Torque is a rotational force that is calculated by multiplying the applied force by the distance (lever arm) from the axis of rotation. A higher torque allows more force to be applied but at a lower rotational speed. For Lance's mountain climb, a fixed gear bike with a smaller front sprocket will provide more torque for climbing but at a lower speed than a larger sprocket. The smaller sprocket multiplies the torque applied by the rider over a shorter lever arm, generating more force at the chain.

1. 
Torque this!
What is torque?

2. A B
Lance needs to climb the Pyrenees. His only options are fixed gear
bikes. Which one should he choose for the mountain climb? Why?

3. Torque (Rotational Force)
Torque is the effect of a force applied on a body at some
distance from the axis of rotation of that body (c.w. or
c.c.w.). Ex: Torque wrench or large pipe wrenches.
Torque = Force * Lever arm (length)
Unit of measurement:
English = Ft lbs SI = Newton meters

4. How is it calculated?
 As you apply a force to any point on a lever arm
(FxL) it gives you a Torque value that is “in waiting”
at the point of rotation.
 If you try to “feel” or re-apply that torque at any
other lever distance from the axis of rotation, the
torque is the distributed along the lever length (L).
 The shorter the Lever or smaller the sprocket, the
greater the Force that is applied from Torque.

5. In each case, the same torque
gets “loaded” into the drive
hub at the front sprocket. But
A the torque then gets re- B
applied through the length of
lever arm. Depending on the
length you’ll get some kind of
Force (T/L=F)
Because Lance loads the same amount of torque into the drive hub the
smaller front sprocket distributes the torque less, so more force is
“conserved” and is applied to the chain.

6. Force Transformers – Belt Drive
Drive Driven
Force: Since the two pulleys are connected by a common belt the Force In = Force Out
Lever Arm: The distance from the center of the pulley to the outside rim (radius).
Angular Speed: If the output pulley is twice as big as the input pulley, then the output pulley
would only make ½ revolution for every revolution of the input pulley.
Torque: Torque in = Fin x Lin Torque out = Fout x Lout
Mechanical Advantage = Torque out / Torque in
Mechanical Advantage: Since the Forces of the two pulleys are equal, then the lever arm
(radius) of the pulleys must determine mechanical advantage.

7. Torque Transformer -Gear Drive
Drive =18 Teeth Driven =24 Teeth
1. Force: Since the gears are directly connected the force from the drive gear is directly transferred to the driven
gear. In other words Force In=Force Out
2. Gear Ratio: Drive (input) gear = 18 teeth: Driven (Output gear) = 24 teeth
Gear Ratio = (Driven Gear / Drive Gear)
= 24 / 18 or = 1.33 to 1
3. Lever Arm: The distance from the center of the gear to the gear tooth (radius).
4. Angular Speed: If the drive gear makes one revolution, the output gear would make ¾ (.75) revolution). If
the input gear was spinning at 1000 rpm the output gear would be spinning at 750 rpm
5. Torque: Torque in = Fin x Lin Torque out = Fout x Lout
6. Mechanical Advantage: Determined by the Gear Ratio ( or ratio of the radii)

8. A bicycle is a combination of a gear drive and
belt (chain) drive system
200 N
1200N•10cm=12,000N•cm
of torque at driven hub
Calculate for both: 6000N•cm/5cm=1200N
1) Torque at hub of 10 cm (force transferred) 20 cm
drive gear
2) Force transferred
from drive to driven Pedal Length = 30 cm
gear 200 N
3) Torque at hub of
driven gear
6000 N•cm
of Torque in 20 cm 10 cm
each case:
(200N•30cm)
Note: 200 N = about 45 lbs of force

9. Torque vs. Speed
Greater Torque
Less Speed
Less Torque
Greater Speed

10. Basso’s Challenge
If the input (drive gear) is spinning
Clockwise at 20 rpm how fast and
what direction is the output gear
spinning?
N-is the number of teeth
 http://auto.howstuffworks.com/gears.htm
 http://www.howstuffworks.com/transmission.htm
 http://www-education.rec.ri.cmu.edu/multimedia/cgr.shtml