Would there be any advantages to a wing with a concave upper surface?

A wing with a concave upper surface could have the same area as one with the normal convex shape of an aerofoil.

I can think of many potential disadvantages: additional complexity of design and construction, reduced volume for fuel tanks, having rain fill up rather than run off the the wing.

Could there be any advantages to such a design? Has it ever been tried, or studied?

For clarity, this is the kind of cross-section I have in mind. Yes, it's ugly, and I don't think that better draughtsmanship would improve it.

• aerodynamics-wise you would have earlier flow separation (another disadvantage), if I understood you correctly. Otherwise, you you are speaking of "upside-down" airfoils, they produce less (or more negative) lift given the same AoA. Jul 28, 2016 at 21:04
• No, I don't mean upside-down aerofoils - I mean an aerofoil that has the same upper and lower area as a "normal" one, but that achieves that on the upper surface by curving back inwards, rather than outwards (yes, it would look ghastly). Jul 28, 2016 at 21:11
• I'm pretty sure this would create a lot more drag than lift, wings are curved outwards on the top for a reason, even in nature. Jul 28, 2016 at 21:22
• It's used when lift must be oriented down, like for a "car rear wing/airfoil"..
– mins
Jul 28, 2016 at 22:02
• @mins -- or a horizontal stabilizer? Jul 28, 2016 at 23:22

The idea behind this design seems to be that the principal cause of lift of a wing is that the top has a larger area than the bottom, so if we substitute a top surface with a different shape but the same area, we will still get similar lift.

This is the idea behind the equal-transit-time theory of lift, which is incorrect, disagreeing in several ways with with actual observations of air flowing past airfoils and the lift forces that result. NASA has produced a basic but thorough refutation of this theory; among the points they make are

The lift predicted by the "Equal Transit" theory is much less than the observed lift, because the velocity is too low. The actual velocity over the top of an airfoil is much faster than that predicted by the "Longer Path" theory and particles moving over the top arrive at the trailing edge before particles moving under the airfoil.

and

There are modern, low-drag airfoils which produce lift on which the bottom surface is actually longer than the top.

What you generally want in an airfoil is for it to establish streamlines that carry the air at very high speed over the top and shoot it downward past the trailing edge. The speed is not determined by the surface area or length along the top surface; the speed is determined by other things, and two air molecules that start near each other but go on different sides of the wing (one on top, one on the bottom) get to the trailing edge when their respective speeds carry them there, generally not at the same time as each other.

Putting a big hollow space on top of the wing where the air can pile up and then forcing it over a second hump to get to the trailing edge seems counterproductive. It might just lead to the wing stalling at relatively low angles of attack, which would limit the amount of lift you can get from it. But I am not an airfoil designer, and I don't know exactly what the result would be.

• The equal transit theory isn't really itself part of the question - the main point is that instead of continuing to go up at a certain point on the wing, its curve would go down (so all other things remain equal, as much as possible). The latter part of your answer is the thing I am hoping for some enlightenment upon - what would the air do in that hollow? And would it have some dramatic effects around/above mach 1? Jul 29, 2016 at 10:49
• @DanieleProcida Why don't we just put the wheels on top of the car? It shouldn't matter since we have the same amount of wheels either way. Oct 11, 2016 at 9:20
• @immibis What is the point of that sort of sarcastic remark? Oct 11, 2016 at 17:12
• @DanieleProcida You are saying that a concave wing should work if it has the same surface area. I am saying that a top-wheeled car should work if it has the same number of wheels. In both cases, we have focused on something that is mostly irrelevant to the actual problem at hand. Just because a new wing or car design has the same surface area or number of wheels as one that already works doesn't mean the new one will also work, Oct 12, 2016 at 1:49
• @immibis No, I wasn't 'saying'. I was asking. It was a question, about something that seemed interesting to me. That is what StackExchange is for. You'll notice that although StackExchange has a points system, you don't get points by making sarcastic comments about other people's questions. Oct 12, 2016 at 8:09

A wing with an inward (concave) surface on the top will generate negative lift for many positive angles of attack, and really not much lift at all. Curving the top surface is basically creating an upside down airfoil (because lift is negative).

Take a look at a 0° angle-of-attack on a wing with a -14.24% camber:

You can see we are generating a lot of negative lift (-3955 lbs) and a lot of drag, resulting in a large (negative) L/D ratio.

Lets increase the AoA until we get a slightly positive lift coefficient:

You can see that the AoA is extreme for a small amount of lift, barely overcoming drag. The AoA of 15.2° is required which brings the airfoil basically into stall because the flow is going to quickly separate from the wing.

Compare all this to a "normal" airfoil:

At a small 3.5° AoA, you are generating 1000+ lbs of lift and only 90lbs of drag, with a L/D ratio of 11+.

If you would like to play around with airfoils and see the results like I have above, you can download NASA's FoilSim Program

• Thanks for this detailed answer, and the reference to the FoilSim program. (I've downloaded it and after much fighting with Java have it running.) It's interesting - but in fact, I don't think it's even possible to model the shape I'm describing in the question. Jul 28, 2016 at 22:03
• @DanieleProcida How did you get FoilSim working?? I've had the program files sitting there for months now after giving up on getting them working even after changing Java settings Aug 1, 2016 at 12:32
• @Xylius I downloaded it, opened the OS X Java system preferences, added Foil.html to the list of specially-allowed applications, and opened that in Firefox (it didn't work in Safari). Aug 1, 2016 at 15:16
• @DanieleProcida Note taken, thanks! Aug 2, 2016 at 10:08

Well, wing produces lift by accelerating the air downward. That's a result of third law of motion (principle of action and reaction). And it applies at each point along the wing—the lower the pressure, the higher the lift, but also the downward acceleration of the air flowing over the wing.

Now that only works to a certain point. If the surface curves too fast, the air won't be able to follow it any more due to inertia, will detach and the pocket underneath will fill with stagnant air at ambient pressure, eliminating the suction and the lift with it. That is stall.

Normal wing distributes the acceleration of the air along the chord. However, as the air follows your shape, it would accelerate downward a lot in the first part, then return up somewhat before the second hump and accelerate downward a lot again over the second hump.

Your wing needs higher curvature at the two humps to compensate for the concave part generating negative lift. Mainly the first hump is critical, because increasing angle of attack only increases the curvature near the leading edge (while flaps increase it further aft). So I would expect your wing to stall earlier.

I would also expect the wing to have higher form drag, because there would be more changes to the flow conditions and each such change means losing some energy to viscosity.

Also above compares wings with the same coefficient of lift. To achieve it, your wing would probably have to be thicker as it needs to compensate for the negative lift in the middle part. Which is another reason for having higher form drag, too.