Advanced Aerodynamics 2

1. AF 202 – Chris Dimoulis Advanced Aerodynamics 2

2. Objectives Review Vectors Forces in climbs and turns Stability Vg diagram

3. 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

4. To Accelerate or not…? Acceleration: 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

5. Weight 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.

6. Lift Opposes Weight Must EQUAL weight for level flight 2 principles cause lift: Bernoulli’s Newton’s 3rd law

7. Lift Four ways to control lift Pilot Controlled: Change Speed Change Angle of Attack Non-Pilot Controlled Change Wing Surface Area Change Air Density

8. The Lift Equation L=1/2 (CL V² Ρ A) V = √2L/ (CL Ρ A) CL = 2L/(V² Ρ A)

9. Lift Equation 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

10. Uses of the Lift Equation 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.

11. Drag Opposes Thrust 2 Types Parasite Drag Induced Drag

12. Parasite Drag 3 Types Form Skin-Friction Interference Parasite drag INCREASES as speed increases

13. Induced Drag 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.

14. Parasite vs. Induced Drag

15. Region of Reverse Command 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)

16. Thrust 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.

17. Thrust

18. Propeller Efficiency No Propeller is 100% Efficient Effecitve Pitch Geometric Pitch Slippage

19. Turning Tendencies Asymmetrical Thrust (P-Factor) Gyroscopic Precession Spiraling Slipstream Torque from the engine

20. Adverse Yaw 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

21. VectorsForces in Climbs

22. Vectors Remember that a force can be considered a vector Vectors consist of magnitude and direction They can be broken down into components

23. Vector The components are PERPENDICULAR to each other You can add 2 vectors together by adding the horizontal vectors and vertical vectors

24. Forces in a Climb As a climb begins, lift BRIEFLY exceeds weight.

25. Forces in a Climb 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?

26. Forces in a Climb Weight now has a rearward component

27. Forces in a Climb 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.

28. Forces in a Climb Thrust and Lift now have vertical and horizontal components

29. Forces in a climb Therefore you can say… The vertical component of lift PLUS… The vertical component of thrust EQUALS… The total weight

30. Forces in a climb 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.

31. Forces in Turns

32. Forces in Turns Lift remains perpendicular to the wings When the aircraft is banked, lift can be broken down into components

33. Forces in Turns Once in a turn, the horizontal component is responsible for turning. The vertical component is opposing weight and responsible for pitch.

34. Forces in Turns 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.

35. The Math of Turns The angle of bank EQUALS the angle between the Total lift and Vertical Component of lift. 30 bank 45 bank 30 45

36. The Math of Turns Right Triangles: cos θ = A/H sin θ = O/H H = Hypotenuse A = Side adjacent to θ O = Side opposite to θ

37. The Math of Turns 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. { {

38. Forces in Turns 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

39. Forces in Turns 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

40. Forces in Turns 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.

41. Load Factor 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

42. Load Factor LF = Wing Loading/Gross Weight Wing loading = 4800 lbs Gross Weight = 2400 lbs Load Factor = 4800/2400 = 2g BASICALLY – LF = Lift/Weight

43. Load Factor In a turn, Load Factor is equal to the Total Lift.

44. Load Factor 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

45. Stability

46. Stability The axes of an airplane Lateral Longitudinal Vertical

47. Stability Stability about the lateral axis affects pitch Stability about the longitudinal axis affects roll Stability about the vertical axis affects yaw

48. Types of Stability Static Stability – The initial tendency back to equilibrium Dynamic Stability – The tendency over time of the aircraft to return to equilibrium

49. Types of Stability 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