Flight Mechanics 12

Balance of Forces

If the tailplane is producing a balancing force, this will add to or subtract from the lift force.

For a down load:	Lift	-	tailplane force	=	Weight
For an up load:	Lift	+	tailplane force	=	Weight

ANGLE	STALL ANGLE
OF
ATTACK
	CONSTANT
	LIFT
Vs	I AS

Figure 12.3 Variation of angle of attack with IAS

For steady level flight at a constant weight, the lift force required will be constant. At a steady speed the wing will give this lift at a given angle of attack. However, if the speed is changed, the angle of attack must change to maintain the same lift. As the lift changes with the square of the speed, but in direct proportion to the angle of attack, the angle of attack will vary as shown in Figure 12.3 to give a constant lift.

For steady level flight at a constant speed, the thrust must equal the drag. Drag increases with speed (above VMD) and so to maintain a higher speed, the thrust must be increased by opening the throttle.

Flight Mechanics 12

THRUST			C			T2
AND				B
DRAG					T 1
			A

I AS

Figure 12.4 Balance of thrust & drag

To fly at the speed at point A, Figure 12.4, requires a thrust of T1 and to fly at point B requires a thrust of T2. If the thrust is increased from T1 to T2 when the aircraft is at point A, the thrust will be greater then the drag, and the aircraft will accelerate in proportion to the ‘excess’ thrust AC until it reaches point B, where the thrust and the drag are again equal. If T2 is the thrust available with the throttle fully open, then the speed at B is the maximum speed achievable in level flight.

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12 Flight Mechanics

Straight Steady Climb

Consider an aircraft in a straight steady climb along a straight flight path inclined at an angle (γ) to the horizontal. γ (gamma) is the symbol used for climb angle. The forces on the aircraft consist of Lift, normal to the flight path; Thrust and Drag, parallel to it; and Weight, parallel to the force of gravity. This system of forces is illustrated in Figure 12.5.

			THRUST
			REQUIRED
	AERODYNAMIC	L	TO BALANCE
			AERODYNAMIC DRAG
	DRAG
			FLIGHT PATH
12			W cos
Flight	BACKWARDS	W	BACKWARDS
Mechanics
	CLIMB ANGLE		EXTRA THRUST
			REQUIRED TO
			BALANCE
	COMPONENT		COMPONENT
	OF W EIGHT	W sin
			OF WEIGHT

Figure 12.5 Forces in a steady climb

Weight is resolved into two components: one opposite Lift (W cos γ) and the other acting in the same direction as Drag (W sin γ), backwards along the flight path. The requirements for equilibrium are: Thrust must equal the sum of Drag plus the backwards component of Weight; and Lift must equal its opposing component of Weight. For equilibrium at a greater angle of climb, the Lift required will be less, and the backwards component of Weight will be greater.

L = W cos γ

T = D + W sin γ

In a straight steady climb, Lift is less than Weight because Lift only has to support a proportion of the weight, this proportion decreasing as the climb angle increases. (In a vertical climb no lift is required). The remaining proportion of Weight is supported by engine Thrust.

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Flight Mechanics

It can be seen that for a straight steady climb the Thrust required is greater than Drag. This is to balance the backward component of Weight acting along the flight path.

	Sin γ =	T - D
		W

The ability of an aircraft to climb depends upon EXCESS THRUST, available after opposing aerodynamic drag. The smaller the Drag for a given Thrust, the greater the ability to climb.

Drag will be less with flaps up, giving a larger climb angle (improved climb gradient).

Climb Angle

Climb angle depends on “excess Thrust” ( T - D ) and the Weight. As both Thrust and Drag vary with IAS, excess Thrust will be greatest at one particular speed. This is the speed for maximum angle of climb, VX. (see Figure 12.28 for the propeller case).

DRAG

THRUST
AND
DRAG	THRUST (JET)

MAXIMUM

DIFFERENCE BETWEEN

THRUST AND DRAG

VX

IAS

Figure 12.6 Variation of excess thrust with speed (JET)

The variation of Thrust with speed will depend on the type of engine. For a jet engine, where Thrust is fairly constant with speed, VX will be near to VMD, but for a propeller engined aircraft VX will usually be below VMD.

Effect of Weight, Altitude and Temperature.

The Drag of an aircraft at a given IAS is not affected by altitude or temperature, but higher Weight will increase Drag and reduce excess Thrust and, consequently, the climb angle.

Thrust available from the engine decreases with increasing altitude and increasing temperature, which also reduces excess Thrust. Climb angle therefore decreases with increasing Weight, altitude and temperature.

12

Flight Mechanics 12

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12 Flight Mechanics

Mechanics Flight 12

Power-on Descent

TOTAL

REACTION

L= W cos

ENGINE THRUST

D

FLIGHT PATH

FORWARD COMPONENT

OF WEIGHT ( W sin )

W

Figure 12.7 Forces in a power-on descent

Figure 12.7 illustrates the disposition of forces in a steady Power-on descent. The force of Weight is split into two components. One component (W cos γ) acts perpendicular to the flight path and is balanced by Lift, while the other component (W sin γ) acts forward along the flight path and ‘adds’ to the Thrust to balance Drag. If the nose of the aircraft is lowered with a constant Thrust setting, the increased component of Weight acting forward along the flight path will cause an increase in IAS. The increased IAS will result in an increase in Drag which will eventually balance the increased forward force of Weight and equilibrium will be re-established.

If the throttle is closed, the force of Thrust is removed, and a larger forward component of Weight must be provided to balance Drag and maintain a constant IAS. This is accomplished by lowering the nose of the aeroplane to increase the descent angle (γ).

•In a descent Lift is less than Weight. This is because Lift only has to balance the component of Weight perpendicular to the flight path (W cos γ).

•In a descent Thrust is less than Drag. This is because Weight is giving a forward component in the same direction as Thrust (W sin γ).

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