Homework: Second Opinions and All That Jazz

[Sorenson]

I dare not put this in GE like I had to do with my last scholarly thread - it wound up becoming nothing more than a running joke about masturbation.

Anyway: as part of my final grade for my Algebra class, I and a partner have to devise a way to determine the cadence of a bicycle rider through the use of speed, tire size, and cog sizes. After a bit of pondering and thinking, I hit upon the idea that it's more or less all about proportion, and devised the following, both in Metric and Imperial. My instructor asked for Imperial, oddly enough (I mean, this is a scientific problem) but I figured I'd add both, both for a bit of clarification and to try and one-up him.

The Metric Method:

c - Cadence (in RPM)
t = Circumference of rear tire (in cM)
s = Speed (in KPH)
r = Rear Cog teeth number
m = Chain Ring teeth number

c = (((s*100000)/60)/t)*(r/m)

Alternatively, I would have:

d = s*100000
e = d/60
f = e/t
g = r/m
c = f*g

The Imperial Method:

c - Cadence (in RPM)
t = Circumference of rear tire (in inches)
s = Speed (in mph)
r = Rear cog teeth number
m = Main gear teeth number

c = ((((s*5280)*12)/60)/t)*(r/m)

Alternatively, I would use:

d = s*5280
e = d*12
f = e/60
g = f/t
h = r/m
c = g*h

Half the equation is converting speed into a flat distance against which I can weigh the chain ring/rear cog ratio I figured was the key to the answer. For the Metric method, this is done in the manner of multiplying speed against the number of centimeters in a kilometer, dividing this by 60 to get distance travelled per minute, divide this by the circumference of the rear tire, then multiply this against the result of dividing the number of teeth on the rear cog by those on the chain ring. For Metric, it's a similar process: speed against the number of feet in a mile, times twelve to get the number of inches covered, divided by 60 to get distance covered in a minute, then divided by the circumference of the rear tire. Again, multiplying this against the result of dividing the rear cog teeth by the chain ring teeth yields the answer.

In the test equations I've run, I've gotten fairly decent results - I'd like to hear some second opinions, however.

[Church-of-Oranges]

We just did a problem like this too....and I forgot. Try solving for the equation by finding the missing variables ( like one of those stupid I give you a formula like E=mc^2 and they tell you to solve for c.)