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.
A full scientific 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 confine ourselves to the consideration of basic concepts, involving simple equations and, where necessary, simplified 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 flight, (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 flight, has increased power, the aircraft will accelerate. If thrust is less than drag the aircraft will decelerate.
Figure 8.1. The propeller of a Sopwith Triplane.
Figure 8.2 The Four forces acting on an aircraft in steady, level flight. (simplified representation)
The exact way in which thrust is developed by an aircraft’s powerplant depends on the type of propulsion system fitted 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).
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 fluid flowing into the streamtube must equal the mass of fluid flowing 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 flowing into the engine (through the turbines or propeller disc) is equal to the mass of air flowing out of the engine. In other words, the mass flow of air is constant.
Figure 8.3 Common types of aircraft propulsion systems. Thrust is the forward-acting reaction to a mass of air accelerated rearwards by a propulsion system.
Furthermore, if we also assume for our purposes that air is an ideal fluid, and, therefore, incompressible and inviscid, the rate of mass flow of air into the propulsion system will be equal to the rate of mass flow 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:
(mVe – mVo) m(Ve – Vo) Rate of change of momentum = 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)
F = lllllllll ...(1)
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
Figure 8.4 A propulsion system generates forward thrust by accelerating a mass of air rearwards.
A change of velocity is, of course, an acceleration. So we may write:
F = mass × acceleration ...(2)
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)
Thrust = llllllll ...(3) t
or
Thrust = mass × acceleration...(4)
Finally, looking at Equation (3), and because we are assuming a constant rate of mass flow 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 airflow is increased – in other words, accelerated - by the action of the propulsion system.
m(Ve – Vo) Thrust = llllllll
t
m
But mass flow ___ = constant
t
Therefore Thrust
h
(Ve - Vo). (the symbolh
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 airflow when the propeller is rotating. So do not be surprised if your flying instructors sometimes disagree on what scientific 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.”Propeller thrust is proportional to the increase in velocity imparted to the air.