Hello, Bob,
You seem to have more information at your fingertips than I have in my books.
You have been sucked in by a difference between cars and airfoils. Somebody correct me if I get this wrong--
First of all, airfoils are two-dimensional and cars are three dimensional. Here are the drag formulas for both:
Cars: D = Cd A 1/2 rho V^2
Airfoils: D = Cd L 1/2 rho V^2
L is the length of the chord line. So, D for an airfoil has units of force per unit length of wing.
The real problem is that the Cds above have different definitions. It may not be possible to translate from one to the other, but let's try. Suppose the car has a rectangular cross-secion of unit width. Then, you could replace the A in the car formula by H, the height of the car. Equating the two drag formulas above gives--
Cd(car) H = Cd(airf) L,
Cd (car) = L/H Cd(airf) For the airfoil, L/H would be the "fineness"
Okay, so how do I translate for a car with a circular cross-section? Let's say that the car and the airfoil have the same drag when they have the same frontal area. Then, I could write an equation--
Cd(car) A 1/2 rho V^2 = Cd(airf) L W 1/2 rho V^2
and A = HW.
W is the length of the wing, or the width of the rectangular car.
We get the same result as before,
Cd (car) = L/H Cd(airf) For the airfoil, L/H would be the "fineness"
Okay, you say there are airfoils of about Cd = 0.0035 for which L/H = 5 about.
So, Cd(car) = 5 x 0.0035 = 0.0175, close to my initial guess. Well, I have settled on the suggestion from (who said it?) and used Cd = 0.025 for analysing the super-efficient rail-car.
Thanks, Bob, your words have been very helpful.
Ernie Rogers
Quote:
Originally Posted by Bicycle Bob
Do you have a reference showing attached flow on such an abrupt shape?
According to "the Theory of Wing Sections" by Abbott & Von Doenhoff, the NACA 66021 has a cd of .0035, but the 66009, twice as fine, gets .003. Even the 63 series is only listed at up to 21% thick, although I think I did OK with a 64025 for a strut.
For a good example of balancing volume with frontal area, I'd look at the Zeppelins. It is unfortunate that so much data on shapes pertains to wings. The earlier NACA series 0010-35 shape, with 10% thickness and a continuous convex curve to the back edge, more like a zeppelin outline, got to .003 cd, but had trouble with pitch instability as a wing.
To modify a pure shape for running near the ground, the bottom is squished in proportion to how low it is. This produces a wing shape, but the lift can be cancelled by a bit of rake and the venturi effect underneath. The overall effect on drag is not as bad as the addition of wheel exposure. Successful LSR cars are not jacked up. One such HPV was made, but it embarrassed the builders.
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