VERTICAL DRAG IN HOVER

Figure 4.4 shows a half-plan view of the example helicopter divided into segments by concentric circles around the rotor mast. Also shown is a side view with wake stations designated below the rotor. The drag coefficient for each segment depends on the shape of its cross section. Drag measurements of cylinders and flat plates under a rotor are reported in reference 4.1. It is concluded in that report that the turbulence in the rotor wake is always high enough to insure that fully turbulent, or supercritical, boundary-layer conditions exist. Supercritical drag coefficients for a number of two-dimensional shapes with flow from above are shown in Figure 4.5. These drag coefficients are based on data presented in references 4.1 and 4.2.

Tilt-rotor aircraft have a large wing to be accounted for. Deflecting a trailing edge flap can reduce its vertical drag penalty but wind tunnel test results reported in reference 4.3 indicate that the optimum flap angle is about 60° rather than the 90° that would be expected to produce less drag.

The measured distribution of dynamic pressure under a full-scale rotor with —4° of twist was shown on Figure 1.19 of Chapter 1. For rotors with different twist, the measured distribution can be modified by multiplying by the square of the ratio of induced velocities calculated by the method of Chapter 1 for the two values of twist. Figure 4.6 shows the —4° twist distributions modified for —10° of twist for use with the example helicopter.

Using the drag coefficients and the dynamic pressure corresponding to each of the airframe segments, the vertical drag penalty can now be calculated by

Radius Station, r/R

Hemispherical Nose Cq = -1

Wheel CD = .25

— 7 Y / і I І і /

___ л і.

FIGURE 4.5 Drag Coefficients of Typical Component Shapes

Note: Drag coefficients are based on super critical flow and on area projected in plan view.

summing the product of the drag coefficient, the dynamic pressure ratio, and the projected area of each segment in the half-plan view:

N

D 2 X (^/D. L.)„A„

v_________ я^І__________________________

G. W Г A

Table 4-1 presents the calculation for the example helicopter, which shows that the download penalty is 4.2% of gross weight.

The saving in power due to the pseudo ground effect of the fuselage on the rotor may be estimated by calculating the ground effect due to a full ground plane at the mean position of the fuselage by the method of Chapter 1 and then multiplying it by the ratio of projected fuselage planform area in the wake to disc area. Thus:

—————- Extrapolated for Rotor with -10° Twist

rlR FIGURE 4.6 Distribution of Dynamic Pressure in Wake

Source: Boatwright, “Measurements of Velocity Components in the Wake of a Full-Scale Helicopter Rotor iri Hover,” USAAMRDLTR 72-33, 1972.

For the example helicopter the mean position of the fuselage is at Z/D = .12 and from Figure 1.41 of Chapter 1:

‘IGE

TABLE 4.1 Calculation off Vertical Drag for the Example Helicopter 1 2 3 4 5 6 7 Airframe Radial Vertical Dynamic Pressure Drag Segment Segment, Position, Position, Ratio, Coeff., Area, n r/R Z/R (q/D. L.)a A. fi2 4x5x6 1 .7 .2 .95 .1 6 .57 2 .6 .2 .80 9 10 7.20 3 .5 .2 .68 .9 12 7.34 4 .4 .2 .55 9 12 5.94 5 .3 .2 .45 9 12 4.86 6 .2 .2 .20 9 12 2.16 7 .2 .2 .20 9 12 2.16 8 .3 .2 .45 .9 11 4.46 9 .4 .22 .57 9 10 5.13 10 .5 .22 .70 .6 9 3.78 11 .6 .23 .83 .5 8 3.32 12 .7 .23 .90 .45 7 2.83 13 .8 .24 1.00 .40 6 2.40 14 .9 .24 0 .35 5 0 15 .97 .25 0 .35 2 0 16 .17 .1 .10 2.0 6 1.20 17 .22 .1 .25 .6 14 2.10 18 .27 .1 -35 .6 12 2.52 19 .27 .1 .35 .1 2 .07 20 .20 .35 .42 2.0 1.5 1.26 21 .3 .4 .47 .25 1.5 .18 Totals 171 59.48

For hovering at Cx/a = .086:

A Cq/o = -.00024

which is the equivalent of 68 horsepower.

The method has been used to correlate with the test data reported in reference 4.4. These tests used a model helicopter suspended under a separate rotor. Both elements were mounted on individual balance systems and wings of various sizes and positions could be installed. Figure 4.7 shows the test results in terms of both vertical drag and pseudo ground effect (which corresponds to the "thrust recovery” of reference 4.4). Also shown are calculated values for the two quantities determined by – the foregoing method. It may be seen that in this case both the download and the pseudo ground effect calculations are optimistic for the fuselage alone, but for the fuselage with the large wing, the download is optimistic whereas the ground effect is pessimistic. Some of the discrepancy may be due to the relatively small size of the model and the possibility that some components actually experienced high drag, subcritical conditions in spite of the wake turbulence.

Measurements of vertical drag in ground effect are reported in reference 4.5 and are. summarized in Figure 4.8, which shows that both the vertical drag and the pseudo ground effect are reduced, or even reversed, when hovering less than a rotor diameter above the ground. Reference 4.6 reports that model tests on the Sikorsky S-76 show that the download ratio changes from +3% out of ground effect to —1% at a wheel height of one foot.