PARASITE DRAG IN FORWARD FLIGHT

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.

Source: Hoemer, “Fluid Dynamic Drag,” published by author, 1965.

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

FIGURE 4.13 Boundary-Layer Thickness

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,

Flat Plates

FIGURE 4.16 Drag Coefficients at 150 Knots

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

.8 –

.6 – .4 –

.2 –

FIGURE 4.19 Engine Nacelle Drag

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.