Calculating Velocity in a Trailing Vortex

[physicsCU]

OK, I am calculating the velocity in a trailing vortex 4 ft laterally from the wingtip at a distance of 1 span behind the wing.
I figured out that V = G/4*pi*r
so in my situation, r = 4 ft, G = 2647.33 ft^2/s (this was found earlier in the problem).

I get a V of ~52 ft/s. What is this? the induced downwash velocity? it seems to be high, my V_0 is 337 ft/s.

I am just trying to get a check on my reasoning here, because this seems to be too high to me. I should mention that lift is assumed to be constant along the span.

But in the case of elliptical circulation distribution, how is there any trailing vortex at the wingtip? since G is 0 there, there is no velocity, and thus no vortex.

 

[Navin A S]

Yes, in the case of an elliptical circulation distribution, there is no trailing vortex at the wingtip. However, there may be a trailing vortex at some distance behind the wing. The velocity at this point will be determined by G/4*pi*r, where G is the total circulation, r is the radial distance from the center of circulation, and 4*pi is a conversion factor.

 

[ravenprp]

Your calculation for velocity in the trailing vortex is correct. The value of V you have calculated is the induced downwash velocity, which is the velocity induced by the wing's lift and circulation. This downwash velocity is typically high near the wingtip and decreases as you move away from the wingtip.

Your V_0 of 337 ft/s is the freestream velocity, which is the velocity of the air approaching the wing before it encounters the wing's lift. This is a different velocity than the induced downwash velocity.

In the case of an elliptical circulation distribution, there is still a trailing vortex at the wingtip. This is because even though the circulation value (G) is 0 at the wingtip, there is still a change in circulation along the span of the wing. This change in circulation creates a trailing vortex at the wingtip.

Overall, your reasoning and calculations seem to be correct. It is normal for the induced downwash velocity to be high near the wingtip and decrease as you move away from the wingtip. And even with an elliptical circulation distribution, there will still be a trailing vortex at the wingtip.