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

Question

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.

Answer 1

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

Answer 2

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.