Originally Posted by
FBinNY
I hate trying to convinced the already convinced, but I'll give it a shot. The reason that ground speed must be figured into the solution, is that while the rider is riding against the wind drag, he's doing all his work levering the bike forward against a fulcrum on the ground. This is very different from an airplane that thrusts against the wind alone.
If you take a minute to draw free body diagrams of both an airplane (in flight) and a bicycle you'll see the difference, and understand why ground force and distance (work) come into play.
I like your idea of drawing a free body diagram.
If we're ignoring rolling resistance (which is already unphysical), then there is no force that depends on speed relative to the ground (consider a hovercraft instead if you prefer).
According to your diagram, what is the difference of the forces acting on a bicycle between (A) a bicycle moving at 30 mph with no wind and (B) a bicycle moving at 10 mph heading into a 20 MPH wind? In both cases, there is a single resistive force of the aerodynamic drag of 30mph acting on a bicycle. In both cases, it takes the same exact effort of the rider.
In reality, rolling resistance is not negligible (and does grow with speed). But even with rolling resistance the OPs numbers do not make sense:
* Into 20 mph wind, riding at 10 mph
* With 20 mph wind, riding at 25 mph
Assuming same aerodynamic positioning, this either suggests that rolling resistance* is much bigger than any of us is considering, or that, well, it wasn't a 20 mph wind.
Cheers,
Charles
* I'm throwing in drive train losses with rolling resistance here.