Basic Aerodynamic Theory and Drag ATC Chapter 1

Aim To review principals of aerodynamic forces

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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)

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!)

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

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

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