1. Aerodynamic Theory Review 1
ATC Chapter 6

2. Aim
To review climbing and descending

3. Objectives State the forces in a climb Define rate and angle of climb
State the forces in a descent
Define rate and angle of descent

4. 1. Forces in a climb
What are the four forces acting on our aircraft in straight and level?
R.A.F L T D
1) Weight acts down towards the earth.
2) Drag acts to pull the aircraft back. R1 = W + D.
3) If we recall the definition of a climb the aircraft is still in equilibrium, therefore there must be a force equal an opposite to R1... R2.
4) R2 = L + T.
5) But T > D. Some other force must also be acting to pull the aircraft back down.
6) Weight can be divided into W1 and a rearward component of weight (RCW) – consider a car rolling backward down a hill...
7) T = RCW + D.
8) But L is also < W so how does the aircraft climb?
9) Some other force must also be acting to pull the aircraft up vertically  Thrust.
10) So climb performance depends on excess thrust  power available. Consider a rocket, it has no wings but can still climb  or consider tilting the lift vector back until the aircraft is climbing due to thrust alone  F/A 18 Hornet.
11) We use full power in light aircraft to climb. W

5. 1. Forces in a climb
We can see weight is acting at an angle to all the other forces so we can break it up into a Perpendicular Component of Weight and a Reward component of weight
R.A.F L T D
RCW
1) Weight acts down towards the earth.
2) Drag acts to pull the aircraft back. R1 = W + D.
3) If we recall the definition of a climb the aircraft is still in equilibrium, therefore there must be a force equal an opposite to R1... R2.
4) R2 = L + T.
5) But T > D. Some other force must also be acting to pull the aircraft back down.
6) Weight can be divided into W1 and a rearward component of weight (RCW) – consider a car rolling backward down a hill...
7) T = RCW + D.
8) But L is also < W so how does the aircraft climb?
9) Some other force must also be acting to pull the aircraft up vertically  Thrust.
10) So climb performance depends on excess thrust  power available. Consider a rocket, it has no wings but can still climb  or consider tilting the lift vector back until the aircraft is climbing due to thrust alone  F/A 18 Hornet.
11) We use full power in light aircraft to climb.
PCW W
RCW

6. 1. Forces in a climb We can now resolve the force vectors
Is the aircraft in equilibrium?
R.A.F R1 L T D
RCW
1) Weight acts down towards the earth.
2) Drag acts to pull the aircraft back. R1 = W + D.
3) If we recall the definition of a climb the aircraft is still in equilibrium, therefore there must be a force equal an opposite to R1... R2.
4) R2 = L + T.
5) But T > D. Some other force must also be acting to pull the aircraft back down.
6) Weight can be divided into W1 and a rearward component of weight (RCW) – consider a car rolling backward down a hill...
7) T = RCW + D.
8) But L is also < W so how does the aircraft climb?
9) Some other force must also be acting to pull the aircraft up vertically  Thrust.
10) So climb performance depends on excess thrust  power available. Consider a rocket, it has no wings but can still climb  or consider tilting the lift vector back until the aircraft is climbing due to thrust alone  F/A 18 Hornet.
11) We use full power in light aircraft to climb.
PCW W R2
RCW

7. The aircraft is now in equilibrium
1. Forces in a climb
We must increase the power to overcome the RCW
R.A.F R1 R1 L T T D
RCW
1) Weight acts down towards the earth.
2) Drag acts to pull the aircraft back. R1 = W + D.
3) If we recall the definition of a climb the aircraft is still in equilibrium, therefore there must be a force equal an opposite to R1... R2.
4) R2 = L + T.
5) But T > D. Some other force must also be acting to pull the aircraft back down.
6) Weight can be divided into W1 and a rearward component of weight (RCW) – consider a car rolling backward down a hill...
7) T = RCW + D.
8) But L is also < W so how does the aircraft climb?
9) Some other force must also be acting to pull the aircraft up vertically  Thrust.
10) So climb performance depends on excess thrust  power available. Consider a rocket, it has no wings but can still climb  or consider tilting the lift vector back until the aircraft is climbing due to thrust alone  F/A 18 Hornet.
11) We use full power in light aircraft to climb.
PCW W R2
RCW
The aircraft is now in equilibrium

8. The aircraft is in equilibrium
1. Forces in a climb
In Summary:
R1 = R2
L < W
T = RCW + D
R.A.F R1 R1 L T D
RCW
1) Weight acts down towards the earth.
2) Drag acts to pull the aircraft back. R1 = W + D.
3) If we recall the definition of a climb the aircraft is still in equilibrium, therefore there must be a force equal an opposite to R1... R2.
4) R2 = L + T.
5) But T > D. Some other force must also be acting to pull the aircraft back down.
6) Weight can be divided into W1 and a rearward component of weight (RCW) – consider a car rolling backward down a hill...
7) T = RCW + D.
8) But L is also < W so how does the aircraft climb?
9) Some other force must also be acting to pull the aircraft up vertically  Thrust.
10) So climb performance depends on excess thrust  power available. Consider a rocket, it has no wings but can still climb  or consider tilting the lift vector back until the aircraft is climbing due to thrust alone  F/A 18 Hornet.
11) We use full power in light aircraft to climb.
PCW W R2
RCW
The aircraft is in equilibrium

9. 2. Rate and angle of climb
We can describe climb performance as either Rate of Climb or Angle of Climb
Rate of climb is the altitude gained over time. Expressed in feet per minute (fpm).
Altitude
1) We can describe a climb as either RoC or AoC. 2) AoC – Altitude gain over distance. Expressed as an angle. 3) RoC – Altitude gain over time. Expressed in feet / min (fpm).
Time

10. 2. Rate and angle of climb
We can describe climb performance as either Rate of Climb or Angle of Climb
Rate of climb is the altitude gained over time. Expressed in feet per minute (fpm).
Angle of climb is the altitude gained over distance. Expressed as an angle
Altitude
1) We can describe a climb as either RoC or AoC. 2) AoC – Altitude gain over distance. Expressed as an angle. 3) RoC – Altitude gain over time. Expressed in feet / min (fpm).
Angle of Climb
Distance

11. 2. Rate and angle of climb Definition of Power Work Power = Time
Power is supplied by the engine and can be described as the amount of work that can be done in a given amount of time
Work
Time
Power =
Work = Force x Distance
Force x Dist.
Time
Power =
A climb is an increase in altitude at a constant heading, airspeed and power setting with the aircraft in balance.

12. 2. Rate and angle of climb Definition of Thrust
Thrust is the force applied to the Airflow by the propeller As we increase speed less thrust will be imparted on the airflow Thrust is limited by the Power Available
A climb is an increase in altitude at a constant heading, airspeed and power setting with the aircraft in balance.

13. 2. Rate and angle of climb Best Rate of Climb Pa-Pr RoC = 33000 x W
Maximum altitude gain over a given time.
Achieved by flying at best RoC speed also known as Vy.
For the C172SP Vy is 74 KIAS at Sea Level
Our best Rate of Climb (VY) occurs at the point of Max Excess Power
Pa-Pr W
RoC = x
For the same time period, the aircraft flying at Vy will travel further horizontally and gain more altitude than the aircraft flying at Vx. The aircraft flying at Vx, however will have a greater AoC and may avoid obstacles.

14. 2. Rate and angle of climb Best Angle of Climb Thrust - Drag
Maximum altitude gain over a given distance.
Achieved by flying at best AoC speed, Vx.
For the C172SP Vx is 62 KIAS at Sea Level
Best Angle of Climb occurs at Max Excess Thrust
Thrust - Drag W
AoC = Sin x
For the same time period, the aircraft flying at Vy will travel further horizontally and gain more altitude than the aircraft flying at Vx. The aircraft flying at Vx, however will have a greater AoC and may avoid obstacles.

15. 2. Rate and angle of climb
Comparison of altitude and distance gained over the same time period at Vx and Vy.
For the same time period, the aircraft flying at Vy will travel further horizontally and gain more altitude than the aircraft flying at Vx. The aircraft flying at Vx, however will have a greater AoC and may avoid obstacles.

16. 3. Forces in a descent
What are the forces acting on our aircraft in S&L? L D
1) Weight acts towards the earth
2) From our definition of a descent, the aircraft is still in equilibrium, so W is opposed by an equal force, R.
3) R = L + D
4) But what makes the aircraft go forwards?... W can be divided into W1 (force opposing lift) and forward component of weight (FCW).
5) FCW = D
6) In a powered descent D= FCW + T W
R.A.F

17. 3. Forces in a descent
Again we can see weight is acting at an angle to our other forces so we can break it up L D
FCW
PCW
1) Weight acts towards the earth
2) From our definition of a descent, the aircraft is still in equilibrium, so W is opposed by an equal force, R.
3) R = L + D
4) But what makes the aircraft go forwards?... W can be divided into W1 (force opposing lift) and forward component of weight (FCW).
5) FCW = D
6) In a powered descent D= FCW + T W
R.A.F
FCW

18. The aircraft is now in equilibrium
3. Forces in a descent
We can now resolve the forces R L D
FCW
PCW
1) Weight acts towards the earth
2) From our definition of a descent, the aircraft is still in equilibrium, so W is opposed by an equal force, R.
3) R = L + D
4) But what makes the aircraft go forwards?... W can be divided into W1 (force opposing lift) and forward component of weight (FCW).
5) FCW = D
6) In a powered descent D= FCW + T W
R.A.F
FCW
The aircraft is now in equilibrium

19. The aircraft is now in equilibrium
3. Forces in a descent
In Summary:
L < W
R = W
D = FCW R L D
FCW
PCW
1) Weight acts towards the earth
2) From our definition of a descent, the aircraft is still in equilibrium, so W is opposed by an equal force, R.
3) R = L + D
4) But what makes the aircraft go forwards?... W can be divided into W1 (force opposing lift) and forward component of weight (FCW).
5) FCW = D
6) In a powered descent D= FCW + T W
R.A.F
FCW
The aircraft is now in equilibrium

20. 4. Rate and angle of climb
Like a climb we can describe descent performance as either Rate of Descent or Angle of Descent
Rate of descent is the lost gained over time, expressed in feet per minute (fpm).
Altitude
1) We can describe a climb as either RoC or AoC. 2) AoC – Altitude gain over distance. Expressed as an angle. 3) RoC – Altitude gain over time. Expressed in feet / min (fpm).
Time

21. 4. Rate and angle of climb
Like a climb we can describe descent performance as either Rate of Descent or Angle of Descent
Rate of descent is the lost gained over time, expressed in feet per minute (fpm).
Angle of climb is the altitude gained over distance. Expressed as an angle
Altitude
1) We can describe a climb as either RoC or AoC. 2) AoC – Altitude gain over distance. Expressed as an angle. 3) RoC – Altitude gain over time. Expressed in feet / min (fpm).
Angle of Descent
Distance

22. Questions?