Part 3: Turning Performance roll rates and wing loading
Flight paths of aeroplanes are controlled primarily varying the magnitude and direction of tge lift vector and by varying the thrust or power contributed by the engines.The magnitude of the lift vector is a direct function of the angle of attack (alpha) or the lift co-efficient C^L.Alpha is controlled by pitching moment contributed by the horizontal tail, to achieve the desired C^L.Tail load is varied by changing elevator angle.
In a steady level flight Lift L= W Weight.When pitching up Lift will be greater at highet alphas and will exceed the weight.The ratio of the L/W is the LF Load Factor.Since weight is force due to gravity when L=W lift =1 g.If lift is 3 times the weight it means the aeroplane is subject to 3 g's.
A stable aeroplane adjusts its speed and flight path angle quite rapidly and subsequently settles down at the speed for which lift equals weight and at the flight path angle FPA for which forces are in climb or descent equilibrium as the case might be.The essence of the equilibrium is that the speed is determine by the L=W condition (i.e by C^L), and the FPA is determined by the thrust.Therefore speed is determined by the position of the elevators and the flight path angle by the throttle.
The Direction of the lift vector is perpendicular to the wing plane. The wing Angle if Bank ( theta) is controlled by aileron controls via their assymmetric deflection.The resultant Rolling Moment banks the aeroplane and tilts the lift vector to one side. The horizontal component of the Lift vector (L sin× theta) accelerates the plane laterally and curves the flight path. Its vertical component (L cos x theta) balances the weight-if sufficient in magnitude.In a turn if radius R, the lateral force,L sinx theta ( theta=bank angle), must balance the centrifugal force in the aero plane ( equal and opposite outward of the turn).For a level turn the weight must be equal to the vertical component if lift. For a 45 degree bank the Lift is 41% greater thsn the weight and the aeroplane is subjected to 1.41 g's.Therefore in a turn the stalling speed is increased and is one if the reasons fir maintaining a speed margin of 20% to 30$ above the level flight stall speed for takeiff and landing.This margin us required fir maneuvering that may become necessary to avoid an obstacle along the flight"s tragectory.
The turning performance of an aeroplane in level flight can be related to the rate of turning or "Roll rate".The radius of turn is reduced and the rate of turn is increased by INCREASING the LF.The design maneuvre LF is 2.5 for transport aircraft ,upto 3.8 for small G.A. aircraft, and upto 7 to 8 for combat aircraft! The minimum turn radius for a given speed is obtained eith a high CL max, high q ( dynamic pressure) and LOW wing loading.With a fixed speed q decreases with high altitude.So an aeroplane with a high C^L max and low wing loading ( which is a case for Boeing 727 wing ).When looking at the Maneuver V-n diagram, the "corner" velocity,i.e. fastest rate of turn is at the intersection of the C^L max curve and maximum velocity structural limits.
High speed aircraft often have wings that are sufficiently flexible so that aileron effectiveness is seriously reduced due to wing twist under load.The aileron lift at the rear if the outer panel may twist the wing to a lower angle of attack,which counteracts much of the aileron lift.In extreme cases ,the net effect may be even reversed ("aileron reversal") so that a positive aileron angle might actually reduce the outer panel wing lift.In such design (B727 in case),the outboard ailerons are utilized only during low speed regime, and high speed roll control us obtained by small inboard ailerons fir gentle maneuvres and by spoilers for HIGH RATES OF ROLL.