Fourthbook wrote:
With so much time/$$$/attention given to reducing bike weight and streamlining it for aerodynamics, I’d like to better understand the relative role of the various factors that affect the work/effort necessary to propel a bike. Perhaps someone knows the equation and can provide general/typical values for the primary coefficients so we know where best to concentrate our efforts (other than on personal fitness).
As usual, the answer is on Sheldon Brown's site.
http://sheldonbrown.com/rinard/aero/formulas.htmRainer Pivit is a university type guy in Germany and has measured exactly what you're asking: typical values for the various forces that oppose a cyclist. His equation is:
(quote)
The force resiting the motion of the bicycle Ftotal consists of the sum of rolling friction Froll, aerodynamic drag Fwind, the force needed to accelerate Faccel, the upward slope resistance Fslope, the bearing friction resistance and the drive efficiency h. Unlike the other quantities, acceleration and upward slope resistance can also be negative - usually a positive thing for the cyclist - thus propelling rather than retarding the bicycle. Naturally the drive losses h apply only if the bicycle rider really pedals the bicycle and does not just let it roll. Bearing friction, such as friction in the hubs, is usually added to rolling friction; accordingly the bearing friction forces in the drive train are added to the drive efficiency h, specifically, pedals, bottom bracket, freewheel and partially also the hubs (the additional forces on the hub due to chain tension). Thus one arrives at the formula:
Ftotal = (Froll + Fslope + Faccel + Fwind)/h
where h : drivetrain efficiency, dimensionless.
(end quote)
Also there are two charts, Figure 1 graphically showing the Forces in the equation above, at different speeds, for a "typical" rider on flat goround. This might be the "work" you're asking about.
The second chart, FIgure 2, graphically shows the Power needed to overcome those Forces, again at different speeds, for a "typical" rider on flat ground. This might be the "effort" you're asking about.
What's interesting to me is that: you're right, aero is a bigger source of resistance than weight. But remember these charts are on flat ground, where weight only affects rolling resistance; on uphills, low weight really starts to matter. (On down hills, heavier is actually better!)
The usual question is, since we can all agree that aero+heavy is faster on the flats, and non-aero+lighter is faster up very steep hills, at what gradient does lighter weight become more important than good aerodynamics...?