Special Performance Problems
The previous chapters described methods for estimating the performance of the helicopter as an aircraft that hovers or simply flies from one place to another. Frequently, however, it is necessary to analyze the performance from other aspects. The aspects that will be discussed in this chapter are:
Turns and pullups Autorotation Maximum accelerations Maximum decelerations
Optimum takeoff procedure at high gross weights
TURNS AND PULLUPS
Load Factor Relationships
Conditions in a steady turn or in a symmetrical pullup are similar to conditions in level flight except that the rotor thrust is significantly higher than the gross weight and the rotor has a pitching velocity that relieves the retreating tip angle of attack. The rotor thrust must overcome the vector sum of weight and centrifugal force, as shown in Figure 5.1
or, in terms of the bank angle:
»Шгп = V1 + tan2 Ф = —
The centrifugal force is:
where (0 is the rate of turn and jRturn is the radius of the turn. But
Kmrn © = V
Yet another form of the equation can be written in terms of the rate of pitch, 0, by noting that
0 = 0) sin Ф
(in a vertical bank the rate of pitch would be equal to the rate of turn), but
J n2 — 1 radian/sec
The rate of pitch, 0, which is inherent in all these maneuvers, has a relieving effect on the retreating tip angle of attack. The rotor, which is producing the pitching motion of the helicopter, must precess itself nose up as a gyroscope; this requires increasing the angle of attack of the advancing blade with cyclic pitch while decreasing the angle of attack of the retreating blade. The change in cyclic pitch required to precess the rotor can be determined by setting the change in aerodynamic moment from trim equal to the gyroscopic moment. If the pitching velocity is constant, with no pitching acceleration, then no additional hub moment is required except for a small one due to damping moments from the fuselage and horizontal stabilizer. The analysis of the rotor with pitching velocity will be found in Chapter 7, "Rotor Flapping Characteristics.” From that analysis:
. 16 ‘
ДВ, ———– — 0 radians
For the example helicopter in a turn at 115 knots with a load factor of 1.2, the pitch rate is 0.08 rad/sec and the decrease of cyclic pitch required due to this rate is 0.2 degrees, which decreases the retreating angle of attack by this amount and thus allows the rotor to develop somewhat more thrust before stalling than it could in static conditions such as in a wind tunnel test.
The power required during a steady turn may be estimated from the level flight characteristics by using an effective gross weight equal to the actual gross weight multiplied by the load factor. Using this method and the information in Figure 4.38 of Chapter 4, the example helicopter requires a total power of 3,170 h. p. in a 1.2-g turn at 115 knots, compared to 1,470 h. p. for level flight at the same speed. Sometimes for demonstration purposes, it is permissible to lose some speed and some altitude during a "steady” turn. In this way, a significant amount of power can be extracted from the changes in kinetic and potential energy in order to demonstrate higher load factors within the installed power limitations. Assuming that a speed, AV, is lost during a 180° turn, the change in kinetic energy is:
and, combining equations derived earlier, the time to make the 180° turn is:
Thus the gain in power is:
Ah. p.„ = 2 —————— *———-
Similarly, the power associated with a loss of altitude during the same 180£ turn is:
For the example helicopter in a 1.5-g, 180° turn starting at 115 knots, ending at 100 knots, and losing 50 ft of altitude, the increment of available power due to the change of speed is 656 h. p. and due to the change in altitude, 230 h. p.
For analysis of nap-of-the-earth flight, it is necessary to consider load factors less than 1 developed during a pushover as would be used to fly over the top of a hill and into the valley beyond. For this case:
(h) 2 J?
^ ^ ^ -*v pushover
This can be used to calculate the load factor associated with flying over a hill with a given radius of curvature.