The C-T-M lines are a simple way of predicting how CAS TAS and Mach number vary in a climb or descent.
Draw a vertical line (Y axis) at the left of your page to represent altitude. Moving up this Y axis means that altitude is increasing. Moving down means that altitude is decreasing.
From the base of the Y axis, draw a horizontal (X axis) to the right to represent speeds along the base of the page. Moving left to right means that the speeds are increasing. Moving right to left means that they are decreasing.
The C-T-M lines are three straight lines fanning out as they go upwards from the X axis. Below the tropopause in the ISA they always fan outwards as they go up the graph. The order of these lines is C for CAS on the left, T for TAS in the centre, and M for Mach at the right.
To find out what happens (for example) in a constant Mach climb (or descent) just draw the Mach line straight up the graph. Now draw the other two lines in the correct order, fanning away from it. Moving up the graph you will see that both the CAS and TAS lines are sloping to the left. This means that CAS and TAS decrease as altitude increases in a constant mach climb.
To see what happens in a constant Mach descent just observe what happens as you move down the graph. CAS and TAS both slope to the right, meaning that they increase as altitude decreases at constant Mach.
The method for constant CAS or TAS is the same. Just draw a vertical line to represent whatever is being held constant. Then draw the other two lines in the correct order, fanning away from it. To see what happens in a climb move up the graph. To see what happens in descent move down the graph.
The straight line C-T-M sytem is only accurate for ISA conditions below the tropopause, but can easily be modified to take account of inversions and isothermal layers.
As we climb in an isothermal layer the pressure continues to decrease, but the temperature is constant. The relationship between CAS and TAS is determined by density (and hence pressure), so the CAS and TAS lines still move apart in an isothermal.
But the TAS at any given mach number is related to temperature. Temperature is constant in an isothermal layer, so the mach number at any given TAS is constant. This means that the Mach and TAS lines are parallel to each other in an isothermal layer. It is also worth noting that the biggest isothermal layer in the world is (the stratosphere) above the tropopause.
So to modify the CTM lines to account for an isothermal layer just draw the TAS and Mach lines parallel to each other and the CAS line fanning away to the left as you move up the graph.
In an inversion the temperature increases as altitude increases. This causes the TAS at any given Mach number to increase. So in an inversion the TAS and Mach lines move together with increasing altitrude, as the CAS line fans away to the left as before.
It probably all sounds a bit complicated without drawings but is really very simple and reliable given a bit of practice.
Now getting back to the original question in this string, doing a quick CTM indicates that as altitude decreases in a constant mach glide, the TAS increases. This means that if we want to maintain constant mach in our glide we must make the aircraft go faster. We do this by pushing the nose down. This reduces the angle of attack, thereby reducing drag. But more importantly it makes the aircraft go down a steeper slope. The force making the aircaft fly down the slope is the weight x the sine of the angle of descent. As angle of descent increases, so does the force down the slope. It is this which makes it go faster.
It is important to fully understand these concepts because other questions include such things as "What happens to descent gradient (or glide angkle) in a constant mach glide"?
Any student who is not thoroughly up to speed with things like CTM will be seriously disadvantaged in the POF and PERF exams.
Those students who have done lots of practice using the standard feedback lists might like to try these questions. None are direct feedback, but they are all inverted versions of real feedback. If the original feedback question asked about a climb for example, I have changed it into a question about a descent.
I have produced them to help students to fend of the temptation to simply learn the answers and ignore the concepts. Those of you who get consistently high scores using standard feedback might find the results of this test rather surprising.
1. Given the following data calculate the maximum allowable take-off mass for the aircraft in a 5 kt headwind?
LIMIT FLAP 5 FLAP 15 FLAP 25
Field limited TOM 66000 Kg 69500 Kg 71500 Kg
Climb limited TOM 73300 Kg 68900 Kg 65600 Kg
Wind corrections: +120 Kg/Kt headwind -360 Kg/Kt tailwind
a. 66600 Kg.
b. 70100 Kg.
c. 72100 Kg.
d. 68900 Kg.
2. How do VX and VY compare?
a. Vx is always greater than or equal to VY.
b. VX is always less than VY.
c. VY is always greater than or equal to VX.
d. VY is always less than VX.
3. The reduced thrust take-off procedure?
a. Improves engine life.
b. Cannot be used in low ambient temperatures.
c. Requires at least 10 Kts headwind component.
d. Can be used if TOM is greater than performance limited TOM.
4. VS will not be decreased by?
a. Increasing flap angle.
b. Decreasing weight.
c. Increasing altitude.
d. Moving the C of G aft within the allowable range.
5. The TOD at ISA msl on a flat hard dry runway with no wind is calculated to be 800m. What would it be in the following conditions?
Assume + or – 20m/1000 ft elevation, + 10m/Kt tailwind,
+ or – 5m/10C ISA deviation and the standard slope adjustments.
2000 ft airfield Elevation. QNH = 1013.25 mb. 5 Kts tailwind.
210C ambient temperature. Dry hard runway. 2% upslope.
a. 832m.
b. 954m.
c. 1034m.
d. 1195m.
6. How can the climb limited TOM be increased?
a. Reduce V2.
b. Reduce VR.
c. Reduce V1.
d. Reduce flap angle and increase V2.
7. Which of the following approximates to VMD for a turbojet aircraft?
a. 1.32 VS.
b. 1.35 VS.
c. 1.5 VS.
d. 1.6 VS.
8. A jet aircraft is climbing at Vx and constant powers setting. If speed is increased while power setting held constant?
a. Climb gradient and ROC will increase.
b. Gradient and ROC will decrease.
c. Gradient will increase and ROC will decrease.
d. Gradient will decrease and ROC will increase.
9. An aircraft is gliding at its best range glide speed. If angle of attack is decreased?
a. Glide speed will decrease.
b. Glide endurance will increase.
c. Glide range will decrease.
d. Glide range will increase.
10. How do IAS and drag vary as a flight progresses for a jet aircraft flying at its maximum range cruise speed?
a. Increase, Increase.
b. Increase, Decrease.
c. Decrease, Decrease.
d. Decrease, Increase.
11. What is the tyre speed limit?
a. Max VLOF in ground speed.
b. Max V1 in TAS.
c. Max V1 in ground speed.
d. Max VLOF in TAS.
12. The long range cruise speed for a jet aircraft gives?
a. 1% increase in TAS.
b. 1% increase in IAS.
c. 1% increase in ground speed.
d. 99% of maximum cruise range with an increase in IAS.
13. An aircraft is gliding at its best range glide speed. If angle of attack is increased?
a. Glide speed and range will decrease.
b. Glide speed and endurance will increase.
c. Glide speed will decrease and range will increase.
d. Glide speed will increase and range will decrease.
14. When descending at constant mach number IAS…… and the margin to low speed buffet ………?
a. Increases, Increases.
b. Increases, Decreases.
c. Decreases, Decreases.
d. Decreases, Increases.
15. A jet aircraft is climbing at Vx and constant powers setting. If speed is reduced while power setting held constant?
a. Climb gradient and ROC will increase.
b. Gradient and ROC will decrease.
c. Gradient will increase and ROC will decrease.
d. Gradient will decrease and ROC will increase.
16. Distance available for a jet aircraft planning to land on a wet runway?
a. Must be at least 15% greater than the dry landing distance.
b. May be less than 15% greater than the dry landing distance, provided such data is included in the flight manual.
c. May be less than 15% greater than the dry landing distance, provided the airport authority gives approval for the landing.
d. May be less than 15% greater than the dry landing distance provided the operating company gives approval for the landing.
17. Maximum endurance may be achieved by?
a. Carrying out a steady climb followed by a steady descent.
b. Flying at the absolute ceiling for as long as possible.
c. Flying at constant altitude and constant speed using minimum fuel flow.
d. Flying at VMRC in straight and level flight.
18. Which of the following statements is true?
a. Best range speed is lower than best endurance speed.
b. Best prop range speed is equal to best glide range speed.
c. Best range speed and best endurance speed are the same thing.
d. Best glide speed is approximately 1.32 VMD.
19. Which of the following balance thrust in a steady climb?
a. Weight.
b. Drag.
c. W sin Gamma.
d. Drag + W sin Gamma.
20. How will variations in C of G position within authorised limits affect the fuel consumption in terms of ANM/Kg?
a. Forward movement will increase ANM/Kg.
b. Forward movement will decrease ANM/Kg.
c. There is no relationship between C of G position and ANM/Kg.
d. Rearward movement will decrease ANM/Kg
21. In order to achieve maximum glide range an aircraft must be flown at?
a. VIMP.
b. VIMD.
c. VX.
d. VY.
22. If a pilot elects to land with flap 35 instead of flap 25 the field limited landing mass will……. and the climb limited landing mass will………?
a. Increase, increase.
b. Increase, decrease.
c. Decrease, decreases.
d. Decrease, increase.
23. Which of the following statements is true of two identical aircraft of different masses when descending at idle power setting at any given angle of attack?
a. The heavier aircraft will have a greater forward and greater vertical speed than the light aircraft.
b. The heavier aircraft will have a lower forward speed but greater vertical speed than the light aircraft.
c. The lighter aircraft will have a lower vertical speed but greater forward speed than the heavier aircraft.
d. The lighter aircraft will have a greater forward speed but a lower vertical speed than the heavier aircraft.
24. To maintain a lower speed greater than VS, when flying at the back of the drag curve?
a. More flap is required.
b. Less thrust is required.
c. Less flap is required.
d. More thrust is required.
25. Which of the following conditions might cause V2 to be limited by VMCA?
a. High ambient pressures.
b. Low ambient temperatures.
c. High flap setting.
d. All of the above.
26. What happens to the descent angle as an aircraft descends from FL370 to FL250 at constant Mach number then from FL250 to FL 100 at constant CAS?
a. Increase, increase.
b. Increase, constant.
c. Decrease, decrease.
d. Decrease, constant.
27. How is SFC affected by C of G movement?
a. SFC is not affected by C of G position.
b. Forward movement increases SFC.
c. Rearward movement increases SFC.
d. Rearward movement decreases SFC.
28. If a pilot elects to land with flap 35 instead of 25 flap the landing distance will……. And the go-around performance will………?
a. Increase, increase.
b. Increase, decrease.
c. Decrease, decreases.
d. Decrease, increase.
29. When carrying out certification test flying to establish VMCG, why is nose-wheel steering considered to be inoperative?
a. Because nose-wheel steering is ineffective after VR.
b. Because nose-wheel steering would not be used in the event of an engine failure during the take-of run.
c. Because VMCG must be valid for both dry and wet runway conditions.
d. Because aircraft may be operated with defective nose-wheel steering.
30. What would be the obstacle clearance in a 5% gradient take-of climb given the following data?
Obstacle height 160m above the airfield elevation.
Obstacle 5000m from the screen.
Screen height 50 ft.
a. 90m.
b. 105m.
c. 200m.
d. 250m.
1. d
2. c
3. a
4. c
5. c
6. d
7. d
8. d
9. c
10. c
11. a
12. d
13. a
14. a
15. b
16. b
17. c
18. b
19. d
20. c
21. c
22. c
23. a
24. d
25. d
26. b
27. a
28. c
29. c
30. b