Gear Ratio Math Problem

[g4drive]

I've been checking out this forum for over a year now and each time it tells me, "Our records indicate that you have never posted to our site before! Why not make your first post today by saying hello to our cycling community" ... So hello everybody ... I'm from the U.K. (Essex boy) but have been living in NJ, USA for many years. So on to my question:

I just came off the trainer and was trying to figure out my average MPH ...

Chainring: 39T
Rear Cog: 14T
Inches/Revolution: 75
Average Cadence: 105 rpm
Distance covered in a minute = (75 * 105)/63,350 = 0.12429 miles
Average speed = (0.12429 * 60) = 7.46 mph

Given the effort i had to put in, 7.46 mph doesn't seem like the right reward. Can anyone tell me what is wrong ... my gut feel is that this should have been at least 20 mph.

Thanks in advance

 

[graf zeppelin]

I've been checking out this forum for over a year now and each time it tells me, "Our records indicate that you have never posted to our site before! Why not make your first post today by saying hello to our cycling community" ... So hello everybody ... I'm from the U.K. (Essex boy) but have been living in NJ, USA for many years. So on to my question:

I just came off the trainer and was trying to figure out my average MPH ...

Chainring: 39T
Rear Cog: 14T
Inches/Revolution: 75
Average Cadence: 105 rpm
Distance covered in a minute = (75 * 105)/63,350 = 0.12429 miles
Average speed = (0.12429 * 60) = 7.46 mph

Given the effort i had to put in, 7.46 mph doesn't seem like the right reward. Can anyone tell me what is wrong ... my gut feel is that this should have been at least 20 mph.

Thanks in advance

I get 22.9 mph and I agree with you: based on gut instinct that also sounds about right. I didnt do the math though lol. I could likely figure it out, but I took the lazy route:

http://www.soulbikes.com/gears/

You can choose your crank length and wheel/tire size, and have it step cadences in intervals that would be helpful to you. It will give you average speeds for your two highest gears and then your lowest, and then all kinds of metrics for the entire cassette. If you are looking for speed data on a particular gearing, just pretend you have a single gear and put 39 in row one (for the chain rings) and 14 in row two (for the cassette).

 

[andrello]

I just came off the trainer and was trying to figure out my average MPH ...

Chainring: 39T
Rear Cog: 14T
Inches/Revolution: 75
Average Cadence: 105 rpm
Distance covered in a minute = (75 * 105)/63,350 = 0.12429 miles
Average speed = (0.12429 * 60) = 7.46 mph

Your first mistake is ignoring the gear ratio in your calculation. Your calculation assumes a one-to-one ratio. This would be correct if your crank was directly on the wheel like in the old days of high-rollers (you can see how inefficient those were). This is compounded in your second mistake which is using an average distance. This is irrelevant since you already know your average cadence.


Speed is a function of gearing, cadence and circumference of the tire:

speed in MPH=[# teeth chainring]/[# teeth sprocket]*[cadence in RPM]*[circumference of tire in meters]/26.8(<---unit conversion factor)
I'm using meters here because it makes the conversion factor a more reasonable number.

If your wheel circumference is correct (75inches=1.905meters) your average speed = 39/14*105*1.905/26.8=20.8MPH.


But beware - this does not necessarily translate to speed on the road because it may likely be easier to spin your wheel 20MPH on the trainer than it is on the road. To check, go out and see if you can hold that cadence for that gearing on a flat road.

Is your trainer listed here?:
http://www.geocities.com/almost_fast/trainerpower/
The Kurt Kinetic Road Machine (post-2004 models) supposedly has the most road-accurate resistance.

Anyway, if you're getting cadence you must have a computer. Why don't you use it on your rear wheel when on the trainer? If it's wireless and the signal is too weak to make it to the computer from the rear you can move the computer from your handlebars to your top tube or seatpost.

 

[g4drive]

Your first mistake is ignoring the gear ratio in your calculation.
...
Speed is a function of gearing, cadence and circumference of the tire:

speed in MPH=[# teeth chainring]/[# teeth sprocket]*[cadence in RPM]*[circumference of tire in meters]/26.8(<---unit conversion factor)
...

If your wheel circumference is correct (75inches=1.905meters) your average speed = 39/14*105*1.905/26.8=20.8MPH.

Andrello,

Thanks very much for your reply. I did not ignore the gear ratio. When I said "inches/revolution" that is the distance traveled with one revolution of the pedals ... i.e. =[# teeth chainring]/[# teeth sprocket]*[circumference of tire in inches] = (36/14) * 26.9685 = 75.13 (or 75 as stated)

Therefore, using your formula, I get:

39/14*105* (26.9685 inches converted to meters = 0.685m) /26.8 = 6.9mph ... back to my confusion.

 

[g4drive]

Thank you graf zeppelin,

The link you posted helped me figure out my problem:

The "inches/revolution" number I have was taken from a gear ratio table, where (39T chainring / 14T sprocket) * wheel diameter = 75 inches ...
of course I was thinking that the tables would use wheel circumference so that the result would be distance traveled in that gear from one turn of the cranks ... would make sense. So real distance traveled from one revolution of cranks is: (39/14) * 26.8 * 3.14159 = 234.54 inches and MPH = (inches travel per revolution * cadence * 60) / #inches-in-a-mile = (234.54 * 105 * 60) / 63,360 = 23.32 mph

Mystery solved. Thanks again.