Math problem: 17060 rph or 5430 rph?
 

I've confused myself, and maybe some of you can help: I was just messing around with this new unit converter (mph to kph, fahrenheit to celsius etc) and decided to figure out some bike stuff. I wanted to see how many crank rotations it takes me to go a mile. Here's how I broke it down:

If I have 48x17 gearing with 700x23 tires, I know that I am traveling 74.3" per rotation.

74.3" is 0.0011726641 miles.

0.0011726641 goes into 1 (mile) 852.759115 times (I rounded to an even 853 for this thing here), so 853 rotations of the cranks will take me 1 mile, right? OK, so let's continue:

If I am traveling at the rate of 20mph, I would multiply 20 (miles) x 853 (rotations) to get 17060 rph (rotations per hour) right? OK... so here's where I get confused.

If I'm traveling at 20mph, my cadence is roughly 90.5 rpm. If I multiply 90.5 x 60 (minutes in an hour) I get 5430.

Where am I messing up? If I figure out my rotations per hour by distance, I get a very different figure than when I figure it by time. I am hoping that someone here can help me figure this out, it will bug me enough that I will try to count my rotations on my next hour ride!:twitchy:

Anybody?

Gear inches is not the distance you travel per rotation. Gear inches is the equivalent diameter of a penny farthing type bike (aka no gears just one giant direct drive wheel)

so the distance you travel is 74.3" * pi or 233.42" which is .003684 miles
this is 271.4 rotations for a mile (3 minutes/mile)

20 miles at 271.4 rotations gives 5428 which is the same as your 5430

When you said "gear inches is not the distance you travel…" I immediately started googling to prove you wrong, but instead I found that it is I who had been mixed up for all these years. I didn't even know there was a thing called development, but that's what I had always been attributing the value of gear inches to. Thanks for setting me straight there.

So knowing gear inches is actually kind of worthless. I mean, knowing how far I will go on a crank's rotation = useful. Knowing how big my wheel would be if it were a penny farthing = stupid. Why do people care at all about gear inches? Why isn't development the number that is thrown around all the time?

I guess it gives a constant you can compare against I guess. It does give you a piece of information that is "standard".. given a direct drive wheel how big of a diameter would it be to travel the same distance as with gearing, useful dunno.. but I guess you can always just take the gear inches and multiply it by about 3 (pi to be exact) and get the distance traveled.

Not sure why it is the one people care about most