Last week when we talked about coefficients, I very briefly touched on something that really deserves some extra attention.
I used an example of finding a lift coefficient to show what these unitless numbers represent. We took the surface area of our wing, as well as our dynamic pressure—the pressure exerted by all those air molecules moving—and divided our lift measurement by both values.
What if you’re not testing a wing, though? Cars have aerodynamics too, and they don’t have wing surface areas to use. Are you just stuck?
That’s why we don’t actually refer to surface area when talking about coefficients. Instead, we use the term reference area—that is, the area we’re using to take all of our forces and moments and turn them into coefficients, and back again.
For aircraft, the reference area is nearly always the wing planform. If you took an airplane and positioned a light directly above it so that its shadow was in sharp relief on the ground, and then drew an outline around just the wing section (including the parts inside the fuselage), that would be your planform.
For cars, the reference area is the projected frontal area of the vehicle—if you drove the car through a giant sheet of paper, the frontal area is the hole you’d leave in the paper.
We don’t just have a reference area, though. When we go to make coefficients out of our moments, we have that extra length unit in there we need to get rid of.
So we have two other values:
- A reference span, the length straight across from left wingtip to right wingtip
- A reference chord, the length of the wing cross-section, or airfoil, from leading edge to trailing edge
Together, these three values are called the reference quantities. They’re the basic geometric dimensions that every aircraft needs for any aerodynamic analysis. Reference chord is especially necessary because it gets used when calculating our center of gravity.
For good, representative analysis, these reference quantities should be accurate to the aircraft you’re making.
But this starts to get complicated:
- If your wing isn’t straight across but tilts up, is the wing planform the full area of both wings, or is it just the projected horizontal part?
- When your wing is swept back, what’s your true span? The full length of both wings, or the actual tip-to-tip measurement?
- A lot of airplanes have different chord lengths at the wing root and the wing tip. So what the heck do we use as a reference?
This is why I said these quantities should be accurate to your aircraft—but this isn’t as critical as you think.