So I made an equation...
 

for climbing.

First off, I apologize for the mixed units. They are just what I'm most familiar with...
v= speed in mph
P= power in watts
m=mass (weight) in lbs.
g=grade (6% grade would be entered as 6)
d=distance in miles of the climb
t= time in minutes to get to the top

first:

v=50P/(m*G)
t=1.2dmg/P

Boring I know but here's what i've learned:

For my weight (200lbs including the bike) and a 7% grade, losing 10 pounds off my ass or my bike is the same as increasing my power by 20 watts. 5 pounds gets me 10 watts.

For a climb that generally takes me 11 minutes, I can cut 17 seconds off that time by losing 5 lbs. or gaining 10 watts of power.

This is in the context of climbing and thus ignores air resistance.

hope it's helpful to someone.

B.

It's also assuming that the weight lost is not muscle, because the real key is watts per kg. Sometimes losing weight will actually lose you watts as well.

/\word.

You might want to look at http://www.analyticcycling.com. They've done the work for you and you get to include all effects in all conditions without having to assume any, e.g. rolling resistance, are negligible.

holy sheep. that website rocks. still proud of my work but thanks for the link.

If you want to play with the formulas more on your own, get from the library or buy a copy of Bicycling Science 3rd edition from MIT Press. An entire chapter is devoted to the bicycle power equation; that plus the info on analytic cycling and a good spreadhseet or graphing program and you can spend hours at least as productively as on bf :)

also take a look here http://www.kreuzotter.de/english/espeed.htm

Yeah, that's a better resource. Upon a cursory look, the OP's equations look correct, but the full-blown equations are 2nd order ODEs that need to be numerically-integrated due to their non-linear nature - so that'll give you much more accurate results.

thank god there are online calculators for this. Calculus was way too many years ago.