ppl_05_e2

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CHAPTER 7: WEIGHT

Figure 7.7 If the aircraft were to be suspended through its Centre of Gravity, the aircraft would hang in perfect balance.

All aircraft have published weights, such as Basic Empty Weight, Maximum Gross

Weight, Zero Fuel Weight, Maximum Take off Weight, Useful Load, Maximum Landing Weight, etc. (In JAR-FCL/EASA examinations, you will mostly fnd the word mass substituted for weight for reasons we have just discussed.) Furthermore, because, during fight, the aircraft consumes fuel, the weight of the aircraft constantly changes.

As fuel tanks empty, the distribution of the weight throughout the aircraft, and, thus, the position of the aircraft’s centre of gravity, changes, too.

As you will learn in the Mass & Balance section of this series, because weight acts through the centre of gravity, the position of the centre of gravity along the aircraft’s longitudinal axis affects the stability of the aircraft. Therefore, there are forward and aft limits (See Figure 7.8), calculated by the aircraft designer, within which the centre of gravity must remain throughout a fight. These centre of gravity limits are established in order that the pilot may have suffcient elevator authority in all phases of fight, to control the aircraft in pitch. If the centre of gravity exceeds the forward limit, the aircraft is said to be nose heavy. If the centre of gravity is too far aft, the aircraft is said to be tail heavy. An aircraft which has its centre of gravity outside the aft limit may be dangerously unstable in pitch and display unfavourable stall and spin characteristics.

A nose-heavy

aircraft is very stable in pitch

and will require

greater elevator displacement to control in pitch.

An aircraft

which is tail heavy may be

dangerously

unstable in pitch and display unfavourable stall and spin characteristics.

Figure 7.8 Representative fore and aft limits of the centre of gravity for a PA28.

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CHAPTER 7: WEIGHT

Beware, the centre of

gravity may be outside limits,

even if the maximum take-off weight (mass) is not exceeded.

A pilot must ensure, before

every flight, that the weight

(mass) and centre of gravity limitations are not exceeded.

In addition to such weight information as Useful Load, and Maximum Take Off Weight (Mass), the Pilot’s Operating Handbook (POH) may contain separate details of the weight that may be loaded in the aircraft’s baggage compartment. This is a detail that the pilot must not neglect because carrying too much baggage could move the centre of gravity too far aft, even if the Maximum Take-Off Weight (Mass) is not exceeded.

The POH may also specify such details as minimum crew weight for solo fight.

Weight, then, although not aerodynamically generated, as are lift, drag and propeller thrust, is a fight force which the pilot must fully understand. Maximum and minimum weights (or masses) must be observed in loading an aircraft. Weight is a crucial concept, both in itself and in its effect on the position of the centre of gravity.

It is one of the pilot’s major responsibilities when preparing his aircraft for fight to confrm that the centre of gravity is situated within the limits stipulated in the Pilot’s Operating Handbook.

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CHAPTER 7: WEIGHT QUESTIONS

Representative PPL - type questions to test your theoretical knowledge of Weight.

1.Choose the correct statement option below:

a.Weight and mass are conceptually the same.

b.Weight and mass are both forces.

c.Weight and mass are two different concepts; weight is a force and mass is a quantity of matter.

d.The weight and mass of a given body will be equal only in deep space.

2.Choose the correct statement option below.

a.The scientifc unit of mass is the Newton.

b.The scientifc unit of force is the kilogram.

c.The scientifc unit of force is the metre per second2

d.The scientifc unit of mass is the kilogram.

3.The weight of an aircraft is:

a.The force acting on the aircraft’s mass and directed towards the centre of the Earth.

b.The same as the aircraft’s mass.

c.The mass of the aircraft when the aircraft is assumed to have zero weight.

d.The force acting on the aircraft to accelerate it in the horizontal plane.

4.Choose the correct statement option below.

a.A body always possesses the same mass and weight whatever the strength of the gravitational feld.

b.The mass of a body is dependent on the strength of the gravitational feld in which the body is situated.

c.A body always possesses the same mass but in zero gravity will have no weight.

d.The weight of a body is independent of the strength of the gravitational feld in which the body is situated.

5.Choose the correct equation below.

a.weight (Newtons) = mass (kg) × linear acceleration (m/s2)

b.weight (Newtons) = mass(kg) × acceleration due to gravity (m/s2)

c.weight (kg) = force (Newtons) × acceleration (m/s2)

d.weight (Newtons) = mass (kg)

6.On Earth:

a.weight (Newtons) = mass(kg) × linear acceleration (m/s2)

b.weight (Newtons) = mass (kg) × 32 m/s2

c.weight (Newtons) = mass (kg) × 9.81 m/s2

d.weight (Newtons) = mass (kg) × m/s2

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CHAPTER 7: WEIGHT QUESTIONS

7.On the moon:

a.the weight of a body will be approximately 1/6 of its weight on the Earth.

b.the weight of a body will be approximately 6 times its weight on the Earth.

c.the weight of a body will be the same as its weight on the Earth.

d.the mass of a body will be approximately 1/6 of its mass on the Earth.

8.When considering the linear acceleration of a body under the action of a given force:

a.It is the body’s weight that will determine the magnitude of the acceleration.

b.Neither the body’s mass nor its weight affects the magnitude of the acceleration.

c.It is the body’s mass that will determine the magnitude of the acceleration.

d.A force cannot cause a linear acceleration

9.When considering lifting a body in a gravitational feld:

a.It is the body’s mass which is crucial to the consideration.

b.Neither a body’s mass nor its weight affects the consideration.

c.A body of fnite weight cannot be lifted in a gravitational feld

d.It is the body’s weight which is crucial to the consideration.

10.Despite the difference in concepts between weight and mass, weight may be expressed in kilograms on Earth because:

a.In a constant gravitational feld mass is always equal to weight.

b.Given that the acceleration due to gravity is constant at 9.81 m/s2, mass is directly proportional to weight, and, therefore, weighing devices may be calibrated to read mass in kilograms.

c.In a constant gravitational feld there is no difference between mass and weight.

d.In a constant gravitational feld mass and weight have no meaning.

Question	1	2	3	4	5	6	7	8	9	10
Answer

The answers to these questions can be found at the end of this book.

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CHAPTER 8

PROPELLER THRUST

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CHAPTER 8: PROPELLER THRUST

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CHAPTER 8: PROPELLER THRUST

INTRODUCTION.

The technical description of the propeller and the engineering aspects of its operation are covered in the book in this series entitled ‘Aeroplanes’. This chapter looks at propellers solely from the point of view of the Principles of Flight.

Figure 8.1. The propeller of a Sopwith Triplane.

A full scientifc explanation of the function of a propeller is complex, requiring an understanding of quite advanced mathematics, and is, therefore, beyond the scope of this book. Here, we will confne ourselves to the consideration of basic concepts, involving simple equations and, where necessary, simplifed mathematics. You will not, however, need to understand the equations or the mathematics to learn from this chapter the principles of operation of the propeller that you are required to know, in order to pass your pilot’s licence theoretical knowledge examinations.

THRUST.

The force which propels an aircraft through the air is known as thrust. As you have learnt, thrust, together with lift, drag and weight, is one of the four principal forces which act on an aircraft in fight, (Figure 8.2). At any constant airspeed, thrust is equal and opposite to the force of drag. If thrust is greater than drag, for instance, because the pilot, in level fight, has increased power, the aircraft will accelerate. If thrust is less than drag the aircraft will decelerate.

Figure 8.2 The Four forces acting on an aircraft in steady, level flight. (simplified representation)

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CHAPTER 8: PROPELLER THRUST

The exact way in which thrust is developed by an aircraft’s powerplant depends on the type of propulsion system ftted to the aircraft. Common types of aircraft propulsion systems are: the Piston Engine/Propeller combination, the Pure Turbojet, the By-pass Turbojet and the Turboprop (Figure 8.3).

Thrust is the forward-acting

reaction to a mass of air

accelerated rearwards by a propulsion system.

Figure 8.3 Common types of aircraft propulsion systems.

But, whatever the type of powerplant, thrust is always generated by one aspect or another of the application of Newton’s 2nd and 3rd Laws (see Page 14). For all types of propulsion systems, a mass of air is accelerated rearwards by the system, as depicted in Figure 8.4, and the reaction to this rearwards acceleration gives rise to the thrust force which drives the aircraft forwards.

Acceleration is, of course, just another name for change in velocity. Figure 8.4 depicts how a given mass m of air is accelerated from velocity Vo to velocity Ve, as it passes through a propulsion system. Vo is the velocity of the air entering the propulsion system and Ve is the increased velocity of the air after it has passed through the propulsion system.

In the chapter on Lift, you met the Principle of Conservation of Mass which states that, when we consider a closed system such as a streamtube, the mass of fuid fowing into the streamtube must equal the mass of fuid fowing out of the streamtube. Now, a propulsion system, such as a jet engine or piston-engine/propeller combination may be considered, for our purposes, to be a closed system, so that the mass of air fowing into the engine (through the turbines or propeller disc) is equal to the mass of air fowing out of the engine. In other words, the mass fow of air is constant.

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CHAPTER 8: PROPELLER THRUST

Figure 8.4 A propulsion system generates forward thrust by accelerating a mass of air rearwards.

Furthermore, if we also assume for our purposes that air is an ideal fuid, and, therefore, incompressible and inviscid, the rate of mass fow of air into the propulsion system will be equal to the rate of mass fow of air out of the system. In other words:

mass

_____ = constant time

From your science lessons at school, you may recall that mass × velocity is called momentum, and that momentum is a concept which says something about the quantity of motion of a moving mass. In accelerating the air rearwards, the propulsion system imparts a rate of change of momentum to a mass, m, of air. In other words, if, in a given time lapse, t, the momentum of the air is increased from m Vo to m Ve, the rate of change of momentum of the air can be expressed by:

Rate of change of momentum =	(mVe – mVo)	m(Ve	– Vo)
	llllllllll or	llllllll
	t	t

Now, Newton’s Second Law states that the force acting on a body is equal to the rate of change of momentum of that body, so in the expression:

m (Ve	– Vo)	..............(1)
F = lllllllll
t

F is the force imparted by the propulsion system to the mass of air in order to accelerate it.

m (Ve – Vo)

Now F = lllllllll express a change in velocity over a given time. t

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CHAPTER 8: PROPELLER THRUST

A change of velocity is, of course, an acceleration. So we may write:

F = mass × acceleration

..............(2)

Propeller thrust is

proportional to the increase in

velocity imparted to the air.

Equations (1) and (2), then, are expressions of Newton’s 2nd Law and describe the force exerted by the propulsion system on the air to accelerate it rearwards. It is at this point that we apply Newton’s 3rd Law to the situation in order to explain the generation of forward-acting thrust. Newton’s 3rd Law states that every action has an equal and opposite reaction and acts on different bodies. So the force imparted to the air by the propulsion system to accelerate it rearwards induces a reaction force, equal in magnitude to the accelerating force, and acting on the propulsion system, in the opposite direction (in this case forwards), to give us thrust.

We may, therefore, re-write Equations (1) and (2) as:

m(Ve – Vo)	(3)
Thrust = llllllll ..............
t
or
Thrust = mass × acceleration............	(4)

Finally, looking at Equation (3), and because we are assuming a constant rate of mass fow of air, m/ t , through the propeller disc, we can see that the size of the the thrust generated by any aircraft powerplant depends solely on the amount by which the velocity of the rearwards airfow is increased – in other words, accelerated - by the action of the propulsion system.

	Thrust =	m(Ve – Vo)
		llllllll
			t
	But mass fow	m	= constant
		t

Therefore Thrust h (Ve - Vo). (the symbol h means “proportional to”.)

Or, stated again, in plain language: thrust is directly proportional to the increase in velocity imparted by the propulsion system to the air.

PROPELLERS.

The propulsion system which powers most light aircraft is the piston engine/propeller combination*. The piston engine causes the propeller to rotate, and, by producing thrust, the propeller acts is such a way as to convert the power developed by the engine into propulsive power. As you will discover, the exact nature of the thrust force developed by a propeller is very complex. As well as accelerating air rearwards, propeller blades are also aerofoils, and are, therefore, as you learnt in the Chapter on Lift, also able to develop thrust in the form of a “horizontal lift” force because of the favourable pressure distribution over the blades created by the relative airfow when the propeller is rotating. So do not be surprised if your fying instructors sometimes disagree on what scientifc explanation best accounts for the thrust developed by a propeller.

*“engine” from Latin ingenium meaning ingenuity or cunning (or its product), via Old French ‘engin’; “propeller” from Latin pro + pellere “to drive” meaning “to drive forward.”

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