Introduction

Manoeuvrability is a measure of the open-loop capabilities of an aircraft. The objective is quickness and the more available the better. In contrast, handling qualities involves the specification of open-loop parameters which have been correlated with desirable closed-loop performance. The objective is a proper combination of quickness and precision. There is usually an upper and lower bound on quickness associated with a given degree of desired precision. Too slow, and the pilot considers the aircraft “sluggish” and may have a tendency to over-control. Too quick, and the pilot finds the aircraft “jumpy” or “oversensitive.”

In Aircraft Research & Development studies Manouevrability primarily under three considerations

1. How to specify requirements for maneuverability in new aircraft..
2. How to design for better maneuverability in new aircraft, and ..
3. How to evaluate the maneuverability of existing aircraft.

Flight Testing directly involves the last point stated above, while also building up on the knowledge-base for the first two study areas. In the operational scenario, we would like to determine how to use a manoeuvrability advantage over an adversary (or counter a disadvantage) in tactical situations.

#### Turn Performance Analysis

Unlike the V-n diagram, sustained turn performance analysis includes the thrust capability of the aircraft. This performance is defined at the point where thrust equals drag in a level turn at a specified power setting (usually MAX power). We see then that aircraft sustained turning performance may be lift limited, structurally limited, or thrust limited depending on the aerodynamic design, structural strength or thrust capability.

Sustained/Stabilized Turns

The sustained or the stabilized turn test is usually performed at several different altitudes with a series of turns flown at each altitude. If airspeed and altitude are constant during the maneuver, the Specific Excess Power, Ps, is 0.

This test is good for hand-held data acquisition and is usually performed to spot check values that have been determined from dynamic performance models or the level acceleration test. Three techniques are used to obtained the stabilized turn data

• The stable g method is flown by holding a target load factor and allowing the airspeed to stabilize. Once the airspeed has stabilized for a minimum of ten seconds, the load factor (n) and velocity are recorded. The stable g method is used on the ‘front side’ of the turn performance curve. The aircraft, is accelerated out to Vmax and then the aircraft g is increased incrementally taking data at each g level established. As the aircraft is on the front side, each increase in g will result in a new, and reduced, stable airspeed. At some g level the airspeed will no longer stabilize and will continue to decrease. At this point the aircraft will transition to the backside and the backside technique (Constant Airspeed Method) will be used. Knowing n and V allows computation of rate of turn (ω) and radius of turn (R).

• The constant airspeed method is flown by holding a target airspeed and recording the resulting load factor. Normally, conditions (g level and airspeed) need only be held constant for approximately ten seconds. The constant airspeed method is typically used on the back side of the turn performance curve, but may be used also on the front side. As with the stable g method, the airspeed and corresponding load factor to hold that airspeed are the data of interest. Typically, the constant airspeed method is started at some airspeed greater than the 1-g backside stable point airspeed and incrementally increased to the point where any increase in airspeed results in a drop of g to hold a stable condition. This indicates that the aircraft has transitioned to the front side.

• The timed turn technique is a variation of the constant airspeed method. It is normally used at low airspeeds and for g levels (n) < 2. It is also used if either there is no available measurement device for g or if only a coarse or inaccurate method of measuring load factor is available. For a timed turn manoeuvre, the power is set and the aircraft is established in a bank angle and the airspeed allowed to stabilize, or the velocity is held constant using bank angle. The turn is maintained through 360° and the time to accomplish the turn is recorded. From this, the rate of turn, ω, can be calculated. With ω known at that airspeed (V), n and R can be calculated.

Theoretical Basis

The total energy of the aircraft, $E ={1 \over 2} mV^2 + mgh$

This can be divided by the weight of the aircraft to give the specific energy,

$E_s ={V^2 \over 2g} + h$

Taking the derivative with respect to time gives

$P_s ={V \over g} {\dot V} + {\dot h}$, the specific excess power.

This quantity identifies the rate at which the aircraft is losing or gaining energy.

From the force equations, we can also find the standard expression for specific excess power as

$P_s ={V \over mg} ({T – D})$

$T$ is the thrust along the fight path, a function of throttle setting, altitude, Mach number, angle of attack, and thrust vectoring deflections.

If the tangential thrust and drag forces are expressed as functions of V, ω, and $p$ (rollrate about forward axis) for a specific altitude and throttle setting, then surfaces of constant Ps can be generated in the maneuver space. The Ps = 0 plot for maximum thrust bounds the region of sustainable maneuvers (i.e, by definition, the thrust boundary). Along with the maneuver performance envelope (V-n diagram), this determines which maneuver states are sustainable, which are achievable instantaneously, and which are unattainable.

With the known relationships between True airspeed (V) and cockpit load factor (n) on radius of turn(R) and turn rate (ω), a generic carpet plot can be made. For a specific altitude, M can be used instead of V to plot the relationships. The Ps=0 curve can then be overlaid on this plot as shown.

The above plot yields three Mach numbers of interest. The point where Ps = 0 curve is tangent to a constant load factor line (point a ) yields the Mach for max sustained g for that configuration. The peak of Ps=0 curve (Point b) yields the Mach for maximum turn rate, and the point where the Ps = 0 curve is tangent to a value of constant turn radius (Point c) is the Mach for minimum turn radius. By examining the Ps = 0 plot above, it can be seen that for each level of load factor there are two Mach values where the aircraft can stabilize. The higher one is called front side and the lower one is the backside ( ..of the curve). [Recall the drag polar – thrust line intersection]

Thrust Limited or Lift Limited ?!!..

The thrust limited turn is one in which the aircraft thrust is insufficient to maintain the turn up to the lift limit of the wing. The lift limited turn is one in which the thrust capability to sustain a turn exceeds the capability of the wing to generate lift.

We can superimpose a Ps = 0 curve on the V-n diagram to examine the difference between thrust and lift limited turns.

Note that Ps = 0 plot A extends to the left of the lift limit boundary. This shows that A at a given load factor, would be accelerating (positive Ps) as the aircraft stalled. Whereas the Ps =0  plot of B indicates that at the same load factor, the aircraft would be a ‘negative’ Ps =0 (meaning Ps <0) when it reached the stall. In other words,

• the lift limits sustained turn capability in case A, and
• the thrust limits sustained turn capability in case B.

To determine the limiting factor of the aircraft, we have to examine which parameter, at a given airspeed, is reached first (stall or Ps = 0) at a set load factor.

In the next and final part we shall discuss the flight testing for investigation into the lift and thrust boundaries

This is the third part of a four part tutorial.

PART-4: Flight Testing for Lift & Thrust Boundaries

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