Aircraft Wake Turbulence and Its Detection pp 157-169 | Cite as

# The Effect of a Drooped Wing Tip on Its Trailing Vortex System

## Abstract

The effect of wing tip droop on the structure and position of its trailing vortex is studied. Spanwise load distributions determined by vortex lattice theory show that the stronger vortex moves from the tip of the wing to the hinge of the drooped tip as the droop angle increases. Experimental results on model wings are given which present the strength and the induced velocity profiles of the rolled-up vortex as a function of tip geometry. These results confirm at least qualitatively, the analytical prediction. It is concluded that a droop angle of approximately 90° is optimum and results in a maximum induced velocity which is half of that produced by a plane wing.

## Keywords

Control Point Horseshoe Vortex Vorticity Distribution Model Wing Helicopter Rotor## Nomenclature

- a
core radius where v(r) is a maximum

- A
aspect ratio = b

^{2}/S- b
wing span

- c
local wing chord

- C
_{ι} section lift coefficient

- L
lift per unit span

- r
radial coordinate

- R
radius

- s
semispan

- S
wing area

- v(r)
tangential velocity at radius r

- v
_{max} maximum value of v(r) = v(a)

- V
free stream velocity

- W
downwash velocity

- x, y, z
coordinates of the control point

- y′
spanwise coordinate of the wing

- X=x/y
_{v} nondimensional coordinates of the control point

- Y=y/y
_{v} nondimensional coordinates of the control point

- Z=z/y
_{v} nondimensional coordinates of the control point

- Z
_{1} distance downstream of wing trailing edge

- y
_{v} semiwidth of the horseshoe vortex

- θ
droop angle

- α
angle of attack

- Г(η)
circulation at the section η

- η
y′/(b/2) nondimensional spanwise coordinate

- ζ
vorticity at any radius r

- ζ
_{max} center value of ζ (r=0)

- i, j
number of chordwise and spanwise locations of control points

- ι, m
number of chordwise and spanwise locations of vortices

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## References

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