Category Helicopter Performance, Stability, and Control

INTRODUCTION [9] [10]

• A low pitching moment to minimize blade torsion moments and control loads.

• An aft aerodynamic center position to minimize the nose ballast required to balance the blade.

• Enough thickness for efficient structure.

• Easy-to-manufacture contours.

Unfortunately, because many of these requirements are conflicting, the choice of the best airfoil is not easy. (This situation is not unique to helicopters. For even such simple aircraft as sailplanes, there is no single airfoil that is considered optimum by a consensus of designers.) It is, however, possible to use wind tunnel Results to show the effects of various physical parameters on the static aerodynamic characteristics, and to a lesser extent on the dynamic aerodynamic characteristics, for use either in the analysis or in the design process. For a discussion of airfoils in general* especially as viewed by the airplane aerodynamicist, the reader is referred to reference 6.1.

Could a helicopter do steady inverted flight? Theoretically, yes; practically, no. A rotor could produce enough negative thrust to support the helicopter’s weight if it

were designed with enough negative collective pitch range. Some radio-controlled helicopter models have demonstrated this capability. No actual helicopters are rigged in this manner, for two reasons. First, it would require a collective control system with twice the normal travel and thus would require more space and weight than a normal system. Second, it would lose the important safety feature of having the down collective stop approximately corresponding to the right position for autorotation.

A rather complex indication of the maneuverability of a military helicopter is the return-to-target maneuver. In this maneuver, the helicopter passes over a spot (target) in forward flight and then tries to return to that same spot in the shortest possible time. The most critical ground rule is that the whole maneuver must be done at constant altitude. This simulates a nap-of-the-earth maneuver in which the "target” might be hostile and capable of destroying the helicopter if given the opportunity. Shorter times could be achieved if the maneuver were done with a zoom and a dive.

The optimum return-to-target maneuver at constant altitude consists of a combined deceleration and banked turn until the flight path is pointed back at the target followed by a level flight acceleration. A discussion of the maneuver in reference 5.18 points out that the deceleration could be increased by sideslipping to increase the parasite drag, but that flight tests using this technique revealed the danger of the pilot becoming disoriented and losing the target. For this reason, calculations should be done assuming a zero sideslip turn during the banked deceleration phase.

The maximum rotor thrust for the deceleration phase may be taken from the isolated rotor charts of Chapter 3 as the zero torque value at the upper stall limit (ACq/g = 0.008). The calculated ground path for the example helicopter doing this maneuver is shown in Figure 5.17. The procedure for the step-by-step calculation was as follows:

• At the initial tip speed ratio, find CT/amix from Chapter 3 rotor chart at Cq/g = 0, and ACq/g = 0.008.

• Find dxpp from charts.

• Calculate load factor:

Cl/®mix COS ClTpp

П — ———– ———-

Cyr/G

• Example Helicopter

• Initial Speed = 115 к

• G. W. = 20,000 lb

• Sea Level, Std. Day

• Acceleration Done at Takeoff Power Rating

• Deceleration Done in Autorotation at 100% rpm

• Calculate radius of turn:

• Calculate deceleration:

• At end of time increment, А/, calculate:

57.3 VAt,

— R——— ,deg

Ал – = VAt cos |/, ft Ay = V А/ sin |/, ft

• Repeat the procedure using the appropriate rotor chart as speed decreases until |/ is in the third quadrant and

tan |/ =

• If the speed drops below the autorotative limit as defined in Figure 5.12, a powered, steady turn at this speed should be used with the corresponding load factor taken as the ratio of maximum gross weight to actual gross weight from a power required curve such as Figure 4.24 at the appropriate engine power rating.

• Use an acceleration curve such as Figure 5.14 to continue the flight path until the origin is reached.

Helicopters are occasionally used for towing in special situations such as minesweeping, rescue, or salvage operations. The maximum towline tension that can be maintained is a function of the maximum rotor thrust and the angle the towline makes with the horizon. For most towing operations, the speed will be slow enough that hover conditions can be assumed to apply. The equation for the towline tension can be derived from the balance of forces acting on the helicopter as shown in Figure 5.18. When the equations for the vertical and the horizontal

components of the forces are solved simultaneously, the ratio of towline tension to gross weight is:

Figure 5.18 shows this ratio as a function of у for several ratios of maximum thrust to gross weight. The example helicopter at sea-level conditions can develop a maximum net rotor thrust of 27,800 lb out of ground effect, as shown in Figure

4.35. If it is flown at a gross weight of 17,000 lb and the towline is kept as flat as possible, it can maintain a towline tension of 22,000 lb.

Although aerobatic maneuvers are not considered to be normal helicopter flight conditions, loops and rolls are quite possible and have been done by a variety of designs.

Loops

A well-done loop does not put excessive loads on any of the aircraft components. Figure 5.19 shows a loop being done by an airplane, which, having a separate

propulsion device, is easier to visualize than a helicopter. The loop shown is idealized in that a constant speed is being maintained and the flight path is a perfect circle. The highest load factor is at the bottom of the loop, where it is only 2 g. Although no airplane or helicopter can do such a perfect loop, nevertheless any loop can be considered to be a relatively mild maneuver as far as loads go.

There is, however, a problem with respect to control. At the top of the loop, where the rotor thrust is zero or at least very low, all helicopters have reduced control power in pitch and roll; some—those with teetering rotors—may have none at all. If the pilot wants to make a cyclic correction in this situation, he might be surprised by how far he has to move the stick in order to get a response. The rotor will respond readily to the cyclic pitch and may tilt further than the designers made provision for. This is the classic setup for mast bumping on teetering rotors and for droop stop pounding on fully articulated rotors.

Reference 5.19 describes the piloting technique required to loop the Sikorsky S-67:

The loop is initiated from a slight dive at approximately 175 knots. The cyclic is pulled aft and collective lowered slightly to limit control loads. As the aircraft passes the 90° point (straight up), collective is added to maintain positive g. Airspeed at the inverted point in the maneuver averages 50 knots. The average time to execute a loop is 21 seconds. The load factor range for the maneuver runs from 2.5 plus g at the entry to 0.7 g inverted to 2.5 plus g during the recovery.

Rolls

A roll is similar to a loop, as shown in Figure 5.20. Most aerobatic airplanes rely on substantial fuselage sideforce to support them when the wings are straight up and down. The Sikorsky description of the maneuver in the S-67 is:

The roll maneuver is conducted to the right only to eliminate the problem of interference between the collective stick, pilot’s left leg, and the cyclic stick. Generally the maneuver is started from 150 knots in level flight. The aircraft is pulled to 20° nose up and the pitch rate is reduced to a minimum. As the airspeed reaches 130 knots, full right and a slight amount of aft cyclic are introduced. As the aircraft reaches the 270° point (three-fourths of the way through the roll) lateral cyclic is returned to neutral and additional aft cyclic is introduced to counteract the nose tucking that initiates at approximately the 270° point. The roll takes an average of 6 seconds to complete and the load factor ranges from 0.8 g to 1.7 g for the maneuver.

A study of the takeoff maneuver of helicopters too heavily loaded to hover out of ground effect is reported in reference 5.17. The conclusions of that study are that the shortest—and safest—takeoffs are achieved by accelerating into forward flight with as much ground effect as possible until reaching a rotation speed and then climbing out at that speed. An equation for the distance required to accelerate from hover to a given forward speed can be derived by considering that the acceleration capability is linear with speed. That this is a satisfactory assumption is shown by Figure 5.14. If x is the distance, then x is speed and x is acceleration. Between hover and VmiX (or xmix), the equation for acceleration is:

dx.

X = *HIGE + X

where dx/dx is a negative number.

The solution to this differential equation is:

Combining these last two equations gives the equation for the distance, x, required to accelerate to the speed, x:

Once the helicopter is accelerated to the rotation speed, x rot, a climb is started. The additional distance to climb over an obstacle with height h is:

where an approximation to the rate of climb from momentum considerations an be used:

where

Ah. p. h. p.avai| h. p. flt@irot

The total distance required for the maneuver is thus:

The optimum rotation speed depends on the height of the obstacle to be cleared. For a low obstacle the rotation speed will be low, but for a high obstacle (such as a mountain) the speed will be that for maximum climb angle, which could be found from a plot of rate of climb versus forward speed as in Figure 4.48 as the speed at which a ray from the origin is tangent to the curve. Calculations have been done for the example helicopter at a gross weight of 28,000 lb—a weight just above that at which hover out of ground effect is possible on a sea-level standard day according to Figure 4.35. Figure 5.16 shows the results of the calculations: First the distance required to clear a 50-ft obstacle as a function of the rotation speed, and then the optimum rotation speed and minimum distance as a function of obstacle height.

At speeds near hover, the deceleration capability is equal and opposite to the acceleration capability but in high speed flight, the capability may be limited by

Speed, knots

FIGURE 5.14 Maximum Longitudinal Acceleration Capability

rotor autorotation at some overspeed limit usually specified by structural design to be 10-20% over normal rotor speed. The procedure for calculating the deceleration capability under this limitation using the rotor charts of Chapter 3 are, as follow:

• Assume that CT/o = Cr/o.

• For even values of tip speed ratio, find 0O at Cq/o = 0.

• Find СЦ-рр from charts.

Calculate

COS ttTpp

• Find new 0O at Cq/o = 0.

• Convert CT/o to T at applicable tip speed.

• Convert Cj/a to H at applicable tip speed.

• Convert tip speed ratio into speed and dynamic pressure, q.

• Calculate the deceleration capability from the equation:

The ability to increase speed rapidly is important for many types of operations. The maximum level flight acceleration capability is primarily a function of the excess power available. At hover, the maximum acceleration is achieved when the maximum available rotor thrust is tilted until the vertical component is equal to the gross weight.

For this situation, the acceleration is:

where the maximum thrust is taken as equal to the maximum hover gross weight from a hover ceiling plot such as Figure 4.35. From hover, the equation can be used for accelerations rearward and sideward as well as forward. The acceleration capability in forward flight varies from the hover value to zero at Vmix. For speeds between hover and Vmix, the acceleration capability can be computed using the forward flight charts of Chapter 3 with the following procedure:

• Assume that CT/o = Cw/g.

• For even values of tip speed ratio, Find 0O at C2/omax. avaiL t0 main rotor.

• Find Отру from charts.

• Calculate

Cw/g

COS Ct’ppp

• Find new 0O at Cg/Gm, x lvii]..

• Find f/Ah corresponding to Ct/g and 0O.

• Convert tip speed ratio into forward speed and dynamic pressure, q.

• Calculate the acceleration capability from the equation:

acc=ft/scc2

Figure 5.14 shows the acceleration capability of the example helicopter at its design gross weight and at sea level standard conditions.

The ability of the pilot to make a safe entry into autorotation and a safe flare from autorotation depends on both his skill and the physical characteristics of the helicopter. Some helicopters have been found to be reasonably forgiving of sloppy piloting; others are dangerous even for skilled test pilots. This situation leads to the desire to quantify the autorotative characteristics with some sort of simple index number that will indicate how a given helicopter compares to other helicopters in this regard. Since both the entryinto autorotation and the flare from autorotation have to do with the kinetic energy stored in the rotor and the rate it is dissipated, a logical index is the equivalent hover time, or the time that the stored kinetic energy could supply the power required to hover before stalling. This and several other indices are discussed in reference 5.15 but the equivalent hover time appears to give the best correlation with the qualitative opinions of test pilots. In Reference 5.15 the equivalent hover time is called t/k. In this book it will be called /cauiv and defined as:

Although reference 5.15 does not specify what value to use for CT/omax, a reasonable approach would be to use the maximum calculated value from isolated rotor hover charts such as those in Chapter 1. Figure 5.13 is taken from reference

5.15 and represents the correlation of pilot opinion and equivalent hover time for several Bell helicopters. The figure indicates that the design goal for single-engine helicopters should be at least 1.5 seconds in order to be considered satisfactory. It is not yet clear what the corresponding goal should be for multiengined helicopters. For what it is worth, the twin-engine example helicopter has an equivalent hover time of 0.8 seconds. A later study* reported in reference 5.16 results in a simple autorotative index for the landing flare in the form:

where the first term corresponds to the altitude to which all the rotor kinetic energy could lift the aircraft, and the second term is the penalty associated with altitude and disc loading. The study as applied to Sikorsky helicopters indicates that an index as low as 60 is satisfactory for single-engine helicopters and 25 for twin-engined. The calculated autorotative index for the example helicopter is 39.

Equivalent Hover Time, tequiv. sec

FIGURE 5.13 Autorotative Ratings of Several Bell Helicopters

Source: Wood, “High Energy Rotor System,” 32nd AHS Forum, 1976.

The touchdown occurs at the end of the autorotative landing flare in which the helicopter has been brought from steady autorotation with moderate forward and vertical velocities to a condition with little or no velocity in either directiourAn idealized flare maneuver is illustrated in Figure 5.11. It starts with a cyclic flare at

constant collective pitch in which increased rotor thrust and its aft tilt are used to decrease both the vertical and the horizontal velocity components. At the end of this cyclic flare, the aircraft should be near the ground with its vertical component zero—or within the design sink speed of the landing gear—and with its horizontal velocity corresponding to autorotation at the angle of attack to which the rotor has been pitched. The maximum safe flare angle is the highest angle from which

the helicopter can be subsequently rotated nose down to a level attitude during the time that the rotor energy can be used to develop hovering thrust. (Two qualifications should be noted: The flare angle may be limited in an actual case if the pilot fears that he may lose sight of the ground in a machine without good downward visibility; and some helicopters do not have to flare to a level attitude if

they have a tail wheel or skid structurally designed to take high loads.) The final nose-down rotation and collective flare are done during the time required to use up the rotor energy and should result in both the vertical and horizontal velocity components ending up as low as possible.

A method for estimating the final touchdown velocity is as follows:

• Calculate the maximum allowable tip path plane angle of attack at the end of the cyclic flare as a function of the maximum nose-down pitch rate, @m2X, as limited by the longitudinal control power of the helicopter and the time available for the maneuver:

axppm„ = 0m„ А/, deg

where the maximum pitch rate is given by the equation:

• yQ

= —ABv deg/sec

where Bx is the forward cyclic pitch available. See Chapter 7 for the derivation of this equation.

The time for the maneuver is:

At =

In this equation, the maximum value of CT/o at the end of the maneuver can be taken from hover charts such as those in Chapter 1. If the resultant flare angle is more than 45°, use 45° as the value.

• Use Figure 5.12 to find the tip speed ratio, jilut0, at which autorotation can be sustained at the maximum flare angle while still developing a vertical component of rotor thrust equal to the gross weight. Figure 5.12 was produced from the isolated rotor charts of Chapter 3 by letting

Find the minimum touchdown velocity in knots as:

where the term (g/2) tan aTPPA/ is the decrease of forward speed during the nose-

down rotation to the horizontal. Applying this process to the example helicopter gives:

This method assumes an ideal flare maneuver in which a skilled pilot does the right thing at the right time. It is actually a difficult maneuver in which the pilot must simultaneously satisfy the equations of motion for vertical forces, horizontal forces, and pitching moments with only his cyclic and collective controls in order to end the maneuver within narrow limits of height above the ground, rate of descent, and forward speed. Reference 5.13 states the problem thus: "Pilot apprehension is a factor because of ground proximity and rate of closure.”

Although the initial rate of descent does not enter into the calculation directly, it does affect the pilot’s chances of achieving the ideal flare. The higher the initial rate of descent, the less time he has to correct mistakes in control inputs. A study made with a B-25 airplane showed that satisfactory deadstick landings could be made up to rates of descent of 2,500 ft/min. Above that, the quality of the landings decreased. Presumably, helicopters have a similar limit.

Even though the military have had a requirement for many years that the minimum touchdown speed be 15 knots or less, there is a lack of actual test data on the maneuver, so the method has not yet been checked against an actual flare.

At some combinations of altitude and forward speed, it is impossible to demonstrate safe autorotative landings at a vertical touchdown speed within the design limits of the landing gear. The boundaries of these combinations define the

height-velocity diagram or Deadmans Curve. An unsealed height-velocity diagram is shown in Figure 5.7. Since the actual ability to make a safe landing depends on the interaction between the helicopter and the pilot, the height-velocity diagram can only be accurately determined in flight test. Prior to these tests, however, a First approximation can be obtained using a combination of empirical and analytical considerations.

The helicopter aerodynamicist should be aware that there are two different sets of ground rules used in determining the height-velocity diagram. When certificating a civil helicopter, the United States Federal Aviation Agency (FAA) specifies a pilot delay time following the power failure of 1 second along the upper boundary and no pilot time delay along the lower boundary. The United States military branches, on the other hand, specify a 2-second pilot delay at all points in order to define an operational height-velocity diagram. A method for calculating the diagram using FAA flight test data is given in reference 53. This method will be

outlined along with modifications to make it suitable for generating military operational height-velocity diagrams.

The method uses the generalized, nondimensional height-velocity diagram shown in Figure 5.8, which was generated from test data using three single-engine, single-rotor helicopters flown by skilled test pilots in a series of FAA flight test programs. To establish the diagram for a given helicopter, three unique heights and one velocity must be found: hh, £>hi, hcs, and Vcr The low hover height, h]Qi can be calculated by assuming that the entire maneuver is done at a vertical rate of descent equal to the landing gear sink speed, VLG, and lasts as long as the kinetic energy associated with rotor speed can provide power equivalent to that required for hover in ground effect without exceeding a value of CT/<5 of 0.2. The resultant equation based on the analysis of reference 5.3 is:

where Cr/a is the value of Ct/g based on gross weight. Since the tail rotor is not required to balance the main rotor torque during this maneuver, the power required should not include tail-rotor-induced power. A study of height-velocity

Source: Pegg, “An Investigation of the Height-Velocity Diagram Showing Effects of Density, Altitude, and Gross Weight,” NASA TND-4336, 1968.

curves generated by the military test agencies indicate that this equation can be used for military as well as FAA-type time delays.

The analysis of flight test data for the three helicopters at several gross weights each indicated that the critical velocity, VCR, at the nose of the height – velocity curve is a function of the speed for minimum power, Vmin, and the gross weight. The relationships deduced from this test data are plotted in the top half of Figure 5.9. The results, however, cannot be considered to be universally valid. The spread in gross weights for each of the test helicopters was only about 20%, and in this range the speed for minimum power did increase. At higher gross weights this trend would be expected to reverse as a result of blade stall effects, as indicated in Figure 4.24 of Chapter 4. A solution to this dilemma that preserves the method of

FIGURE 5.9 Parameters for Height-Velocity Diagram reference 5.3 is to calculate Vmin from energy considerations that do not include the effects of stall. In Chapter 3 an equation was derived for the main rotor power using energy methods:

where the Induced Efficiency Factor, e, can be estimated from the low |i portion of Figure 3.7 of Chapter 3. The equation can be solved by trial and error procedures. Once Vmia (in. knots) has been determined, Va an be found from Figure 5.9, which is based on a similar figure in reference 5.3. The left-hand side of this figure is valid for the time delay used by the FAA—1 second along the top of the height – velocity curve and no delay along the bottom. The right-hand side applies to the military delay of 2 seconds at all points on the height-velocity curve and was guided by the published data on the Bell AH-lG as tested by the Army and reported in reference 5.11.

The high hover height, hhb as a function of VCr is plotted at the bottom of Figure 5.9 again for both types of time delay based on the test data of references 5.3 and 5.11.

The critical height, hCR, at the nose of the height-velocity diagram can be taken as 95 ft for all single-engine helicopters using the FAA time delay according to reference 5.3. This should be raised to 120 ft for the military time delay.

The failure of one engine on a multiengined helicopter is, of course, less of a problem than on a single-engined helicopter. For this case, the low hover height is:

The study of multiengined helicopters of reference 5.14 recommends that the critical speed, VCr, be taken as half the speed at which the remaining power can maintain a rate of descent equal to the landing gear design sink speed—that is, half the speed at which:

(h. p.rcq. – h. p.lvlil) = Flg. ft/sec

This method of determining VCR should be used for the FAA time delay, but for the military 2-second time delay the critical speed is undoubtedly higher. For want
of a more precise value, it is suggested that the critical speed for this case be taken as equal to the speed at which the remaining power can maintain a rate of descent equal to the landing gear design sink speed.

The critical height, hCR, for multiengined helicopters can be assumed to be 50 ft or h[0, whichever is higher. Until more data are available regarding single-engine height-velocity curves on multiengined helicopters, it may be assumed that there is no difference between the values of hCR that would be obtained using the FAA and military-type time delays.

The methods described here have been used to construct height-velocity diagrams for the example helicopter at sea-level standard conditions and at 4,000 ft, 95° F, for both the FAA and the military time delays. The results are shown in Figure 5.10. At sea level the example helicopter can hover in ground effect with one engine out at its normal gross weight, so there is no single-engine failure envelope for this condition. At 4,000 ft, 95° F, however, the helicopter cannot hover on one engine; thus there is a single-engine envelope, as shown on the bottom set of curves of Figure 5.10.

The high-speed portion of the height-velocity diagram in Figure 5.7 is simply a warning that a power failure at high speed and close to the ground is a dangerous situation. No analytical method has been developed for predicting this portion of the diagram, and some presentations omit it entirely. Two considera­tions regarding the high-speed portion are worth noting. First, for this flight condition, the pilot can be assumed to be alert and able to react quickly to a power failure. Second, for most helicopters, when the rotor slows down at constant collective pitch, the increase in tip speed ratio causes the rotor to flap back so that a pitchup is started, which tends to keep the rotor speed from decaying further and, at high speeds, results in the automatic start of a climb. The height of this portion of the diagram depends only on what is considered prudent. The trend with time has been to decrease the height as shown from the values given in pilot handbooks for the following helicopters:

Following a power failure, the pilot has a limited zone in which to select a suitable landing spot. The radius of this zone is equal to the maximum glide distance from the altitude at which he enters autorotation. This altitude is either the altitude he had at the time of the power failure or the altitude to which he can zoom. The

zoom maneuver is possible when the failure occurs at a forward speed, V0i higher than the autorotational speed, Vv The altitude gained can be related to the kinetic energy made available by decreasing the air speed modified by the power dissipated during the time required by the maneuver:

G-v-(K-F?)-550 j .р.<//, ft

4____________________ J‘Q

G. W.

(Although some kinetic energy might be available beause of a decrease in rotor speed, this should not be included, since the pilot will want to get the rotor speed back up to normal before landing.) For this calculation, the power is assumed to correspond to the average level flight power for the two conditions and the time of the maneuver is the time required to decelerate from V0 to Vx using, the component of gravity along the flight path. Using these assumptions, the equation becomes:

where the climb angle, yn is:

CJo

(CT/o),

A conservative value of (CT/o)max for this calculation is 0.12. The extra glide distance due to the zoom maneuver is:

The analysis has been done for the example helicopter assuming a complete power failure at 160 knots, and the results are plotted in Figure 5.6. The power required was taken from Figure 4.24 and the rate of descent from Figure 5.5. It may be seen that the best autorotative speed is about 87 knots, which is closer to the speed for minimum rate of descent than to the speed for minimum angle of descent.