# Bicycle Mechanics - Maths question! Gear/cadence related

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ronfinch
06-18-08, 07:17 AM
Hi all,
I was wondering if there exists a fairly simple fomula for calculating speed, using gearing, wheel size, crank arm, + anything else that might be pertinent? I realise that get a bike computer is the obvious answer - I am just interested. Searched but failed to find anything, and unfortunately I am not particularly mechanically/mathematically minded so am stuck...

Cheers
Ron

DMF
06-18-08, 07:50 AM
http://www.sheldonbrown.com/gears/

Google on "gear inches" too.

dabac
06-18-08, 07:50 AM
Hi all,
I was wondering if there exists a fairly simple fomula for calculating speed, using gearing, wheel size, crank arm, + anything else that might be pertinent? I realise that get a bike computer is the obvious answer - I am just interested. Searched but failed to find anything, and unfortunately I am not particularly mechanically/mathematically minded so am stuck...

Cheers
Ron

Check out Sheldon Brown's online gear calculator http://sheldonbrown.com/gears/ and set it to display gear units as MHP/KPH at a certain cadence.

cny-bikeman
06-18-08, 07:56 AM
As you asked for something simple a rough calculation can be made based on the fact that a 100 inch gear at 100 rpm is 30mph (50 kph). If you are in a 70 inch gear at 90rpm that makes it 30 x .7 * .9= 19mph (18.9). A 110 inch gear at 120rpm makes it 30x1.1*1.2= 40mph (39.6). Sheldon's and many other sites can produce gear inch tables. If you have access to a computer Sheldon's site is of course the best option but this works on the road, given that you can estimate cadence either way!

Mr. Underbridge
06-18-08, 08:03 AM
This can be found on Sheldon's site, but this is just basic geometry.

For each turn of the crank, you travel the circumference of the wheel multiplied by your gear ratio. If you know the circumference of your wheel (in meters) and your cadence and the size of your chainwheel and cog, then it's just:

You didn't specify, but since you say "maths" instead of "math", I'll assume you want km and m instead of miles and inches:

Speed (km/hr) = 0.06 x cadence(rev/min) x (Size of chainwheel in teeth) / (size of rear cog in teeth) x (circumference of wheel in meters)

Tricky part is wheel circumference - to guesstimate, get the bike on the sidewalk, orient wheel with valvestem down, put a chalk mark under valve, roll bike some number of wheel revolutions, chalk again, measure distance, divide by number of revolutions.

fordfasterr
06-18-08, 08:19 AM
Try this one !!! (http://velocide.com/cadence_calculator_new.html)

OLDYELLR
06-18-08, 08:20 AM
Try this: http://home.earthlink.net/~mike.sherman/shift.html

ronfinch
06-19-08, 07:38 AM
Hi all,
Only just got chance to get back online.
Thank you all very much for your replies - very useful and exactly what I was looking for, both the simpler thing and the more complex explanation on sheldon brown.com.

Cheers