## Chapter 3

## Aerodynamic Forces on Airfoils

## Airfoil terminology

1. Chordline – A straight line connecting the leading edge and the trailing edge of the airfoil

2. Chord – The length of the chordline . Airfoil dimensions are measured in terms of the chord.

## Airfoil terminology

3. Mean camber line – A line drawn halfway between the upper surface and the lower surface.

4. Maximum camber – The maximum distance between the mean camber line and the chordline . The location of maximum camber is important in determining the aerodynamic characteristics of the airfoil.

## Airfoil terminology

5. Maximum Thickness – The maximum distance between the upper and lower surfaces. the location of maximum thickness is also important.

6. Leading edge radius – A measure of the sharpness of the leading edge. It may vary from zero, for a knife edge supersonic airfoil, to about 2% of the chord for blunt leading edge airfoils.

## The four main variables in wing geometry

1. The shape of the mean camber line

if the shape coincides with the mean camber line then the airfoil is symmetrical

2. Thickness

3. Location of maximum thickness

4. Leading edge radius

## Definitions

Flight path velocity – The speed and direction of a body passing through the air.

Relative wind – The speed and direction of the air impinging on a body passing through it. It is equal and opposite in direction to the flight path velocity.

Angle of attack or alpha – The acute angle between the relative wind and the chordline of an airfoil

## Definitions

Aerodynamic force – The net resulting static pressure multiplied by the planform area of an airfoil

Lift – the net force developed perpendicular to the relative wind

Drag – The force parallel to the relative wind which opposes the notion of a body through the air.

Center of Pressure – the point on the chordline where the aerodynamic force acts

## Definitions

Laminar flow – smooth airflow with little transfer of momentum between parallel layers

Streamlined flow is the same as laminar flow

Turbulent flow the the streamlines break up and there is much mixing of the layers.

## The Cylinder

Where the streamlines are scrunched together velocity is very high and pressure is lowered.

Where the streamlines are further apart the velocity is lower and pressure is higher.

## The Cylinder

The important point here is that if the flow patterns are realized around a cylinder in a perfect fluid, then no net lifting force is developed.

The analogy then can be drawn to the symmetrical airfoil with no angle of attack.

In this scenario, there is no lift being generated.

Symetrical Airfoil

## The Cylinder

The drag side of the discussion is that in a real wind tunnel test, there is surface friction which causes a boundary layer to be set up.

Alters the flow pattern around the cylinder in such a way as to increase the friction.

The flow pattern produces drag in addition to the skin friction.

## The Curve Ball

If we were to rotate the cylinder the skin friction would cause an imbalance in the drag profile of the cylinder.

The air would tend to follow the rotation and produce more lift on one side of the cylinder than the other.

The best examples of this are a curve ball in baseball and a slice or hook in golf.

This is called the Magnus effect.

## The Airfoil

In airfoils, the flow pattern is much more efficient for creating lift.

The air is accelerated ahead of the airfoil and over the top of the surface.

However there is a stagnation point in front of the airfoil where the air comes to a complete stop, at this point static pressure is equal to the free stream velocity (Bernoulli’s equation).

## The Airfoil

Furthermore the air is slowed under the airfoil producing higher pressure under the surface (impact pressure).

In some high angles of attack, the stagnation point may even move under the leading edge producing even more lift.

## The Airfoil

Near the max thickness portion max velocity and min pressure will occur (Bernoulli’s equation)

Because of viscosity, the slow air in the boundary layer will slow the upper layers to the point where a high pressure area will show up near the trailing edge.

## The Airfoil

In all cases lift generated by an airfoil, the generated lift will be the net force caused by the distribution of pressure over the upper and lower surfaces of the airfoil.

At high angle of attack near that for maximum lift a positive pressure will exist on the lower surface but this will only account for approximately one third the net lift.

## Center of pressure

The point at which lift or aerodynamic force passes through the chord line.

It is important to know when designing an airplane where in relation to the cg the cp is.

You want the cp behind the cg at all times for stability’s sake.

## Center of pressure

This can be complicated by the cambered airfoil’s pitching moment caused by an imbalance imparted by the cp on top behind the cp on the bottom.

## Aerodynamic Center

For this reason we use the Aerodynamic Center for calculations.

The Aerodynamic Center does not change with changes in angle of attack at a given velocity.

It resides at about 23 to 27% of the chord and 50% of the chord supersonically.