Aerodynamic Theory Review 1 ATC Chapter 6

Aim To review climbing and descending

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

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

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

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

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

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

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

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

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.

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.

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 = 33000 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.

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.

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.

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

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

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

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

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

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

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