1. Basic Aerodynamic Theory and Drag
ATC Chapter 1

2. Aim
To review principals of aerodynamic forces

3. Objectives Define drag and its different types
State the factors effecting airflow
State the different types of parasite drag
State the effect of parasite drag vs. Airspeed (TAS)
Define induced drag and its effect in level flight
State the effect of induced drag vs. Airspeed (TAS)
State the factors effecting induced drag
State the different type of wingtip designs
State the effect of wingtip designs vs. induced drag
Define total drag
Define Drag Coefficient(CD)
Define Lift/Drag Ratio
State the factors effecting the best Lift/Drag ratio

4. 1. Drag
Drag
Newton’s third law states that every action has an equal and opposite reaction
The opposite reaction of an aeroplanes motion through the air is called drag
As drag acts to slow the aeroplane down, the least amount of drag produced will equal the least amount of thrust required.
Total drag is made up of two main types:
Parasite drag and
Induced Drag
Total drag acts parallel to the relative airflow
DRAG

5. 1. Drag Drag Total Drag Induced Drag Parasite Drag Profile Drag
Interference Drag
Skin Friction
Form Drag

6. 2. State the factors effecting airflow
Airflow around an aeroplane
The pattern of the airflow past an aeroplane depends on the shape of the aerofoil and its attitude with respect to the free stream airflow
When the airflow over the wing is smooth it is called laminar flow
Laminar Flow

7. 2. State the factors effecting airflow
Airflow around an aeroplane
The air that is in contact with the upper surface of the wing is called the boundary layer and is only several millimetres thick
The air in the boundary layer is slowed due to friction compared to the free stream air
This causes the air to become turbulent as it attempts to flow back to the region of lowest pressure
The point at which the air becomes turbulent is called the transition point
Transition point

8. 2. State the factors effecting airflow
Airflow around an aeroplane
Once the air has passed the transition point the air flow has changed from laminar flow to turbulent flow
The turbulent airflow acts like a vortex and continues towards the trailing edge
If the region of lowest pressure becomes too strong and the pressure gradient becomes to large the air separates from the top surface of the wing
When this occurs the wing has stalled and due to the separation being aft of the CofP the pressure on the top of the aerofoil increases and overall lift decreased, therefore stalled
Separation point

9. 3. Types of Parasite Drag Parasite Drag
Parasite drag is caused from the free stream airflow being disturbed
The different types of drag are:
Skin friction
Form drag
Interference drag

10. 3. Types of Parasite Drag Parasite Drag – Skin Friction
Skin friction is the force between the free stream air and any object passing through it
An example of this is the boundary layer of an aerofoil
The magnitude of skin friction depends upon:
The surface area of the aircraft
The nature of the boundary layer –i.e. laminar or turbulent flow
The nature of the surface – i.e. smooth or rough
Airspeed

11. 3. Types of Parasite Drag Parasite Drag – Form Drag
Form drag is created when the airflow has actually separated from the aerofoil
This can be thought of as the turbulent wake vortices that are created after the air has separated from an aerofoil
This occurs begins at the separation point
The magnitude of form drag is measured by the pressure differential from in front and behind a moving object
If a flat plate is placed perpendicular to the airflow in a wind tunnel:
The air must flow around the plate creating a disturbance
Once the air has passed the plate, the air separates and form drag is produced

12. 3. Types of Parasite Drag Parasite Drag – Form Drag
The best way to reduce form drag is by streamlining shapes on an aircraft
By streamlining shapes is prevents large changes in the shape of the object and therefore reducing the vortices.
A reduction in vortices = a reduction in form drag
This can be measured by the fineness ratio of an aerofoil
Fineness ratio = Chord Maximum Thickenss
For the best results, the ratio should be about 4:1
This depends on the intended speed range of use

13. 3. Types of Parasite Drag Parasite Drag – Interference Drag
So far we have looked only one item in a free stream airflow
Interference drag is created where two different objects meet and disturb the free stream airflow
This causes different relative airflows to meet at different angles
Examples of this include where:
The wing meets the fuselage
The elevator meets the
fuselage

14. 4. Parasite Drag Vs. Airspeed (TAS)
As we have seen the magnitude of parasite drag is affected by the speed of the free stream air
As parasite drag is directly related to the disturbance of airflow from an object the greater number of air molecules colliding with the object at any one time = a greater amount of parasite drag
Therefore as the airspeed of an aeroplane increases parasite drag continues to increase exponentially
Parasite drag increases exponentially because:
Drag = CD.½. ρ.V2.s
Therefore: drag  V2
Parasite Drag
TAS

15. 5. Induced Drag Induced Drag
Induced drag is a by-product of lift and is directionally proportional
As we have seen to create lift, there must be a pressure gradient between the top and bottom surface of an aerofoil.
Air will always attempt to move towards a region of low pressure
This means that over the surface of an aerofoil, the air attempts to travel from the bottom surface to the top surface.
Spanwise flow on the bottom of the wing moves from the wing root to wing tip
Spanwise flow on the top of the wing moves from the wing tip to wing root

16. 5. Induced Drag Induced Drag
The vortices are the strongest at the wing tip, as the air moves from the bottom of the wing to the top
Therefore are named wing tip vortices
The vortices that are created at the trailing edge and are of a smaller magnitude
These vortices are called sheet vortices

17. 6. Induced Drag Vs. Airspeed (TAS)
The wing tip vortices are the greatest when the spanwise flow is the greatest
The maximum spanwise flow occurs when the greatest pressure differential occurs
This occurs when the aerofoil is producing the highest amount of lift at a constant altitude
Induced Drag
TAS

18. 7. Factors effecting Induced Drag
As the wingtip vortices are created the air spilling over to the top surface adds to the downwash from the trailing edge of the wing
This increase in downwash creates an average local airflow (different from relative airflow)
The local airflow is inclined compared to the relative airflow
Therefore when lift is produced, at the wingtip, the vector is inclined aft.
Using vector addition, if we separate total lift, we have a rearward component of lift
The rearward component of lift is induced drag

19. 7. Induced Drag in Level Flight
Induced Drag Vs. Flight Conditions
Induced drag is proportional to lift
Therefore during any flight conditions in which large amounts of lift are created subsequently will produces large amounts of induced drag
High angles of attack create a greater pressure gradient between the top and bottom surface of the wing, thus stronger wingtip vortices
High angles of attack subsequently increase the amount of downwash from the trailing edge of the wing, which results in an increase in the rearward component of lift
Rearward component of lift = induced drag

20. 7. Induced Drag in Level Flight
Induced Drag Vs. Flight Conditions
Induced drag is proportional to lift
For level flight lift must equal weight
Therefore if the overall weight of an aeroplane is increased either by load or size more lift is required
Any increase in lift will increase the magnitude of induced drag
Therefore the heavier the aircraft the greater the induced drag
Lift = Weight (Straight & Level)
Lift  Weight
Weight = Lift
Lift = Induced Drag

21. 8. Type of Wingtip Designs
Aspect Ratio Vs. Induced Drag
Aspect ratio is the measure of the wing length by the length of the chord
Aspect ratio = Span Chord
Aspect ratio = Span2 Wing Area
From these equations we notice that the aspect ratio of a wing is inversely proportional to its chord length
If the chord length is reduced the magnitude of the wing tip vortices decrease
Therefore a reduction in induced drag
Therefore an aerofoil with a high aspect ratio has a lower amount of induced drag compared to a high low aspect ratio wing
Thus aeroplane manufactures can reduce the amount of induced drag by increasing the aspect ratio of the wing

22. 7. Type of Wingtip Designs
Washout Vs. Induced Drag
As discussed, wing tip vortices incline the lift vector aft at the wing tip
The magnitude of the rearward component of lift can be reduced by slightly twisting the wing at the tip
This is called washout
The benefits of washout are:
Less severe wingtip vortices
Less induced drag
Less bending load on the wing root
More docile behaviour at the stall – allows the inboard section of the wing stall first, reducing the chances of a spin
Angle of Incidence Wing tip
Angle of Incidence Wing root

23. 7. Type of Wingtip Designs
Tapered Wings Vs. Induced Drag
A tapered wing has a smaller chord at the wing tip compared with the wing root
This results smaller chord at the wing tip reduces the strength of the wingtip vortices
Therefore a tapered wing reduces the amount of induced drag
However induced drag is sill inversely proportional to aspect ratio
i.e. a reduction in wing area = a higher aspect ratio
Aspect ratio = Span2 Wing Area
Therefore a high aspect ratio = low induced drag
Tapered Wing
Larger Chord at wing root
Larger Chord at wing root

24. 8. Type of Wingtip Designs
Elliptical Wings Vs. Induced Drag
An elliptical wing is a wing planform shape that minimises induced drag
Elliptical taper shortens the chord near the wingtips
All parts of the wing experience equivalent downwash
The equal downwash and therefore the effective angle of attack is constant across the whole of the wingspan
Therefore there is no change of relative angle attack from the root to the tip
This improves aerodynamic efficiency
Larger Chord at wing root
Larger Chord at wing root
Elliptical Wing
Equal downwash

25. 9. Wingtip Designs Vs. Induced Drag
Wingtip Design Vs. Induced Drag
Modification to the wingtip design will change the magnitude of the wingtip vortices
Modifications are made to reduce and displace the vortices
The reduction in wingtip vortices = less induced drag
The different wing tip designs are:
Plain wing
Wing Fence
Modified wingtip
Winglet
Wingtip tank

26. 9. Wingtip Designs Vs. Induced Drag
Wingtip Design – Plain Wing
Plain wing tips are found on the majority of general aviation wings
Plain wingtips do not change or reduce incused drag

27. 9. Wingtip Designs Vs. Induced Drag
Wingtip Design – Wing Fence
A wing with a wing fence may still have a plain wing tip, however a fence is installed inboard of the tip to reduce the amount of spanwise flow
The spanwise flow at the tip is reduced, causing a reduction in the magnitude of the vortices
The reduction in the magnitude of the vortices = less induced drag

28. 9. Wingtip Designs Vs. Induced Drag
Wingtip Design – Modified Wingtip
A wing with a modified wingtip reduces induced drag by two separate methods
By modifying the wingtip downwards, increases the overall span of the wing
Increase in span = a increase in aspect ratio
Increase in aspect ratio – reduction in induced drag
The additional benefit of bending the wing tip downwards, moves the wingtip vortices away from airflow over the top of the wing
This maintains the laminar flow over the top of the wing longer, in addition to reducing the magnitude of the rearward component of lift

29. 9. Wingtip Designs Vs. Induced Drag
Wingtip Design – Winglet
A winglet design has the same effect as a modified wingtip
Winglets are not all designed the same, however the main benefit is the increase in the overall span of the wing
Any increase in the span will increase the aspect ratio exponentially
Apsect ratio  span2
Therefore for a small increase in the span there is a large increase in the aspect ratio
Large increase in aspect ratio = large reduction in induced drag
Similar to the modified wingtip, the vortices are displaced from the top surface of the wing, which reduces the rearward component of lift

30. 9. Wingtip Designs Vs. Induced Drag
Wingtip Design – Wingtip Tank
A wingtip tank reduces the leakage of air flowing from the bottom surface to the top surface, thus reducing the wingtip vortices
By reducing the magnitude of the vortices, induced drag is reduced

31. 10. Total Drag
Total Drag
Total drag = Parasite/form drag + Induced drag
Note:
At low airspeeds induced drag is high and parasite drag in low
At minimum drag speed both induced and parasite drag are at a minimum
At maximum speed induced drag is low and parasite drag to high
Minimum drag occurs where the induced drag = parasite drag

32. 11. Drag Coefficient(CD) Drag Coefficient (CD) Drag = CD.½.ρ.V2.S
Where: CD - Co-efficient of drag – shape and angle of attack
ρ (Rho) – Free stream air density
V – True airspeed (TAS)
S – Plan view wing surface area
The CD curve directly relates to angle of attack
Therefore: low angles of attack (cruise) = low CD
high angles of attack (climbs) = high CD
Stall CD
Note:
Minimum CD occurs at a slight angle of attack – approximately 4°
-4°
16°
AoA

33. 12. Lift/Drag Ratio Lift/Drag Ratio (L/D Ratio)
The lift/drag ratio = Lift Drag = CL.½.ρ.V2.S CD.½.ρ.V2.S = 𝐶𝐿 𝐶𝐷
If for every angle of attack this equation is calculated it can be determined that the lift/drag ration graph is:
Note:
The lift drag ratio is at a minimum whet CD is at a minimum
(approximately 4° AofA)

34. 13. Factors Effecting Lift/Drag Ratio
Lift/Drag Ratio Vs. Level Flight
In level flight: lift = weight = CL.½.ρ.V2.S
thrust = drag
Thus at the angle attack and airspeed for the best lift/drag ratio:
the lift required to equal weight = minimum drag
thus minimum drag = minimum thrust required to be produced by the propeller
minimum thrust = best fuel economy
Therefore at the best lift/drag ratio the aeroplane achieves the:
Maximum cruising range
Maximum gliding distance
Thrust = Drag (Straight & Level)
Lift = Weight
minimum Lift = Weight (At best Lift/Drag ratio)
minimum Lift = minimum Drag
minimum Thrust = minimum Drag
minimum Thrust = maximum range (more on this later!)

35. 13. Factors Effecting Lift/Drag Ratio
Lift/Drag Ratio Vs. Weight
Throughout a flight fuel is burnt and subsequently the overall weight of the aeroplane decreases
As weight decreases less lift is required to maintain level flight
The lift can be reduced by:
Decreasing the angle of attack
This which will result in an increase in IAS if the power setting is unchanged
As:
Lift = CL.½.ρ.V2.S
Lift  Angle of Attack . IAS
Therefore in order to maintain a constant IAS the power needs to be reduced as fuel is burnt to maintain the best lift/drag ratio
Lift = Weight (Straight & Level)
Weight = Lift required (for best L/D ratio)
Lift required = AoA or IAS

36. 13. Factors Effecting Lift/Drag Ratio
Lift/Drag Ratio Vs. Altitude
As altitude increases the atmospheric pressure decreases and temperature decreases
Pressure is proportional to Density
Air Density = Pressure Temperature
As altitude increases, pressure decreases and density decreases
As density decreases a higher TAS is requires to maintain level flight
As:
Lift = CL.½.ρ.V2.S
 IAS = ½.ρ.V2
ρ decreases and V(TAS) must increase to maintain the IAS for best L/D ratio
IAS is constant
Lift is constant at minimum drag
Therefore in order to maintain the best L/D ratio at a higher altitude, the aeroplane must be flown at a higher TAS

37. Questions?