How does the airfoil pitching moment relate to center of pressure?

Question

I've looked everywhere to find the answer and it's still unclear to me.

How does pitching moment relate to center of pressure? Does it relate to coefficient of lift?

I have made a carbon fiber wing (Eppler E423) and the CM of that wing is around -.22 where i'd be running it on my racecar. Where is the center of pressure so I can put my main mount directly under?

PS: let me reword, I want to calculate where my center of pressure is along the chord. I'd rather use CM to calculate that(if possible), but any other method aside from hand measuring it from a CP plot would be nice.

Answer 1

The pitching moment probably has little (if any) relevance in the case of an airfoil attached to a race car.

In particular, the pitching moment is related to the fact that with a cambered airfoil, the center of pressure will forward and backward depending on the angle of attack at which the airfoil is operating.

In the case of a race car, the angle of attack won't normally vary much, so the pitching coefficient probably isn't very relevant.

I'm not sure it's really relevant, but the aerodynamic center is normally taken as being at 25% of MAC. The C_m basically then defines a torque that's exhibited at the aerodynamic center.

One other point: I'd at least assume that on a race car, the airfoil is mounted upside down compared to an aircraft--that is, it's intended to produce pressure downward, not upward. To the (I think minimal) extent that pitching moment is relevant at all, it'll be positive (whereas it's normally negative for the main wing of an aircraft). That is to say, on an aircraft the pitching moment leads to a force pushing the nose downward, but in your case it'll be a force tending to push the nose up (and the tail down).

Okay, so based on the comment, what's really desired in this case is to compute the location of the center of pressure. To do this, we really need two things: the C_m and the C_L.

For the moment, I'm going to assume a Reynolds number around 500,000 or so. For an E423, your quoted C_m of -0.22 corresponds to an Alpha (angle of attack) of around 5 degrees. With Re = 500K and alpha=5, it looks like the C_L is about 1.6.

The formula we need is:

h_cp = h_ac - C_mac / C_L.

Plugging in the numbers, we get: 0.25 - (-0.22)/1.6.

Running that through the calculator, we get 0.3875. So your center of pressure should be approximately 38.75% of MAC. Of course, you'll need to adjust if you're actually basing your number for C_m on a different combination of angle of attack and Reynolds number.

As noted above, in your case the airfoil is (presumably) upside-down, so that should really be a C_m of +0.22 and a lift of -1.6, but the signs cancel so we get the same result either way (exactly as you'd expect).

References:

1. Airfoil data
2. Computation