ppl_05_e2
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ID: 3658
Customer: Oleg Ostapenko E-mail: ostapenko2002@yahoo.com
Customer: Oleg Ostapenko E-mail: ostapenko2002@yahoo.com
CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
the aircraft, and elevator authority will be poor. An aircraft which has its C of G outside the aft limit may be dangerously unstable and display unfavourable stall and spin characteristics.
Figure 14.4 Representative fore and aft limits of the centre of gravity for a PA28.
Wind.
Wind will also affect aircraft operations. The wind speed (i.e. strength), direction, degree of gustiness, turbulence and the possibility of windshear are all important considerations when deciding whether or not a light aircraft should be fown.
The aircraft that you normally fy will almost certainly have a maximum crosswind limitation placed on it by the manufacturer, established during a series of test fights.
In crosswinds above a certain strength, an aircraft may not possess the rudder authority to keep straight on the runway, during a take-off run, touch-down or landing run. And, of course, even if a strong wind is blowing straight down the runway centre-line, an aircraft still may have to taxy across wind.
Certain light aircraft may also have an overall windspeed limitation; high surface winds could cause the wing to develop suffcient lift with the aircraft on the ground to make taxiing diffcult or even hazardous, with risks of overturning, plus a loss of directional control due to weathercocking. In the air, an approach into a very strong wind would require a much higher power than normal, with eroded margins of control and the risk of turbulence and windshear.
If an aircraft is cruising at its maximum normal operating speed, VNO, and fies through an area of powerful gusts, VNO can be exceeded. That is why, in gusty conditions, it is wise to leave a safety margin between your cruising speed and VNO. Gust loads are dealt with in further detail, below.
Flight and Ground Limitations.
The fight and ground limitations in respect of a particular aircraft can be found in the Pilot’s Operating Handbook and Flight Reference Cards, or Check List, for the aircraft.
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
Representative limitations for a light training aircraft are contained in the table below, at Figure 14.5. These limitations are included here for illustrative purposes only, and must not be taken as authoritative, for any given aircraft. All airspeeds are indicated airspeeds.
REPRESENTATIVE LIMITATIONS FOR A LIGHT TRAINING AIRCRAFT
Velocity Never to Exceed (VNE) |
155 knots |
Normal Operating Speed (VNO) |
124 knots |
Normal Manoeuvring Speed (VA) |
109 knots |
Maximum Velocity Flaps Extended (VFE) |
101 knots |
Take-Off Safety Speed |
65 knots |
|
|
Stall Speed (faps extended) |
46 knots |
|
|
Stall Speed (clean) |
52 knots |
|
|
Maximum Take-Off Weight (or Mass) (MTOW)/ |
2150 lbs |
(MTOM) - Normal Category |
975 kg |
|
|
MTOW/MTOM – Utility Category |
1950 lbs |
|
884 kg |
|
|
Maximum Demonstrated Crosswind |
17 knots |
|
|
Maximum Load Factor (Normal Category) |
+3.8 |
|
|
Maximum Load Factor (Utility Category) |
+4.4 |
|
|
No Negative Load Factors Approved |
- |
|
|
Figure 14.5 Table of representative general limitations for a typical general aviation training aircraft.
MORE ABOUT LOAD FACTOR.
You were introduced to load factor in the chapters on Forces in Flight and The Stall and Spin. Load Factor was also considered above, from the general point of view of fight limitations. Here we will look a little more deeply into the load factor implications of various manoeuvres, but, before continuing, re-read the previous sections on load factor, especially the section in Chapter 13.
As you have learnt, in steady straight fight, with lift equal to weight, load factor is
1, but in any form of manoeuvring, when the direction of the aircraft is changing, with or without an increase in speed, the load factor will be greater or less than 1.
Turning fight and pulling out of dives require positive accelerations which generate load factors greater than 1. It is also possible to apply negative accelerations to the aircraft, such as in an inverted loop, which would produce load factors of less than 1, and most likely negative load factors. (See below.)
You discovered earlier that a 60°- banked level turn requires lift to be twice the magnitude of weight, in order both to support the aircraft’s weight and to give the aircraft the necessary centripetal acceleration for the turn. The inertial reaction to the
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
doubling of the lift imposes a load factor of 2 on the aircraft structure and occupants. This load factor causes the pilot to sense an apparent increase in weight because the inertial reaction to the increased lift force acts in the opposite direction to the lift force, through the vertical axis of the pilot’s body (if the turn is properly balanced), pressing him into his seat (see Figure 14.6).
Figure 14.6 Calculating load factor from angle of bank.
Pulling out of a dive or fying a loop will, generally, subject the aircraft to higher load factors than 2. The derivation of the formula relating load factor to angle of bank, is at Figure 14.6. You are now familiar with the idea that an aircraft’s structure must be able to support the loads to which it is subjected without permanent deformation or failure occurring. As we mentioned above, the “inertial multiplication” of lift and weight during manoeuvring subjects the aircraft to stresses which the designer must take into account when he is calculating the required strength of the aircraft structure. Aircraft must be cleared for any aerobatic manoeuvres that a pilot may wish to carry out. Details of permitted manoeuvres are given in an aircraft’s Type Certifcate, and in the Flight Manual or Pilot’s Operating Handbook. As you can see, the representative training aircraft referred to in Figure 14.5, is cleared for manoeuvres which will impose a maximum positive load factor of 3.8 on the airframe, when the aircraft is being operated in the Normal Category, and 4.4 when it is fown in the Utility
Category. Aircraft Categories are covered in the section on Mass and Balance, in the
‘Aeroplane (General)’ volume of this series.
Load factor limits are technically expressed as numbers only, that is, without units, because they are factors expressing how many times the normal aircraft weight the aircraft’s structure is able to support when manoeuvring, without risk of damage. Load factor can also be expressed in terms of the symbol, g. You have already seen that for a 60°-banked level turn the load factor to which the aircraft is subjected is 2. The reaction of the pilot’s body mass to the load factor will cause him to feel that his weight has doubled, and he may think of the turn as a 2g turn. Though he may not know it, in using the expression, 2g, he is making reference to the fact that what he senses as his normal weight is in fact a 1g acceleration (the acceleration due to gravity) towards the centre of the Earth. When the pilot is standing on the ground, of course, the Earth’s surface prevents him from actually moving towards the centre of the planet. What the pilot feels as his weight is, in fact, the reaction of the ground stopping that motion.
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
When the pilot is airborne and fies a properly balanced 60°-banked level turn (see Figure 14.7), the extra lift force required to execute the turn will give rise to an inertial acceleration, acting on the aircraft and the pilot, of twice the acceleration due to the Earth’s force of gravity. This, then, is the 2g acceleration, or the load factor of 2 which makes the pilot feel that his weight has doubled, and which subjects the aircraft’s structure to the extra stress.
The stall speed in a positive
g manoeuvre is the product of the straight flight stall speed
and the square root of the load factor.
Figure 14.7 In a 60°-banked level turn, the aircraft is subjected to a load factor of 2.
Looked at another way, in a 60°-banked, 2g, level turn the aircraft fies as if it were twice its actual weight, and the air is imposing an increased force (i.e. lift) on the aircraft’s structure in the same proportion: with a load factor of 2.
You may remember, too, from Chapter 13 that, if the aircraft’s straight-fight stall speed occurs at an indicated airspeed of 60 knots, its stall speed with a load factor of 2 in the 60°-banked turn is 85 knots indicated.
Stall speed in turn = Straight fight stall speed × sttttttttttttttttLoad Factor
An aircraft will not be able to support load factors that increase indefnitely. For instance, the structure of the representative training aircraft, whose limitations we looked at above, is not designed to support a load factor of greater than 3.8, when fown as a Normal Category aircraft, or above 4.4, when fown in the Utility Category. Such an aircraft, then, could not safely fy an 80°-banked level turn, even if the aircraft’s engine were powerful enough to enable the turn to be attempted, because the load factor in an 80°-banked level turn is almost 6, (1/Cos 80° ).
The symbol g, then, is used to indicate an acceleration of, 9.81 metres/sec2 or 32 feet/sec2, the acceleration due to gravity. In straight, steady fight, the acceleration acting on the aircraft in the direction of weight force is termed 1g. Therefore as the apparent weight force (equal and opposite to the lift force), in a given turn, increases by a factor which is numerically equal to the increase in g, known as the load factor, identifying the turn in terms of a certain number of g is acceptable, provided we understand clearly the context in which we use the term, g.
In fact, the greatest load factor that an aircraft has been subjected to, during a given fight, is measured on an instrument called an accelerometer, which is calibrated in
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
units of g. This calibration, of course, is possible only because g and load factor are numerically equal.
Accelerometer needles do not return to zero of their own accord; they continue to indicate the maximum positive and negative load factors experienced in fight, until zeroed by the pilot. If a pilot sees that he has exceeded the maximum permissible load factor, he must report that fact to a responsible authority. To zero the accelerometer and say nothing, after having noted that a load factor limit had been exceeded, would be an irresponsible act, and may endanger the life of the next pilot to fy the aircraft. In Figure 14.8, the right-hand needle of the accelerometer shows that the maximum positive
acceleration (load factor), to which the aircraft has been subjected is 2. The lefthand needle indicates that the aircraft has also been subjected to a maximum negative acceleration (load factor) of -0.6. The middle needle shows the current, instantaneous, acceleration.
Negative Load Factors - Negative g.
As we have mentioned above, in certain conditions of fight, load factors may also be less than 1 or even negative. You have doubtless heard mention of the expression “negative g”. So far in this book, we have discussed positive load factors only. But the direction of a positive load may act in reverse; if it does, the load factor is then described as negative, known popularly as “negative g”.
Even in straight and level fight, values of negative g can be experienced momentarily in severe turbulence. And an aircraft fying straight at a steady speed, that is, in equilibrium but inverted, will experience a negative load factor of -1, or -1 g.
Some aerobatic aircraft are capable of fying manoeuvres, e.g. outside loops, which will generate various degrees of negative g. Negative g can be a most uncomfortable experience for pilot and crew, unless prepared for and accustomed to it.
Inertial Loads.
Load factors imposed on an aircraft’s structure are inertial loads (inertial forces) which arise because the aircraft is subject to an out-of-balance resultant force which imparts an acceleration to the aircraft. An inertial load is equal in magnitude to the force causing the acceleration and acts in the opposite direction to the accelerating force. Accelerations may be either positive or negative; (negative accelerations may be called decelerations).
Linear accelerations, along the line of fight (involving increases or decreases in speed), are small enough to be regarded as negligible, but accelerations which change an aircraft’s direction, such as when the aircraft turns, fies a loop, or recovers from a dive, can be considerable. It follows, then, that the inertial forces, and the associated load factors, acting on an aircraft carrying out such manoeuvres can
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
also be of a signifcant magnitude. An aircraft’s structure must possess adequate strength and stiffness to withstand, without suffering structural damage, the inertial forces arising from the manoeuvres for which the aircraft is approved.
The detailed study of the nature of the inertial loads which give rise to load factors is beyond the scope of this book, but a basic understanding of inertial loads is relatively easy to acquire.
PULLING OUT OF A DIVE.
Expressed in the most basic terms, an inertial load is a reaction to an out-of-balance force which causes an acceleration. The magnitude of any accelerating force can be expressed by the equation:
Force = mass × acceleration, which is an expression of Newton’s 2nd Law.
Therefore, the greater the acceleration to which an aircraft of a given mass is subjected, the greater must be the force acting on the aircraft to cause that acceleration.
In order to consider the phenomenon of inertial loading a little more deeply, let us consider the case of an aircraft pulling out of a dive requiring a maximum centripetal acceleration of 3.5g (measured on the accelerometer) towards the centre of an imaginary circle (see Figure 14.9). (Always remember to check the load factor (g) limitations for your aircraft before fying any manoeuvres.)
The actual value of a 3.5g acceleration is 3.5 × 9.81 metres/sec2, which is approximately 34 metres/sec2. This acceleration is necessary to change the direction of the aircraft as it recovers from the dive. The lift force required to produce this acceleration must be a force of a magnitude over and above the lift force required to support the aircraft’s weight in straight fight. This accelerating lift force, then, is the out-of- balance force that we have learnt must be present to cause any acceleration. The equal and opposite reaction to this accelerating force will be the inertial load acting on the aircraft as it pulls out of the dive. That load will be a certain number of times
Figure 14.9 Pulling out of a high-speed dive.
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
the aircraft’s weight; in other words, it will be greater than the aircraft’s weight by a factor that we have already defned as the load factor.
Now, if the aircraft’s mass is 975 kg, its weight is 975 × 9.81 Newtons, which is equal to, approximately, 9565 Newtons. That means that, in straight, un-accelerated fight, the lift force acting on the aircraft’ structure, in order to counterbalance its weight, is likewise 9565 Newtons.
But during the 3.5g recovery from the dive depicted in Figure 14.9 the lift force acting on the aircraft would be:
Lift force = mass × acceleration = 975 kg × 34 metres/sec2 = 33 159 Newtons
This force is, as we would expect with the pilot having pulled 3.5g, 3.5 times the normal weight of the aircraft. This load factor of 3.5 would be just within the permissible limit of 3.8 for the aircraft whose general limitations are shown in the table at Figure 14.5, when it is operating in the normal category
|
Lift |
|
33 159 Newtons |
= 3.5 |
|
Load Factor = Weight = |
9565 Newtons |
||||
|
|||||
But, considering the lift equation, Lift = CL ½ ρ v2 S, it is not too diffcult to imagine that a careless pilot might fy the recovery too abruptly, pulling back too hard on the control column and increasing CL, and, consequently, the lift force, by too great a value, causing the maximum permissible load factor of 3.8 (the design limit load factor) for our Normal Category aircraft to be exceeded, risking structural damage to the airframe.
Now, if the aircraft is ftted with an accelerometer, the pilot would be able to obtain early information from that instrument if he were about to exceed the maximum permissible load factor. (He would also get a clue from his rapidly increasing apparent weight.)
However, the speed that the pilot reads from his ASI would give him no clue at all.
But, if we knew the radius of the imaginary circle that the aircraft is describing as it pulls out of its dive in Figure 14.9, the aircraft’s speed would give us a clue to the lift force, and, hence, load factor, generated by the wings. We can, of course, never know the radius of a recovery from a dive; indeed, the recovery path is unlikely to follow an arc of a single circle. But, at any given moment, including the moment of maximum load factor, the path being followed by the aircraft is an arc of some circle; so let us, for the sake of argument, imagine that we know the radius of that circle. With this information, we may illustrate a very important point about the inertial forces which give rise to load factors or g.
Monitoring Airspeed in a Dive.
From Newton’s 2nd Law equation, force = mass × acceleration, we can derive an expression for centripetal force, FC; in other words, the force that the wings would have to generate to pull the aircraft out of the dive in Figure 14.9.
This expression is:
v2 FC = m × r
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
where m is the mass of the aircraft, r is the radius of the imaginary, circular, recovery path, and v is the highest true airspeed of the aircraft during the recovery manoeuvre. The expression, v²/r , is, in fact, the centripetal acceleration that the aircraft would have towards the centre of an imaginary circle during the pull out.
In Figure 14.9, then, FC is the total lift required to be generated by the wings to recover the aircraft from the dive. The green section of the lift arrow is the extra lift required to recover from the dive, over and above the lift necessary to support the weight of the aircraft. The green section of the arrow acting in the direction of weight is the inertial reaction to the extra lift force generated by the wings in order to recover the aircraft from the dive. The sum of the green and red arrows acting in the direction of weight gives us the load factor acting on the aircraft.
v2
You do not need, at this level of study, to know how the equation FC = m × r
is derived. You can learn that easily enough from any book on A-level Maths or Physics.
Let us, therefore, calculate frst of all the minimum radius of the circular path that the aircraft could follow without exceeding its maximum permissible load factor, if its maximum speed during the recovery were to be 124 knots, the maximum normal operating speed, VNO, of the training aircraft whose limitations are listed in Figure 14.5, when it is operating in the Normal Category.
As we mention above, the v in the equation FC = m × v²/r is the aircraft’s true airspeed. For the moment, though, we will make the assumption that true airspeed and indicated airspeed are the same. This will rarely be the case in real life, but it simplifes our examination of basic principles. We will look at the implications of v being the true airspeed at the end of this section.
We have the following information about the aircraft:
•The positive limit load factor is 3.8, in the Normal Category
•The mass of the aircraft is 975 kilograms
•The weight of the aircraft is 9565 Newtons
•Therefore, the maximum permissible lift force that the wings may safely generate is 3.8 × 9565 Newtons, which is 36 347 Newtons
•The aircraft’s speed 124 knots( VNO) which is about 64 metres/second
The minimum “radius of pull-out” from the dive can be calculated from rearranging
F |
= m × |
|
v2 |
|
to give us r as the subject of the equation: |
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r |
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C |
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r = |
mv2 |
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F |
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C |
mv2 |
975 × 64 × 64 |
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So, |
r = |
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|||||
FC |
= |
36 347 |
= 110 metres (approximately). |
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Customer: Oleg Ostapenko E-mail: ostapenko2002@yahoo.com
CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
So, the minimum radius of pull-out that the pilot may fy without exceeding the positive limit load factor for his aircraft of 3.8, is just a little more that the length of a football pitch. During the recovery, the pilot will have monitored the accelerometer attentively to make sure that he did not exceed the load factor (or g) limitation.
We can see from the above equation for the radius r, that if r were to be reduced, and the pull-out made more abruptly, FC, the lift force, would have to increase to keep the equation balanced. As a consequence, the maximum permitted limit load factor of 3.8 would be exceeded. (Load Factor = Lift/Weight)
But what if the pilot were fying an identical manoeuvre in an identical aircraft, but which was not ftted with an accelerometer? If he were to attempt to do this, he would need to think carefully both about his speed in the dive and about the manner in which he recovers from the dive. For instance, if the recovery from the dive were to follow an identical recovery path to the case we have just considered (radius of pull-out = 110 metres), but the pilot had allowed the aircraft to reach a speed in the dive of 145 knots (75 metres/second), still well below the aircraft’s VNE of 155 knots, the lift force generated by the wings would be:
FC = m × |
v |
2 |
= |
975 × 75 |
× 75 |
= 49 858 Newtons |
r |
110 |
|
||||
|
|
|
|
|||
The weight of the aircraft is still, of course, 9565 Newtons, so, in this case, the aircraft will have been subjected to a load factor of:
Load Factor = |
Lift |
= |
49 858 |
= 5.2 |
Weight |
9565 |
A load factor of 5.2 is signifcantly higher than the maximum permissible load factor of
3.8 for which the aircraft is cleared while operating in the Normal Category.
Consequently, it is of crucial importance for a pilot to understand that excessive speed can cause an aircraft to be subjected to load factors greater than that which the aircraft has been designed to withstand safely.
The limiting speeds which are published in the Pilot’s Operating Handbook and in the Check List, for most light aircraft, are speeds (indicated airspeeds) in respect of straight, steady fight. Positive g manoeuvres, at speeds above maximum manoeuvring speed, VA, require lower limiting speeds to be observed in order to avoid over-stressing the airframe.
True Airspeed and Indicated Airspeed.
Remember, too, that we pointed out that the v, in the equation FC = m × v2/r, is the aircraft’s true airspeed. So, the greater the altitude at which the pull-out manoeuvre that we have been considering is fown, the greater the amount by which true airspeed will exceed indicated airspeed. Consequently, if the pilot pulls out of a dive at higher altitude, fown at the same indicated airspeed and following the same curved path as a similar manoeuvre fown at lower altitude, the higher true airspeed will mean that the force generated by the wings must be greater, leading to a greater load factor being imposed on the airframe during the manoeuvre. It is true that, during the dive, having the same indicated airspeed as at the lower altitude will mean that the aerodynamic forces acting on the aircraft in the dive will also be the same. However, as soon as the pilot begins to recover from the dive, that situation changes. For the pull-out, it is the true airspeed which determines the force required to produce the positive acceleration necessary to recover the aircraft from the dive. If the pilot pulls
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CHAPTER 14: FLIGHT AND GROUND LIMITATIONS
Aerodynamic
forces are proportional to the square
of the indicated airspeed, but inertial forces are proportional to the square of the true airspeed.
If the
maximum permissable load factor
is exceeded, an aircraft must not fly again until it has been examined by a qualified aircraft technician.
out from the dive following the same curved path as at the lower altitude, he will have to pull back on the control column more in order to generate the greater amount of lift required for the recovery. It is at the point of pull out, then, that the situation changes.
Aerodynamic forces are dependent on indicated airspeed, but inertial forces are proportional to the square of the true airspeed.
The accelerometer measures inertial accelerations and, thus, is an indication of load factor.
The Consequences of Exceeding the Maximum Permissible Load Factor.
Exceeding the maximum design limit load to the extent in the example that we have just considered would be extremely hazardous, and would almost certainly cause permanent deformation of the wing structure.
During an abrupt pull-out from a dive, bending moments are high, and are at a maximum at the wing root. (The centre of pressure on both wings lies at about mid-span, whereas the greater part of the aircraft’s total weight will most likely be concentrated in the fuselage. The wings defect under any loading, and, under a load factor of 5.2, the defection in the wings of an aircraft whose positive design load limit is 3.8 may be such as to cause permanent strain in the wing. The upper surfaces of the wing spar, wing skin and fuselage are subject to compression loads under positive load factors, while their lower surfaces experience loads in tension. Many other components of the airframe structure experience bending moments, too. All airframe components must be thoroughly examined by a qualifed aircraft technician after the aircraft has exceeded its maximum permissible load factor, before the aircraft is allowed to fy again.
If the maximum permissible load factor were exceeded by too great a degree, airframe components would fail, probably resulting in loss of the aircraft. Current regulations, world-wide, require a minimum safety factor of 1.5 to be applied to a light aircraft’s designed load limits. Consequently, airframe components should not break on an aircraft with a maximum permissible load factor of 3.8, until a load factor of 5.7 has been surpassed. However, it would be a very foolish pilot who relied on safety factors to preserve him and his aircraft.
Stall Speed During Recovery from a Dive.
While an aircraft is in the straight and steady descent part of its dive, the forces acting on the aircraft are in equilibrium, as shown in Figure 14.10.
In the descent, the lift is a fraction less than the weight because weight is counterbalanced by the resultant of the lift and drag forces, acting together. In the descent, therefore, load factor will be a little less than 1; (Load Factor = Lift/ Weight). But to recover from a dive by “pulling”, say, 3.5g, the lift force obviously has to increase to 3.5 times the aircraft’s weight.
If you consider the lift force equation, Lift = CL ½ ρ v2 S , you see that the factors in the equation which the pilot would be able practically to control in order to increase the lift force to recover from the dive are airspeed, v, and angle of attack, CL. We will assume that the pilot eases back on the control column. At a constant throttle setting, this action will increase angle of attack (and so CL) and decrease speed.
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