Generating the Deadman’s Curve or Height-Velocity Diagram

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

FIGURE 5.6 Benefits of Zoom Maneuver for Example Helicopter with Power Failure at 166 Knots

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

Цг. Vor FIGURE 5.8 Generalized Nondimensional Height-Velocity Curve for Single-Engine Helicopters

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:

Helicopter	Height (ft)	Date Certificated
Hiller 12E	75	1959
Bell 47J-2	50	1959
Bell OH-4A	15	1963
Hughes 500	5	1964