AeroTech wrote:
Hi Chris,
Thanks for the response and apoligies for taking a bit to reply.
My main objection is regarding the normalization, classically "dynamic pressure at infinity," Q_inf = 1/2 rho Vr^2.
Lets consider a cyclist riding at Vc=Vx, and relative to earth, there is a perpendicular wind velocity Vw=Vy, such that Vy/Vx = tan(beta), and Vr = Vx/cos(beta), Vy = Vx tan(beta).
Our wind, as defined, does not add a tailwind or headwind component to the rider, so Fd = -Fx in your Equation (3).
To properly apply Equation (6), we should use Vr = Vx/cos(beta), making it:
Fd = (CdA)_x 1/2 rho Vx^2 /cos(beta)^2
So far nothing has changed from your equations, we just ignore the complication of law of cosines. But many people, particularly those without sensors, incorrectly think of the data as representing
"If I'm riding at 50kph, and the wind appears to me as coming from an angle beta, then my drag is
Fd = (CdA)_x 1/2 rho Vx^2
which should emphasize that Equation (6) hides its inherent beta angle in Vr, but the data was acquired under one specific beta angle... so if we instead choose to be explicit in defining (CdA)_x = (CdA)_{x,beta_i}/cos(beta_i)^2, then the end user merely digests the formula as they imagine it, and further, (CdA)_{x,beta_i} is self documenting as being valid at a specific beta angle. I don't think anyone meaningfully digests the data as side wind + head/tail winds, so analysis and aero specialists can use whatever they like since they're less likely to develop a false intuition from the equations.
One thing I've personally witnessed, is people being surprised by the disconnect between coefficients and the forces they think they represent. Drag force will not be zero for a rider at 50kph and an extreme side gust, and I believe considering CdA_{x,beta_i}/cos(beta_i)^2 communicates that better than the alternative does.