Maximum Speed

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.