Calculating Drag and Lift From Body Shape

The HP Wizard website has an enormous amount of information, and I have a lot of fun playing with their drag calculator. Basically, you choose from various options and it calculates the Cd and Cl of your car. Let’s try this on a Miata.

I set the following options, which gives me a Cd of .380 and a Cl of .32, which is spot on.

  • Shape – Well rounded (2)
  • Front elevation – Low, rounded, sloping up (a)
  • Scuttle and Wing – Flush, rounded top wings (3)
  • Windscreen – Wrapped ends (2)
  • Windscreen peak – Rounded at top (1)
  • Canopy plan – Tapering to front (3)
  • Rear Canopy – Rounded canopy and boot (4)
  • Lower rear quarters – Tapering to rear (1)
  • Underbody – Monocoque RWD (4)
  • Skin friction – Recessed windows w/ mirrors (5)
  • Internal flow – Typical (4)
  • Openings – Closed cockpit (0)
  • Wheels – Fenders only, 205/50-15 (0.046)
  • Lift induced drag – Production model (Cl .32)
  • Frontal area 18.09: height (48.2) width (65.9).

Windows open and top down

Most HPDEs and racing organizations require you to run with open windows, and HP Wizard can simulate that. By changing Openings to “Open window prod car,” the Cd increases to .428. Or if you use the Miata as intended and open the top, then the Cd is .466.

Now this is interesting because my testing showed that opening the windows was much worse than .428, more like .450. In fact, the hard top with open windows measured worse than a completely open top. I’m still trying to get my head around that. I didn’t test an open top without a wing (no time, and it’s not a racy configuration), so it’s possible the wing actually helped the open top create less drag by smoothing airflow behind the car. Dunno.

In Race Car Aerodynamics, Katz measures the effect of open windows on passenger vehicles and race cars, and a typical sedan loses .067 drag to open windows and .09 to removing the top. So again, this is perplexing why the Miata in particular is so bad with open windows and a hard top.

So I’m just going to stick with a closed-windows model for the rest of this investigation.

Lift and downforce

The HP Wizard calculator can also calculate lift. If I choose the standard production model options, then my Miata model has a coefficient of lift (Cl) of .32. That’s pretty accurate based on other data I’ve seen. Let’s use the calculator’s lift options and see what happens to drag and lift as I lower the car and add downforce.

As usual, I’ll also simulate lap times on a race track (this time VIR). I’ll use a stock Miata (2450 lbs, 4.3, 1.0g tires, etc) and try it with 93 hp, and then I’ll add 50 hp because who has a stock Miata?

Lift-induced dragCdClVIR 93 hp143 hp
Production model.380.32151.52141.29
Sport.378.20151.18140.86
High performance.378.151:51.06140.7
Diffuser.377-0.10150.45139.88
Production race car.377-0.50149.57138.67
Speedway Miata (?).503-1.90149.73137.30
High downforce Miata.806-3.50155.35139.88

Reducing lift (downforce) yields faster lap times, to a point. A Speedway Miata (if such a thing exists) needs a lot of power to overcome the drag. The high downforce version has so much drag that even 143 hp is not enough.

Another thing worth calling out is the diffuser. The Miata underbody is anything but flat, and a diffuser would work better with a flat bottom, but this tool doesn’t allow us to make such adjustments. Anyway, the tool says a diffuser will reduce drag slightly and increase downforce by about .25. If that’s true for a Miata, this is totally worth doing.

Reducing drag with a fastback

In the above simulations, drag turned out to be a lot more consequential than I would have thought. Let’s see about reducing drag with a fastback. Based on real-world tests of my fastback, this could be up to a .07 reduction in drag.

First, I’ll modify some values in HP Wizard and change “Rounded canopy and boot” to “Fastback 10-20 degrees,” and the Canopy plan to “Tapering to rear”. Right away the Cd goes from .380 to .333.

The next thing I see on the Miata is the hard top extends wider than the windows, and catches air moving along the car. My fastback doesn’t do that, so I’ll change Skin Friction from “Recessed windows” mirrors, to “Perfectly smooth body with mirrors,” and now Cd is .323.

That’s a total of 0.058 reduction in drag, which is really good. Not quite as good as my fastback, but I’ve also added some vents for internal airflow. So let’s clean up the internal flow from “Typical” to “Good Design” and the Cd drops to .314, which is a .066 reduction, and getting close to the .07 delta between an OEM hard top and my fastback.

So there’s no magic to a fastback’s drag reduction, just some simple things that are easy to calculate. The fact that a fastback also made my wing produce 20% more downforce was a pleasant surprise.

E30 fastback?

I’m not really a BMW guy. My brother used to have a chipped 325e (now with WINsome Racing), and we had that car plus our Miata and MR2 at Thunderhill, 3-mile, all on the same day. I loved the torque and sound of the straight six, and I went fastest in that car. But something about it and me never clicked.

On the other hand, Anthony Zwain is a BWM guy, and owns EDGE Motorsports in Mountain View, California. After the WGI aero test, Anthony and I started fantasizing about turning a E30 convertible into a fastback. The convertibles are heavier due to chassis bracing, which is a good thing, and the fastback roof would offset that by being very light (probably 20-25 lbs total). It could be a shooting brake or fastback. The sky’s the limit with a convertible.

Image result for e30 convertible
Imagine the possibilities….

You wouldn’t necessarily need a convertible to do this. I can imagine someone simply cutting the C-pillar, jumping on the the rear of the roof until it bent to about 12 degrees, and welding it back again. You’d need new side and rear windows, but those should be Lexan anyway.

Anthony. WINsome. Shut Up. One of y’all should do this.

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