Cyclists in the Race Across America complain about crosswinds, not only because of unpleasant nasal effects...
but also because of a perceived kinetic energy penalty. Does a crosswind actually steal energy from a cyclist?
Represent the cyclist and bike as a frictionless cart on a track. The cart has the same drag coefficient for any direction of incident wind. It travels at 20 mph along the track and there is a 20 mph crosswind. (To be clear, the crosswind is perpendicular to the track, and the apparent wind felt by the cart is 45 degrees off straight ahead.) State your case for or against additional drag loss due to the crosswind.
gilbert, this isn't an answer, it's part of my question!
achillesfear, the PATH isn't into the wind, only the attitude. And it's debatable whether the biker crabs his attitude like a plane, even slightly. This would require tire scrub to stay on course, which is where the energy would go. My experience is that I just lean the bike. Anyway, I'm looking for something more fundamental, which is why I asked that you idealize the bike and cyclist as a cart (which can't sideslip or get pushed off the track).
hec, the answer is indeed in the aerodynamics, and the loss of drafting is a good thought. But RAAM riders tend to be loners, at least for most of the long cross-country trip. Maybe I could have been clearer, but I did refer to "the cyclist" and "a cart", and I'm looking for something that affects the single rider.
I hope you and the other answerers feel free to edit their answers if still interested. Here's a hint: Do the math.
melancholygiant, leaning may put you in a suboptimal position making the production of energy less efficient and comfortable (though in a steady crosswind, veteran bikers do a rigid lean, keeping the same relation to the bike). But your argument for more muscular energy is not solid. I asked for a yes or no on more drag force on an inanimate cart, and some math is needed.
This is about the decision below (they only give you 300 characters there). Here is what I was looking for:
Definitions
Vectors, Vw incident wind velocity, Fw air resistance aligned wih Vw
Fw(x) is aligned with motion
|A| is magnitude(A), A/|A| is unit vector along A
Aerodynamics says Fw=K * |Vw|^2 * Vw/|Vw|
Results
No xwind: Vw=[20,0], |Vw|^2=400, Fw=K*[400,0], Fw(x)=400
With xwind: Vw=[20,20], |Vw|^2=800, Fw= K*[566,566], Fw(x)=566
So there's a 41% drag penalty due to the crosswind.
Well, math may be math, but intuition says the Y force should have no effect since it's at right angles to the cart's velocity. But maybe one can appease intuition as follows: Consider a vertical cylinder moving along X. In a given time interval, the crosswind extends the path the cart cuts through the air by a factor of sqrt(2), while the path's width remains the same. So the mass of air subjected to an X-axis momentum change by the cart's passage is also scaled by sqrt(2). That works for me.