I am trying to find if there is an analytical or simpler way to find pressure or force acting on the upper surface of a wing due to the gust wind.
Assuming the wing is not in motion (static case) and it experiences sudden gust from right above it (at 90 degree). The velocity of this gust wind is known, say "V". See figure below.
I want to calculate pressure exerted by this gust wind on the wing lower surface. Don't want to go through simulations now. Just looking for an estimated value.
Is there a way to do so? Bernoulli's principle perhaps but I'm unable to apply it here!
Any insights highly appreciated!
Thanks in advance.
I understand it as a wing moving in a flow perpendicular to its top. Assuming the flow of wind is subsonic and incompressible, to calculate pressure on top surface we can simply apply Bernoulli equation along the flow (i.e perpendicular to surface) . At the wing top surface the velocity is zero (The wing stops the flow from continuing through it ) so we can find the stagnation pressure there Pstagnation = P + 0.5V2
Where P is free stream Pressure. Take it as atmospheric pressure= 101325 Pa
For the Force acting on Top. Product of Pstag with the Wing area should do the job. The pressure at low surface should be something lower than Pstag as the flow from the top should detach and not meet at the bottom.
Hi Nikesh,
if you are interested in the force acting on the plane, you could tentatively use the drag coefficient for a flat plate perpendicular to the flow (c_d approx 1.8 ...2). Since the dependence of c_d from the reynolds number might be small, the trapezoidal shape might also have a small effect on the drag coefficient.
Best regards
Bastian
Dear Nikesh
The force acting on a surface can be computed according to the following formula :
F = 0.5 x Density of air x [(Velocity of wind )^2] x Drag Coefficient x Area
You are talking of a vertical gust on a wing in flight, right. In this case you encounter a speed variation and - more severe - a change of angle of attack. For the first alone the scaling of forces with the square of velocity could be sufficient for a guess, if you want to neglect dynamic effects. But the second cannot be covered by applying Bernoulli's equation. The lift generated by the wing changes dramatically, depending of the variation of the angle of attack (which is the arctan of the ratio of gust to flight velocity). If you stay in the so-called linear part of the polar you can use the approximative functions that you can find in any text book on aerodynamics (like Anderson or Schlichting) assuming a constant CL-a increment, which is itself strongly related to the aspect ratio of your wing. For the drag force you can assume the increment based on the changes of induced drag, which goes with the square of CL and the inverse of the aspect ratio - see also in text books. For the pressure there are no such simple approximations, since they strongly depend on the airfoil shape you have, and I fear you have to do some kind of simulation. Must not necessarily be CFD if you stay in incompressible or pure subsonic. But some panel method should be able to give you some approximations. But again, be aware that there is a strong limitation regarding the strength of the gust to be analysed and you don't cover dynamic effects that can be rather strong.
Thank you all for your answers!
This part is on hold for the moment and I shall re-post on it when I've gotten there in the next month or so.
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