© 2013 Autodesk

Bicycle Gears and Energy

Adam Kenvarg, Joel Rosenberg, and James Regulinski

Autodesk Sustainability Workshop

© 2013 Autodesk

Why Do Different Gears Feel Different?

http://images.nationalgeographic.com/wpf/media-live/photos/000/212/cache/bicycle-rider-and-dog_21256_600x450.jpg

http://www.bicycling.co.za/wp-content/uploads/files/touchline/bicycling/Bonking_4.jpg

© 2013 Autodesk

The definition of a “machine” is “a tool that consists of one or more parts, and uses energy to meet a particular goal.”

For a bike, the energy comes from the bike rider, who gets the energy from eating food.

A Bike is a Machine

(rider low on energy)

© 2013 Autodesk

Mechanical advantage is the main idea behind all machines – what is the output force for a given input force?

There is a tradeoff between output force and movement – the lower the output force, the greater the movement, and vice versa.

Mechanical Advantage

© 2013 Autodesk

Think about your experience biking: When it’s hard to pedal, are you going fast? When it’s easy to pedal, are you going slow? What gears do you use going uphill? Downhill? What makes you the most tired? How do you think that relates to energy?

Biking Fast and Slow

© 2013 Autodesk

This lesson aims to use calculations to help you understand how gears, wheels, and cranks all factor into the mechanical advantage of a bike.

Remember that the calculations are just models that reflect the reality of your experience biking.

Try to imagine what the numbers MEAN in terms of an actual bike.

Physics, Math, Engineering, and Bikes

© 2013 Autodesk

Gear ratio On most bicycles, two gears are linked by a

chain. The gear ratio is the number of teeth on the front gear divided by the number of teeth on the rear gear

Example 1: If the front gear has 44 teeth, and the rear gear has 11 teeth, the gear ratio is 44/11= 4/1 = 4.

Interpretation: When the front gear rotates around once, the rear gear rotates four full times.

We call this “high gear.”http://www.juniorvelo.com/wp-content/

ChainAndGearsMed.jpg

Rear gear Front gear

© 2013 Autodesk

Gear ratio II

Example 2: If the gears are reversed so the front gear has 11 teeth and the rear gear has 44 teeth, the gear ratio is 11/44 = 1/4 = 0.25.

Interpretation: For every complete rotation of the front gear, the rear gear will only rotate one-quarter turn.

We call this “low gear.”

(Note: 11/44 is a lower gear combination than most bikes have even for their lowest gear)

Rear gear Front gear

© 2013 Autodesk

Tire circumference

Tires are designated based in part by their diameter, which is the distance through the center of the circle. So 27” bike wheels have a diameter of 27” (670mm).

The circumference of a circle is the distance around its outside. It is defined as pi x diameter (C = π x d)

So a 670mm tire has a circumference:C ≈ 3.14 x 670mm ≈ 2100 mm = 2.1m

(for 27” tire, C ≈ 85” ≈ 7 feet)http://wpcontent.answcdn.com/wikipedia/commons/thumb/1/1d/CIRCLE_1.svg/220px-

CIRCLE_1.svg.png

© 2013 Autodesk

Tire circumference II

Finding the circumference is like cutting the circle and “unrolling” it to measure its distance around.

Another way to think about it is that if you put some paint at one point of a wheel, the circumference is the distance that will be between dots on the ground.

http://www.jasminesadler.com/blog/wp-content/uploads/2013/03/pie_crust_circumference1.jpg

© 2013 Autodesk

“Meters of development” To calculate how far the bike moves for each

front gear rotation, multiply the gear ratio by the wheel circumference:

For 760mm wheel, gear ratio 4 (48/12, “high gear”):

Meters of development= C x gear ratio= 2.1m x 4= 8.4m

For 760mm wheel, gear ratio 0.25 (12/48, “low gear”):

Meters of development= 2.1m x 0.25= 0.53m

© 2013 Autodesk

“Gain ratio”

The “gain ratio” relates the distance the pedal moves to the distance the rear wheel moves:

Gain ratio = wheel radius x gear ratiocrank length

http://mywheelsandmore.com/Images/bicycleParts/chainset/Bike-Crank-Arm-length-Determination.jpg

© 2013 Autodesk

“Gain ratio” II – High Gear

Example 1: A road bike in a high gear (44/11), that has 760mm wheels (r = 380mm) and crank length 170mm:

Gain ratio = (380mm/170mm) x (44/11)≈ 2.24 x 4≈ 9

Interpretation: In high gear, the wheel moves 9 times as far as the pedal.

© 2013 Autodesk

“Gain ratio” III – Low Gear

Example 2: A road bike in a low gear (11/44), that has 760mm wheels (r = 380mm) and crank length 170mm:

Gain ratio = (380mm/170mm) x (11/44)≈ 2.24 x 0.25≈ 0.56

Interpretation: In low gear, the wheel moves 0.56 times as far as the pedal.

© 2013 Autodesk

Another Gain Ratio Example

http://en.wikipedia.org/wiki/File:Bicycle_mechanical_advantage.svg

Below is a bike shown with two different gear settings. The gain ratio can be calculated directly from the info given, since it relates the pedal and wheel distances moved.

Lower gear gain ratio Higher gear gain ratio34cm/15cm = 2.27 68cm/15cm = 4.53

© 2013 Autodesk

The “easiness of pedaling” is measured by mechanical advantage (MA). This is the inverse of the gain ratio (1/gain ratio). It is defined as M.A. = Fout / Fin

Lower gear M.A . Higher gear M.A.1 / 2.27 = 0.44 (easier) 1/ 4.53 = 0.22 (harder)Fout = 1000N x 0.44 Fout = 1000N x 0.22

= 440N = 220N

Mechanical advantage

© 2013 Autodesk

So now we see that in high gear, for an increase in distance we get less force out (and it’s harder to pedal).

The higher the gain ratio, the lower the mechanical advantage.

Force/distance tradeoff

© 2013 Autodesk

In mechanical systems, energy = force x distance.

Input energy = 1000 N x 0.15 m= 150 Nm = 150 J

Output energy= 440 N x 0.34 m = 220 N x 0.68 m= 149.6 Nm ≈ 150 J = 149.6 Nm ≈

150J

What Does This Have to Do With Energy?

© 2013 Autodesk

If a biker is pedaling with a constant speed and input force, they are providing a constant amount of energy.

This input energy can be split between distance and force, depending on the gear ratio, wheel size, and crank length.

Energy input = Energy output!

© 2013 Autodesk

Like a bike, a car is just a more complex machine. Let’s compare the two to see some similarities:

Bike Car• Food is energy source • Gasoline is energy source• Biker’s muscles • Internal combustion engine• Gears help make bike • Gears help make engine

easier to pedal run efficiently (transmission)

How a Car is Like a Bike

https://secure.flickr.com/photos/gfreeman23/2992812856/lightbox/

© 2013 Autodesk

In this Inventor activity, you’ll be using Design Accelerator to alter the chain drive and observe the effects. You’ll also be measuring the diameter of the back wheel and the length of the crank.

Then we’ll tie our measurements to the math and see how everything relates.

So Let’s Get to It!

© 2013 Autodesk, Inc. All rights reserved.

Autodesk is a registered trademark of Autodesk, Inc., and/or its subsidiaries and/or affiliates in the USA and/or other countries. All other brand names, product names, or trademarks belong to their respective holders. Autodesk reserves the right to alter product and services offerings, and specifications and pricing at any time without notice, and is not responsible for typographical or graphical errors that may appear in this document.