Bicycles, The Earth & Basic Trigonometry

Contents

The first bikes and the fixie folks

Penny Farthers

Surplace

Bike Calc

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;