Finite Wings

Question 1

What is downwash and how is it created?

Answer 1

Down wash referes to the induced velocity created as a consequence of the wing tip vorticies. These vorticies induce a velocity downward over the whole wingspan.

Question 2

What is induced drag and how is it created?

Answer 2

In 2D wing theory the static pressure of the free stream is recoverd behind the wing, Thus the kinietic energy induced in the flow is converted back to pressure energy, and zero drag is resulted.
For a finite wing the generation of tip vorticies requiers a quantity of kinetic energy that is not recovered by the wing. This energy appears to the wing as induced drag..
Draw geometerically how we find D_i.

Question 3

What is meant by effective angle of attack?

Answer 3

The downwash, w, has the effect of reducing the angle of the oncoming flow. This means that an vehicle can be traveling at a geometerical angle of attack however the incidence angle the airfoil experiences is different. This makes it necessary to intruduce the concept of an effective angle of attack.

Question 4

What is the ground effect?

Answer 4

If a point vortex is placed at a height h above a horizontal plane and an equal but opposite vortex is placed below it. The vertical velocity from one vortex on a point on the plane is equal but opposite to the effect fom the other vortex. Thus the vertical velocity is zero. This shows that the mirror vortex is equivalent in effect to a solid boundry.

However the mirror image of the horseshoe vortex reduces the downwash on the wing, hence the power requierd is reduced.

Question 5

What are the effects of asspect ratio?

Answer 5

reduced down wash=> less induced drag => higher aerodynamic efficiency eta.

Question 6

What is the general idea of Prandtl’s lifting line theory?

And what is the goal?

Answer 6

To replace the wing with a vortex system that effects the surrounding flow similarly thus generating similar forces..

Prandtl’s theory shows how 2D airfoil characteristics can be used to the determine the characteristics of a finite wing.

Question 7

What are the components of the vortex system?

Answer 7

• The starting vortex
• Trailing /wing tip vorticies
• The bound vortex

Question 8

Describe how the starting vortex is created.

Answer 8

Circulation isn’t genertaed imidiatley. Due to the direction change of the SL at the TE high local accelerations are created therefor very large viscous forces. The air is unable to turn around the TE. Instead it leaves the surface creating a vortex.

The vortex left behind is equal in strength and opposite in direction to the circulation around the wing.

Question 9

Describe how wing tip vorticies are created.

Answer 9

high pressure on the lower surface, and low pressure on the upper surface. At the wing tip this pressure differences is tried to be evened out. Air from the lower surface moves towards the low pressure regin at the top thus creating a vortex.

Question 10

Describe the bound vortex system.

Answer 10

The bound vortex system is a theoretical arrengemtn of vorticies that are used to replace the physical wing. Wing thickness is negelected just like for thin airfoil theory.

Question 11

What is a point vortex?

Answer 11

A point vortex is considered to be a string of rotating particles surrounded by fluid moving irrotationally under its influence.

Or a more general definition is that a vortex is a flow system in which a finite area, in a normal section plane contains vorticity.

Question 12

What are Helmholtz theorems about?

Answer 12

The 4 fundamental theorems govering vortex motion in an inviscid flow.

Question 13

What are Helmholtz 4 theorems?

Answer 13

1. A fluid particle in motion posses all or some of the following:
   - Linear velocity.
   - Vorticity.
   - Distortion.
2. Vortex continuity.
   The strength of a vortex cannot grow or diminish. along its axis or length. A vortex line cannot end in a fluid. Must form a closed loop or start/end in a discontinuity in the fluid such as a solid body.

3-4.

• There is no fluid interchange between a vortex tube and surroundings.
• The strength of a vortex remains constant as the vortex moves through the fluid.

Question 14

What is Biot-Savart’s law?

Answer 14

The relationship between the induced velocity by a vortex tube and the tubes strength (Circulation).

Question 15

What is the induced velocity by a semi-infinite vortex?

Answer 15

v=gamma/(4pir)

r=perpendicular distance.

Question 16

What is the induced velocity by a infinite vortex?

Answer 16

v=gamma/(2pir)

r=perpendicular distance.

Question 17

What are the two main consequenes of downwash?

Answer 17

1. The downwash at a point has the effect of tilting the resultant oncoming flow at the wing through the angle epsilon. Thus reducing the effective incidence. For the same lift as the equivilent infinte wing (2D) at incidence alpha_inf an incidence of
   alpha=alpha_inf+epsilon
   is requierd for the finite wing.
2. Induced drag. In 2D wing theory the static pressure of the free stream is recoverd behind the wing, Thus the kinietic energy induced in the flow is converted back to pressure energy, and zero drag is resulted.
   For a finite wing the generation of tip vorticies requiers a quantity of kinetic energy that is not recovered by the wing. This energy appears to the wing as induced drag..
   Draw geometerically how we find D_i.

Question 18

What are some characterisitcs of the elliptical circulation distribution?

Answer 18

• It is the only circulation distribution producing a constant downwash along the span.
• It produces the minimum induced drag of any possible lift/circulation distributions. (For a planar wing.)

Question 19

Why do the even terms disapear for a symetrical loading?

Answer 19

Since we choose to describe the general loading case with fourier series the even terms are infront of sin(2theta) and sin(4theta) etc and these terms disapear when you integrate from 0-pi.