Co-ordinated Turn Systems10.5 CO-ORDINATED TURN SYSTEMS10.5.1 IntroductionA co-ordinated turn is one in which both the lateral acceleration, a, and thesideslip velocity, v, are zero. In such a turn the lift vector is perpendi&!lar to theaircraft axis OY. Co-ordinated turns reduce adverse sideslip and, therefore, rollhesitation. In such turns, there is minimum coupling of rolling and yawingmotions. Provided that the side force due to aileron, Y:, and the side force dueto the yaw rate, Y, are both negligible, then zero sideAslip angle (P = 0), zerosideslip velocity (v = P/Uo = O), and zero lateral acceleration (a, = 0) areall equivalent conditions.
Sometimes, particularly in early textbook? On flyingtechniques, a co-ordinated turn was assumed to be one in which the lateralacceleration experienced in the cockpit was zero - a condition displayed to pilotsby the turn-and-bank indicator, with its black ball centred between the verticallines.
However, this condition is not one which finds much use in AFCS studiessince the acceleration at the cockpit is a function of the distance from theaircraft's c.g. Generally, the acceleration at the pilot's station features in AFCSwork only in relation to ride control systems, which are dealt with in Chapter 12.10.5.2 Conditions Needed for a Co-ordinated TurnFor a body axis system the side force equation is: Y = m ( W- P + UR)Following the development detailed in Section 2.4 of Chapter 2, it can be seenthat the rate of change of sideslip angle can be expressed as in eq.
(2.75), i.e.:If R0 = 0, WdUo = a0and, if a co-ordinated turn is achieved, i.e. If: p =0then:If the aircraft has been trimmed so that olo is zero, then:336 Attitude Control SystemsTherefore, in a co-ordinated turn, the rate of turn develops in proportion to thebank angle, 4. Of course, neither Yv nor YzA is generally zero, nor may they beneglected. Consequently, if p is to be zero, so that eq. (10.35) obtains, a steadydeflection of the ailerons is required to maintain the co-ordinated turn. The valueof aileron deflection required is given by:There are a number of factors which may delay the establishment of a co-ordinated turn. They include the following:1.
An aileron deflection usually induces a yawing moment.2. The build-up of yaw rate, as a result of any change in bank angle, is delayed by aerodynamic lag.3. The action of the yaw damper, which is commonly fitted to aircraft, tends to reduce any transient yaw rate.As an illustration of how these factors affect the turn, consider an aircraft, such asCHARLIE in Appendix B, in which:NkA 0 (10.37)Whenever a positive roll rate is required i.e. BA 0and N$ 0, it is then evident that the sideforce contributions of the tyres ofthe undercarriage contribute to the damping of the motion during groundroll.
However, suppose V represents the ground speed and Vw represents thecomponent of headwind which arises when the aircraft is moving on the runway inthe presence of a wind. Equation (10.79) then becomes:The presence of the headwind now results in the real root of the characteristiccubic being finite, rather than zero, with the possibility of some stability in track.When the headwind is positive, the real root is stable if:Therefore, it can be deduced that N b stabilizes the ground tracking mode whereasN; destabilizes it.
Vishnu G Nair
A discussion of the dynamics of aircraft rotation and lift-off can be foundin Pinsker (1967).10.8 CONCLUSIONSAutomatic control systems for maintaining the attitude angles of an aircraft, orfor changing an aircraft's attitude to a new commanded value, are introduced. Toemphasize the principles of negative feedback control which are common to themany varieties of attitude control system used on aircraft, the pitch attitudecontrol system is dealt with extensively. The use of a pre-filter in conjunction withthese types of AFCS to obtain the required handling qualities in the controlledaircraft is briefly dealt with, before a roll angle control system is considered. Theuse in such systems of phase advance compensation networks, or a roll ratedamper as an inner loop to achieve the required dynamic response is dealt withand gain scheduling as a means of maintaining the same closed loop performanceover as much of the flight envelope as possible is also treated.
The unwantedresults of tight roll control, such as roll ratchet or pitching motion due to rolling,are treated briefly before the means of achieving automatically controlled co-ordinated turns by a variety of methods is explained. The chapter concluded withthe important subject of controlling direction stability during ground roll.10.9 EXERCISES+,10.1 A transport aircraft, flying at a Mach number of 0.8 and a height of 10000 m has as its transfer function, relating bank angle, to aileron deflection, SA, Gl(s) asExercises 353as defined below. When the aircraft flies at half the height and at a Mach numberof 0.4 its transfer function becomes G2(s).The block diagram of the bank angle control system used on the aircraft is shownin Figure 10.24.
Controller Aircraft dynamics I m lAttitude gyroFigure 10.24 Block diagram of a bank angle control system for Exercise 10.1.+,(a) Determine the closed loop transfer function relating the bank angle, to +,-the commanded bank angle, for flight condition 1. (Hint: make reasonable simplifying assumptions.)(b) What is the effect upon the dynamic response of the bank angle control system if the aircraft flies at flight condition 2? Assume the controller gain, K+, remains unchanged.(c) If the value of K+ is 2.5, and if the value of the commanded bank angle is 5.0°, sketch the closed loop response for both flight conditions.10.2 If the experimental VTOL aircraft of Exercise 2.7 is flying at 15 m s-l, and has the same stability derivatives that were listed in that question, calculate the lateral acceleration at its c.g. For a flat, co-ordinated turn in which the yaw rate is 0.33 rad s-l. (The aircraft may be assumed to have zero sideslip velocity.)10.3 In the sideslip suppression system, represented by the block diagram in Figure 10.25 a sideslip signal is used as feedback to drive the rudder so that sideslip is eliminated. The wash-out filter in the inner loop can be regarded as a blocking filter for constant manoeuvre commands, i.e. Yaw rate feedback operates only during changes of the flight state.
The dynamics associated with the rudder servo are negligible.
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