# Calculating Wing Downforce

How much downforce does your car wing make? Mathematically, you can calculate downforce using this formula:
`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 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, then your area is about 4 square feet (64″ x 9.1″ / 144 ).
• `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`. Multiplying by 1 is easy, and I’ll explain later why this is also a reasonable value.
• `V^2` – Velocity in feet per second, squared. For this you need to know that 1 mph = 1.467 feet per second.

OK, so let’s figure out about how much downforce a 4 square-foot single-element 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. I’ve also added the Reynolds number (Re) at that speed for later discussion.

If we assume that tire grip is linear with weight (it’s not, but I’m simplifying it), 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.

You can see that at low speed, downforce isn’t very effective, and you might question its use for autocross (40 mph avg). To be fair, drag isn’t very consequential at low speed, so as long as your aero parts aren’t heavy, or at the polar ends of the car (which they usually are), then low speed aero is somewhat useful.

At medium speeds, downforce is a noticeable advantage. If you’re looking at this table and thinking 3% grip isn’t that big of a deal, it is. On a Miata, that’s the difference of about one second at most race tracks.

At high speed, over 100 mph, aero is a game changer.

## Coefficient of Lift

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. When I swapped roofs, there was probably a degree or two of change in the angle of air moving over the roof, but that wasn’t going to change things 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 single element wing, on a Miata. For a properly designed dual element wing, you can use an equally rough value of Cl 1.5. My original dual element wing measured more like 1.3, but I’ve made more modifications since, and it’s probably closer to 1.5 now.

In another post on low speed wings, I investigate how wing chord and speed affect the Reynolds number, and that wings perform better at high Re numbers (faster speed or larger chord). Conversely, low speeds and narrow wings generate lower Re numbers. You could use that to fudge the calculation slightly. For example, for a Reynolds number around 300k or less (low speed or narrow chord), use a coefficient of lift of 0.8 or so, and for a Re of over 800k (high speed or big wing), use 1.1.

Since coefficient of lift is affected by roofline shape, use the following modifiers when you calculate downforce for a Miata:

• If you have an open top convertible, divide the wing’s downforce by 2.5.
• With a choptop (or a hardtop with the window removed), cut downforce 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 wing shapes, angles, turbulence, and lift using the NACA wing calculator and see for yourself. If you want real values, you don’t do calculations, you hire a professional (not me) to measure the real-world differences on your car.

## 2 thoughts on “Calculating Wing Downforce”

1. jimmy says:

what does p refer to

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1. john hayes says:

p = penis (haha had to)
ρ = m/V
where
ρ = density, units typically [kg/m3] or [lb/ft3]
m = mass, units typically [kg] or [lb]
V = volume, units typically [m3] or [ft3]

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