Low Speed Wings, Part 1

I live near two very different tracks, Watkins Glen International and Pineview Run. WGI is the fastest track in North America, and Pineview might be the slowest. When I run racing simulations in OptimumLap, Watkins Glen is one of the few tracks where drag matters. On any other track I can increase drag quite a bit and it’s not a big factor. Conversely, at Pineview Run, drag is almost inconsequential, and the same would be true on an autocross course.

I’ll run a quick simulation and show you what I mean. Here’s a Miata at three local tracks, Watkins Glen International (WGI), Pineview Run (PV), and New York Safety Track (NYST) using drag coefficients of .45 and .495 (110%).

WGI .45WGI .495PV .45PV .495NYST .45NYST .495
Lap time140.58141.3473.8573.8998.7699
Max speed120.61117.8875.2274.96106.8105.49
Effect of adding 10% drag.

At WGI, adding 10% drag is a difference is .76 seconds and almost 3 mph top speed. That’s the difference between winning and losing. Conversely, at Pineview, it’s only .04 seconds and not worth talking about. I put NYST in just to show what an average track is like, and here the added drag is only a quarter of a second.

So when optimizing for low speed aerodynamics, let’s ignore drag and go for as much downforce as possible.

Aspect Ratio

Wings make most of their downforce in the middle of the wing; the further you move from the center, the less downforce the wing makes. This is because the ends of the wing create vortexes that destroy lift.

Wingtip Vortices
Image from Flight Literacy

Therefore, for a given area, a longer wing makes more lift than a shorter wing, simply because the ends are further from the center. You may have heard of a high aspect ratio wing; that’s a wing that is very long and thin, such as on a sailplane, or glider. Theoretically, you might think that would be a good wing on a racecar.

Glider (sailplane) - Wikipedia
Thanks Wikipedia for the image.

Well, not necessarily. For one, racecar wings (and most airplanes these days) use endplates, which keep the upper and lower pressure zones from creating the lift-destroying vortexes. So you don’t need to have a really long wing to avoid losing lift. Just use a big enough end plate.

Another reason a high aspect ratio wing would be difficult for cars is construction. Building a really long wing with a narrow chord is going to be a noodle. The stiffness of a wing is the thickness cubed multiplied by the chord, and so a high aspect ratio wing would be fragile or at least very flexible.

Another reason a high-aspect ratio wing isn’t ideal is because the mass is high up and away from center. Mass centralization is important for handling, and a high-aspect ratio wing is the antithesis of that.

Finally, probably the most significant reason a high-aspect ratio wing won’t work well at low speed is it would generate low Reynolds numbers. What?

Reynolds Number

I’m not going to go into a deep explanation of what a Reynolds (Re) number is, but I think of it as a resistance number. At low speed, air doesn’t have much resistance; you can put your hand out the window as if it were a wing, and at 5 mph change the angle of attack freely. Do that at 60 mph and you’ll feel a lot of drag. At that speed, air seems to have the same resistance as moving your hand through water.

Likewise, a smaller hand will have less resistance out the window than a larger hand. So you can probably tell that the Re number depends on the chord of the wing (the size of your hand), and the density of air (which is basically the speed you’re moving).

Let’s see the relationship of chord and speed on the Re number. I’ll take three wings: a high-aspect ratio 4″, an in between 6″ (eBay single wing), and a more standard 9″ wing (9 Lives Racing is about that), and see what the Re numbers are at 62 mph (the average minimum corner speed at Mid-Ohio, and also 100 km/h for the metric people).

Wing chordMPHReynolds Number
4″ (.102m)62 187k
6″ (.152m)62280k
9″ (.23m)62420k
Reynold’s numbers with different chords

In the table above, you can see that the 4″ wing has a Re number of just under 200k. The 9″ wing has a Re approaching 500k. OK, so how is this significant?

Look at the image below, which shows a Selig S1223 wing at three different Re numbers. The gold line represents a Re of 1 million, the purple line is 500k, and the green line is 200k. The lines show the coefficient of lift divided by the coefficient of drag (Cl/Cd), which you can simply think of as how efficient the wing is at making lift. The higher the Re number, the more efficient this wing is. At 200k, the wing just isn’t working that well. At 500k, it’s about 130% better, and at 1 million, it’s better still.

Reynold’s number of 200k (green) vs 500k (purple) vs 1 million (gold).

All of this means that for a wing to be useful at low speed, it needs a really large chord. For argument sake, I’m calling this 16″. This drives up the Reynold’s number to where the wing is more efficient. In addition, flow separation is delayed at higher Reynolds numbers, which means you can use a low-aspect ratio wing at a higher angle of attack. (And if you grok what I’m saying about the Reynolds number, you understand that you can also use more wing angle at higher speed.)

Wing Shape

The Airfoil Tools website has a pretty good search function, you can look for wings of different profiles and sort on factors like thickness, camber, and even Reynolds number. I started by searching for wings that had the highest lift/drag ratio (Cl/Cd) at 500k Re, using this search. That returned a lot of results, some of them rather strange. Next I looked at the Cl vs Alpha graph, and many of them peak around 1.5.

But what I’m specifically looking for are high lift wings. I don’t want a wing that’s the most efficient at low Re, I want one that has the highest lift at low Re. So I changed the search parameters to use a minimum thickness or 10% and minimum camber of 8% (both values that should drive up lift) to find wings that have a Cl of 2:1 or greater. (Note that single wings have peak downforce at about 12 degrees, but double wings and low Re numbers can use a thicker wings for more angle.)

That search returned four pages of results, and after culling those, the ones I’ll use for this investigation are the Church Hollinger Ch10, Eppler 420, and Selig S1223. (There are other potentially good ones I didn’t look into, such as FX 74-Cl5-140 MOD, FX 72-MS-150B AIRFOIL, GOE 525, etc.)

Airfoil Tools allows you to compare wings by clicking Add to comparison. So let’s do that for each wing. You get a view like so, with the corresponding data.

Wings compared

Turbulence

Wings work best when they can have laminar flow. Conversely, when the air is turbulent, it increases drag and decreases lift. Airfoil Tools allows you to simulate turbulence using the Ncrit value. An Ncrit of 9 is like a wind tunnel, or about what you’d experience on a race track, on a still day, with no other cars in front of you. In other words, pretty unrealistic.

To simulate what your wing is doing behind your car’s canopy, during a race, possibly in the wake of another car, you need to use a Ncrit value of 5 or less. Unfortunately, Airfoil Tools doesn’t give you all the Ncrit values, and depending on which wing you choose, 5 might be as low as you can go.

Head to Head on Reynolds

I’ll use these three wings and then compare the various graphs at a Ncrit value of 5, starting with Re 200k, then 500k, and finally 1 million. In the graphs below, Cl is lift, Cd is drag, and Alpha is the angle of attack.

Re 200k

A Reynolds number of 200k is absurdly low, and for our theoretical wing of 16″ chord (.41 m) represents a speed of less than 20 mph. Still, this is useful to look at because most people don’t have a 16″ wing, and so this represents how these wing shapes would perform at a more standard 9″ chord and around 30 mph.

At 200k, the S1223 wing is clearly ahead of the CH10 and E420 in both Cl and Cl/Cd, which are the most important factors. (Sorry about the colors, I can’t choose them.)

Re 500k

A 16″ wing at 41 mph would have a Re of about 500k. Pineview Run’s average minimum cornering speed is around 43 mph, so this is a close approximation for that track, or for an autocross.

The S1223 wing is winning on Cl and Cl/Cd. This is a good wing for low speed applications. The E420 is starting to diverge from the CH10, showing a bit more promise at higher wing angle. Where the CH10 wing shines is in lower drag, but we don’t care about that for this application.

Re 1 Million

At this point the 16″ wing is traveling at 87 mph, which is not what I’d call low-speed cornering, but it’s worth looking to see how the wings perform at higher Reynolds.

Conclusions

  • S1223 looks like the low-speed wing of choice. It has the highest lift, but also the highest drag by a fair amount. This might be a good all-purpose wing on a powerful car that can overcome drag, but not one of my underpowered Miatas.
  • CH10 looks like it would be a great low-drag wing for a momentum car. It’s very efficient and seems tolerant of wing angle. This looks like the best wing for a “set it and forget it” mentality. The 9 Lives Racing wing profile is a lot like the CH10, but 9LR has more camber. Camber is good, it makes more downforce. This is one of those situations where I look at the 9 Lives Racing wing and say to myself, why the fuck am I doing anything with wings?
  • E420 splits the difference and seems like a great choice for an all-purpose wing. It’s thicker than the other wings, and would probably be a better choice for a double wing setup, where that can be exploited for more wing angle and downforce.

What Next?

In Part 2 of this series I’ll build one of these wings, and in Part 3 I’ll test it at a low-speed venue. But while the S1223 is a clear winner, I’m not exactly sure how I can build it strong enough, it’s just so damn thin at the end.

S1223 the right way up

The S1223 also comes in a Richard T. LaSalle modified version, which is slightly thicker and has more camber. This wing generates even higher lift and can be used at 15 degrees angle of attack, but it does so with more drag. This would definitely be a low-speed application, especially on a Miata.

S1223 vs S1223-RTL at 500k Re

One thought on “Low Speed Wings, Part 1”

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