Can we use multi element wing for slow flight planes, like F1 multi element rear wing?

If we know that pressure act prependicular to the surface why this two upper elements are "almost" vertical?

It seems to me that they produce "tons" of drag instead lift.Resultant force point to far back,instead down!

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  • $\begingroup$ Note that in f1 a secondary goal of the wing is to spoil the airflow for the next car. $\endgroup$
    – Sanchises
    Aug 7, 2020 at 8:10
  • $\begingroup$ @Sanchises they do that in yacht racing too! $\endgroup$ Aug 7, 2020 at 19:30
  • $\begingroup$ @Sanchises this is not true at all. To spoil the airflow for the next car, the leading car has to remove energy from the flow. Unless the leading car can remove energy efficiently and for a beneficial reason (e.g. generating downforce), what's the point in removing that energy if it will then take away some of your work (engine power) to do?? $\endgroup$ Aug 8, 2020 at 6:55
  • $\begingroup$ @StuartBuckingham It's not about straight-line performance but about cornering. See this article roadandtrack.com/motorsports/a18209365/… (no affiliation, just the first search result I found that illustrated my point). $\endgroup$
    – Sanchises
    Aug 10, 2020 at 10:12
  • $\begingroup$ @Sanchises absolutely. When testing aero, we test through many different Yaw, Steer, Roll and Rideheight combinations. In fact, the straight ahead accelerating conditions (Yaw 0, Steer 0, Roll 0, nose-up pitch) will have 0 weighting towards the weighted downforce numbers (in-fact, some teams will negatively weight these points, as increased downforce here = more rolling resistance). These points are still looked at though because the rear wing & diffuser see much straighter flow than the front of the car in cornering conditions. $\endgroup$ Aug 10, 2020 at 14:13

3 Answers 3


Excellent application inverted on the drag racer, which brings home the point perfectly. If you have enough excess thrust, devices like these can dramaticly increase Coefficient of Lift, but at the cost if loss of lift efficiency, or lower lift to drag ratio.

In the case of the dragster, more propulsion efficiency is lost if tires break loose from the pavement, so the drag of the "inverted Fowler flap" is an acceptable trade-off to the downlift increasing traction.

As mentioned in comments, this is why the Fiesler Storch requires 240 HP to achieve its legendary STOL performance.

And just as flaps 10 is better for lift than flaps 30 for taking off, one might question the need for the second and third flap on a lifting wing, but heavy airliners love them when coming in to land as Fowler flaps.

  • $\begingroup$ @RobertoDigiovani, How upper element produce lift/"downforce" if stay almost vertical,so resultant force is point almost back from direction of travel, instead down? $\endgroup$
    – user50657
    Aug 7, 2020 at 5:41
  • $\begingroup$ @Roberto.I edit my picture.look at it.. $\endgroup$
    – user50657
    Aug 7, 2020 at 5:56
  • $\begingroup$ @Noah Prandtl there must be drag to create lift. The slots help eliminate turbulence behind the wing (rather than having one solid piece). This application needs to press down on the tires as much as possible, even at the expense of drag. So when you draw the resultant force vector for all 3 "wings", it is very much down. $\endgroup$ Aug 7, 2020 at 10:12
  • 1
    $\begingroup$ Slot gaps do not eliminate turbulence behind behind the wing. In fact, by having a slot gap, the boundary layer growth rate on the element behind would be higher than if there was no slot gap. Turbulent boundary layers grow at a rate of Re^-0.2, so one continuous section creates less turbulence. Commonly, people say that "slot gaps re-energise the boundary layer", but in reality, it is throwing away the old boundary layer and starting a new boundary layer. The reason for slot gaps is to have a higher energy boundary layer so the flow stays attached (for a particular camber). $\endgroup$ Aug 7, 2020 at 15:19
  • $\begingroup$ @Stuart Buckingham "higher energy boundary layer so the flow stays attached", ergo less turbulence where it counts. You can argue this one with the birds, they have Fowler flaps too. $\endgroup$ Aug 7, 2020 at 19:17

This looks very much like a Formula Student/Formula SAE wing!

The idea of the multi-element wing is for all three elements to act together, rather than as seperate sections. If you look at all of the elements joined together (imagine there are no slot gaps), the suction surface should form a constant curve* which is informally known as the camber line.

The unified camber line produces would produce a huge amount of load if the flow could stay attached to it. Unfortunately it is far too aggressive for the flow to stay attached. By splitting the section into multiple small sections, the boundary layer that has lost a lot of energy are shed, and a new higher energy boundary layer is started.

The last part of the first element, and then each element after it are there to "recover" pressure from the suction peak that should be on the first element where the ground clearance is at a minimum. Therefore the peak (negative) Pressure Coefficient on subsequent elements should always be getting smaller (closer to zero). Note on the third CFD picture, the cutaway 3D wing, there is a pressure spike on the suction surface of the second element that is higher (more suction) than the first element. This means that the first element is not working hard enough, and needs more camber, and the slot gap needs more overlap so that the suction peak on the second element increases the dumping velocity of the first element.

Unfortunately the first design is badly separated on the second and third elements. This is very commonly done by Formula Student Engineers, who chase headline numbers, rather than designing an efficient aero package.

For using a multi-element wing for slow flight airplanes, unfortunately these aggressive designs create lots of load, but also lots of drag. For an F1 car, the drag polar can be anywhere between 3.5 and 5 depending on the configuration. FS/FSAE designs like you have shown are going to have drag polars are in the range of 5~10 for a front wing with the benefit of in-ground effects, and down to 2 for a rear wing!

There is a fantastic paper called High-Lift Aerodynamics by A. M. O. Smith which I highly recommend you take a look at. It takes you through all of the theory and examples of how and why multi-element wings work.

* The curve should actually have small steps in it to give space to the extra mass-flow that comes through the slot gap.

  • $\begingroup$ @NoahPrandtl is there anything this doesn't answer that's stopping you from accepting this answer? $\endgroup$ Aug 8, 2020 at 8:16
  • $\begingroup$ ,all answers are correct so I dont know which to choose $\endgroup$
    – user50657
    Aug 8, 2020 at 16:07

No, it is not if you are not limited in wing area and / or wingspan.

The other answers already do a splendid job explaining how this multi-element airfoil works and that it creates a lot of drag.

Now look at slow flight airplanes – they all use high aspect ratio wings without complex flap systems. Doing this gives them better efficiency. Yes, they need more wing area and wing mass to achieve enough lift, but at low speed the friction drag increase caused by the larger surface is small. On the other hand, their induced drag, which is dominant at low speed, is kept small by the high wing span.

The induced drag of the multi-element airfoil, on the other hand, is prohibitive, as is the pressure drag caused by the incidence of the rear elements (which actually is induced drag) and possible flow separation on the upper surface. This makes the multi-element airfoil less efficient: It needs much more power for the same lift. With race cars that makes sense: The wing cannot be wider than the car itself, and in order to develop the maximum possible downforce, an inefficient way of producing it has to be selected. With airplanes, no such restrictions exist and the glider-like wing is the better choice.

  • $\begingroup$ Totally agree. Only tidbit is that there shouldn't be flow separation on the suction surface of a well designed wing no matter if it is single or multi-element. $\endgroup$ Aug 7, 2020 at 15:52
  • $\begingroup$ @StuartBuckingham: Yes, looking closely at the CFD result doesn't show separation, but is is only CFD. Real flaps achieve their highest lift with a bit of separation. $\endgroup$ Aug 8, 2020 at 8:01
  • $\begingroup$ @PeterKämpf yes this is the unfortunate situation that many up-and-coming engineers find themselves in. As I explained in my answer, some engineers chase the headline numbers rather than focus on good engineering principles. Despite this, at the end of the day, the section best designed using aero principals will out perform the airfoil just chasing headline numbers. $\endgroup$ Aug 8, 2020 at 8:09
  • $\begingroup$ Also, real-world restrictions for your third paragraph scenario definitely exist. An infinite span is not realistic. A multi element wing may still be the best design decision depending on the design constraints (weight, vehicle width etc.) imposed. $\endgroup$ Aug 8, 2020 at 8:23

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