Swedish Simulations

Every year my sister Mia gives me Swedish Fish in my Christmas stocking. This year I’m in Florida (I’ll be racing Sebring next week), and I won’t get any candy. Instead of getting something Swedish, I’ll give something.

The other day, Torbjörn Linderson (I’ll call him Torb hereafter), from Sweden, asked a question on the Miata Race Prep group about aero modifications vs weight and should he do them. The question started vague, and with limited information I said do the wing, based on the fact that in every racing simulation I’ve run, a car with a wing beats a car without a wing. Another person with more knowledge and less science said that a low-drag wing (like my 9LR) doesn’t do anything until 80-90 mph, and that he wouldn’t use one.

That’s an interesting statement, and it begs the question, at what speed does aero start working? To see if aero helps at a lower speeds, I’ll do a quick simulation in OptimumLap. Using a stock Miata (with windows open) and some round numbers: .50 Cd, -.50 Cl, 2450 lbs, 1.1g static grip. I’ll run this car through a low-speed corner (T1 Pineview) and it goes 66.25 mph. Now I’ll use a Miata with airdam (no splitter) and 9LR wing for .05 Cd and +0.68 Cl (OptimumLap reverses the lift number). Now the car goes through the corner at 66.80 mph, a difference of .55 mph.

You might be thinking that half of a mile-per-hour is nothing, but it works out to 104.58% more grip, which is not nothing. But I’m citing a car modified with airdam and wing, not just simply the addition of a wing and no front aero. But at least we answered the question of, is aero useful at less than 80 mph, and the answer is yes.

Torb gave us more details on his car and the rules he races under, and that made things even more interesting. Blog post interesting.

The rules and the car

Torb races under the Roadsport C rules, which are a bit like NASA ST/TT rules, using kgs/hp with allowances for minor tuning. Without getting too deep in the details, his car would be at the class limit with 147 hp and 2367 lbs. That’s a pretty decent Miata, right between NASA TT5 and TT6.

The rules allow aero mods that don’t protrude from the body as seen from above. This is a lot of leeway, and would allow him to use an airdam, or an OEM-style front end with a splitter, as long as the splitter doesn’t protrude beyond the front bumper. He can also use a spoiler and flat bottom for free. So right away I’m thinking this: build a Supermiata with a flat floor! I’m a big fan of spoilers myself, and that may yet be the conclusion, but let’s move on.

The rules don’t allow him to change the roofline shape, and so a chop top or fastback are not allowed. But he could remove the rear window from a OEM hardtop and get the slightly better lift value of the chop top.

But Torb is interested in a wing. The wing needs to be mounted within the shape of the body as seen from the top, which is about 60″ (same as my wing). The wing needs to be 2″ below the roofline, and I can’t simulate that and will just use the roofline. The end plates can measure up to 10×10 square, which is within an inch of mine. The major problem with a wing is that it incurs a a 5% weight penalty.

As the car sits, Torb can just squeeze below min weight limit. However, it would be really easy to add weight. Starting with a 40-lb lead-acid battery instead of the 2-lb race battery he has now. The wing and stanchions are about 20 lbs, and a flat floor made out of metal could easily bring the weight up, and ballast would do the rest.

Front end options

Torb needs to keep the front-end aero within the lines of the stock bodywork, when viewed from above. In addition, if he adds rear downforce, he needs to balance that in front. The two obvious front-end options are a vertical airdam, and an OEM bumper with a splitter that extends only to the front bumper.

That’s exactly how my car is currently set up, see the pic below. In addition, I have a splitter extension I can add to this, it bolts on underneath. This can be easily adjusted so that the length is flush with the front bumper, when viewed from above, or to any length I want.

Such a front end would have more drag, but also more downforce, than an airdam. I haven’t tested this myself, but CFD from Hancha/Velox came to this conclusion. Compared to the airdam, they said it would have .01 more drag and .07 more downforce. These seem like reasonable numbers, I’l use them.

Swedish tracks

Torb sent me details on the three tracks he races on. If you follow the links below, you’ll see different cars with lap times which lists the power/weight ratio of the car, and what kind of tires the car is using. Hallelujah for good data!

• Kinnekulle Ring is a short 1.28 miles, lots of flowing corners, very little braking. The best Miata lap on slicks is just under a minute. At the other end of the spectrum, a 1990 Miata with 19 lbs/hp lapped at 1:06.17, which is another useful data point. So far this is looking a bit like Lime Rock, which is slightly longer (1.47 miles) and faster.
• Mantorp Park is 1.93 miles, with a long uphill straight. Watch a Civic K20 do this in 1:26.55. It’s a bit like Thunderbolt without the chicanes, but the speeds look more like Summit Point.
• Gelleråsen Arena is 1.57 miles and Torb does around a 1:17 lap. The track has three 2nd-gear corners where aero wouldn’t do much, but it starts end ends with a complex of of 3rd gear corners where aero would help. Waterford Hills is 1.4 miles and tighter, but this is probably the closest approximation.

Car builds and simulations

There are four configurations worth testing here. I’ll name them so it’s easy to follow.

1. OEM – Open windows destroy a Miata’s drag and lift numbers. I’ll be kind and call this Cd .50 and Cl -.50, 147 hp, 2367 lbs.
2. SuperM – I don’t have real numbers for the Supermiata formula of an airdam and spoiler. I do have comparative data from my car, plus drag and lift numbers from cars that have similar aero. I’ll call this Cd .50, Cl .40. 147 hp, 2367 lbs.
3. Sp-SM – As above, but with an OEM front end and splitter (not the airdam). Cd .51, Cl .47. 147 hp, 2367 lbs.
4. Ad-Wing – This version uses an airdam (no splitter) and wing. This is actual data from my car with OEM hard top. Cd .49, Cl .68, 147 hp, 2485 lbs. This version should also use a flat floor, since Torb needs to add weight anyway, but I don’t know what that would do for drag and lift, so I won’t factor that in.
5. Sp-Wing – As above, but swap the airdam for an OEM front end with a splitter. Cd .50, Cl .75. 147 hp, 2485 lbs.

In all cases I’ll use 1.3g grip. Torb sees spikes higher than that, and the class limit is 1.4g, but in steady cornering 1.3g seems a good value.

At Lime Rock (which I’m using to simulate Kinnekulle), the average speed is around 90 mph, and you can see that the airdam-wing setup is almost a half second faster than the airdam-spoiler version. In addition, the OEM front end with a splitter is another .1 seconds faster.

It’s not really worth mentioning stock aero, because it sucks. All of the aero options beat the OEM bodywork by over two seconds.

OEM	SuperM	Sp-SM	AD-Wing	Sp-Wing
62.39	60.20	60.08	59.74	59.64

At a lower speed track, like Waterford (which I’m using to represent Gelleråsen) average speeds are around 70 mph. But it’s pretty much the same relationship with the wing coming out on top, despite the extra weight. The gap isn’t as great, however.

OEM	SuperM	Sp-SM	AD-Wing	Sp-Wing
76.75	74.90	74.78	74.61	74.50

Another thing worth noting is that on the cars with a spoiler, the OEM front with the non-protruding splitter is .12 seconds faster than the one with the airdam. It’s weird that it’s the same time difference at both tracks, but the airdam is always slower. I’m not sure this would bear out in the real world, though.

Oh shit, OL has Swedish tracks

I went looking for more track maps and OptimumLap has seven Swedish tracks! Among them is Torb’s home track, Linköping, and his favorite track, Kinnekulle Ring. I re-ran the simulations again, and while the results were the same for Kinnekulle Ring, at Linköping the wing versions did not win!

OEM	SuperM	Sp-SM	AD-Wing	Sp-Wing
65.13	64.11	64.06	64.17	64.12

Conclusions

In all but one of the scenarios, the wing wins. But that’s making the assumption that the wing is not affected by mounting it 2″ below the roofline, and it might be. And even though this is a simulation based on scientifically acquired data, it is a simulation. YMMV.

If this was my car, I might choose an adjustable spoiler, primarily because I’m lazy. The car is already at the class limit, and a spoiler is less work. The wing is more expensive, and would require modifying the car. Although that would provide an opportunity to use a flat floor, and add ballast where I wanted it. If Torb adds a flat floor to the spoiler version, he needs to remove weight to offset that. If that proves difficult, the wing is the obvious choice.

Torb had also asked about using a hardtop without a rear window, and if you’ve read my results on that, the answer is yes if you’re not using a wing, and no if you are using a wing. I don’t know what the answer is with a spoiler, but it would be fun to A/B test it.

Regardless of what happens at the back, I would use an OEM front end with an adjustable splitter and vertical end plates, rather than an airdam. While the airdam has slightly less drag, the adjustability and extra downforce could be more useful. It’s also easier to load on a trailer with less overhang. And let’s face it, everyone can use .12 seconds.