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I would like to know how far above and below a wing's surface an observer must look in order to see no change to the airflow. Not simply visually but mechanically, assuming a perfect scenario. I am not particularly adept at mathematics, so if there is a rule of thumb, or a general upper boundary, that would suffice for the figure I need.

For a visual representation, a wind tunnel with smoke trails. At some point distant from the top and bottom of the wing in the tunnel, all flow lines will be identical again, implying that wings have an area of effect. How far is this point from each respective surface?

Another way to ask would be to say how far apart must biplane wings be (in a perfect scenario) for them to have no effect on each other?

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  • $\begingroup$ I don't know the answer, but I will assume that the person who does will need to differentiate between a discussion about boundary layers and wake. Just like a boat in water, the distance away that water flow is affected by the passing hull depends on the time that has passed since the boat disturbed the point that is lateral to that wake as it moves outward. For biplane wings, I would guess no more than two feet would probably do the trick. $\endgroup$ – Ryan Mortensen May 8 '16 at 20:55
  • $\begingroup$ I guess ground effect could be used, at least as a rule of thumb... i.e. if the aircraft is within a certain distance of the ground, an increased lift effect becomes noticeable. (Due to changes in the flow patterns around the wing.) $\endgroup$ – Andy May 9 '16 at 9:48
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A precise answer would be: Only outside of the supersonic shock cone. In subsonic flow the change has unlimited range, but dies down with the inverse of the distance.

A mathematical description is possible with the Biot-Savart law. It was first formulated for calculating the magnetic field induced by a current, but can equally well be applied to aerodynamics.

Now it depends on how much error you still accept. If you need the interference-free distance between two biplane wings, express that distance in multiples of the wingspan - that is how it scales. A few wingspans of vertical separation should be enough to make the interference between wings negligible. In flow direction the distance must be much larger: Munk's displacement law postulates that in inviscid aerodynamics the distance in flow direction between two wings makes no difference. In reality, air traffic control requires a separation of up to 8 nautical miles between heavy airplanes for the turbulence to die down or be washed away by wind.

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  • $\begingroup$ Ok then let's elaborate slightly. If I have a wind tunnel and I place a wing inside, how far away from the sides of the tunnel would the wing have to be for the pressures on the tunnel caused by the wing to be negligable? Ten wing thicknesses? Twenty? Exactly five metres? Please forgive my naivety and lack of mathematical prowess. $\endgroup$ – Stephanie-may Shellam May 9 '16 at 10:49
  • $\begingroup$ What I need is to be able to say something like: "In normal air at sea level, for a wing of 3cm thickness, the area of effect would be about 10 cm above and below" .. sort of thing, This is a model so it does not need to be precise. $\endgroup$ – Stephanie-may Shellam May 9 '16 at 10:57
  • $\begingroup$ Any other wing inside of those 10cm would therefore experience lifting issues, and any outside would experience little to no interference. Obviously it isn't 10cm, it would be some function of the air density and distance; the scale of the wing compared to the tunnel environment so to say. If the wing is 'this big', how big does the tunnel have to be to satisfy negligible interference. It must be a fairly standard thing? $\endgroup$ – Stephanie-may Shellam May 9 '16 at 11:23
  • $\begingroup$ @Stephanie-mayShellam: Windtunnels use correction factors to compensate for the tunnel wall influence. Windtunnels are too small to ever have a distance to the wall where no wall influence remains. $\endgroup$ – Peter Kämpf May 9 '16 at 19:43
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    $\begingroup$ @Stephanie-mayShellam A 1mm wing in a 1000mm wind tunnel would cause negligible interference. While theory would still show a minute difference, it would be unmeasurable. However, a 1mm model is completely impractical and would be dwarfed by the sting it needs to ride on. The sting would still cause measurable interference. $\endgroup$ – Peter Kämpf May 10 '16 at 4:15
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2 cents here: One of the first homework assignments of our aerodynamics class was to calculate the lift of an airfoil by using the pressure data of the wind tunnel walls. Any wing shape would generate a pressure variation (if it's generating lift) at the boundaries of the tunnel. (Unmeasurable it may be)

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