Category Helicopter Test and Evaluation

Delay time is simply defined as the time between an engine failure and the pilot commencing corrective action by rapidly lowering the collective lever. Hence the maximum delay time is the delay that causes the rotor speed to reach the minimum power-off transient value before rising to achieve a stable autorotative condition. Since entry into power-off flight will inevitably involve some change in rotor speed it is common practice to relate key instances to the corresponding rotor speed, see Fig. 2.26.

Having worked-up to a repeatable collective lever lowering rate (by routinely acquiring zero ‘g’ for example) and with reference to a sensitive rotor speed gauge a test pilot will incrementally reduce NRl until NR3 equates to the transient power-off minimum rotor speed. Alternatively the test may be curtailed before the minimum is reached if a sufficiently long delay time has been demonstrated. The model developed in the previous section can be used to show the effect of increasing delay time, see Fig. 2.27. Note that a maximum delay of 1.5 s is possible with the example rotor. Figure 2.28 shows the rotor speeds NRl and NRj in the form of an in-flight cross-plot or ‘how – goes-it ’ chart. Test teams often use this style of chart to get some idea of the effect of increasing delay time on the minimum rotor speed. They can, therefore, ensure that the minimum rotor speed limit is approached in a safe manner by using the chart to select the next incremental reduction in NR . It is worth reminding the reader that in flight the test team will use values of NR to progress the evaluation. The delay times would be determined from appropriate post-flight analysis.

Whilst the simplistic analysis detailed above gives a basic guide to the factors affecting the time taken for the rotor speed to decay to the minimum permissible value it does not take account of important additional factors. These include the action of the pilot in attempting to contain the rotor speed within limits and the effect of rate of descent on the angle of attack of the rotor blades. To investigate these effects further it is necessary to construct a more detailed model of a rotor entering a vertical autorotation. As before consider the three-quarter radius as being representative of the conditions on the complete rotor blade. Now:

T = L cos ф — D sin ф

Q = 0.75R(D cos ф + L sin ф)

Using basic aerofoil theory it can be shown that: L =1 pV0275 abcRa015

D = 2 PV2.15 bcRCD

Now the angle of attack and airflow velocity will depend on the blade pitch, the vertical velocity and the rotational velocity at the three-quarter radius. Assuming a linear twist :

00.75 = 00 + °.7501

and:

V0275 = (0.75R ))2 + (V + vih) 2

The effect of changes in thrust developed and torque required on the vertical velocity and the rotor speed can be determined by assuming constant acceleration over a short time interval, St:

[Vc ]t+st = [Vc ]t +[T ~mgl St m

[)]t + St = [)]t – Q St

A more detailed study of the situation following an engine failure (see Fig. 2.25) highlights the role of the rate of descent in changing the magnitude and direction of the forces acting on the rotor blades and thus the unbalanced torque causing the rotor speed to decay. It can be seen that the speed of a rotor initially operating at 35 rad/s, with an inertia of 6000 kg m2, stabilizes at 21.5 rad/s once the vertical rate of descent has reached 1500 ft/min. It should be remembered that the analysis presented ignores the effect of entry into the vortex-ring condition. In reality the pilot will attempt to arrest the rotor speed decay and contain the NR within narrower limits by rapid reductions in collective pitch. This has the effect of increasing the rate of descent and unloading the rotor blades thereby reducing, and ultimately reversing, the decelerating torque applied to the rotor. Since prompt action following an engine failure is often vital to success it is important to know if the pilot has sufficient time to identify a problem with the powerplant(s) and take corrective action. This is determined by measuring the delay time.

2.12.1.1 Minimum rotor speed and rotor inertia

It is vital that the RRPM does not decay too far following a loss of power as it may then be impossible to establish the aircraft in a stabilized autorotation. The rate of rotor speed decay is therefore a very important factor, and the minimum rotor speed below which recovery is impossible is of critical concern to the rotor system designer. It is rather difficult to determine the minimum rotor speed accurately but by making some reasonable assumptions it is possible to get a basic understanding of the issue. Suppose the minimum allowable rotor speed ()min) corresponds to the maximum mean lift coefficient achievable by the rotor (CLmax). Now the rotor thrust, T, is given by [2.25]:

T = 2 pV 2bcRCL

If the thrust is assumed to remain constant during the initial phase of the power failure [2.25] and the inflow velocity is small compared with the rotor speed, then:

P )2»m bcR3CLnom =

p nmin bcR3cL

max

L max

where )nom = rotor speed at instant of power failure and CLnom = average lift coefficient at instant of power loss.

In addition if the torque coefficient remains unchanged [2.25], then:

where Qnom = torque required at instant of power failure and Qmin = torque required at minimum rotor speed.

Hence the torque required to drive the rotor at any instant following the power failure will be given by:

2

Q = Q

nom

In the absence of any shaft power from the powerplants the torque requirement will tend to cause the rotor speed to decay. Thus:

Q

I

Reorganizing, integrating and applying the initial condition that at t = 0, ) = )nom, gives:

t = I)2m /1 _ 1

Qnom V ^ ^nom /

Therefore, the time taken for the rotor speed to reduce to the minimum permissible value can be obtained from:

Thus we see that tmin is dependent on the rotor inertia, the rotor speed and torque requirement at the instant of power loss and the ratio of the thrust required to the maximum thrust the rotor can produce. Consider the effect of changing some of these variables on a 4-bladed rotor of 6.5 m radius and 0.4 m chord with a lift curve slope of 6 per radian operating in the hover, see Table 2.1. Note that from the simplistic analysis detailed above the minimum rotor speed for this example helicopter is 18 rad/s based on a nominal mass of 5000 kg. The data in Table 2.1 indicates that the decay time can be lengthened by increasing the rotor inertia, increasing the nominal rotor speed or by reducing the thrust that the rotor has to produce under normal power-on conditions.

Assessment of rotorcraft performance following an engine failure is necessary to ensure its safe operation. For single-engined rotorcraft an engine failure will result in

a forced, or engine-off, landing (EOL). For multi-engined helicopters, however, it is still necessary to assess the ability of the aircraft to continue flight particularly in critical areas of the flight envelope. In any event the pilot must react quickly to avoid loss of control and prevent the rotor speed from decaying below acceptable minimums. As the power fails directional control will go out of trim and the residual anti-torque moment will yaw the helicopter, generating additional sideslip that may possibly induce a roll if no corrective action is taken. (An undemanded yaw may be the first indication to the pilot that a power failure has occurred.) The rotor speed decay rate can be estimated by applying simple rotational mechanics to the problem. Now:

Q = I®

Thus:

d) Q

оо = — = rotor speed decay rate =—-j

where Q= rotor torque and I= moment of inertia of rotor system.

Thus reducing the rotor torque will reduce the rate of rotor speed decay. This can be achieved by reducing the blade pitch in order to decrease the rotor drag. In steady autorotation a given value of collective pitch will cause the helicopter to settle on a unique descent speed and rotor speed combination. The pilot can therefore control the rotor RPM using collective pitch – the lower the pitch the higher the rotor speed – but in practice the usable range of RRPM is very restrictive. If the rotor speed is too low the blade will stall and lose lift; too high and there will be excessive loading on the rotor hub and blade roots. The safe range is typically within 80% and 120% of the nominal power-on speed for transient excursions and between 90% and 110% for stabilized conditions.

Empirical measurements suggest that for a conventional helicopter significant penetra­tion into the vortex ring condition can be made without hazard. It is possible therefore

to examine the incipient stages of the condition without compromising a safe recovery. Any theoretical vortex ring boundary should therefore reflect this reality by showing contours of increasing vortex strength. Model tests on a rotor, with — 8° of linear twist, operating at a range of collective pitch settings in a vertical descent highlight a correlation between vortex strength and thrust fluctuation [2.24], see Fig. 2.22.

The trend in thrust fluctuations implies that the worse case situation occurs with a RoD equal to approximately 0.8vih, slightly lower than the theoretical value of vih. Figure 2.22 also shows that for rates of descent less than 0.3vih and greater than 1.5vih only 1% thrust fluctuation occurs which might be equated to the incipient stage of the vortex ring condition. Based on the vertical flight data shown in Fig. 2.22 and using the boundary shape suggested by Peters and Chen [2.22], a series of contours can be drawn (Fig. 2.23). Note that if the rate of descent is low (around 0.5vih) glideslopes steeper than approximately 60° will cause the helicopter to enter the incipient stage of the vortex ring state. Also note that if an approach angle of less than 10° is used vortex ring can be almost completely avoided thus the simple rule-of-thumb of ‘no more than 500 ft/min below 30 kts’ is sound since it gives an approach angle of 9°. Figure 2.24 presents the same information in a slightly different manner and also illustrates the 30 kts/500 ft/min rule of thumb for vih between 15 m/s and 50 m/s. Here normalized glide velocity (Vg/vih) and glide angle (y) are used to show the vortex ring boundary. The figure clearly shows that for glide angles of less than 60° incipient vortex ring can be completely avoided. Also if a modest rate of descent (around °.3vih) is generated from the hover (glide angle equals 90°) then the vortex ring condition can be explored with a degree of safety provided the helicopter is sufficiently high to initiate recovery by generating forward speed. Note that for rotorcraft with high disk loading and consequently high values of vih the rule of thumb cannot be guaranteed to keep the helicopter clear of the vortex ring condition.

The ‘Wolkovitch’ boundaries although based on a detailed representation of the vortex-ring condition fail to match empirical data. Experience gained from wind tunnel experiments and flight test suggests that the vortex-ring condition can be escaped by allowing a forward velocity component to develop. Thus the lower boundary should show that as the horizontal velocity (q) is increased higher rates of descent (q) are required to enter the vortex-ring state. This can be achieved if the Wolkovitch approach is modified to account for the effect of forward speed on the wake geometry, see Fig. 2.20.

Figure 2.20 shows that the magnitude and direction of both the freestream flow and the wake can be represented by vectors:
a = freestream flow = vV2 + Ц2 b = wake = V^2 + (v _ q)2
Now the dot product (b^a) can be thought of as the magnitude of one vector multiplied by the component of the other vector in the direction of the first. Thus in this context the dot product represents the magnitude of the wake velocity multiplied by the component of the freestream in the direction of the wake. Hence:
b-a TbT
component of freestream flow in direction of wake
b-a_ p x p + (v _ q) x_ q = + q(q _ v) Ib I Vp^+Cv^n)2 Vp2 + (v _ q)2
The Wolkovitch approach assumes that the vortex-ring state begins when the velocity of the vortex tube relative to the actuator disk is zero, that is:
t2 + q(q _v) VTJT(v_f
Therefore: p2 + q(q _ v) + p2 + (v _ n)2 = 0 2p2 + 2q2 + v2 _ 3qv = 0
or:
3 1 p2 = 2 qv _ q2 _ _ v2
(2.23)
As before from momentum theory, 1 = v2(p2 + q2 _ 2qv + v2), thus:
1 = v2 (3qv _ q2 _ 1 v2 + q2 _ 2qv + v2 ) = v2 (1 v2 _ 1 qv
2 = v4 _ qv3 2 q = v v3
And, returning to Equation (2.23):
A V 1 2 = 1 4 v v3 ) 2v v2 v6
3	2

Therefore the lower vortex-ring boundary is given by:

2

ц = v——

VJ

2 1 4

p = 7 – V6-

The upper vortex boundary is obtained in an analogous manner, by replacing v with kv in Equation (2.23). As mentioned above, Wolkovitch recommended k = 1.4 as denoting the edge of the fully developed vortex ring condition. Peters and Chen [2.22], on the other hand, prefer k= 2 as indicating the condition beyond which no vortex is present anywhere in the streamtube. Hence Equation (2.23) becomes:

31

p2 = 2 ^2v) — ц2 — ^(2v)2 = 3^ — ц2 — 2v2

Once again from momentum theory, 1 = v2(p2 _|_ ц2 — 2^ + v2), thus: 1 = v2(3^ — ц 2 + ц2 — 2v2 — 2цv + v2)

1 = v2^v — v2) = — v4

1

Ц = v + —

v3

Consequently:

Therefore the upper vortex-ring boundary is given by:

1

Ц = v + —

v3

These boundaries are shown in Fig. 2.21. Clearly the lower boundary approximates to the empirical trend whereby with forward speed higher rates of descent are required to enter the vortex-ring state. There are, however, two issues that remain unresolved. First the upper and lower boundaries should predict the same forward velocity, above which vortex-ring can be completely avoided. Secondly the upper boundary is based on entry to the windmill-brake state (Vv = 2vih in the hover) whereas the lower indicates entry into fully developed vortex-ring (V = 0.7vih in the hover). In order to resolve these problems the lower boundary must be further modified to start at p = 0, ц = 0. This is achieved by noting that a vortex will appear in the streamtube when (b-a)/ Ib|< 0. Thus the lower boundary should be given by:

p2 + ц(ц — v)

V^2 + (v — ц)2

Applying momentum theory gives:

1 = v2(^v — Ц + Ц — 2qv + v2)

1 = v2(v2 — цу)

1

Ц = v ——

Consequently:

^2=3v (v—УЗ)—(v—УЗ)— 2у2=У2—У6

Therefore the complete criteria, see Fig. 2.21, for the vortex-ring state are:

1

Ц = v±—

2 1 1

^ = 7 — У6

These criteria can be used to predict a complete and coherent boundary for the onset of the vortex ring condition [2.22].

Perhaps the most accurate predictions of the flight conditions that lead to vortex-ring can be obtained by considering so-called dynamic inflow [2.22]. Dynamic inflow attempts to account for the effect of the vortex-ring condition on the inflow character­istics through the whole rotor. Wolkovitch [2.23] analysed the vortex-ring state by considering a slipstream that is surrounded by a protective tube of vorticity, see Fig. 2.18.

It can be seen that the vortices descend at an average speed of 0.5 v — g or vi/2— Vg sin у relative to the rotor, whereas the rotor itself descends at a speed Vg sin у. Thus for low rates of descent the vortex-ring will move away from the rotor and steady flow can exist. If, however, the glide slope is too steep the relative velocity of the vortices will fall to zero and they will remain within the rotor disk resulting in the vortex-ring condition. This critical condition can be expressed in terms of a critical glide speed ^гіt:

Kdt 2 sin у

or normalizing using the induced velocity in the hover (vih): Vcrit sin у Vv

v

or:

(2.19)

To express Equation (2.19) in a more convenient form it is necessary to rewrite it in terms of horizontal velocity (Vf = Vg cosy) and vertical velocity (Vv = Vg siny). This is achieved by use of momentum theory, since:

T = 2p AvV’

Since noting that thrust and weight must balance both in a steady descent and in the hover (neglecting the effects of download and vertical drag), we can write:

vV ‘=^-7 = v2 2pA h

Now from Fig. 2.19 it can be seen that for a gliding rotor: V ‘ = W2 + (Vv – v, )2

Thus:

v2h = vi Vf + (Vv – v,)2 v2h = v, Vv2 + VV – 2Vvv, + v2 v4h = v2 (vf2 + v2 – 2vvv, + v2)

Now from Equation (2.18) the vortex-ring condition is entered when: 2Vv = v,. Hence the lower vortex-ring boundary will be represented by:

v4h = 4 v2 (vf2 + vv2)

1 = 4^2^2 + 4^4

Thus:

22^4 + 22^2^2 – 1 = 0

If the rate of descent is allowed to increase and the blade pitch is reduced the helicopter will eventually enter the windmill-brake state. Wolkovitch [2.23] recommended that the upper vortex-ring boundary be represented by:

1.4v

q = —

Again we can recast this equation, since:
< = v2(Vf + V – 2Vvvi + v2)

or:

1 = v2(^2 + q2 – 2^v + v2)

Therefore substituting for q using Equation (2.21) and simplifying:

302q4 + 702q2^2 – 492 = 0 (2.22)

It has already been seen that the vortex-ring state can cause a lifting rotor to lose effectiveness in descending flight. Likewise vortices can lead to tail rotor stall and a consequent loss of yaw control. Any situation that causes the tail rotor to pump air into an oncoming airstream has the potential to generate a vortex ring state. Sideways flight, rapid spot turns or out-of-wind hovering are situations when the tail rotor is operating in a state equivalent to either a climbing or descending rotor. If flow into the rotor opposes the inflow (the descending case) then a vortex ring may form which reduces the ability of the tail rotor to generate an anti-torque thrust. Depending on the size and loading of the tail rotor it may be possible for the pilot to detect the incipient stages of this phenomena by observing unusual activity in yaw or by feeling irregular buffeting of the tail cone. Failing either of these cues the pilot may only become aware that something is amiss when full pedal deflection has no effect in arresting an unwanted yaw rate. In this situation the tail rotor is effectively power settling and the only course of action left is to reduce the anti-torque requirement by either lowering the collective lever or closing down the engine(s).

1.8 POWERED DESCENTS

Prior to analysing the performance characteristics of a helicopter in an autorotation it is necessary to consider the limits on stable descent. Two basic conditions exist: descent under power characterized by the rotor imparting a downwards induced velocity vector on the upward moving flow, and autorotation when smooth momentum flow takes place with the rotor blades generating thrust via a transfer of energy from the airstream to the rotor. Descent under power from the hover or at low forward speed can lead to the potentially hazardous flight regime of vortex ring therefore determining the combination of airspeed and RoD that leads to the vortex-ring state is important.

Earlier the vortex-ring state was mentioned in association with purely vertical flight when it was concluded that for rates of descent between zero and 2vih, a vortex would exist somewhere in the streamtube passing through the rotor. This broad definition was further refined by the realization that stable rotor behaviour was only in question when a vortex existed close to the disk. Consequently the danger area was reduced to vertical rates of descent between 0.7vih and 1.5vih. It is now necessary to determine the effect of a forward speed component on the rates of descent that can generate this potentially hazardous situation.

In the hover the tail rotor will be rotating about a fixed point in space and will not, therefore, be subjected to any form of oncoming airflow. Thus the tail rotor power will be given by:

2 A + 8 pSTR ATR ()R)tR CD

2PA 8 TR TR TR D

1.7.4 Power required by the tail rotor in forward flight

In forward flight the tail rotor will be subjected to an oncoming air stream in much the same manner as the main rotor. If we ignore the effects of compressibility and

blade stall then it is possible to determine the tail rotor power increment using a similar approach as that taken for the main rotor [2.4]. Thus the tail rotor profile power will be given by:

and the total tail rotor power will be:

where the induced velocity viTR is given by:

Figure 2.17 shows a typical variation of tail rotor power with forward speed. The power is expressed as the ratio of the tail rotor power to the total power required. Note the rapid reduction in power with forward speed and that although there is an increase in power after a minimum is reached it is not as steep as the main rotor power. This trend is due to the effects of forward speed on the induced velocity of the tail rotor.

1.7.5 Unloading the tail rotor

The variation of power depicted in Fig. 2.17 has been calculated assuming that the tail rotor provides all the anti-torque force required (no fin contributions). Typically
as the forward velocity of a helicopter increases the vertical stabilizer or fin generates an aerodynamic force that acts in sympathy with the tail rotor thereby reducing its loading. In fact, for many helicopters operating close to their cruise speed, the tail rotor is completely unloaded with the fin providing all the anti-torque force required. Layton [2.4] quotes a recent military specification that requires that a helicopter be capable of an 80 knot run-on landing with no tail rotor. He concludes that the vertical stabilizer must generate sufficient sideforce at 80 knots to balance the main rotor suggesting that the tail rotor is fully unloaded at that speed and that above that speed reversed pedal is required.

The discussion so far has only been concerned with determining the power required by a single main rotor. Such a rotor system will generate a torque reaction in the fuselage and without some form of anti-torque device the fuselage will spin uncontrollably. The most common anti-torque system is a small rotor affixed to a tail boom and orientated so that it generates a moment as it rotates which acts in opposition to the torque reaction. Alternative systems based on ducted fans, or fenestrons, and pressurized air (the NOTAR) have been used with great success. It should be remembered that tail rotors are required mainly in low speed flight when there is insufficient airflow over the fin to generate a side force that can oppose the torque reaction.

The tail rotor power can be estimated by considering the torque it must oppose. The main rotor torque is responsible for the torque reaction and thus the tail rotor thrust can be found by a simple balance of moments. Therefore:

T і — q — PMR 1 TR »TR — QMR — 0

“MR

where, in forward flight:

pmr — pAMR ()R)Mr or, in axial flight:

PMR — pAMR ()R)Mr

MR