# How to calculate the forces and moments required to aerodynamically actuate slats?

I am trying to make a wing where slats automatically deploy once it hits a higher angle of attack, let's say right before stall. I need to roughly estimate the forces and moments acting on the undeployed slat.

Here is a sample airfoil with the pressure distribution superimposed:

Source: own work

I plan to operate at a Reynolds number of 100,000 at stall speed, and the preliminary dimensions for the slat position are 10% for the width, 1.5% for the depth and 2% for the gap, all in chord percentage. Refere to the image below for the definition of the dimensions:

Source: Effect of Slot Span on Wing Performance, J.Granizo

I think the next step is to use the following equations for the slat alone:

Source: Fundamentals of Aerodynamics 6th edition

However, I only know the pressure and friction coefficients on the top surface (marked in red line). Do I assume that the entire bottom surface (marked in blue line) is at atmospheric/freestream pressure?

A point in the right direction would be appreciated.

• This doesn't sound very simple. What will be the distance of the slat from the airfoil? What is your Reynolds number? How the slat will be moving? It would be nice to put more details to your problem for people to point you in the right direction. The above equations are just a high-level force analysis on the slats assuming you know the $\Delta C_p$, $c_f$ etc.
– ares
Commented Nov 4, 2018 at 6:15
• I have provided more information in the post. The plan is to have the slats held by a cantilever snap-fit joint inside the main airfoil (like a pen cap). I want to know if the suction force is strong enough to pull the slat off of the joint, which I measured to be around 2N of force Commented Nov 4, 2018 at 23:20
• As a pilot, I don't want anything uncommanded going on with wing surfaces. Maybe have a pressure sensor that lights to indicate it might be a good idea to deploy the slats? There are some light aircraft that have permanently mounted slats like you drew. Here is an article the Zenith STOL CH 701 that uses them zenithair.com/stolch801/design/slats-vs-vg-design.html Commented Nov 5, 2018 at 4:18

Very interesting challenge and very interesting design approach.

I've read this had been done few times with TE flaps but not with LE slats. If i were you I would take the following approach to figure a way out.

1. In Javafoil you can model open slat multi element air-foil. The results are not very accurate at your Reynolds number if there is a huge separation bubble though. xfoil does not support this feature at the moment but if you are thinking of using TE Flap your best bet is to use xfoil). Calculate several slat gaps by geometrically altering the input file for a list of angles of attack.

2. You can easily export the local CPx data to a text file in Javafoil. Then use these data to find out how much of aerodynamic force the slat generates by integrating the local surface slope and CPx values for each slat-gap, alpha pair.

3. Then this data-set could be interpolated to find out what would be the slat-gap distance for given angle of attack for a given spring constant and substantially to find L/D for each angle of attack.

Hope this helps. ABCD

PS: One example of automatic TE flap deflection is discussed here. I think LE slat would be much more effective because $$Cp_\alpha$$ near the LE is much higher than that of the TE

• Your example of "automatic TE flap deflection" involves a high speed launch, but for a smaller model might work with rubber bands. Spring loaded leading edge slats have been around for a while. Commented Nov 6, 2018 at 4:50

Curious as to the application and how the slats would extend (springs, electric motor, actuated by pressure sensor). What is most interesting is the choice of wing. Thin undercambered wings, which could be considered a wing with slat and flap already deployed, have amazing low speed lift performance, but generate so much lift at higher speeds that they become impractical.

If one studies wing evolution in aircraft wings, thin under camber gave way to flat bottom, then semisymmetrical, then thinner as speed continually increased. Modern airliners are perfect examples of slow to fast every flight. They reconfigure for LESS lift and drag so they can speed up and fly efficiently at cruise speed. But an 800,000 lb 747 dropping to 1/3 of cruise speed (1/9 lift!) and reconfiguring to the days of Bleriot with (Fokker Triplane) Fowler flaps is an engineering marvel indeed.

Modern "slipper" glider wings are not nearly as undercambered. So what will this plane be?

So, as far as the right direction, I would look into air foil tools on the Net and check out some existing designs for your application.

If you want to slat the wing you have, spring loaded automatically deploying (probably by lower air pressure) slats have been used on fighter planes such as the Sabre jet. But the wing you have will be very good for slow flight as it is.

• It's for a design challenge in which the goal is to get the highest score - which is to maximize the area under the L/D vs AOA curve from 0 to 20 deg, normalized with the airfoil's cross-sectional area. So the best score will be obtained by having a good L/D performance for a wide range of AOA & lowest wing volume. I figured I can try to increase the L/D at higher AOA with slats to improve my score because they will be using the cross-sectional area of the airfoil w/ undeployed slats, and wanted to ask if the suction will be strong enough (2N of force) that I can get away w/ not using springs. Commented Nov 5, 2018 at 23:02
• Chord length is capped at 10cm, so it will be hard to find small diameter springs to fit inside the main airfoil. Commented Nov 5, 2018 at 23:03
• Ok! Lift of this type of wing will start at negative AOA. If unable to make it retractable, maybe fixed slat (slot) like Fiesler Storch and birds! Good luck. Commented Nov 5, 2018 at 23:19