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NACA Wing Shapes and Airfoil Tools

Airfoil Tools is a really neat site. It serves as a catalog of existing airfoil shapes, and allows you to compare them, simulate different speeds and angles of attack, and draw and plot your own wing shapes. Naturally most of these wings are designed for airplanes, but some have been used on cars (upside down) to create downforce. Cars don’t go nearly as fast as planes, and so the ideal shape of a car wing is different, and optimized for Reynolds numbers on the lower side of the spectrum.

The Reynolds number isn’t easy to explain, so I won’t. But it’s worth noting that the airfoil tools calculator has values that can be used to simulate car speeds. For example, a wing with a 10″ chord that is traveling through the air at 67 mph, and at 68-degrees F has a Reynolds numbers of around 500,000. Doubling the speed doubles the Reynolds number. You’ll only need this number if you’re using the Airfoil Tools, otherwise forget it.

In Competition Car Aerodynamics, , Simon McBeath frequently uses the NACA wings as examples, such as the NACA 6312, so let me explain a bit about how NACA 4-digit wings are designated. The first digit is the camber as a percentage, the second digit is the location of camber in relation to the chord length, the third and fourth digits are the percent thickness of the chord. So, a NACA 6312 wing has 6% camber, the max camber occurs at 30% of the chord length (from the front), and the thickness of the wing is 12% of the chord length.

McBeath discusses these form factors and how they allow a wing to generate more downforce.

  • More camber creates more downforce, but too much and you get separation underneath at the trailing edge.
  • Moving camber rearward generates more downforce, but further forward is more efficient for low-drag, low-angle applications.
  • A thickness of around 12% is quoted as being best for flow separation, but a thicker wing doesn’t create much more drag at car speeds, and could be better when run at a high angle of attack. The author suggest around 16-18% thickness as being ideal.

First I want to give a shout-out to 9 Lives Racing who makes a very strong, economical, and proven wing. I believe it was copied from an IMSA car, and I don’t know if it originated from a NACA profile before that. I’ve tried to find a NACA shape that’s the same, but I can’t find an exact match.

For fun, I’ll plot a wing that looks similar. Start at the NACA 4-digit airfoil generator and plug in some numbers. At first I’ll try 8% camber, 50% chord position, and 12% thickness and I get a wing that looks kind of like the 9LR wing (although 9LR has more camber).

Now I want to take McBeath’s advice and increase the thickness to 16% and I’ll add as much camber as the tool allows (9.5%).

To my eye it looks chubby. The leading edge also bucks with the latest trends which have a much sharper leading edge. Anyway, neat tool.

It’s a lot of effort to build a wing, and it would take a lot of trust to build one based on an online calculator and other people’s suggestions for what might work. A couple proven wing shapes I’m interested in building are the Eppler E423 high lift airfoil, and the Chuch Hollinger CH 10-48-13 high lift low Reynolds number airfoil. And then again there’s the smart move, which is to buy the 9 Lives Racing wing and move onto other projects.

Another thing I discovered using the Airfoil Tools page is that mosts wing shapes operate best in a fairly narrow range of angle, and that this angle of attack is dependent on speed. Let’s see what the Airfoil Tools page can show us on how wing angle affects downforce and drag.

First I’ll select a wing, and the NACA 6412 is as good as any for this demonstration. Next I’ll set the Reynolds number from 50,000 to 200,000 and the NCrit range between 5 and 7. Click Update Range and look at the resulting graphs.

First up is Cl vs Alpha. Cl is the coefficient of lift, which is downforce to you and me, and Alpha is the wing’s angle of attack. The more wing angle, the more downforce, up until about 10 degrees. After that flow separations occur and the wing creates less downforce.

Next take a look at Cd vs Alpha, which is drag vs wing angle. This wing has the least drag around zero degrees. There are three lines in these graphs that represent different speeds, but you can see that drag goes up quite a bit after 10 degrees.

The next one I’m interested in is Cl/Cd vs Alpha, which is how efficient the wing is at different angles. At slow speed (bottom line), the wing is most efficient at around 5 degrees angle of attack, and at higher speed, more like 6-7 degrees.

So you might think to set this wing at about 6 degrees, so that the wing performs at its best lift/drag ratio over a range of speeds. However, this isn’t necessarily the best setting for your car.

  • Racing is about balance and you might want more or less rear downforce to achieve that balance.
  • More downforce, even at the expense of more drag, is almost always faster. You can read more about that in Downforce vs Drag.
  • Having an over abundance of rear downforce will make the car understeer at high speed (safer), which means you can tune the car for oversteer at low speed (funner).

If you look at the CFD data for the 9 Lives Racing wing, it also operates in a similar range for angle of attack. It makes more downforce at 10 degrees than 5 degrees, but not a lot more. I suspect that above 12 degrees the wing starts to stall. You can run the wing at higher angles, but you’d need a Gurney flap or dual element wing to keep the air attached.

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Splitter Length and Side Fences

In this post I’ll examine several aspects of splitter design, starting with length. Some racing organizations regulate the maximum size of a splitter, for example:

  • Supermiata S2, NASA ST6 – airdam, but no splitter
  • Supermiata S1, NASA ST5 – 4″ max
  • Champcar – 12″ max (wow)

In Race Car Aerodynamics, Katz states that the splitter length should be double the chord length, the chord being the distance from the splitter to the ground. So if your car has 4″ of ground clearance, the splitter should be 8″ long. That seems rather long to me, but this rule of thumb may depend on the shape of the nose, and for a vertical airdam, perhaps shorter is ok.

In Competition Car Aerodynamics, Simon McBeath cites a CFD study done on a NASCAR model, using splitters of 2″, 4″, and 6″. In this case the ideal splitter length was 4″, producing the most downforce, and best L/D ratio.

  • The yellow line represents the total downforce, and you can see that the 100mm splitter is just slightly higher than 150mm.
  • The blue line shows downforce increasing fairly linearly up to 100mm, and then leveling out at 150mm. So you don’t want to go longer than 6″ (at least not on this stock car).

In the NASCAR CFD study, the splitter added 10% more downforce than using the airdam alone. This is in contrast to the Hancha Group’s CFD work, who’s theoretical airdam produced 34% more downforce with a splitter than with just an airdam. A Miata isn’t a stock car, and this is all calculations, so YMMV.

The same NASCAR CFD study found that extending the splitter rearwards underneath the car had further benefits, and the longer the better. This isn’t surprising, because it’s effectively creating a flat bottom. The interesting part was that lengthening the splitter rearwards made the splitter less effective, because of a build-up of pressure in the engine bay. Overall downforce did increase, but this was because of body interaction. The CFD model was revised to add vents in the hood, and then the splitter and underbody panel both made more downforce. Hood vents are not just for cooling!

Another unexpected result comes from Competition Car Aerodynamics. In Chapter 9 McBeath explains the wind tunnel work done at MIRA using a championship winning Integra Type R (which always makes me want to go all Dor-Dori and shout “Inte-R!” in a Japanese accent). In the wind tunnel, they experimented by putting different ends on the splitter, with ramps of different sizes, and with and without a vertical fence on the end. Each time they measured the result for drag and lift.

The configurations were as follows, and correspond to the image below:

  1. Shallow ramp.
  2. Baseline configuration with no ramp or fence.
  3. Medium ramp.
  4. High ramp.
  5. High ramp with vertical fence.
  6. Vertical fence alone, no ramp.
  7. Vertical fence, shallow ramp.

In the image above, the total amount of front downforce is the yellow line, and configuration 6, a simple vertical fence, is the winner. Adding a small ramp (configuration 7, which is pictured above), or large ramp (configuration 5) in front of the vertical fence actually reduced downforce and increased drag (the black line). Who’d have thunk it?

McBeath doesn’t reveal the actual numbers (it was a private test, they hold the cards close to their chest), but he did say that the best configuration reduced total drag on the car by 4.8%, and more significantly, total downforce increased by 50%!

I’ll conclude this post with some generalizations about splitter design:

  • You can make your the splitter as long as your rules allow, but the longer it is, the more it will affect the front/rear balance. Also note that it may work just as well at a shorter length. If you want to choose a length and not experiment with it, 4″ seems a safe bet.
  • Extend the splitter rearwards as far as the rules allow. But note that this may increase pressure under the hood, and then hood vents may be necessary.
  • Extend the rearward edge of the undertray as close to the leading edge of the front tires as possible. You can generate downforce from wheel wash.
  • If the undertray curves upwards at the rear, it will accelerate the air in front of it, creating more downforce and drag. McBeath quotes a value of about 4% increase in downforce and 1.5% increase in drag. For me, the effort wouldn’t be worth it, and I’d just use a flat undertray and perhaps rake it slightly.
  • Your splitter may create over 200 lbs of downforce, and so if you can’t stand on it, it isn’t strong enough.
  • Many people use birch plywood for the undertray and splitter, but mahogany marine plywood is better. I suggest Okume or Meranti BS-6566, it’s more weather resistant than birch and 33% lighter. I’d go with 9mm-15mm thick depending on if it’s just an undertray or splitter.
  • The front edge of the splitter should be radiused on the underside to avoid separation of flow. Sharp on top, radiused on the bottom.
  • Add vertical fences on the sides of the airdam to shield the tires and increase downforce.

Miata Airdam and Splitter

Look at an NA Miata front end and you’ll notice that you can see the front tires exposed to airflow. Rotating wheels are terrible for aero, and this is made worse by the shape of the nose, which forces more air at the exposed tires and also under the car. Under the car, the spinning wheels put the airflow in yaw, making things even worse. For drag and lift reduction, the Miata’s front end is the clearly place to start. Each generation of Miata has gotten progressively better in this regard, and so you can see Mazda agrees.

Image result for miata front view na
Bad nose shape and exposed tires.

Mazda’s partial solution to this was the R-package front lip, which reduces the amount of air going under the car, and directs some towards the brakes. But the tires are still very exposed.

Image result for miata front view na
R-package front lip.

The are a number of aftermarket companies making Miata front ends, and many address this problem. The DIY solution is a vertical sheet of plastic, which you can buy at Speedway Motors for $20. I’ll always refer to this as the Supermiata Airdam, because Supermiata did a lot to popularize this style. 9 Lives Racing sells a pre-cut piece that will save you some headaches.

Supermiata airdam, function is fashion.

To mount the airdam you should use a sturdy undertray. Some racing rules limit the rearward length of the undertray, and so most of them start at about the front axle. If the rules permit it, most people simply extend the undertray in front of the airdam making it into a splitter. Trackspeed engineering makes an undertray/splitter bracket, which greatly simplifies building one.

Airdam and splitter, and wow.

The Hancha Group did a cool CFD study on Miata front-end design, and you should read Splitter or Airdam, Which is Best?, on their site. I’ll post their images and chart here.

1. Stock, 2. Lowered, 3. Lip, 4. Lip + splitter, 5. Airdam, 6. Airdam + splitter
Supermiata airdam and splitter FTW

Let’s take those drag and lift values, put them in OptimumLap, and see the results at my local race tracks. I’ll use a Miata with 100hp, 2400 lbs, and tires that grip at 1g.

SetupPineviewNYSTWatkins Glen
184.40111.27153.52
284.24111.01153.58
383.96110.09151.30
483.68109.43150.42
583.74109.55150.44
683.60109.16149.70

Setup #1 is stock. Setup #2 is lowered to 4″, and this causes more drag, but also less lift, and that’s why it’s faster than #1. The exception is at Watkins Glen, where drag is more important. (Yes, lowering a car has other benefits, but I can’t simulate that in OptimumLap.)

Setup #3 is significantly faster. I don’t know if Hancha used the R-package front lip for the CFD, or if they calculated a chin-style airdam that completely covers the front wheels. Setup #4 adds a splitter to the chin airdam, and you can see it makes more downforce, without adding drag.

Setup #5 is a Supermiata style airdam, and it’s just a bit slower than #4. Add a splitter and you get Setup #6. Adding the splitter to the airdam reduced drag by 6.5%, and increased downforce by 34%. At a short and slow track like Pineview, this is only worth .6 seconds compared to a lowered Miata. At a track like WGI, it’s 3.8 seconds. Astonishing!

But probably not accurate in the real world. Add over 200 lbs of downforce to the front of the car and it’ll oversteer. So a real-world figure would be less. But then of course you’d balance that with a spoiler or wing, and go even faster, right?

Miata Spoilers

If you’re serious about downforce, use a wing; it can generate more downforce, and is around 5x more efficient than a spoiler. It begs the question, why would anyone want a spoiler?

  • Spoilers are usually cheaper than wings.
  • Some racing rules don’t allow wings, but allow spoilers (Supermiata S2, for example).
  • A small spoiler can reduce both drag and lift.
  • Wings are often gaudy on a street car, but spoilers almost always make a car look cool. Not only my opinion, but NASCAR fans as well.

I’m going to build an adjustable-height fixed-angle spoiler so I can find out what’s ideal on a Miata. But before that it’s worth looking at the existing literature and products.

How a spoiler works

As the name implies, a spoiler “spoils” the airflow coming over the top of the car, fooling the air into behaving as if the car has a different rear profile. This creates an earlier separation of flow, with consequently less drag and lift.

Image result for with and without spoiler airflow
How a spoiler works.

Spoiler height

Let’s take a look at what the pundits say. In Race Car Aerodynamics, Katz shows two different graphs for spoilers. The first is based on spoiler height alone, at a fixed angle of 20 degrees from vertical, or what I’d call 70 degrees.

I’ve put some pencil marks on the graph and drawn some conclusions.

  • A low spoiler about 1″ tall reduces drag the most. It also adds a bit of downforce. From a drag and downforce perspective, it’s a win-win!
  • A 3″ spoiler doesn’t add any drag, and doubles the downforce of the low spoiler. In other words, you get something for nothing!
  • A taller spoiler adds downforce and drag, but downforce increases more rapidly than drag. The gift that keeps on giving!

So no matter what height spoiler you chose, it has a benefit. Based on theory alone, we should all have low spoilers on our street cars, and taller spoilers on our race cars (rules permitting).

Spoiler angle

Katz includes another graph on spoiler angle, this time using a fixed-height spoiler. Confusingly, this time the angle is measured from horizontal, not vertical, and the 70-degree angle from the previous graph isn’t included.

Some observations of this data:

  • Drag increases about linearly with angle.
  • Lift-drag ratio seems best at a very shallow angle, but this may simply be the low overall height of the spoiler. Also note that L/D ratio doesn’t get any better than about 3:1, whereas a wing can be like 15:1. Which is why you use a wing if you’re serious about downforce.
  • Increasing spoiler angle to 60-degrees or more increases downforce, but at a diminishing return.

Spoiler height and angle combined

Next I’ll look at my other favorite reference, Competition Car Aerodynamics. McBeath cites CFD work done on NASCAR spoilers, in which they changed both the spoiler height and angle.

I’ll use the above results to compare spoilers of different lengths and angles that result in a similar total height above the deck. Which in turn allows me to figure out the most efficient spoiler angle.

  • 160mm spoiler, 20 degree angle, 54.7mm total height
  • 80mm spoiler, 40 degree angle, 51.4mm total height
  • 60mm spoiler, 60 degree angle, 52mm total height

It’s a bit difficult to see in this graph, but a 60mm spoiler set at 60-degrees is slightly better than a 160mm spoiler set at 20 degrees, even though the longer spoiler is a little bit taller. In other words, a higher angle works better.

Spoiler conclusions

Based on Katz and McBeath, here are some conclusions:

  • Downforce increases fairly linearly with either spoiler length or angle. In other words, it’s all about the height of the spoiler.
  • For any given length, increasing spoiler angle increases efficiency.
  • Downforce tails off slightly at the steepest angle and longest length.
  • There is no one answer for how high or at what angle you should run your spoiler, it’s all about tuning the aerodynamic balance. The easiest way to find out is use an adjustable spoiler built by Blackbird Fabworx and sold through Good-Win Racing, etc.

NASCAR spoilers

NASCAR used rear wings for a short period of time and then switched back to spoilers. Not because they could get better performance from a spoiler, but because the series is always looking for ways to make racing both closer and safer, and the wing did neither. In addition, the fans didn’t like the look of a wing. To be fair, the CoT wing was hideous, see for yourself.

Cot_spoiler_medium
Yuck.

So we can’t look to NASCAR for the most effective spoiler design, because we know their priorities lie in close racing rather than outright speed. But it’s worth noting a few things about NASCAR spoilers.

  • NASCAR probably knows more about spoiler design than any other race series, and they still don’t settle on one design. In fact, the regulations change almost yearly. Looking only at the height, in 2016 it was 3.5″, in 2017 2.375″, and in 2019 8″.
  • Some years the spoilers were adjustable for angle, some years they were fixed, and there have been different heights, widths, and shapes throughout the years.
  • NASCAR uses the spoiler to balance not only the overall aero package, but as a way to balance the performance between different cars, and at different tracks.
  • When NASCAR reverted from rear wings to spoilers, they set the spoiler angle at 70 degrees. In 2019 the fixed angle remains 70 degrees. Interesting.

Here’s an excellent article on A comparative look at NASCAR’s new spoiler, old spoiler, and wing.

Nscs-newspoiler2010hi_medium
Click image to enlarge.

NASCAR spoiler shapes

The 2019 spoiler is flat across the top, but different shapes have come and gone.

Image result for nascar spoiler shape
Curvy, almost bat-wing style.
Image result for nascar spoiler shape
Convex top edge.
Image result for nascar spoiler
Concave top edge.

The size and shape of Miata spoilers

So now that we’ve looked at spoiler theories and real-world examples from NASCAR, let’s get down to what matters: Miata spoilers.

  • Miatas have a roofline that is peaked in the middle, and you might imagine that the ideal spoiler shape has a matching convex arc to it. Although like all things aerodynamic, this could be totally false, and maybe the sides should be taller?
  • The rear edge of the trunk is curved and so a curved spoiler would look more natural, and could be an easier DIY project as well. Also, a curved spoiler would be more rigid than flat. But will curved work better?
  • There’s no reason to “spoil” the air coming along the sides of the car, and so a spoiler much wider than the rear canopy seems like a waste. Although the exposed spoiler ends are probably better at adding downforce. Albeit not very efficiently, and at probably a different angle than is ideal for spoiling the roofline shape.

Miata products

This IKON spoiler is an attractive design, with a convex top edge and curved profile. It would be neat to see something like this with a flat extension that’s adjustable for height.

The Rocket Bunny spoiler is more NASCAR; flatter across the top, taller, and with a steeper angle. I’d guess it’s slightly more effective than the Icon, but it has a tacked-on look that doesn’t really appeal to me.

And then there’s this JSP spoiler that looks like a wing, but isn’t (air isn’t going to flow under it, hence not a wing). The shape follows the curvature of the sides and roof, and this may be an efficient design.

Of course all of these spoilers have a fixed height and angle, so there’s no way to adjust the aerodynamic balance. On the other hand, the Blackbird Fabworx spoiler is large and adjustable for angle. It’s also a lot more expensive, but you get what you pay for.

Spoiler done right.

Spoilers by the inch

One of my favorite websites and resources is Ballistics by the Inch. They start with a long gun barrel and shoot different ammo out of it, keeping track of velocity. Then they cut the barrel 1″ shorter and repeat the process. In the end, they know exactly how different ammo performs, and which is best, from any particular length barrel.

And so I’m going to do… spoilers by the inch! Start with a short spoiler and keep making it taller, all the while keeping track of drag and downforce. In the end I should know what’s the best size spoiler for a standard Miata. And as I repeat this experiment with different front ends (R-package lip, airdam, splitter), I should be able to know what’s about the right size spoiler for different aero packages.

But first I need to make a spoiler with adjustable height. In fact I’ll probably make two, a small one that’s adjustable from 1-4″ and another for 5-12″ or so.

DIY adjustable spoiler

I like building things and I’ve never seen an adjustable-height fixed-angle spoiler, so I’m going to make one. My construction method of choice is a lightweight core (luaun plywood in this case) wrapped with fiberglass or carbon fibre.

  1. I started with an old fiberglass trunk lid I’d made previously. This was an easy project in itself, using release wax and a couple layers of fiberglass on top. I’m not using the trunk any more, so I cut the rear of the trunk lid off to serve as the base of the spoiler.
  2. Next I cut a 42″x8″ piece of 1/4″ lauan plywood, and held it up against the trunk at about 70 degrees so I could trace the rough curvature of the rear trunk using a sharpie.
  3. I then drilled holes in the center and ends of the plywood, and matching holes in the trunk lid.
  4. Next I put safety wire (zip ties also work great) through the holes and pulled them tight. This makes the plywood conform to the shape of the trunk lid.
  5. I then filled the gaps between the plywood and trunk lid using a mixture of epoxy and silica microballoons (a lightweight filler and thickener). The beauty of working with epoxy is you can be sloppy, and gaps up to 1/4″ are fine.
  6. After drying, the wire stitching can be removed and the rest of the gaps filled.
  7. I cut the top slightly convex so it matches the roofline. The spoiler is 5″ tall in the center, which seems pretty tall, but I’m going even higher with a Lexan extension.
  8. Next a layer of fiberglass on either side for strength.
  9. Finally I’ll add another layer of thickened epoxy to fill the fiberglass weave, and make it easier to sand.

Spoiler Adjustments

I’m using a Lexan plate to change the height of the spoiler in 2″ increments. I think 12″ is as high as I need to go.

PlateAdjustmentHeightNotes
NoneZero4″Base height of spoiler
6″Zero6″
6″+2″8″
10″Zero10″
10″+2″12″13″ is max size for SM2

Downforce > Drag

I have two Miatas, and even my faster one is slow. Adding an airdam, splitter, side skirts, wing, and all the other aero bits add weight, and some of them increase drag as well. The last thing you want to do to an underpowered car is add more weight and drag, right? Maybe.

Drag reduction matters most when accelerating on a straight, but pretty much everywhere else downforce is preferable to drag reduction. Even still, there are times when drag reduction is more important, such as in an endurance racing strategy where you want to do one less pit stop. It also seems logical that at a high-speed track you’d want to skew your aero package towards top speed and reduced drag, especially in an underpowered car.

Or so you’d think. But like most things aerodynamic, what seems obvious could be completely wrong. So let’s examine downforce vs drag on a very fast racetrack that is dominated by long straights and top speed.

I did a motorcycle track day at Portland International Raceway, and I’ll describe it like this: it has a really long and boring front straight, a couple corners, another long and slightly less boring back straight, and a couple corners. If ever there was a track where you’d want to reduce downforce and optimize for less drag, this is probably it.

In Race Car Aerodynamics, the author Joseph Katz calculated lap times for a generic prototype race car at Portland International Raceway factoring in grip and drag. Take a look at the track layout in the chart inset, it’s like I said. The full results are in SAE Paper 920349, but this is what I make of it.

At this track, you might think that you should set your aero for the least possible drag, thereby attaining the highest top speed. But that actually sets the worst lap time, some 6 seconds off the pace. Or you might think to optimize for the highest L/D ratio, and with that you’d at least be within the same second as the fastest cars.

But somewhere in the neighborhood of maximum downforce, that’s where the fastest lap time was. On any other track I’d guess that maximizing downforce is the right thing to do, but I’ve raced down the front straight on this track (which is nearly a mile long), and the results are surprising.

This is a calculation, albeit a very sophisticated one, and it’s based on a race car with a lot of power that can overcome drag. Still, it makes me wonder if we should chase all the downforce we can and not worry about drag reduction at all. Miatas are all about cornering anyway, and we’re used to getting passed on the straights!

Miata vs RX-7 Aero

Not so different. Yet so different.

In 1993, the Mazda Miata had a coefficient of drag of .38, and the RX-7 had a Cd of .29. Same manufacturer, same year, both two-door sports cars, and yet the RX-7’s had 20% less drag.

There’s nothing magical about the RX-7 shape, and if you compare its Cd to new cars, it’s only so-so. In The Most Aerodynamic Cars You Can Buy Right Now there are many cars with Cds from .27 down to .22, and a unicorn at .189. (Follow along in this Aero Timeline and see how Mercedes has incrementally improved their aero from high .4s down to .24 complete with wind-tunnel smoke trails.)

But let’s stick with the same year and manufacturer, and see what would happen if you could magically put a RX-7 body on a Miata, and what that would do for performance and fuel economy.

Calculating top speed

To calculate top speed, I’ll use the RSR Bonneville Aero-Horsepower & Drag Loss Calculator. I’ll enter data for a 1993 Miata, with frontal area of 18 sq feet and a Cd of .38. Miatas of that vintage had about 116 crank hp, and if I multiply by .82 to simulate driveline losses, that’s about 95 hp at the rear wheels. (You can argue driveline losses, I’m using figures from Competition Car Aerodynamics.)

First I want to calculate top speed, so I’ll throw some numbers into the calculator until the Horsepower Needed field reads 95. Turns out that 116 mph is the top speed.

Now I’ll drop a RX-7 body on the Miata, and drop the Cd to .29. The top speed goes up by 10 mph to 126 mph. Wow!

However, top speed is rarely important, so I’ll plug in some more common values. I’ll use 60 mph to represent the exit of a corner, and 90 mph to represent a faster section of track. How much power is required to go that fast, and how much power remains?

CdHP to go 60 MPHHP RemainsHP to go 90 MPHHP Remains
.3816.578.546.848.2
.2913.881.237.857.2

At 60 mph, the low-drag RX-7 body has an additional 2.7 hp available over the standard bodywork. Meh. At 90 mph, there’s an additional 9 hp available from the sleek RX-7 body. Wow! Obviously, the faster you go, the more important drag becomes.

Simulating lap time

Drag is obviously important, but more important is lift (downforce). We need the numbers for both drag and lift in order to calculate a lap. I don’t have any published numbers for lift on a Miata, but the Hancha group did CFD testing and I’ll use their lift value of 0.27. In Race Car Aerodynamics (p. 19) Katz lists the RX7 at .24 lift, and AutoSpeeds article on Aero Testing ven breaks that down into front lift vs rear. Let’s plug these values into OptimumLap and simulate lap times at my local track, Watkins Glen International.

MiataRX7 Miata
Drag.38.29
Lift.27.24
Lap2:34.932:33.38

So a Miata with a RX-7 body would go over 1.5 seconds per lap faster than a stock Miata. Some people would give their left nut for 1.5 seconds.

Fuel economy and race strategy

In sprint racing, fuel economy is meaningless, but in endurance racing, it can be important. Especially if longer stints will allow you to do one fewer pit stop during the race, or if your car is right on the cusp of doing the maximum allowed stint. OptimumLap shows a 2.5% decrease in fuel economy using the RX7 body. That doesn’t seem like much, but it can be a big difference.

Let’s use my race Miata as an example. It burns about 7 gallons per hour, and with its 12.7-gallon gas tank, it can go about 1:50 before the tank runs out. This is not a problem in AER where stints are 90-minutes long. But in Champcar or Lucky Dog, stints are two hours long, and I end up doing an extra stop. In cases like this, 2.5% fuel economy can be a huge deal.

So not only is the RX7-bodied Miata going 1.5 seconds faster per lap, it’s doing that while burning 2.5% less fuel. Calculate the total number of laps per stint and the driver in the stock Miata can do 42.6 laps per stint. The driver in the RX7-bodied Miata can do 44.1 laps.

Calculating Cd using body shape

A Miata’s drag and lift values aren’t terrible, but the RX7 shows us that it could be a lot better. What body can you make, and how much would that affect drag and lift?

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 of your car. Let’s try this on a Miata.

I set the following options, which gives me a Cd of .376, which is close enough to a Miata’s .38 that I feel satisfied:

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

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 .426. Or if you use the Miata as intended and open the top, then the Cd is .464.

So let’s see about reducing the drag. In the drag calculator I used “Rounded canopy and boot” to represent the Miata, let’s give the Miata a RX-7 top and change the Rear Canopy to “Fastback 10-20 degrees,” and the Canopy plan to “Tapering to rear”. Right away the Cd goes from .378 to .340. As a side note, the worst possible angle for the rear window is 30 degrees – you can see that in the drag calculator – and if you measure a Miata’s rear window, it’s about 30 degrees.

The next thing I see on the Miata is the hard top extends wider than the windows, and catches air moving along the car. The RX-7 doesn’t do that, so I’ll change Skin Friction from “Recessed windows” mirrors, to “Perfectly smooth body,” and now Cd is .331.

The drag calculator doesn’t allow me to address the Miata’s terrible front end, so I can’t get down to the RX-7’s .29. That’s a subject, and a test, for another time.