Training & Nutrition - Spin rate, gears = MPH?

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View Full Version : Spin rate, gears = MPH?

WonderMonkey
03-04-08, 07:53 PM
Is there a general formula that equates spin rate plus gear selection to miles per hour for the different size bikes? Is this a reasonable hope?

There is some music available that is a certain beats per minute and is used for training. If I knew I could set the major gear to 3 and the minor gear to 5 (for example) and ride at a certain BPM I could keep myself at a certain speed.

Make sense? No?

supton
03-04-08, 08:07 PM
I use a quick-hand formula (usually have Excel or a calculator handy):
kph = cadence * 60 * chainring / rear_cog * 2.1 / 1000
mph = 0.62 * kph

Boiling it down a bit:
mph = 0.07812 * cadence * chainring / rear cog

Bike size doesn't matter. 26" and 700c tires are nearly the same diameter, so the equation holds. 650c, I'd have to rework the math but it should be close enough for a workout.

However, as you tire, your BPM goes up for the same power output (or speed). Or, your speed will go down as you tire, if you hold the same heartrate.

WonderMonkey
03-04-08, 08:10 PM
I use a quick-hand formula (usually have Excel or a calculator handy):
kph = cadence * 60 * chainring / rear_cog * 2.1 / 1000
mph = 0.62 * kph

Boiling it down a bit:
mph = 0.07812 * cadence * chainring / rear cog

Bike size doesn't matter. 26" and 700c tires are nearly the same diameter, so the equation holds. 650c, I'd have to rework the math but it should be close enough for a workout.

However, as you tire, your BPM goes up for the same power output (or speed). Or, your speed will go down as you tire, if you hold the same heartrate.

Wow, thanks! How did you come up with that? Just a knowledge of how bike gears work? I'm obviously ignorant of bike math. How do you know to divide the chainring by the rear cog? Standard stuff?

Trucker_JDub
03-04-08, 08:13 PM
Better yet: http://sheldonbrown.com/gears/

Check out Sheldons site. There is more then just the gear calculator. You could spend days reading about just about any thing bike related in there.

WonderMonkey
03-04-08, 08:27 PM
Better yet: http://sheldonbrown.com/gears/

Check out Sheldons site. There is more then just the gear calculator. You could spend days reading about just about any thing bike related in there.

OVERLOAD! That calculator has too many things to enter that I don't know the answer to.

barba
03-04-08, 08:30 PM
The math isn't too hard. You need to know your gear, the diameter of your wheel/tires and cadence. Send me a PM and I can email you an Excel spreadsheet I made to calculate either speed from cadence or cadence from speed for a given gear combo.

WonderMonkey
03-04-08, 08:31 PM
OK I went and looked up the specs to my bike and have MOST of the information. As much as my feeble brain can derive.

supton
03-04-08, 08:36 PM
Pretty much basic physics.

Think of it this way. It may help if you have your bike in a trainer, so you can stand next to it.

Start with the chainring in a small diameter gear. Each revolution of the crank will pull so many chain links. If you go to a larger chainring, it will then pull a proportionate number more. So, as the chainring goes up in size, bike speed tends to go up also.

Now, look out back at the cassette. If you shift from a smaller cog to a larger cog, it takes more chain links to get a full revolution of the wheel and tire. The speed of the bike is inversely related to the cassette gear. Ergo, the speed is related to chainring divided by cassette gear.

Now, using that info, we can determine how many times the wheel will turn for each revolution of the crank. The wheel itself will propel the bike a certain distance for each time it turns. That distance is the tire diameter times pi (which is approximately 3.14). If you spin the crank so many times per minute, you will move such and such a distance. If you multiple by 60, you will find the distance moved per hour.

The first formula I posted can be broken down as this:

cadence * 60 = crank revolutions per hour
chainring / rear_gear (cassette gear) = step up ratio of the drivetrain
2.1 is the approximate distance that the bike moves for each revolution of the wheel (in meters)
1000 is the number to convert from meters to kilometers
0.62 is the conversion factor from kilometers to miles

twobikes
03-05-08, 08:39 AM
Try this for a simpler formula. Multiply your speed in miles per hour by the constant 336 and divide by your gear in inches for your cadence. Factor the equation if you already know your cadence, but want to know your speed in miles per hour. (Cadence multiplied by gear in inches and divided by 336 equals speed in miles per hour.) Because your gear in inches has already been adjusted for your wheel size, the formula works for any bike.

WonderMonkey
03-05-08, 09:28 AM
I will give that a try as well, thanks for the info.

WonderMonkey
03-05-08, 09:29 AM
In addition to the good information I have received in this thread, I have this chart produced from the sheldonbrown.com site. I put in the information and got the below back. What does it mean?

http://www.henrynet.com/stuff/gearchart1.jpg

supton
03-05-08, 10:20 AM
Did you select gear development? It looks like that, although it could be gear ratio. "gear development" is how far the bike rolls (typically measured in meters) for each revolution of the crank. "gear ratio" is merely the step up ratio between the chainring and the cassette cog.

The % numbers shows the percentage difference between the gears. If you were to shift and use the same cadence in either gear, your speed would change by that %.

03-06-08, 07:10 AM
Not sure if you are interested but when I bought my bike last summer I had them put a Cateye computer on with cadence. I think it was around 45.00. Didn't really think I would need it, but it sure is nice to just look down and see your cadence instead of looking at watch, counting crank revs. and then multiplying. Just a thought.

Now, since this will only be my second year of biking I would like to learn more about the gearing on my bike to take advantage of all that it offers. And by the way, I'm not really eligible for the 50+ forum but I enjoy the info and friendly banter. The road forum is sometimes over my head but I do get lots of good info there as well. Just have trouble communicating as I have much to learn about biking.

Have a great day all.

twobikes
03-06-08, 07:14 AM
To use the formula I gave, you need to specify results in gear inches when you use Sheldon Brown's on-line gear calculator.

sch
03-08-08, 05:45 PM
A nominal easily remembered constant is 100rpm in 100gear/in is 30mph. The
hassle is figuring out your gear/in and cadence. Easier just to look at the speedo.

mdcrisp2000
03-08-08, 06:16 PM
Is this the sort of thing you're looking for?

http://www.kc-bike.net/topspeed/

WonderMonkey
03-11-08, 07:50 AM
Similar. A member here in the forums sent me their Excel spreadsheet which was a fantastic start. I then modified it a bit to get closer to how I would like to see it. If anybody wants it I'll ask him if it's ok. It allows you to put your crank and cog settings in and gives you MPH or Cadance in a nice display.

WonderMonkey
03-11-08, 07:51 AM
A nominal easily remembered constant is 100rpm in 100gear/in is 30mph. The
hassle is figuring out your gear/in and cadence. Easier just to look at the speedo.

I only wear my speedo when in France.