AF 202 – Chris Dimoulis. Advanced Aerodynamics. Objectives. A little bit of Theory A little bit of Physics A little bit of Math A whole lot of fun!. Definitions. Leading edge Trailing edge Chord Line. Definitions. Relative Wind Angle of Attack. Aerodynamic Forces. What is a force?
A little bit of Theory
A little bit of Physics
A little bit of Math
A whole lot of fun!
Angle of Attack
What is a force?
Any influence to an object that causes a change in speed, direction, or shape.
What is acceleration?
A change in velocity (speed and direction)
An unbalanced force is required for an acceleration.
Force, acceleration, velocity are ‘vectors’
The most known force formula:
Force = Mass x Acceleration
You can rewrite this to say that:
Acceleration = Force/Mass
The 4 Airplane Forces are:
Remember what an acceleration is
Change of speed and/or direction
Requires and unbalanced force
Opposing forces must be equal
Thrust = Drag
Lift = Weight
If weight and lift are not balanced…
Weight > Lift = Airplane decends
Lift > Weight = Airplane pitches up (NOT CLIMB!!!!)
If thrust and drag are not balanced…
Thrust > Drag = Aircraft speeds up
Drag > Thrust = Aircraft slows down
It is simply a matter of adding the vectors together…
The resulting force is…
This will produce an acceleration in the direction of that force.
Weight is a force
The acceleration in F=ma is the pull of gravity (9.8 m/s2)
The total weight of your plane is the downward force applied at the center of gravity (CG).
We feel weight
It is equally opposed by the ground.
Therefore there is no acceleration
Acts perpendicular to the flight path
Occurs at the center of lift/pressure
Two principles are used to explain lift:
Newton’s 3rd law of motion
When the velocity increases the pressure decreases
High pressure always seeks a low pressure
High pressure below the wing applies a force upward
For every action there is an equal and opposite reaction
What ways can lift be changed?
Change Angle of Attack
Change Wing Surface Area
Change Air Density
L=1/2 (CL V² Ρ A)
CL= Coefficient of Lift
V = Velocity (ft per sec)
1 knot = 6076 ft/hr = 1.68527 ft/sec
P = Air Density
A = Wing Surface Area (sq.ft.)
The coefficient of Lift increase as Angle of Attack increases
Velocity also has a great impact.
Velocity increases – Lift Increases
Air density and the design of the wing have an affect, but cannot be changed by the pilot
Altitude Density Speed of Sound
(Feet) (d) (Knots)
0 .002377 661.7
1,000 .002308 659.5
2,000 .002241 657.2
3,000 .002175 654.9
4,000 .002111 652.6
5,000 .002048 650.3
Angle of Attack = 5 degrees
Coefficient of lift = .4
Airspeed = 100 knots = 607600 ft/hr = 168.7 ft per sec
Air density = .002175 (3000 feet)
Wing surface area of 172 = 174 sq.ft.
L = .5(.4 x 168.72 x .002175 x 174)
Lift = 2154 lbs
Increase the speed to say… 150 knots and let’s see what happens
150 knots = 253.167 ft/sec
L = .5(.4 x 253.1672 x .002175 x 174)
L = 4853 lbs
THAT’S 2G’S AT FULL WEIGHT
With just a little rearranging we can learn other wonderful things about lift
Rearrange for velocity and we can see what angle of attack will do to it (assuming you remain level)
Rearrange for Coefficient of Lift to see what Angle of Attack you need for a given Air speed
Keep L = 2154 lbs. for level flight
V = SqRt(2L/ (CL Ρ A))
Make the Angle of Attack 10 degrees
Coefficient of lift = .8
V = SqRt(4308/(.8 x .002175 x 174))
V = 119.2 ft/sec
V = 70 knots
Once again keep lift at 2154 lbs.
CL = 2L/(V² Ρ A)
Slow airspeed from 100 to 80 knots
80 knots = 135 ft/sec
CL= 4308/(1352 x .002175 x 174)
CL = .62
Angle = 8 degrees
ASSUMING LEVEL FLIGHT IS MAINTAINED
Velocity Angle of Attack
100 5 degrees
90 6 degrees
80 8 degrees
70 10 degrees
60 13 degrees
50 16 degrees
As Angle of Attack increases we decrease speed
As speed decreases we need to increase angle of attack to maintain lift
As speed increases we must decrease angle of attack.
Airplane stalls at Critical Angle of Attack
An airplane can stall at any airspeed
Why then do we have Vso and Vs?
The Airplane will stall at the critical angle of attack regardless of
Angle of Bank
Below Vso and Vs you the required angle of attack to produce lift is beyond the critical angle of attack
Types of stalls
Drag is the rearward acting force opposing thrust
Three Types of Parasite Drag
Increases when speedincreases (exponential)
Inherent whenever a wing produces lift
Increases when speed decreases
As speed decreases we need to increase angle of attack
Induced drag increases as AOA increases
Induced Drag is also caused by wingtip vortices
High pressure below the wing is pulled toward the low pressure above the wing.
D =1/2 (Cd V² Ρ A)
Cd = Coefficient of Drag
V = Velocity (ft per sec)
P = Air Density
A = Wing Area (Sq.Ft.)
Speed = 100 knots = 168 ft/sec
Air Density = .002175
Wing Area = 174 sq.ft.
Angle of Attack = 2 degrees
Coefficient of Drag= .03
D = .5(.03 x 1682 x 174 x .002175)
D = 160 lbs of Drag
After a certain speed drag increases and so the required thrust increases.
Region of reverse command refers to the need for MORE power to fly SLOWER speeds
This is reversed from normal (hopefully that is obvious to you)
As one enters ground effect, much of the downwash, upwash, and wingtip vortices are reduced effectively increasing your Coefficient of Lift
Forward force pulling/pushing plane through the air.
Thrust is most easily described as lift in the horizontal direction
The propeller aerodynamically functions similar to a wing
By spinning it creates its own relative wind.
Why does the propeller have a twist in it?
Just like with lift, thrust on the propeller increases with angle of attack and with speed.
The outside of the propeller spins faster thus requiring a smaller pitch
No Propeller is 100% Efficient
Asymmetrical Thrust (P-Factor)
Torque from the engine
When pitching up, the angle on the DOWNWARD moving blade is greater than that on the upward moving blade. Causes a left yaw.
A gyroscope is basically something that spins
A force applied to a spinning object is felt 90 degrees in the direction of rotation.
Pitch up – right yaw
Pitch down – left yaw
The slipstream strikes the left side of the rudder yawing tail right and the nose left
The engine is rotating Clockwise from a pilot’s view. The opposing reaction makes the plane want to bank left