Flight with Asymmetric Thrust

Mechanics Flight 12

Yawing Moment

The yawing moment is the product of thrust from the operating engine multiplied by the distance between the thrust line and the CG (thrust arm), plus the drag from the failed engine multiplied by the distance between the engine centre line and the CG. The strength of the yawing moment will depend on:

•how much thrust the operating engine is developing (throttle setting and density altitude).

•the distance between the thrust line and the CG (thrust arm).

•how much drag is being produced by the failed engine.

The rudder moment, which balances the yawing moment, is the result of the rudder force multiplied by the distance between the fin CP and the CG (rudder arm). This statement will be modified by factors yet to be introduced. Thus, at this preliminary stage, the ability of the pilot to counteract the yawing moment due to asymmetric thrust will depend on:

•rudder displacement (affecting rudder force).

•CG position (affecting rudder arm).

•the IAS (affecting rudder force).

Flight Mechanics 12

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Mechanics Flight 12

Flight Mechanics

Critical Engine

One of the factors influencing the yawing moment following engine failure on a multi-engine aircraft is the length of the thrust arm (distance from the CG to the thrust line of the operating engine).

In the case of a propeller engine aircraft the length of the thrust arm is determined by the asymmetric effect of the propeller. At a positive angle of attack, the thrust line of a clockwise rotating propeller, when viewed from the rear, is displaced to the right of the engine centre line. This is because the down-going blade generates more thrust than the up-going blade (Chapter 16). If both engines rotate clockwise, the starboard (right) engine will have a longer thrust arm than the port (left) engine.

If the left engine fails, the thrust of the right engine acts through a longer thrust arm and will give a bigger yawing moment; a higher IAS (VMC) would be necessary to maintain directional control. So at a given IAS, the situation would be more critical if the left engine failed, Figure 12.23.

The critical engine is the engine, the failure of which would give the biggest yawing moment.

To overcome the disadvantage of having a critical engine on smaller twins, their engines may be designed to counter-rotate. This means that the left engine rotates clockwise and the right engine rotates anti-clockwise, giving both engines the smallest possible thrust arm. Larger turbo-props (e.g. King Air etc. and larger) rotate in the same direction. In the case of a fourengine jet aircraft the critical engine is either of the outboard engines.

Note: If all the propellers on a multi-engine aircraft rotate in the same direction, they are sometimes called ‘co-rotating’ propellers.

LONGER

THRUST

CRITICAL ARM

ENGINE

Figure 12.23 Critical engine

Flight Mechanics

Balancing theYawing Moments and Forces

Although the moments are balanced in Figure 12.22, the forces are not balanced. Consequently, the aircraft is not in equilibrium and will drift, in this case, to the left. The unbalanced side force from the rudder can be balanced in two ways:

•with the wings level and

•by banking slightly towards the live engine (preferred method).

Rudder to StopYaw -Wings Level

Rudder is used to prevent yaw, and the wings are maintained level with aileron. Yawing towards the live engine gives a sideslip force on the keel surfaces opposite to the rudder force,

Figure 12.24. If the sideslip angle is too large, the fin could stall. The turn indicator will be central and so will the slip indicator.

Note: Asymmetric thrust is the exception to the rule of co-ordinated flight being indicated to the pilot by the ball centred in the inclinometer.

This method of balancing the side force from the rudder gives reduced climb performance because of the excessive parasite drag generated so is not the recommended method for critical situations, such as engine failure just after take-off or go-around.

YAWING MOMENT

RUDDER MOMENT

Figure 12.24 Wings level method

The only advantage of the ‘wings level’ method of balancing the forces is the strong visual horizontal references available to the pilot, both inside and outside the aircraft.

The disadvantages are that if the sideslip angle is too large, the fin could stall plus the ability to climb is reduced due to excessive parasite drag.

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Mechanics Flight 12

Lift

RUDDER

FORCE

Weight

Figure 12.25 Maximum 5° bank towards live engine

Rudder to Stop Yaw - Bank Towards Live Engine

It is more aerodynamically efficient to balance the rudder sideforce by banking towards the live engine, Figure 12.25, so that lift gives a sideways component opposite to the rudder force. The angle of bank must not exceed 5°, to prevent excessive loss of vertical lift component.

Banking towards the live engine also reduces the side force on the fin from sideslip, which minimizes VMC, effectively reduces the yawing moment and gives more rudder authority to stop the yaw.

The cockpit indication will be the turn needle central with the slip indicator (ball) one half diameter displaced towards the live engine. The ‘ball’ is not centred, but the aircraft is not sideslipping. This method produces minimum drag and gives the best ability to climb and is therefore the preferred method of putting the aircraft in equilibrium following engine failure.

Roll andYaw Moments with AsymmetricThrust

The rolling and yawing moments and the power of the flight controls to balance them will determine the controllability of an aircraft with asymmetric thrust. Rolling and yawing moments with asymmetric thrust are affected by:

•Thrust on the live engine

The greater the thrust, the greater the yawing moment from the live engine. The further the engine is mounted out on the wing (increased thrust arm), the larger the yawing moment. Thrust is greatest at low speed and full throttle.

•Altitude

Thrust reduces with increasing altitude and/or increasing temperature (high density altitude). The worst case for engine failure is low density altitude, e.g. immediately after take-off on a cold day at a sea level airport.

Flight Mechanics

Minimum Control Airspeed

It has been shown that when a multi-engine aircraft suffers an engine failure several variables affect both the yawing moment and the rudder moment which is used to oppose it. It has also been shown that there is a minimum IAS (VMC), below which it is impossible for the pilot to maintain directional control with asymmetric thrust.

Airworthiness Authorities, in this case the EASA, have laid down conditions which must be satisfied when establishing the minimum airspeeds for inclusion in the Flight Manual of a new aircraft type. As in most other cases, the conditions under which the minimum control airspeeds are established are ‘worst case’. A factor of safety is built into these speeds to allow for aircraft age and average pilot response time.

Because there are distinct variations in the handling qualities of the aircraft when in certain configurations, minimum control airspeed (VMC) has three separate specifications:

VMCA (CS 25.149 paraphrased)

VMCA is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative and maintain straight flight with an angle of bank of not more than 5°.

VMCA may not exceed 1.13VSR with:

•maximum available take-off power or thrust on the engines.

•the aeroplane trimmed for take-off.

•the most unfavourable CG position.

•maximum sea level take-off weight.

•the aeroplane in its most critical take-off configuration (but with gear up); and

•the aeroplane airborne and the ground effect negligible; and

•if applicable, the propeller of the inoperative engine:

•windmilling

•feathered, if the aeroplane has an automatic feathering device.

The rudder forces required to maintain control at VMCA may not exceed 150 lb nor may it be necessary to reduce power or thrust on the operative engines.

Note: There is no performance requirement, just directional control.

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Mechanics Flight 12

Factors AffectingVMCA

Angle of Bank

Banking towards the live engine reduces the rudder deflection required and so allows a lower VMCA. 5° maximum is stipulated because larger bank angles would significantly reduce the vertical component of lift; the angle of attack would have to be increased with the added penalty of higher induced drag.

CG Position

Because the aircraft rotates around the CG, the position of the CG directly affects the length of the rudder arm and, thus, the power of the rudder and fin to maintain directional stability and control. The ‘worst case’ is with the CG at the aft limit. If the requirements can be met in this configuration, the ability to maintain directional control will be enhanced at any other CG location.

Aileron Effectiveness

At low airspeed, dynamic pressure is low which reduces the effectiveness of all the flying controls for a given angle of displacement. This effect on the rudder has already been discussed, but the ailerons will be affected in a similar way. In Figure 12.24 and Figure 12.25 (right roll input) the wings are maintained either level or at the required bank angle with the ailerons. At reduced airspeed, greater right roll aileron displacement must be used to keep the wings in the required position. The ’down’ aileron on the left side will add to the yawing moment because of its increased induced drag. At low IAS (increased CL ), the large angle of down aileron could stall that wing and give an uncontrollable roll towards the dead engine. VMCA must be high enough to prevent this unwelcome possibility.

Flap Position

Flap position affects lift / drag ratio, nose-down pitching moment and the stalling speed. With asymmetric thrust, flaps reduce climb performance, increase the margin above stall, but do not directly affect VMCA. However, if take-off flap is used, the difference in lift between the two wings due to propeller slipstream is further increased. This increases the rolling moment, requires increased aileron deflection and indirectly increases VMCA.

Undercarriage

The undercarriage increases drag and reduces performance. The increased keel surface in front of the CG decreases directional stability slightly, thus the fin and rudder are opposed in sideslip conditions, and this will slightly increase VMCA.

Altitude and Temperature

VMCA is affected by the amount of thrust being developed by the operating engine. As altitude and/or temperature increases, the thrust from an unsupercharged engine will decrease. Therefore, VMCA decreases with an increase in altitude and/or temperature.

Relationship between VS and VMCA

VS is constant with increasing altitude, so can be represented by a straight line in Figure 12.27. (It was shown in Chapter 7 that stall speed does increase at higher altitudes, but for this study, we are only dealing with lower altitudes). Figure 12.27 shows that at about 3000 ft, VS and VMCA typically correspond. So above this altitude, the stall speed is higher than VMCA. If the aircraft is slowed following an engine failure with full power on the operating engine, the aircraft can stall before reaching VMCA. The margin above loss of control is reduced; in this case by stalling.

Vs IAS

Figure 12.27 VS and VMCA

VMCG (CS 25.149 paraphrased)

VMCG, the minimum control speed on the ground, is the calibrated airspeed during the takeoff run, at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane using the rudder control alone (without the use of nose wheel steering) to enable the take-off to be safely continued using normal piloting skill. The rudder control forces may not exceed 150 pounds (68.1 kg) and, until the aeroplane becomes airborne, the lateral control may only be used to the extent of keeping the wings level. In the determination of VMCG, assuming that the path of the aeroplane accelerating with all engines operating is along the centre of the runway, its path from the point at which the critical engine is made inoperative to the point at which recovery to a direction parallel to the centre line is completed may not deviate more than 30 ft (9.144 m) laterally from the centre line at any point. As with VMCA, this must be established with:

•maximum available take-off power or thrust on the engines.

•the aeroplane trimmed for take-off.

•the most unfavourable CG position.

•maximum sea level take-off weight.

Factors Affecting VMCG

Altitude and Temperature

VMCG is affected by the amount of thrust being developed by the operating engine. As altitude and/or temperature increases, the thrust from an unsupercharged engine will decrease. Therefore, VMCG decreases with an increase in altitude and/or temperature.

Flight Mechanics 12

Mechanics Flight 12

Rudder Arm

When the aircraft is on the ground it rotates about the main undercarriage, which is aft of the CG. Therefore the rudder arm is shorter when the aircraft is on the ground. It will be found that on most aircraft VMCG is higher than VMCA.

VMCL (CS 25.149 paraphrased)

VMCL, the minimum control speed during approach and landing with all engines operating, is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the aeroplane with that engine still inoperative and maintain straight flight with an angle of bank of not more than 5°.

VMCL must be established with:

•the aeroplane in the most critical configuration for approach and landing with all engines operating,

•the most unfavourable CG,

•the aeroplane trimmed for approach with all engines operating,

•the most unfavourable weight,

•for propeller aeroplanes, the propeller of the inoperative engine in the position it achieves without pilot action and

•go-around power or thrust setting on the operating engines(s).