Category Helicopter Performance, Stability, and Control

The following information has been graciously provided by the manufacturer of each helicopter.

AGUSTA A1Q9

[1] (B2-x20)

[2] Constant chord

• Linear twist

[3] 0O, collective pitch that is required to produce enough rotor thrust to balance the weight and to compensate for the inflow.

• 01} blade twist.

• ax and bx , tilt of the tip path plane with respect to the shaft that is required to produce enough moment about the center of gravity to balance or trim the helicopter.

• Ax and Bv cyclic pitch required to compensate for the unsymmetrical velocity pattern and to produce the amount of als and bXs required to trim.

[4] = Іо^Уо + 4h + 2уг + 4уз + 2ул + 4уъ + 2Уб + 4уі + 2у% + 4y* + Уі

where in this casсу is the calculated value of dCT/o/dr/R. The root and tip losses can be handled as trapezoidal corrections to the total integral:

A method for making a rough estimate of the vertical drag penalty in hover was given in Chapter 1. This method will now be refined in order to raise the confidence level in the hover performance calculations. The method consists of the following steps:

• Divide the plan view of the airframe into segments.

• Estimate the drag coefficient of each segment as a function of its shape.

• Determine the distribution of dynamic pressure in the rotor wake.

• Sum the effects of each segment.

[6] Calculate the rotor thrust as the sum of the weight and the vertical drag.

• Correct the rotor power at this thrust for the "ground effect” due to the airframe.

The questions most asked of the helicopter aerodynamicist concerning auto­rotation are:

• How much does the rotor speed decay following a power failure before the pilot can react?

• What is the minimum steady rate of descent?

[8] How far can the helicopter fly following the power failure while the pilot looks for a – suitable landing spot?

The interest of the helicopter aerodynamicist in airfoils is either for the analysis of an existing rotor or for the design of a new one. In the first case, he may acquire the data he needs either directly, from two-dimensional wind tunnel tests or from whirl tower tests of a rotor with the specific airfoil, or indirectly, from test results of similar airfoils modified by empirical or theoretical means. For the design of a new helicopter, he may select one of the many airfoils already investigated or design an entirely new airfoil to incorporate characteristics he considers desirable. Since a blade with a good airfoil costs little or no more to build than one with a poor airfoil, there is strong motivation for improving airfoils even if the expected performance benefits are relatively small. A good airfoil for a rotor has:

• High maximum static and dynamic lift coefficients to allow flight at high tip speed ratios and/or at high maneuver load factors.

[10] A high drag divergence Mach number to allow flight at high advancing tip Mach numbers without prohibitive power losses or noise.

• Low drag at moderate lift coefficients and Mach numbers to minimize the power in normal flight conditions.

[11] +

Since both a0 and vl are direct functions of rotor thrust:

AAx = (n — 1) Л.

Maneuver ‘ 7 1 level flight

[12] Plot pitching moment versus angle of attack with stabilizer off and with stabilizer on at several incidence settings, as in Figure 8.16 (page 502).

• At each intersection the lift of the horizontal stabilizer is zero so the downwash angle must be equal to the geometric angle of attack of the stabilizer:

£fH CLp + Ifl

• Plot Єрн versus aF and determine ePa o and (deF/daF)H Span Efficiency Factor

Since the stabilizer lift distribution is usually strongly affected by flow irregularities coming back from the fuselage and rotor, it is not certain that

[13] far, this study has been limited to the longitudinal mode, but it is evident that the lateral mode in hover could have been treated in the same manner by using the moment of inertia in roll instead of pitch in the equations. For a simple analysis, it is again necessary to assume that the pilot holds heading by adjusting tail rotor

Design gross weight, G. W. Minimum operating weight Power plants Fuel tank capacity Parasite drag area, /

Vertical drag ratio, Dv/G. W.

Main Kotor Radius, R Disc area, A Tip speed, flR Chord, c No. of blades, b Solidity, a Blade area, Ah Airfoil Twist, 0г

Blade cutout ratio, xQ Hinge offset ratio, f/R Blade-flapping inertia, ly Lock no., у

Polar moment of inertia, J Shaft incidence, /

Height above C. G., hM

Ml L-STD-1374 PART l-TAB GROUP WEIGHT STATEMENT PAGE MO

NAME WEIGHT EMPTY MODEL

DATE REPORT

MIL-STO-1374

З

MIL-STD-1374 PART I-TAB

NAME

DATE

os

^1

^1

Fuselage Station

FIGURE A.1 Example Helicopter

FIGURE A.4 Fuselage Lateral-Directional Aerodynamic Character­istics

Just as a horizontal stabilizer is not absolutely necessary on a helicopter, neither is a vertical stabilizer, since the tail rotor alone can produce adequate directional stability. Nevertheless, most modern helicopters do have a vertical stabilizer. Depending on the helicopter, the vertical surface may be used to: streamline the tail rotor support, supplement the directional stability produced by the tail rotor, unload the tail rotor in forward flight, support a T-tail, or stabilize the fuselage in case the tail rotor drops off completely.

Because of the low dynamic pressure behind the fuselage and hub, as illustrated by the measured data of Figure 8.9, many designers use vertical surfaces on the ends of the horizontal stabilizer to put them into relatively clean air. In this configuration, they are also out of the way of the tail rotor’s induced flow, and

they increase the effectiveness of the horizontal stabilizer by acting as end plates. This configuration, however, is probably heavier than a centrally located fin.

As long as the vertical surface is there, it can be used to unload the tail rotor in forward flight by including camber or an offset incidence angle. The primary purpose is to increase the fatigue life of the tail rotor by minimizing the oscillatory flapping loads. Unloading the tail rotor in this manner may not save on total power, since now the induced drag of the vertical surface must be overcome by the main rotor. If the span of the vertical surface is much less than that of the tail rotor, the power tradeoff will probably be unfavorable.

Some recent specifications for combat helicopters have asked the designers to configure the aircraft so they could be flown home in case the tail rotor were completely shot off. In a sideslip, a big enough vertical surface could produce enough antitorque force to do this. Unfortunately, several development programs, such as those reported in references 10.8 and 10.13, have demonstrated that this much area can cause large blockage problems, especially in sideward flight. As a result no helicopter has this desirable characteristic at this writing.

A wing is a convenient place to hang external stores or to carry fuel. From an aerodynamic standpoint, however, it is usually detrimental unless used in conjunction with a forward propulsion system in a compound helicopter configuration. The penalty in hover is due not only to the structural weight of the wing but also to its aerodynamic download. In high-speed forward flight, a lifting wing that is used to unload the rotor may actually increase the retreating blade angle of attack, leading to premature stall. This happens because the partially unloaded rotor must be tilted further forward to produce the required propulsive force that now must compensate for the drag of the wing in addition to the drag of the basic helicopter. This requires increased collective pitch to overcome the inflow and increased cyclic pitch to keep the rotor in trim. In many applications, these two effects will combine to increase the retreating tip angle of attack more than the decrease made by unloading the rotor. In some cases, if the requirement is for a high transient load factor during a pullup, then the addition of a wing may be justified.

If a wing is to be used, its incidence should be chosen so that at high speed it is operating at its best angle of attack. By analogy with biplanes, for minimum induced drag, the wing and the rotor should be sharing the lift such that their ratio is:

The wing should be located with its aerodynamic center behind the most aft center of gravity of the helicopter so that it acts as a stabilizer rather than a destabilizer.

A large wing may cause a problem in autorotation. If the wing supports a large portion of the gross weight, the rotor will be starved for thrust and will not be able to maintain autorotation. If this situation is possible, some means of reducing wing lift will have to be used, such as reverse flaps, spoilers, or incidence changes.

Auxiliary propulsion in the form of propellers, ducted fans, or jet engines can be used to relieve the rotor of part or all of its propulsive requirement. The limit to this is the wingless autogiro, where no power at all is required by the rotor. The use of auxiliary propulsion to overcome drag reduces the needed forward tilt of the rotor, thus decreasing its collective and cyclic pitch requirements and relieving the high angle-of-attack pattern on the retreating side. This permits this type of aircraft to operate at very high tip speed ratios. Autogiros built in the 1930s routinely operated at tip speed ratios above 0.5, which is considered today to be the upper limit for "pure” helicopters.

An auxiliary propulsion system acting as a separate, controllable longitudinal force system can be used to change the aircraft pitch attitude at any speed. This is especially attractive for combat helicopters. In a hover, for example, this type of helicopter can be held either nose up or nose down to increase the usable field-of – fire. Another use is as a speed brake in forward flight. This is a valuable attribute where rapid and precise decelerations and descents are required to accomplish a mission.

The power to operate the propulsive devices depends on their thrust-to – power ratio. For propellers and ducted fans, this ratio is primarily a function of their diameter—the bigger, the better. Such a system does have its disadvantages, of course. Its weight subtracts from the payload that can be hovered; unless it is declutched in hover, it will reduce the power available to the main rotor, thus creating an even higher payload penalty.

The compound helicopter is even more vulnerable than the pure helicopter to the generality that whatever helps the high speed capability hurts the hovering capability, and vice versa.

The complexity and weight penalties of compounding by using both a wing and an auxiliary propulsion system are justified only when the aircraft require­ments combine higher speeds than can be achieved by a pure helicopter with helicopter-type performance in the lower speed regimes. If the rotor is completely unloaded, all the limitations based on blade element angles of attack are eliminated. At some forward speed, the advancing tip Mach number will approach drag divergence; at that point, however, the rotor can be slowed down to alleviate even this problem.

Despite the possibility of unloading the rotor completely, analysis shows that a lifting rotor acts as an efficient large-span wing compared to the typical wing that might be used on this type of configuration. For most effective use of the power, the main rotor should be loaded as highly as possible. This is done by adjusting the collective pitch to some value above flat pitch. In this sense, the collective control is something like the flap setting on an airplane.

The U. S. military has developed a standard weight reporting format known as a Group Weight Statement. The weight equations given earlier have been applied to the example helicopter and its Group Weight Statement is included in Appendix A.

The best position for the center of gravity on a single-rotor helicopter is slightly ahead of the main rotor shaft. Even when the designer has good intentions and achieves this goal during preliminary design, experience indicates that before the helicopter is ready for production, its average center of gravity (C. G.) will have drifted aft and settled down somewhere behind the shaft. In some cases, this aft C. G. position is forced by design considerations even during preliminary design. A classic example of this is the Sikorsky UH-60A. As explained in reference 10.13, this helicopter was limited in overall length by the requirement to load it into a C-130 without major disassembly. With the rotor sized by the vertical climb requirement, the air transportability requirement dictated a short nose. This and the desire to carry all the fuel behind the main cabin, led to a center of gravity range of more than 15 inches; all located aft of the main rotor. Sikorsky more or less satisfactorily solved the resultant trim problem by canting the tail rotor, as explained during the discussion of tail rotor design.

The longitudinal position of the center of gravity of the empty helicopter is calculated from the sum of the static moments about some arbitrary point contributed by each group that makes up the empty weight divided by that weight.

The arbitrary point should be selected ahead of and below the nose so that all parts of the aircraft will have positive locations. Figure 10.10 shows the scheme as it applies to the example helicopter. Since the center-of-gravity position with respect to the main rotor is of prime importance, it is convenient to chose the origin so that the hub falls on an easily remembered point. For the example helicopter, this has been chosen as Fuselage Station 300 and Waterline 200. The calculation that yields the center-of-gravity position for the empty helicopter is presented next.

Calculation for Center-of-Gravity Position of Empty Example Helicopter

Note that as the design progresses, this calculation can become more and more precise by expanding it to account for the weight and location of each component of each group.

A plot of the longitudinal center of gravity position as a function of gross weight is known colloquially as the "C. G. potato.” It is generated by loading items of the useful load into the empty helicopter in the most forward manner and then in the most aft manner. Figure 10.10 shows the location and weights of the useful load items of the example helicopter. The fuselage station for the center of gravity as the loading proceeds is obtained from the equation:

N

Total Moment, empty + ^ JF„(Fuse. Sta)„

Fuse. Sta. n = ———————————- ——^——————

Empty Weight + J Wn

n =1

The resulting C. G. diagram is shown in Figure 10.11 (page 667) for loading starting from the front and for loading starting from the rear. Any other loading sequence would place the center of gravity inside the diagram. For this case, the maximum possible C. G. excursion is 28 inches ahead and 37 inches behind the main rotor. This extreme result of "indiscriminate loading” might be marginally acceptable for the forward condition, where a nose-up rotor flapping of about 6° would be required to trim, with substantial resulting blade loads. The far aft position would certainly be unacceptable because of even greater flapping as well as the destabilizing effect of the aft C. G. In operation, a helicopter of this size would probably be limited to not more than ±10 inches from the shaft, which means that the loading would have to be monitored and controlled by the crew.

HOW TO’S

The following items can be evaluated by the methods of this chapter:

Sikorsky has used tail rotors canted 20° down to the left on both the UH-60A and the CH-53E, as may be seen in Appendix B. Reference 10.13 cites the advantages

of this concept as the more efficient use of hover power sfnce the tail rotor thrust vector has an upward component, the ability to tri^ with a center-of-gravity position behind the main rotor, and the alleviation of unsteadiness in the vortex ring state in sideward flight. The primary disadvantage is the development of a longitudinal response with directional control inputs. This can be mechanically compensated for in one flight condition, but not in all. In weighing the advantages against the disadvantages, reference 10.13 concludes: "Although the UH-60A control and Automatic Flight Control System (AFCS) design solved the coupling problems associated with the canted tail rotor, the feeling is that unless forced into an aft c. g. problem by other constraints, the canted tail rotor should not be considered.”

A horizontal stabilizer is not absolutely required on a helicopter. Helicopters designed before I960 were unlikely to have them but were nevertheless considered successful. A stabilizer does, however, make an order-of-magnitude improvement in the flying qualities in forward flight and is used routinely in modern designs.

The analytical methods of Chapters 8 and 9 can be used for guidance in choosing the area and fixed incidence that will provide acceptable static and dynamic longitudinal stability in high-speed forward flight at the most aft center – of-gravity position, but the stabilizer s effect on hover and low-speed flight should also be considered. The primary effect is the possibility of erratic longitudinal trim shifts when going from hover to forward flight if the main rotor wake impinges on the surface and produces a high download. There are three possible factors that might contribute to this problem: a large fixed incidence stabilizer located behind the main rotor wake in hover, a high rotor disc loading, and low control power. When one or more of these factors is significant enough to create a problem, designers have adopted three different approaches. One, favored by Bell, places the surface forward on the tail boom so that it is in the rotor wake in hover and thus does not experience a sudden change in download during the transition. The second method uses a T-tail with the horizontal stabilizer mounted at about the same height as the main rotor so that it does not feel the wake until high speeds are reached where the induced velocities are small. The third approach uses a movable incidence stabilator that can be aligned with the local flow during transition either by being permitted to float free or by being programmed as a function of flight parameters. A discussion of the development of the Hughes AH-64, which had both a T-tail and a stabilator during its development, can be found in reference 10.14. In this case, the incidence of the stabilator was programmed to be a function of air speed, collective pitch, and aircraft pitch rate, as shown in Figure 10.9. The air speed input is the primary means of changing incidence during the transition. The collective pitch input is used to reduce the upload in autorotation, and pitch

Source: Prouty & Amer, “The YAH-64 Empennage and Tail Rotor—A Technical History,” AHS 38th Forum, 1982.

rate is used to make the surface into an "active control,” which allows its area to be significantly less for the same level of dynamic stability than if the incidence were fixed.

A similar stabilator schedule for the Sikorsky UH-60 is found in reference

10.15.

The pitch range designed into the tail rotor must provide for both maximum antitorque capability and adequate control in all flight regimes. On the negative side, the critical condition is directional control in autorotation. Experience indicates that a value of —10° to —15° at the 75% radius station is adequate for this. The tabulation of Appendix В lists values used on contemporary heli­copters.

On the positive side, the collective pitch must be at least high enough to develop the maximum value of CT/oT used earlier when calculating the required tail rotor solidity. A check should then be made for right sideward flight conditions to determine if this pitch is high enough to account for the increased inflow while still providing a thrust adequate for both antitorque and maneu­vering. Choosing a higher value than necessary will cause a problem for the designer of the tail rotor drive system. During a fast hover turn with torque, the tail rotor pitch is very low. If the pilot quickly stops the turn by using maximum pitch, the angles of attack on the tail rotor blades will initially increase by that change before the final inflow pattern an establish itself. This angle may be enough to stall the tail rotor transiently, with a resulting high torque spike in its drive system. Designing for a torque that is caused by a maximum pitch higher than absolutely required for normal operation will increase the helicopter’s weight and cost. A discussion of this problem faced during the development of the Hughes AH-64 will be found in reference 10.8.

Dividing the total blade area up into a finite number of blades is the next decision. The fewer the blades, the cheaper the tail rotor is to build and maintain; but if the

result is a very stubby blade, high tip losses may penalize performance. Most designers will select the number of blades to satisfy an aspect ratio (radius/chord) criteria of 5 to 9.

TWist

High twist is beneficial on the main rotor for improving hover performance and for delaying retreating tip stall in forward flight. High twist also helps tail rotor hover performance; but, as mentioned in the discussion of tip speed, even untwisted tail rotor blades will not have high retreating tip angles of attack. Thus part of the usual advantage of high twist does not apply. A further consideration, reported in wind tunnel tests in reference 10.12 and in flight test observations in reference 10.8, indicate that untwisted rotor blades go through the vortex ring state more gracefully than twisted blades do. This then is a consideration regarding the ability of the new design to fly steadily in sideward flight.

With the diameter and tip speed chosen, the next task is to choose the tail rotor solidity. The criterion that most often dictates this is the ability of the tail rotor to balance the torque of the main rotor in a full-power vertical climb at a specified density altitude with at least a 10% thrust margin remaining for maneuvering before stalling. During the analysis of lateral-directional trim in hover in Chapter 8, it was shown that the required value of tail rotor thrust just to balance main rotor torque was:

Qm

It ~ їм

From this, the minimum tail rotor solidity can be obtained as:

CT/oTmxTRj{ilR)j^lT — lM)

The critical condition may be either at low altitudes, where the power available is a maximum, or at high altitudes, where the density is low. The minimum solidity, of course, should be increased for design purposes to account for the 10% maneuvering margin and for any blockage effects of the fin, as discussed in Chapter 4. A further check should be made for right sideward flight (assuming "American” rotation of the main rotor) since the tail boom drag may be high as a result of main rotor wake impingement, as discussed in reference 10.11. The required blade area depends not only on the maximum thrust but also on the maximum usuable value of Cr/ox, which in turn depends on the airfoil section. It is generally true that compressibility effects on tail rotors are limited to relatively small power penalties, and so it is permissible to choose a thicker airfoil for the tail rotor than would be desirable for the main rotor, in order to take advantage of the higher maximum lift coefficient.

The charts of Chapter 1 give the maximum predicted values of CT/o for rotors with the NACA 0012 airfoil. The charts can be used directly if the actual airfoil has similar maximum lift characteristics, or they can be modified up or down to account for the difference between airfoils as measured in two-dimensional wind tunnel tests.

The choice of tip speed for the tail rotor is usually based on just two conflicting considerations: a low tip speed minimizes noise, and a high tip speed minimizes weight. Aerodynamic factors are less important than they are on the main rotor. High tip speeds are not so likely to generate serious Mach tuck problems because the blades are stubbier and thus torsionally stiffer; and low tip speeds are not likely to produce retreating tip stall problems because the tail rotor operates in a nonpropulsive mode with a more benign angle of attack distribution. How designers have decided in the past is indicated by the tail rotor tip speeds used on contemporary helicopters as listed in Appendix B.

The choice of tail rotor diameter will be influenced by the following considera­tions:

Advantages of a Large Diameter Advantages of a Small Diameter

Low power required in hover Low tail rotor and drive system weight High directional control power Helps solve perpetual tail heavy problem High stability in forward flight Low hub drag

Although these conflicting considerations would seem to leave every designer on his own, a study of existing helicopters reported in reference 10.10 indicates a remarkably good relationship for the ratio of tail rotor diameter to main rotor diameter as a function of the main rotor disc loading. Figure 10.8 shows that small tail rotors are used with low main rotor disc loadings and big tail rotors are used with high disc loadings. There are probably three reasons for this:

1. With a high disc loading, the main rotor is requiring so much power that saving power with a big tail rotor is attractive.

2. With a low main rotor disc loading, the tail boom is very long and the difficulty of balancing the helicopter with the center of gravity near the main rotor is made easier by using a small tail rotor.

3. When looking at other helicopters, the observed trend becomes aesthetically pleasing.

The trend in Figure 10.8 is expressed approximately by the equation:

DT _ 1

DM ~ 7.15 — .27 D. L.M

It may be significant that both the Hughes AH-64 and the Bell OH-58 as originally designed had directional control problems that were made less severe by increasing the diameter of the tail rotor to make it closer to the trend line.

Source: Wiesner & Kohler, “Tail Rotor Design Guide,” USAAMRDL TR 73-99, 1973.

Many designers in the past compromised the main rotor transmissions to obtain a "traditional” direction of rotation, although that mattered very little, while letting tail rotors turn in either direction even though that was an important decision. Experience gained during several recent development programs has proven that tail rotors should rotate with the blade closest to the main rotor going up to alleviate the instability and unsteadiness associated with the tail rotor vortex ring state in sideward flight (left sideward flight for helicopters with the "American” direction of main rotor rotation). A discussion of this subject will be found in Chapter 2. Figure 2.10 showed the dramatic improvement resulting from reversing the direction on the Lockheed AH-56. With the original—and wrong—direction, going from hover into left sideward flight not only required an unstable pedal travel but actually used up all the available control before reaching 15 knots. Not shown was the great unsteadiness that existed from 10 to 30 knots. When the rotation was reversed, the pedal displacement became stable, a good control
margin remained, and flight was much steadier. Similar experiences can be cited by engineers at Bell, Westland, Aerospatiale, and Mil. This main rotor/tail rotor interference phenomenon is not well understood, and as yet there is no analysis that will provide quantitative results.

If steadiness in left sideward flight is not enough reason for selecting a preferred direction, perhaps noise reduction is. Tests performed at Westland and reported in reference 10.9 have shown that noise in forward flight is lower if the tail rotor blade on top is going aft since it is not slicing through the main rotor wake quite so violently..