AF 202 – Chris Dimoulis. Advanced Aerodynamics 2. Objectives. Review Vectors Forces in climbs and turns Stability Vg diagram. Force. Force: Any influence to an object that causes a change in speed, direction, or shape. The 4 forces of flight Weight Lift Thrust Drag.
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Forces in climbs and turns
Any influence to an object that causes a change in speed, direction, or shape.
The 4 forces of flight
A change in speed OR direction which requires an unbalanced forces
Straight, level, and constant speed flight required an equilibrium balance of the forces
Opposing forces are equal
Lift = Weight, Thrust = Drag
Weight is a force
In F=ma, the acceleration is the pull of gravity
As long as an object has mass (and is on earth) there is the downward force of gravity.
Must EQUAL weight for level flight
2 principles cause lift:
Newton’s 3rd law
Four ways to control lift
Change Angle of Attack
Change Wing Surface Area
Change Air Density
L=1/2 (CL V² Ρ A)
V = √2L/ (CL Ρ A)
CL = 2L/(V² Ρ A)
L - Total lift
CL - Coefficient of lift increases as Angle of attack increases
V – Magnitude of velocity (speed)
A – Area of the Wing
P – Air Density
To simulate level flight, keep L the same value
We can see how the angle of attack MUST increases as speed slows
We see that as angle of attack decreases we must increase speed to maintain lift.
Parasite drag INCREASES as speed increases
Inherently created when lift is produced by use of angle of attack
As angle of attack increases, induced drag increases
Since angle of attack increases when speed degreases, induced drag ALSO increases when speed decreases.
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)
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.
No Propeller is 100% Efficient
Asymmetrical Thrust (P-Factor)
Torque from the engine
When rolling into a bank…
Lift is increased on the outside wing
Lift is decreased on the inside wing
When lift changes so does drag
Drag is increased on the outside wing
Drag is decreased on the inside wing
The aircraft pulls outside of the turn
Remember that a force can be considered a vector
Vectors consist of magnitude and direction
They can be broken down into components
The components are PERPENDICULAR to each other
You can add 2 vectors together by adding the horizontal vectors and vertical vectors
As a climb begins, lift BRIEFLY exceeds weight.
The brief increase in lift increases drag
If you do not add power you will slow down
Once established, angle of attack decreases which decreases drag
Total drag still remains higher. It does not return to normal…WHY?
Weight now has a rearward component
Total drag now equals the Drag vector PLUS the rearward component of weight
This is why adding power is needed to MAINTAIN airspeed in a climb
Thrust = drag + the rearward component of weight.
Thrust and Lift now have vertical and horizontal components
Therefore you can say…
The vertical component of lift PLUS…
The vertical component of thrust EQUALS…
The total weight
Or more simply that the OPPOSING forces in a constant rate constant speed climb are equal.
But lift does NOT necessarily = weight and thrust does NOT necessarily = drag
Thought the values of some of the forces may be generally lower than in straight and level flight.
Lift remains perpendicular to the wings
When the aircraft is banked, lift can be broken down into components
Once in a turn, the horizontal component is responsible for turning.
The vertical component is opposing weight and responsible for pitch.
For the vertical component of lift to equal weight, Total Lift must be increased.
This is done by increasing angle of attack
This increases induced drag which will slow us down
And so we need to add power to maintain speed.
The angle of bank EQUALS the angle between the Total lift and Vertical Component of lift.
cos θ = A/H
sin θ = O/H
H = Hypotenuse
A = Side adjacent to θ
O = Side opposite to θ
So we can say this
cos θ = Vertical Lift / Total Lift
sin θ = Horizontal Lift / Total Lift
Total Lift x cos θ = Vertical Lift
Vertical Lift / cos θ = Total Lift
Total Lift x Sin θ = Horizontal Lift
Horizontal Lift / sin θ = Total Lift
θ = The angle of Bank.
What happens when we bank without increasing lift (Use 1.0g for lift)
Total Lift x cos θ = Vertical Lift
1.0g x cos 15 = .96g
1.0g x cos 30 = .86g
1.0g x cos 45 = .70g
Vertical Lift does NOT equal weight
Vertical Lift must equal weight. Make vertical lift = 1.0g and see what total lift you get.
Vertical Lift / cos θ = Total Lift
1.0g/cos 15 = 1.03g
1.0g/cos 30 = 1.15g
1.0g/cos 45 = 1.41g
So we can see that as the angle of bank increases, the more TOTAL LIFT we need to remain level
So as bank angle increases, angle of attack must increase also.
Opposing total lift is something called Load Factor.
Load Factor is measured in g’s. If the load on the airplane is Xg’s then the load factor is X times it’s weight.
The ratio between total load on wings and the gross weight of aircraft
LF = Wing Loading/Gross Weight
Wing loading = 4800 lbs
Gross Weight = 2400 lbs
Load Factor = 4800/2400 = 2g
BASICALLY – LF = Lift/Weight
In a turn, Load Factor is equal to the Total Lift.
So using our formula for Total lift, we also know the Load Factor
Load Factor at 60 degrees?
1.0g/cos 60 = 2.0g
1.0g/cos 70 = 2.9g
The axes of an airplane
Stability about the lateral axis affects pitch
Stability about the longitudinal axis affects roll
Stability about the vertical axis affects yaw
Static Stability – The initial tendency back to equilibrium
Dynamic Stability – The tendency over time of the aircraft to return to equilibrium
Positive Stability – Tendency to return to equilibrium
Neutral Stability– Tendency to remain in new condition
Negative Stability – Tendency to continue to away from equilibrium
e.g. – Negative Static or Positive Dynamic
The quality of an aircraft that permits it to be maneuvered easily and to withstand the stresses imposed by maneuvers
The quality of the aircraft’s response to the pilot’s control application when maneuvering the aircraft.
Longitudinal stability is about the lateral axis
Three things affect Longitudinal Stability
Location of Wing with respect to CG
Location of the Horizontal Stabilizer with respect to CG
Area of size of the tail surface
Downwash of air from the wings strikes the top of the horizontal stabilizer producing downward pressure.
Lateral stability is about the Longitudinal axis.
Lateral Stability is most commonly attained by adding a dihedral to the wings
Wings are built 1-3 degrees above perpendicular to the longitudinal axis
Wind striking the plane may cause one wing to rise putting the plane in a bank.
With Dihedral the wind strikes the lower wing with a higher Angle of Attack
Vertical Stability is about the vertical axis.
It is the vertical stabilizer that gives the aircraft stability
Like a weather vane
Like the keel on a ship