumference29 = pi*29 circumference700c = pi*27
circumference26 = 81.6814 circumference29 = 91.1062 circumference700c = 84.8230
For a fixed speed, which wheel is rotating faster?
Today, geared bikes are sometimes measured in gear inches
% Number of teeth in front: 42 num_front_teeth = 42; % Number of teeth in rear: 20 num_rear_teeth = 20; gear_inches26 = diameter26 * num_front_teeth / num_rear_teeth gear_inches700c = diameter700 * num_front_teeth / num_rear_teeth gear_inches29 = diameter29 * num_front_teeth / num_rear_teeth
gear_inches26 = 54.6000 gear_inches700c = 56.7000 gear_inches29 = 60.9000
devs26 = pi*diameter26 * num_front_teeth / num_rear_teeth dev700c = pi*diameter700 * num_front_teeth / num_rear_teeth dev29 = pi*diameter29 * num_front_teeth / num_rear_teeth
devs26 = 171.5310 dev700c = 178.1283 dev29 = 191.3230
% road num_front_teeth = 52; num_rear_teeth = 11; % mtn num_front_teeth = 22; num_rear_teeth = 34;
earths_diameter_eq = 24900; earths_diameter_eq_plusonefoot = 24900 + 1/5280; avg_dist_earth_moon = 238857; avg_dist_earth_sun = 93020000; dist_newyork_los_angeles = 2462;