## CHAPTER 4

LIFT AND STALL

**X-4 and X-5**

The X-4 was a semi-tailless design that proved it was not suitable for speeds near Mach 1

Only with computer flight controls is this system viable

The X-5 was a variable swept wing demonstrator

The wings pivoted from 20° to 60°

It took about 20 sec to make the full travel and had a hand crank in case of electrical failure

The drag axis, the thrust axis and the principle axis were all different

Had really poor spin characteristics and you guessed it they lost one in a spin

However drag reduction and high speed performance improvement data was good enough to use for development of the F-111, the F-14 and the B-1

http://www.youtube.com/watch?v=sU2ts77Dp54&NR=1&feature=endscreen

## Factors in Lift and Drag equations

1. Airstream velocity V (knots)

2. Air density ratio (sigma)

3. Airfoil planform area square feet

4. Profile shape of the airfoil

5. Viscosity of the air

6. Compressibility effects

7. Angle of attack (degrees)

## Factors in Lift and Drag equations

1. Airstream velocity V (knots)

2. Air density ratio (sigma)

3. Airfoil planform area square feet

4. Profile shape of the airfoil

5. Viscosity of the air

6. Compressibility effects

7. Angle of attack (degrees)

Items 1 and 2 define dynamic pressure

Items 4,5 and 6 explain drag on an airfoil

## Coefficient of Lift

Is a measurement of lift at a certain angle of attack or said another way, it is the ratio of the lift pressure and dynamic pressure and is a function of the shape of the wing and angle of attack.

**Dynamic Pressure and Lift**

Recall that the dynamic pressure possessed by a moving fluid is equal to the density ratio (sigma) times the velocity squared in knots divided by 295.

## Dynamic Pressure and Lift

It is also true that when dynamic pressure is exerted over a certain amount of area measured in square feet, it yields a force proportional to the amount of the area. F=pressure x area

## Dynamic Pressure and Lift

The amount of lift obtained from a wing should thus be proportional to the dynamic pressure and the wing area.

It is not exactly equal to the product of these 2 quantities so the difference is made up by the CL in this equation:

## The lift equation

The equation says that lift is equal to the lift coefficient times the dynamic pressure times the wing area.

The CL can be thought of as a measure of how efficiently the wing is transforming dynamic pressure into lift.

It can also be thought of as the ratio between the lift pressure and the dynamic pressure

## The lift equation

Lets say we have a wing that has an area of 2 square feet, is subjected to a dynamic pressure of 1.5 psf and yields a lift force of 1.2 pounds.

The CL would be determined as:

## The lift equation & CL

This result would be obtained at a certain angle of attack.

At a higher angle of attack the same wing and dynamic pressure would have a higher CL up to the point of stall.

Each angle of attack produces a particular lift coefficient since the angle of attack is the controlling factor in the pressure distribution.

If the curve starts at 0 the airfoil is symmetrical

**Stall α**

Note how some of these airfoils start in the negative numbers (cambered)

An airfoil always stalls at the same α

At the stall α the airfoil achieves its maximum CL

This is referred to as it’s maximum lifting ability or CL(MAX)

## CL change for flaps up and flaps down

1. A very sharp drop off would indicate a sudden stall whereas a softer curve indicates a more benign stall.

2. You can tell if the airfoil has a camber to it because of the zero lift angle hits base line in the negative numbers.

3. The very top of the curve indicates the CLmax or maximum lifting ability.

**CL change for Camber**

Note the 0012 is a symmetrical airfoil

The 4412 and the 0012 are 12% of the chord

So the max thickness is the same

However the max camber of 4% occurs at 40% of the chord for the 4412

So clearly, more lift per same given α out of the cambered wing

Also the cambered airfoil has a lower stall speed

**CL change for Thickness**

Note by the NACA number, the 4412 is 12% of the chord thick

The 4406 is just 6% of the chord thick

Both airfoils have max camber of 4% located at 40% of the chord

The 4412 produces more lift but will also produce more drag

## Stall Facts

Remember stall AOA does not change for weight, attitude or altitude.

Stall Speed does change with weight, density altitude and Load factor or G loading

## The V stall speed occurs at CLmax so the equation is:

## Load factor = G’s x weight

2gs x 2150 = 4300

All factors being equal the stall speed varies as the square root of the lift.

The equation is:

Where W2 is current weight and W1 is max gross weight

This formula works for Va, approach speed, gust penetration speed and stall speed

## The Controversy:

So in steady flight the only variables in the equation are CL and V

Since AOA sets the value of CL speed is now a constant linked to AOA

Dole – AOA is the primary control of airspeed in steady flight. Rate of climb or descent is controlled by power

A blend of pitch and power should be used to control altitude and airspeed.

To rely on AOA for airspeed control only would result in rough control technique.

AOA indicators are used to determine Vx, Vy and max range.

Also AOA indicators may be used on final approach as well

**Boundary ****Layer Theory**

Boundary layer is important to understanding what happens to flow at and above stall AOA

Viscosity causes air to stick to the wing surface

Air velocity at the surface is therefor 0

As we move away from the surface, velocity begins to pick up slowly due to friction with the non moving air particles

The layer of air from the airfoil surface to the point at which no slow down occurs is the boundary layer

The nature of the boundary layer determines CLmax and the stall characteristics

**Laminar Flow**

Defined as a very thin layer of smooth flow where the layers do not intermix

As the airflow moves aft the boundary layer thickens and becomes unstable

Mixing of the layers occurs which causes *Turbulent Flow*

**Boundary layer**

velocity profiles for laminar and turbulent flow (pg 50)

Cessna Corvalis

Laminar flow wing

235 kts

TSIO-550

310 hp

**Reynolds Number**

Osborn Reynolds found the boundary layer was laminar or turbulent is dependent upon 3 things:

1. The fluid velocity

2. The distance downstream

3. The kinematic viscosity.

The formula is as follows:

Where:

Rg = Reynolds number

V= stream velocity (fps)

x = distance downstream

v (nu)= kinematic viscosity ft2 /sec

**Reynolds Number**

Probably the main use for the RN is in analysis of skin friction.

Since laminar flow indicates small values of skin friction then a lower RN is desirable.

The higher the RN the more chance of developing a turbulent flow and a correspondingly higher value of skin friction.

**Reynolds Number**

The higher RN indicates the turbulent flow closer to the leading edge.

RN’s less than 500,000 indicate mostly laminar flow

RN’s from 1 and 5 mil are partly laminar and partly turbulent

RN’s above 10 mil give mostly turbulent boundary flow

## Reynolds Number

RN varies directly with velocity and distance back from the leading edge and inversely with viscosity.

The curve indicates lower CDrag with increasing RN’s because the velocity gradient decreases as the boundary layer thickens.

## Reynolds Number

High RN’s are obtained from large chord surfaces, high velocity and low altitudes.

Low RN’s are obtained from small chord surfaces, lower velocity and higher altitudes.

Remember high altitudes produce higher values of kinematic viscosity (the air is less thick).

**Mooney Acclaim**

Fastest GA airplane

Laminar flow wing

242 kts

TSIO-550

280 hp

## Adverse Pressure Gradient

Basically the lower pressure gradient on top of the airfoil causes the airflow to want to separate from the airfoil.

As the air flows back on the airfoil pressure increases until at the trailing edge, pressure should more or less equal.

The more the pressure is reduced the slower the velocity.

## Adverse Pressure Gradient

In fact near stall conditions, the airflow can actually reverse and flow backwards up the wing.

Where these two meet is where airflow separation will take place.

The boundary layer is acted on by 2 things:

1. friction

2. adverse pressure gradient

## Adverse Pressure Gradient

Laminar flow will lend to earlier airflow separation because of lower energy velocity

Turbulent flow will resist early airflow separation because of higher energy forces.

## Stall

Stall is airflow separation of the boundary layer from a lifting surface. Stall starts at the trailing edge and advances forward.

The accelerated stall is where airflow separation occurs at the leading edge first because the air can’t make the corner.

## High CL Devices

Camber changers:

Flaps – Plain, Split, Slotted, Fowler

Leading edge slats and flaps

## Helio Courier

## The Advantage of Leading Edge Slats

It is a 6-place bush/utility/sport-utility aircraft that features the 350 horsepower turbo charged six-cylinder Lycoming TIO-540 engine.

It is designed to have a minimum controllable airspeed of 26 knots and a cruise speed of 147 knots.

The Helio Courier is anticipated to have a useful load of 1,700 pounds and a range of 912 nautical miles with standard fuel capacity.

It can safely operate out of a 500 foot unimproved clearing at full gross weight and take-off and land in areas otherwise only accessible to aircraft such as 2-place Piper Super Cubs.

The Helio Courier is capable of safely taking off and landing in less than 250 feet.

On floats, it can land on and take off from many smaller lakes (not accessible with the de Haviland Beaver and Otter or the Cessna 180/185 and 206).

## The Vx Takeoff Looks a Little Different eh?

## High CL Devices

Energy Adders

Vortex generators stir up the boundary layer mixing higher velocity air higher up in the boundary layer with lower velocity air lower in the boundary layer.

Reduces takeoff and landing dis. and speeds

## Vortex Generators

These are mounted on a J3 Cub, lowering stall speed 5 – 6 kts! Like mini-wingtip vortices. Note how the vortex brings the high energy air closer to the wing surface, lowering drag.

## High CL Devices

Leading edge slot may allow airflow through to energize airflow pattern over the wing.

## High CL Devices

Boundary Layer Control is when a vacuum pump is used to suck faster moving air closer to the wing to artificially raise boundary layer velocity

Sometimes using pressurized air usually from the turbine is directed over the wing energizing the airflow