How much downforce does your wing make? Mathematically, you can calculate downforce using:
downforce = 1/2p * A * Cl * V^2.
If that means anything to you, then you don’t need this website. If that calculation scares the shit out of you, read on.
You can break this formula into four parts:
1/2p– I’ll simplify this as a constant value of
.00119. That’s all you need to know about
1/2p. (OK, someone actually asked about this, it’s air density, which changes due to elevation, temperature, and humidity. If you want to calculate the downforce at sea level, on a cold and wet day, versus a hot and sunny day in the mountains, go ahead. Or just accept my static value and move ahead.)
A– This is the area of the wing in square feet. If you have a 64″ 9 Lives Racing wing (10″ chord), then your area is 4.44 square feet (64″ x 10″ / 144 ). If you have a 72″ 9LR wing, that’s 5 square feet.
Cl– This is Coefficient of Lift. It’s a tricky value because it changes with different shapes of wings, how fast you’re going, the wing angle, and turbulence. For the time being, you can use a value of
1.0. I’ll explain later why this is a good value.
V^2– Velocity in feet per second, squared. For this you need to know that 1 mph = 1.46667 feet per second.
OK, so let’s figure out about how much downforce a 64″ x 10″ wing produces at different speeds. Three things will remain constant, the
1/2p value, the wing area
A, and the coefficient of lift,
Cl. Multiply all those factors together and you get a value of
.00528836. Now all we need is to multiply
.00528836 by the velocity in feet per second, squared.
|40 mph||3441.8||18.2 lbs|
|60 mph||7744.0||40.9 lbs|
|80 mph||13767.2||72.8 lbs|
|100 mph||21512.1||113.8 lbs|
|120 mph||30976.0||163.8 lbs|
How Much Added Grip?
If we assume that tire grip is linear, we can calculate the amount of grip you gain at different speeds. Downforce helps lighter cars more than heavy cars, because the percentage gain is greater. I’ll use the same wing and speeds to illustrate this.
|Speed||2400 lb car||3000 lb car|
Coefficient of Lift = 1.0
In the above calculations, I chose a Cl value of 1.0. In reality, a good single-element wing in free-stream air, at high velocity (high Reynolds number), can create 50% more downforce than that (Cl 1.5). Meaning that if we can place the wing in non-turbulent air, and drive faster (creating a larger Reynolds number), the wing will be at peak performance.
In the real world, you can’t get to peak performance. There is always some degree of turbulence, whether from your roofline, the wake of other cars, crosswinds, etc. Turbulence destroys lift. I saw this firsthand when I changed only the roofline shape on my car and back-to-back tested them: no roof was a 250% loss in rear downforce. A fastback was a 130% gain in rear downforce. Turbulence is a HUGE factor in generating lift.
The fact is that a wing doesn’t perform the same in free-stream CFD as it does at roofline height on your car. I changed only the roofline shape and made downforce go up and down by over 400% (Cl rear .23 to 1.09). There’s probably a degree or two of change in the wing angle due to the angle of air moving over the roof, but it’s not on this order of magnitude.
So this is a very long-winded way of saying that a coefficient of lift of 1.0 is fine for rough calculations on a hardtop Miata.
- If you have an open top, divide the wing’s downforce by 2.5.
- With a choptop, cut it in half.
- With an OEM hard top (also probably applies to a convertible with the roof up), use the figures in the table as is.
- With a fastback, multiply by 1.25.
If you want to nerd out on it, you can experiment with turbulence and lift using the NACA wing calculator (change the NCrit value) and see for yourself. If you want real values, you don’t do calculations, you hire a professional to measure the real-world differences on your car.