Bicycles, The Earth & Basic Trigonometry
Contents
- 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?
The first bikes and the fixie folks
How fast can my bike go?
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
Vertical speed = radius x angular speed (rpm)
For a fixed speed, which wheel is rotating faster?
Gear Inches
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
Development: How far you go with one rotation
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
Climbing & Passing Gears
% road num_front_teeth = 52; num_rear_teeth = 11; % mtn num_front_teeth = 22; num_rear_teeth = 34;
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?
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;