Category Helicopter Performance, Stability, and Control

A fallout of the calculations for power required is the collective and cyclic pitch associated with the trim points. Figure 4.41 shows these for level flight at sea level at the example helicopter’s design gross weight.

Cruising Flight

There is no single accepted definition of cruise speed. Depending on the situation, it may mean the speed for maximum range, the speed for 99% of maximum range,

the speed at maximum continuous power, or any other continuous speed required to do a specific mission.

The speed for maximum range may be determined using a plot of fuel flow vs. forward speed such as the one for the example helicopter on Figure 4.42. The speed for maximum range is the speed at which a ray through the origin is tangent to the fuel flow curve for this case, 114 knots. Note that this is slightly faster than the speed for maximum equivalent rotor lift-to-drag ratio in Figure 4.40. The reason is that a turbine engine is more efficient at high power than at low power because of the fuel flow that must be used just to keep the gas generator spinning, regardless of the power output. The effects of head – and tailwinds are also shown. A headwind requires a higher cruise speed than no wind, and a tailwind a lower speed. The specific range, S. R., is the distance flown whil? burning one unit of fuel. It is generally expressed in nautical miles (N. M.) per pound of fuel and is determined as:

s R Ground speed RM./hr N. M.

Fuel flow Tb/h^ ’ lb

If one knows the engine power required as in Figure 4.38 and the engine fuel consumption characteristics as in Figure 4.3, the specific range can be determined

as a function of gross weight, altitude, and forward speed. (Note: For multiengine helicopters, divide the power required by the number of engines before going to the fuel flow curves.) The calculation has been done for the example helicopter, and the results are plotted on Figure 4.43. At low gross weight, maximum range is obtained at high altitude whereas at high gross weight it is obtained at sea level. At low gross weight and low altitude, the average blade element angle of attack is below the condition for the maximum lift-to-drag ratio. For this case, a higher value of CT/o obtained by flying at a higher altitude is beneficial. This is analogous to the dependency of hover Figure of Merit on CT/o, which was discussed in Chapter 1. The better specific range at low gross weight and high altitude can be important during a long flight in which the helicopter is allowed to drift up as fuel is used. One word of caution: if the cruise altitude is expected to be over 15,000 ft, oxygen should be provided for the crew.

The speed for maximum range corresponds to the maximum specific range, but it is common to use the speed to the right of the peak where the specific range is 99% of maximum, the rationale being that the mission time can be shortened with little sacrifice of economy by flying at this speed.

Figure 4.44 is a cross-plot of Figure 4.43 showing the effects of gross weight and altitude on the 99% maximum specific range value. The cruise performance is better with one engine than with two. This is due to the characteristics of a turbine engine, which is more efficient near full power than at partial power since a large part of its energy is consumed internally in driving the compressor. (This effect is not so pronounced on reciprocating engines.) The single engine advantages are generally not used because of the risk of not being able to restart the dead engine in an emergency. It does, however, give the pilot an option—for example, in stretching the range at the end of a long over-water flight.

The distance traveled at the speed for 99% maximum specific range while burning a given amount of fuel can be found by integrating the area under the specific range curves of Figure 4.44, since:

The power-required curves of Figure 4.38 and the power-available curves of Figures 4.1 and 4.2 can be used together to find the maximum speed. A procedure for generating the curve of maximum speed as a function of altitude requiring a minimum of interpolation is as follows:

• Select even values of G. W./p/p0.

• Calculate the density ratio, p/p0 = G. W./(G. W./p/p0).

• Use the atmospheric charts of Appendix C to find the altitude.

• Use the engine curves to find the total power available.

• Divide the power available by the density ratio, h. p.lvlillbl9/p/p0.

• Match the basic power required curves with the power available to obtain a first estimate of maximum speed.

• Determine additional compressibility losses as a function of temperature, G. W./p/p0, and estimated

• Subtract additional compressibility losses from power available and rematch on power required curves to obtain corrected value of Vmix(If the compressibility correction is large, this process may require some iteration.)

The result of using this procedure for the example helicopter is given in Figure 4.39. Figure 4.1 shows that the example helicopter has a transmission torque limit that prevents the pilot from using full takeoff power below about 1,200 ft on a standard day. This is a fairly common limitation and—if the pilot observes it—accounts for the takeoff power lines on Figure 4.39 having different slopes at low altitudes.

Many design studies require estimates of the effects of installed power, weight, or parasite area on maximum speed. Good examples would be studies of the feasibility of retracting the landing gear or of installing larger engines. For this purpose, three partial derivatives should be evaluated: dVmJd h. p., dVmiJdG. W., and dV^Jdf The first two can be evaluated from a power-required plot such as Figure 4.38. For the example helicopter at initial conditions of 20,000 lb, 160 knots, and 3,920 h. p. (intermediate installed power rating), the derivatives at sea level are:

д V

0. 009 K/h. p.

d h. p. д V

їла* ± 0.005 к/lb

d G. W. ‘

A study of Figure 4.38 shows that these derivatives are strongly dependent on the initial trim point.

Standard Day

The parasite power area derivative can be found from the isolated rotor charts by noting that:

a Kmax, _ d h-p. d df df d h. p.

рЛ/ft/?)3 d Cq/g d h. p. 550 d 6

The trim condition is near |i = 0.4 and CT/o = 0.085. From the isolated rotor charts:

co/° ■

Є

Thus

d h. p. 285,000(0.0012) . , ‘

—TT~ =——- —7;—- = 89 h. p./ft2

d f 240(0.016) r

and

Equivalent Rotor Lift-to-Drag Ratio

The helicopter aerodynamicist is occasionally aske. d to calculate the lift-to-drag ratio of a rotor (including hub and shaft) to compare its forward flight efficiency with that of another rotor or of an airplane wing. The lift-to-drag ratio of a wing is relatively straightforward to determine; but because a rotor provides both lift and forward thrust, it presents a bookkeeping problem. Although several procedures have been suggested in the past, the following seems to be generally accepted at this writing:

Equivalent lift: The vertical component of rotor thrust.

Equivalent drag: The difference between the main rotor power divided by forward Speed and the parasite drag of the rest of the helicopter (not including main rotor hub and mast.)

Figure 4.40 shows the results of this procedure applied to the example helicopter.

Power Required

Charts representing the nondimensional forward flight performance of isolated rotors and the iterative procedure for determining the trim conditions for the entire helicopter were developed in Chapter 3. These charts and procedures have been used for the example helicopter with appropriate accessory and transmission losses to calculate the engine power required in level forward flight for several gross weights. The results are presented in Figure 4.38. The basic curves show the power required assuming an advancing tip Mach number of 0.7 and the supplementary curves give the additional compressibility corrections as a function of temperature and gross weight based on actual advancing tip Mach number and the method of Figure 3.43, including the secondary effect of increased tail rotor power due to increased main rotor torque.

Also included in the figure are lines representing "upper and lower stall limits” where the increments of the profile torque coefficient, Cg/o0, at the most

critical azimuth position are 0.004 and 0.008, respectively. These limits are from the isolated rotor charts of Chapter 3, corrected for the twist effect as outlined in the discussion of those charts. The presence of these lines is not truly a limit, but simply a warning that many rotors suffer from high blade loads, high control loads, high vibration, and/or erratic flapping due to retreating blade stall in this regime. On the other hand, many rotors have proved relatively stall-tolerant to much higher levels. The aerodynamicist should assume that the rotor designers and dynamicists will provide such a rotor and that he can ignore the stall limits for purposes of estimating performance. An optimistic discussion of the aerodynamic capability of rotors will be found in reference 4.25.

The power required curves of Figure 4.38 as shown apply directly to sea level, standard, conditions but can also be used at other conditions, as follows:

Notes: • Example Helicopter

• Chart Method of Chapter 3

• Out of Ground Effect

• Basic Curves Based on M^qq = 0.7

True Speed, knots

FIGURE 4.38 Normalized Engine Power Required in Forward Flight

/

A momentum method for computing the power required in a vertical climb in excess of that required to hover at the same conditions was derived in Chapter 2. The equation is:

This equation has been evaluated for the example helicopter by equating it to the excess power available and the resultant vertical rate of climb as a function of altitude is shown on Figure 4.36.

Figure 4.37 shows the same calculations as a function of gross weight at two conditions of usual interest: sea level, standard; and 4,000 ft, 95°F.

For purposes of illustration, the parasite drag of the example helicopter has been estimated using the methods and data presented in the preceding section.

For hover in ground effect, no vertical drag or pseudo ground effects have been used. The ground effect has been taken from Figure 1.41 of Chapter 1 for a 5-ft wheel height.

The corresponding tail rotor power required is found by calculating the net tail rotor thrust required to balance the main rotor torque:

550 h. p.^ RM

T"’t== (SlR)M lT

or for the example helicopter:

TT = 0.69 h. p.M

act ■*

The gross tail rotor thrust due to fin interference is:

and the tail rotor power is:

h-P-T = 0.94[h. p. for rTjJ

The resultant tail rotor power corresponding to the main rotor power of Figure 4.29 is shown in Figure 4.30. A comparison of the hover values of CT/o on the main and tail rotors of the example helicopter reveals a mismatch that would probably generate a redesign effort in an actual project. This comparison, shown in

Figure 4.31, indicates that at high gross weights the tail rotor is more heavily loaded than the main rotor—especially when compared to their respective maximum capabilities, which were shown in Figure 4.28. This means that the high gross weight or altitude performance will be limited by the tail rotor rather than the main rotor. Possible redesigns include increasing tip speed, chord, radius, or some combination of these to lower the tail rotor CT/c.

The engine power measured at the torquemeters is the sum of the main rotor, tail rotors, transmission, and accessory powers. For the example heli­copter:

The engine power required in hover in and out of ground effect is shown in Figure 4.32 as a function of gross weight. The next step is illustrated by figures 4.33 and 4.34, where the power required for various density ratios is plotted. The curves for

density ratio other than unity have been simply ratioed from the basic curve. Altitudes corresponding to the density ratios have been taken from the atmospheric charts of Appendix C. The ratioing procedure is valid except for those cases in which the tip speed is so high that a decrease in temperature will start to produce significant compressibility penalties For this situation, the hover curves of Chapter 1 for various tip Mach numbers can be used. Also shown in Figures 4.33 and 4.34 are the installed power ratings, which are 98% of the ratings from Figure 4.1.

The information from Figures 4.33 and 4.34 has been cross-plotted on Figure 4.35 to give the hover ceiling as a function of gross weight in and out of ground effect. It may be seen that the example helicopter can hover OGE at sea level, standard conditions at a gross weight of 27,800 lb and has a hover ceiling of

7,0 ft. at its design gross weight of 20,000 lb on a 95° day.

Figure 4.27, taken from reference 4.24, presents the state of the art of parasite drag of both helicopters and airplanes with several levels of aircraft cleanliness. This plot can be used to make first estimates of the drag of a helicopter in the early stages of the preliminary design. Table 4.3 lists published drag breakdowns for three typical helicopters, which can also be used to guide first estimates. (Note of caution: I have never known of an airplane or a helicopter drag estimator who was pleasantly suprised by flight test results showing that he had overestimated the drag of the aircraft. The estimating methods outlined in this chapter must be considered to produce minimum estimates and thus are suitable for the wishful – thinking phases of proposals and sales brochures. For realistic engineering estimates, I recommend that at least another 20% be added to the total to include those items that were not initially included or that will grow during the normal development of the helicopter.)

Source: Rosenstein & Stanzione, “Computer-Aided Helicopter Design,” AHS 37th Forum, 1981.

In addition to the major drag items discussed earlier, a modern helicopter has many minor sources of drag, individually small but significant in total. A partial list of these miscellaneous items includes:

Windshield wipers External store mounting points

Source: Pruyn and Miller, “Studies of Rotorcraft Aerodynamic Problems," WADD TR 61-124, 1961.

Overflow drain tubes Abrasive walkways

Lights: anticollision, formation, landing Fueling receptacles Ground electrical receptacles Skin gaps, steps, and mismatches

Most of these items have characteristic dimensions of less than 4 inches and thus operate at subcritical Reynolds numbers at normal flight speeds, with corre­spondingly high drag coefficients. The data and methods of reference 4.2 can be used to evaluate the drag of these items. Such an evaluation for the Lockheed AH 56A "Cheyenne” produced an estimate of slightly more than one square foot of flat plate area.

Less obvious sources of drag are those due to cooling and leakage. When air is taken aboard to cool or to ventilate and then dumped overboard with less velocity than the forward speed of the helicopter, its loss of momentum manifests itself as a drag force. Similar drag will be produced by air that simply leaks into the aircraft at one point and out another without serving any useful purpose.

Wheels alone:

Cq (Based on b x d)

L

-4 ^

Tubular

FIGURE 4.26 Landing Gear Drag

Source: Hoerner, “Fluid Dynamic Drag,” published by author, 1965; Sweet & Jenkins, “Wind – Tunnel Investigation of the Drag and Static Stability Characteristics of Four Helicopter Fuselage Models,” NASATN D 1363, 1962.

Compared to a solid wind tunnel model, the actual helicopter in flight has some of the characteristics of a sieve. Some indication of the magnitude of miscellaneous and leakage drag can be obtained from the wind tunnel tests of a Bell UH-1 fuselage, reported in reference 4.15. When all gaps were sealed and all protuberances removed, the drag was reduced by more than 2 square feet of equivalent flat plate area.

Cooling and leakage drag are difficult to estimate without a detailed thermodynamic and internal aerodynamic analysis. During preliminary design, they are usually accounted for by increasing the basic fuselage drag by 10-20%.

The fuselage is not the only component that can suffer from leakage. If a rotor blade has a passageway through its entire length, the rotor will act as a centrifugal pump, taking air in at the root and expelling it at the tip. Unless the air is turned at the tip to align it with the external velocity, losses can be substantial, increasing the power required by as much as 20% in extreme cases. For this reason, blades should be sealed, especially at the root. If a blade is open at the root but sealed at the tip, the centrifugal forces will compress the air inside the tip to a value equal to the dynamic pressure corresponding to the tip speed, about 3-5 psi for most rotors. These pressures were sufficient to collapse solid ribs in early built-up rotor blades. The solution to this problem was to open up a spanwise air passageway, a design feature that is no longer necessary since most modern blades are ribless.

The exhaust system of a turboshaft engine as installed on a helicopter can also be a source of drag. If the rearward speed of the exhaust gas relative to the aircraft is higher than the forward speed, the engine will produce positive residual thrust. The engine installations on turboprop airplanes are generally designed so that this is true even for their highest speeds. The exhaust system on a helicopter, however, is usually designed to produce relatively low exhaust velocities in order to optimize the hovering performance. Thus there is residual thrust only up to some forward speed; beyond that speed there is residual drag. This drag, which may amount to several hundred pounds, can be estimated by the engine manufacturer for a particular engine installation. If the exhaust stack is canted away from straight back, a further drag can be produced corresponding to the loss of the rearward momentum of the air passing through the engine. Thus the exhaust drag is:

Dex = m (V – Vtx cosx)

where m is the engine mass flow in slugs per second and % is the exhaust cant angle.

A large portion of the drag of a helicopter is due to the bluff body drag of the rotor hubs and landing gear. The main and tail rotor hubs are bluff bodies, which,

because of their rotation and function, are impossible to fit with simple streamline fairings that might keep the flow from separating. This is especially true at high speeds when the rotor is tilted nose down. Wind tunnel tests have generally led to the conclusion that streamlining individual bits and pieces without unduly blocking possible air paths between them leads to the lowest hub drag. A summary of published wind tunnel tests of both faired and unfaired rotor hubs is shown in Table 4.2. For comparison purposes, the drag values are presented for zero angle of attack and zero rpm.

The obvious way to minimize the hub drag is to keep the relative size of the hub as small as possible, as on the Vertol CH-47 and on the Hughes OH-6A. The effect of angle of attack and rotor speed on hub drag is shown in Figure 4.22 for an unfaired hub and for a faired hub. At least part of the difference between hubs is due to the lift-induced drag on the faired hub.

The drag of the rotor shaft can be estimated from the cylinder drag data of Figure 4.23. The total drag of the rotor hub and mast in close proximity to a fuselage or mast pylon may be higher than if they were isolated. This is due to separation on the fuselage or pylon triggered by the neighboring bluff body wake

“shaft = 0°

.85

I

.80

0 20 40 60 80 100

Percent rpm

FIGURE 4.22 Effect of Angle of Attack and rpm on Hub Drag

Source: Linville, “An Experimental Investigation of High-Speed Rotorcraft Drag,” USAAMRDL TR 71-46, 1971.

on the hub. Obviously, this interference drag is a function of the exact configuration, but one set of tests reported in reference 4.21 and summarized in Figure 4.24 may be taken as typical. One way of decreasing the interference drag is to suck off the low energy boundary layer, as was done on the S-58 wind tunnel model in Table 4.2. Another way of doing the same thing—though perhaps not as effectively—is to use a pylon cap, as on some Sikorsky and Yertol helicopters. This

Source: Hoerner, “Fluid Dynamic Drag," published by author, 1965.

cap acts as a low aspect ratio wing whose tip vortices energize the boundary layer on the aft portion of the pylon and thus delay separation. A comprehensive survey of hub drag, along with suggestions for minimizing it, is to be found in reference 4.22.

Yet another interference drag is caused by the rotor downwash on the aft fuselage, which can induce areas of local separation. Figure 4.25 shows test results from reference 4.23 of this drag for one configuration. The interference drag increases with increasing angle of attack, apparently because the aft portion of the fuselage becomes more susceptible to separation triggered by wake turbulence as its pressure gradient becomes more and more unfavorable. The wake behind the hub constitutes a low-pressure sink that can draw the flow off of the upper fuselage, thus producing separation. Again it is obvious that this type of interference drag is highly dependent on the configuration; but in order to evaluate it accurately for a specific design, rather elaborate wind tunnel models are required with a rotor that has the correct disc loading mounted separately from the drag model, but in the correct relative position. In lieu of this, it is suggested that Figure 4.25 be used for most applications.

Nonretracting landing gears also generally produce bluff-body drag. Reference 4.2 gives the drag coefficients of several types of wheeled landing gear. Several of its examples are shown in Figure 4.26. Skid gear are combinations of tubes and struts of various shapes, and two examples are also shown in Figure 4.26. Measurements of landing gear drag on small-scale wind tunnel models may be high

Source: Keys & Wiesner, “Guidelines for Reducing Helicopter Parasite Drag,” JAHS 20-1, 1975.

because of the low test Reynolds numbers of the components. Figure 4.23 can be used to estimate this effect.

The parasite drag of a helicopter consists of two types of drag: streamline drag, where the flow closes smoothly behind the body; and bluff body drag, where the flow separates behind the body. The difference in drag between these two types is dramatically illustrated by Figure 4.11, which shows three two-dimensional bodies with equal drag. The strut has streamline drag, the flat wire has bluff body drag, and the round wire has a combination of both.

Streamline Drag

The primary component of streamline drag is skin friction, which is produced by the surface capturing air molecules and slowing them down—with respect to the aircraft—to zero velocity. At the nose of the body only the layer of molecules immediately adjacent to the surface is slowed. Further downstream, the slowed air

molecules themselves have a slowing effect on molecules further from the surface, finally building up a boundary layer of air with a velocity distribution varying from zero at the skin surface to the free stream velocity at the outer edge. Skin friction is a measure of the total momentum that has been lost by the air in being slowed down. The magnitude of the skin friction is a function of the Reynolds number:

p VL

——- = 6,400 VL at sea level

M where p is density in slugs/ft3, |i is dynamic viscosity, V is velocity in ft/sec, and L is length in ft.

The skin friction also depends on whether the boundary layer is laminar or turbulent, as shown in Figure 4.12 taken from reference 4.2. This figure shows the skin friction coefficient for a smooth, flat plate and is based on many measurements made in the last hundred years. Airplane wings and helicopter rotor blades operate in the range of Reynolds numbers in which natural transition will occur somewhere on the surface. The so-called laminar boundary layer airfoils are designed to operate as far down the laminar line as possible. Long bodies such as the fuselage of a large jet transport operate at Reynolds numbers in the neighborhood of 109 and thus experience low skin friction coefficients even though the boundary layer is almost completely turbulent.

Natural transition from laminar flow to turbulent flow is not limited to the flow across surfaces. It can be readily observed in the smoke rising from a cigarette in a calm room. The smoke rises a few inches as laminar flow until its critical Reynolds number is reached based on velocity, density, viscosity, and distance traveled. At this point it spontaneously and suddenly becomes turbulent.

Surface imperfections such as riVet heads, skin joints, gaps, and so on produce drag according to their effective frontal area and the local dynamic pressure. If the imperfection extends through the boundary layer into clean air flow, the drag will be almost the same as if it were entirely in free air. If, on the other hand, the local boundary layer is several times deeper than the imperfection is high, the local effective dynamic pressure will be low, and so will the drag. The equation for the drag ratio given in reference 4.2 is:

^freestream

where b is the height of imperfection and б is the thickness of the boundary layer.

For turbulent boundary layers:

6-^L

R1/7

VAT

where * is the distance from the leading edge and Rx is the Reynolds number based on X.

For an aircraft at 150 knots, Figure 4.13 shows the boundary layer thickness over a 50-foot distance, and Figure 4.14 shows the ratio of actual drag coefficient to free stream drag coefficient for surface imperfections with heights of 0.05 and

0. 25 inches. These figures show that even when the boundary layer is 5 inches thick, a rivet head with a height of 0.05 inches has a drag coefficient that is 16% of what it would be in the free stream. Thus flush riveting reduces drag even near the

rear of the fuselage. Some surface imperfections will exist even on well-designed aircraft. They may be accounted for individually by the methods outlined earlier or more simply by increasing the computed skin friction coefficient by a factor that is a function of the relative dirtiness of the aircraft. For example, the analysis in reference 4.2 for the ME-109, a propeller-driven World War II fighter, increased the calculated skin friction drag of the fuselage by 12% to account for surface imperfections.

Besides the effect of surface imperfections, streamline aircraft components have more drag than calculated from the drag of a flat plate because of form drag. This is caused by the increased velocities over the thick part of the body and the forced thickening of the boundary layer due to the slowing of the air to free stream velocities as the contours are brought together at the rear. This applies to both two – and three-dimensional bodies as shown in Figure 4.15. This figure and Figure 4.16 show the dilemma the aerodynamicist faces in using small-scale models in low-speed wind tunnels for drag measurements. Such testing is necessarily done at lower Reynolds numbers than on the full-scale aircraft, and thus the drag coefficient is higher. In some cases the helicopter aerodynamicist will use the high measured drag of the wind tunnel model on the basis that the model does not have surface imperfections of the actual aircraft—thus two wrongs make a right. A more realistic view of the situation, however, is that absolute full-scale drag values

cannot be obtained from a small-scale wind tunnel test and that only approximate

changes in drag due to changes in.

For the purposes of preliminary ac> ^ ^ afag can be estimated from past experience on other fuselage^ ■ SWS drag coefficients

measured in wind tunnels for several alfr ^ ^ ^ ^Pter fuselages at zero lift and reported in references 4.9, 4.10, 4.1*> a ‘ * s * Reference, a minimum drag based on theoretical skin friction a Упо s number of 7 x 107,

Source: Harris et al., “High Performance Tandem Helicopter Study,” USATREC TR 61-42, 1961; Harned, “Development of the OH-6 for Maximum Performance and Efficiency,” AHS 20th Forum, 1964; Foster, “Tilt-Pylon and Wind Tunnel Tests,” Bell R&D Conference, 1961; Perkins & Hage, Airplane Performance Stability and Control (New York: Wiley, 1949).

corresponding to a fuselage length of 45 ft and a speed of 150 knots is shown, and also a line representing minimum skin friction and form drag for streamline fuselages. It is suggested that, for analysis of a new design, this figure be used at a level of aerodynamic cleanliness corresponding to that for one of the known aircraft.

The change of fuselage drag with angle of attack can be estimated for a given helicopter by comparing with the fuselage shapes and the corresponding nondimensionalized curves of Figure 4.18, which are based on wind tunnel tests of both model and actual helicopter fuselages reported in references 4.10, 4.13, 4.9, 4.14, 4.15, and 4.12. The drag of externally mounted nacelles can be estimated using Figure 4.19, taken from reference 4.16.

The drag of wings and stabilizer surfaces consists not only of skin friction but of induced drag as well. The total drag equation is:

where Cdo is the drag coefficient at zero lift, A is the projected area, qjq is the ratio of local dynamic pressure at the component to free stream dynamic pressure, L/b is

.6 – .4 –

.2 –

Source: Keys & Wiesner, “Guidelines for Reducing Helicopter Parasite Drag,” JAHS 20-1, 1975.

the span loading, and e is the Ozwald efficiency factor which accounts for the change in form factor with lift and the fact that the surface probably does not have an ideal elliptical lift distribution. For preliminary drag estimates, experience has shown that an Ozwald efficiency factor of 0.8 for both wings and stabilizers is a valid assumption. The dynamic pressure ratio may be taken as unity for a wing but for both vertical and horizontal stabilizers on helicopter fuselages, the dynamic pressure ratio can vary from 0.8 to 0.5, depending on the size of the wake generated by all of the aircraft components ahead of the stabilizers and how much of the area of the stabilizers this wake affects. Some experimental data on this problem will be found in Chapter 8.

Some military helicopters are designed with flat plane canopies which are intended to reduce detectability by limiting the reflection of the sun to a narrow viewing range. Experience with these canopies, both in wind tunnel tests and in flight test, show that they produce a drag penalty primarily due to separation behind the sharp front corners. Wind tunnel tests on a World War II fighter reported in reference 4.2 showed that a flat panel canopy has five times the drag of a rounded canopy. The results of another wind tunnel test, this time of a helicopter, are shown in Figure 4.20 from reference 4.16, where the drag coefficient of the entire fuselage is plotted as a function of the corner radius ratio. The substantial increase in fuselage drag when going to sharp corners shown in Figure 4.20 has been substantiated by the flight test program reported in reference

4.17 in which a YOH-58A was equipped with a flat panel canopy with sharp forward corners. At its cruise speed of 102 knots, the equivalent flat plate area was increased by 0.7 square feet at its forward center of gravity position and by 2.2 at its aft.

Source: Hoermer, ‘‘Fluid Dynamic Drag,” published by author, 1965.

Drag due to the junction of surfaces with the fuselage can be estimated from Figure 4.21, which is based on the test data of reference 4.2.

Another form of interference similar to vertical drag is the mutual interference of the tail rotor and the fin. The interference manifests itself in two ways: as a force on the fin that decreases the effective antitorque force generated by the tail rotor; and as a change in the flow conditions at the rotor that may either increase or decrease the tail rotor power required. Figure 4.9, based on the test data in references 4.7 and 4.8, shows the nondimensionalized interference force on the fin as a function of the blockage area ratio and the separation distance for both pusher and tractor arrangements. The gross thrust required of the tail rotor is:

Source: Cassarino, “Effect of Rotor Blade Root Cutout on Vertical Drag,” AAVLABS TR 70-59, 1970.

Source: Fradenburgh, “Aerodynamic Factors Influencing Overall Hover Performance,” AGARD CP 1111, 1972.

where TT is the net thrust required to balance the main rotor torque.

For a tractor installation (i. e., with the wake blowing on the fin), the tail rotor benefits from a pseudo ground effect just as the main rotor does in the vertical drag situation. For a pusher installation, the fin slows the inflow, thus producing a beneficial pseudo ceiling effect. The fin also puts discontinuities into the flow, which might result in local stall. Figure 4.10 shows one set of experimental results for a tail rotor with and without a fin. For this configuration, the value of F/T from Figure 4.9 is 0.13. The effect of the fin on power may be found by

Source: Lynn, Robinson, Batra, & Duhon, “Tail Rotor Design,” Part I: “Aerodynamics,” JAHS 15- 4, 1970; Morris, “A Wind-Tunnel Investigation of Fin Force for Several Tail-Rotor and Fin Configurations,” NASA LWP-995, 1971.

comparing the power required for the rotor with fin off at a CT/(3 13% higher with the measured power with the fin on. Such a comparison at CT/a = 0.08 shows that the measured power is approximately 94% of what would have been predicted from the fin off data. Based on this one set of test data, it is suggested that the tail rotor hover performance be based on the empirical equation:

The example helicopter has an area ratio, S/A, of 0.25, and a separation ratio, x/R, of 0.3. Thus from Figure 4.9 the interference ratio, F/T, is 0.125. The corresponding equations for the gross thrust and the power are:

Tr = 1.125 Tn

h. p.r = .94 (h. p. for TT(J

Source: Internal Lockheed document.