LESSON 6 Chapter 5 Drag ANA Chapter 1

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Flight Theory

Chapter 5 Drag


First flew June 1959, last flight Oct 1968

354,200 feet Mach 6.7 (4520 mph)

31,275lbs takeoff 12,295 at landing

200mph landing speed

Launched from B-52

57,000lbs of thrust – anhydrous ammonia and lox

The outer skin was nickel chrome alloy called Inconel X

Used conventional controls in atmosphere used hydrogen peroxide thrusters for pitch, yaw and roll

Established benchmark hypersonic data

Stability, control, materials for high heat, shock interaction, hypersonic turbulent boundary layer, skin friction, aerodynamic heating, and heat transfer


Lift, a Brief Review

We know that lift is produced by low pressure above and high pressure below

We also know that lift is the force acting perpendicular to the relative wind

And that any increase in alpha will generate an increase in drag

Drag acts parallel to the flight path

In all steady state flight lift=weight and thrust=drag

–This is true in a descent

–Also true in a steady climb

However in initiating a climb an alpha change is needed to change the pitch

–Once airspeed stabilizes we are again in steady state

Any given alpha has a corresponding airspeed to achieve steady state

–As speed slows, alpha is increased to provide sufficient lift

–As altitude increases, a higher TAS is needed to provide sufficient lift

Remember that if the V is doubled it is at the square so lift goes up 4 times as much


There are 3 basic ways lift is generated on an airfoil:

–Bernoulli’s Principle

–Deflection (Newton)

–Downwash (Newton)

This is a bit of an over simplification of how lift is generated however

Lift generation, the real story

There are 3 concepts to lift generation

–Conservation of momentum

–Conservation of energy

–Conservation of mass

Newton’s laws explain the conservation of momentum

–Every action has an opposite and equal reaction

Bernoulli’s equation explains the conservation of energy

-Static pressure + Dynamic pressure = Total pressure

Euler equations explain the conservation of mass

–This is where it gets messy

Lift generation, the real story

The Euler equations are a series of calculus equations that relate 2 dimensions of velocity along x and y axis along with pressure and density

All equations must be solved simultaneously

This area of study is called Computational Fluid Dynamics

Engineers use this method to determine the conservation of mass airflow around the airfoil

Lift myths

Equal transit theory

Venturi flow

Skipping stone theory

Lift the Coanda Effect

The Coanda effect (pronounced cwanda)

This explains the air’s tendency to stick to a surface and bend around the curved portion of the upper surface

Newton’s law then takes over explaining the force generated by the bending of the air stream

As air flows over a curved surface, a negative pressure results which pulls the flow toward the airfoil’s surface

Drag defined

Drag is the component of the aerodynamic force that is parallel to the relative wind and retards the forward motion of the aircraft.

The Drag equation is: Drag equation

The coefficient of drag is the ratio of the drag pressure to the dynamic pressure.

Drag like lift is proportional to the dynamic pressure of the air and the area on which it acts.

The equation is much like the lift equation except that it measures the force in the stream-wise direction or parallel to the flow.

When talking about drag, there is a problem when determining the area to be used in the equation.

Drag is being generated by a three dimensional body but drag is only proportional to 2 dimensions of the body (length x width).

Use fuselage shape example Top, Side and Front.

As a standard most bluff bodies (fuselage, engine nacelles or landing gear use the projected frontal area or max cross section.

For wing or tail surfaces, the planform or top view is used.

Sometimes engineers will use the wetted area or the area that would get wet if the whole airplane were dunked in water.
Laminar Flow airfoils

When comparing an older 4 digit airfoil to one of the newer 6 series airfoils there is a noticeable decrease in drag coefficient called the drag bucket.

At low AOA the drag remains extremely low because the laminar flow remains laminar so far back.

At high AOA because of the sharper leading edge the CD goes up higher than the 4 digit airfoil.
Lift to Drag Ratio

The lift to drag ratio is a measure of efficiency.

A higher L/D is more desirable and the equation is:

The Curves

This particular curve relates the L/D ratio to α

L/D max is at the top of the curve

Notice the familiar Cl curve

And the Cd curve


1. Highest point on the curve

2. The most efficient alpha

3. Min drag

4. Best glide

5. Max endurance (jet powered)

6. Max range (prop powered)

7. Max climb angle for Jets
Glide Ratio

Glide ratio is numerically equal to the L/D ratio

15/1 is both glide ratio and L/D ratio

Gross Weight does not effect glide performance.

Glide ratio is always the same

At a higher gross weight, V must be higher to achieve the L/Dmax α

What is the Glide Ratio for the B-19?
Induced Drag

Induced drag is drag generated by the production of lift or more accurately by the production of wingtip vortices.

The DI formula is:



Terms pg 65

Average chord – tapered wing take all chord lengths and average them

Aspect ratio = span (b)/chord (c)

high = glider wing

low = jet fighter wing
Induced Drag

Low pressure on top and high pressure underneath induces a vortex to form at each tip, causing a downward push on the air leaving the trailing edge.

This downward component known as downwash, causes the airstream to depart at an angle downward from the incoming air.

The lift vector being perpendicular to the flow, is now tilted backward at half the downwash angle.
Induced Drag

This means some lift is being generated opposite to the flight path this rearward component is by definition drag.

Induced drag is influenced by the CL and aspect ratio.

It increases directly as the square of CL and inversely as the aspect ratio.
Induced Drag

At low speed and low aspect ratio (short wings) induced drag is greatest.

Induced drag varies inversely with the velocity squared.
Ground effect

Ground effect usually happens when within one wingspan of the ground.

The surface actually helps destroy the downwash generated by the wingtip vortices and thus forces the lift vector more to the vertical thereby reducing drag.

Above 1 span length there is little or no ground effect
Ground effect

At 3/10 span length there is a reduction of 20% induced drag

For our planes that’s 9 feet up

At 1/10 span length there is a reduction of 50% induced drag

For our planes that’s 3 feet up
Ground effect

There is also a change in the effective angle of attack. Because of the altered downwash, an angle of attack increase is the result

Pitching moments develop downward for an aircraft entering ground effect because of the wings downwash not being able to help the tail generate lift downward.
Ground effect

Pitching moments develop upward for the aircraft leaving ground effect and may cause an increase in angle of attack such that the corresponding increase in drag may cause the aircraft to settle.

The pitch up and down moments are experienced entering and leaving ground effect

Level flight in ground effect results in a significant pitch up requiring a substantial force on the yoke to keep the nose down

There may be an increase in static pressure if the ports are below the wing. This will result in a decrease of airspeed the closer the plane gets to the ground or water.

Ground Effect Summary

On entering ground effect:

–Induced drag is decreased

–Nose-down pitching moments occur

–Airspeed may indicate slow

On leaving ground effect

–Induced drag is increased

–Nose-up pitching moments occur

–Airspeed may indicate higher

Parasite Drag

Parasite drag is the drag caused by protuberances and increases directly with the velocity squared.

The DP formula is:
Parasite Drag

Skin Friction – Drag caused by rivets, dirty surfaces, effects boundary layer

Form Drag – caused by the shape of the surface

Interference – collision of boundary layers of different surfaces

Leakage – pressure differences inside and outside the plane, like cracks in door seals

Profile – drag with regards to moving helicopter rotors
Definitions pg 72

Total drag

Total drag is the sum of induced drag and parasite drag
Drag Curves

The total drag curve has limitations

1. Parasite drag will be increased as stall alpha is reached because more frontal area is exposed

2. In high speed flight, wave drag may form as a result of compressibility.
The Total drag formula is:

Wing Loading

Power Loading

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