http://www.mathmodels.org/problems/solview.php?solnum=39&probnum=20090&folder=1
http://www2.bsn.de/cycling/WheelAerodynamics.html
http://www.mathmodels.org/problems/comview.php?solnum=1&probnum=20090&folder=2

D. I. Greenwell, et. al., entitled ”Aerodynamic Characteristics of Low-Drag Bicycle Wheels”, Aeronautical J., Vol. 99, No. 983, Mar. 1995, pp.109-120, has a good discussion of the aerodynamics of bicycle wheels. Conclusions by Greenwell et al

http://www.smartcycles.com/bike_weight.htm

But how does this weight difference affect performance? Does removing these few pounds make the bike fly? Is a lighter bike the fountain of youth? The September 2003 Bicycling Magazine has a chart that makes it easy to quantify the performance gains from light weight. James C. Martin, Ph.D., assistant professor in the department of exercise and sport science at the University of Utah provided some interesting calculations that make the cost of weight very clear.

He posited a 5 kilometer, 7% grade. That's a good, stiff climb. The legendary Stelvio climb averages 7.5%. He further assumed a rider who can kick out 250 watts. A 160 pound rider will take 19 minutes and 21 seconds to get up the hill. Every 5 pounds added make the trip up the hill take 30 seconds longer.

That means each added pound adds 6 seconds to the time it takes to get up this hill. That is only 6 seconds on a stiff, 20 minute climb.

So, given our roughly 4-pound range from a full steel bike to a super-light carbon or aluminum bike, the time difference up this hill would be 24 seconds from best to worst.

But, most weight conscious people aren't bringing their bikes down to 15 pounds because down at that weight, the handling gets very sketchy. 17 - 17.5 pounds is the normal range. The real discussion is about 1.5 to 2 pounds.

The performance advantage of a lighter bike is greatest when the hill is steepest. What happens as things flatten out? Then, as the speed of the bike increases, the resistance comes from the wind, tire rolling resistance, bearing drag, etc. Those 6 seconds/pound grow ever smaller.

The variations in body weight, however, being so much greater, make large difference. If that same 160 pound-250 watt rider were to be 220 pounds, he would come in 6 minutes, 10 seconds later.