OPERATING LIMITATIONS

Flight Envelope

An airplane’s flight envelope is the. region on an airspeed-altitude plot in which the airplane is capable of operating. Within this region, an airplane is limited at low speeds by stall and at high speeds by the available thrust. The stall boundary as a function of altitude is easily determined from

V2=(2WSU

yPoC^J a

The high-speed boundary is determined from power-available, power – required curves such as those presented in Figure 7.15. As an example, let us again consider the Cherokee Arrow. Figure 7.25 was prepared using a gross Weight of 11.8 kN, a of 1.6, a constant propeller efficiency of 0.85, and a gea level engine power of 149 kW. The Cherokee is capable of level flight within the region bounded by the two curves labeled “stall” and “maximum” power.

A typical flight envelope for a supersonic aircraft is given in Figure 7.26. At high subsonic Mach numbers, a phenomenon known as buffet can limit flight to speeds higher than the stalling speeds. This type of buffeting is caused by an instability in the position of the shock waves near the trailing edge of the upper and lowej wing surfaces. As the stall is approached, these

Figure 7.25

waves begin to move fore and aft out of phase with each other, producing a periodic flow behind the wing that resembles a Karman vortex street. The tail, in proximity to this unsteady flow, can produce a severe shaking of the airplane.

Also shown on Figure 7.26 is a limit on the maximum dynamic pressure that can be tolerated. This boundary arises from structural considerations and involves items such as flutter, torsional divergence, and static pressure within an engine inlet diffuser.

An aerodynamic heating limit as shown in Figure 7.26 also exists for airplanes designed to operate at high Mach numbers. It is beyond the scope of this text to consider in depth the subject of aerodynamic heating. However, one can gain some appreciation for the problem by calculating the stagnation

(a)

Figure 7.26 Typical aircraft flight envelopes, (a) Subsonic aircraft, (b) Super­sonic aircraft. (L. M. Nicolai, Fundamentals of Aircraft Design, L. M. Nicolai, 1975. Reprinted by permission of L. M. Nicolai.)

temperature as a function of Mach Number. This can be accomplished using the relationships covered in Chapter Five with the results shown in Figure 7.27. Along the leading edge of a wing, these temperatures will be alleviated somewhat by sweep. Nevertheless, temperatures of the order of 250 °С or higher can be expected for Mach numbers exceeding 2.0.

Maneuvering Envelope (V-n Diagram)

The lift distribution on a wing is illustrated in Figure 7.28. If у represents the spanwise distance to the center of lift of one side, the bending moment at the wing root will be given approximately by

M-yf

where L is the total lift on the wing. Generally, L will be greater than the airplane’s weight, in which case the airplane is accelerating upward at a value

so that the bending moment becomes.

The term (1 + alg) is known as the load factor, n.

n = 1 + – (7.56)

g

In this example, the wing bending moment in steady flight is seen to increase by the factor n. Similarly, n is a measure generally of the increase in the loads on any member of the airplane resulting from accelerations. In I, steady, level flight, n is equal to 1. As a result of maneuvering or gusts, n can increase in magnitude to high values and can be positive or negative.

The value of n that can be achieved by maneuvering can be obtained from

But 2WlpSCLmax equals the stalling speed, Vs. Therefore

(7.57)

Since V can be appreciably greater than the stalling speed, Vs, it is not practical to design an airplane’s structure to withstand the highest possible load factors that it could produce. Instead, based on experience, airplanes are certified to withstand different limit load factors, depending on the airplane’s intended use. A limit load is one that can be supported by a structure without yielding. In addition to designing to the limit loads, FAR Parts 23 and 25 require factors of safety of 1.5 to be applied to the sizing of the structure. Since the ultimate allowable stress of aluminum alloys is approximately 50% greater than the yield stress, a factor of safety of 1.5 applied to the limit loads is approximately equivalent to designing to ultimate load factors with no factor of safety.

Civil airplanes are designed in the normal, utility, acrobatic, and transport categories. For the first three categories, FAR Part 23 states:

§ 23.337 Limit maneuvering load factors.

(a) The positive limit maneuvering load factor n may not be less than

[(1) 2.1 + J4’™ for normal category airplanes, except that n need

W t 1U, IHJU

not be more than 3.8;]

(2) 4.4 for utility category airplanes; or

(3) 6.0 for acrobatic category airplanes.

(b) The negative limit maneuvering load factor may not be less than—

(1) 0.4 times the positive load factor for the normal and utility categories; or

(2) 0.5 times the positive load factor for the acrobatic category.

(c) Maneuvering load factors lower than those specified in this section may be used if the airplane has design features that make it impossible to exceed these values in flight.

For the transport category, FAR Part 25 states:

§ 25.337 Limit maneuvering load factors.

(a) Except where limited by maximum (static) lift coefficients, the airplane is assumed to be subjected to symmetrical maneuvers resulting in the limit maneuvering load factors prescribed in this section. Pitching velocities appropriate to the corresponding pull-up and steady turn maneuvers must be taken into account.

(b) The positive limit maneuvering load factor n for any speed up to VD may not be less than 2.5.

(c) The negative limit maneuvering load factor—

(1) May not be less than -1.0 at speeds up to Vc’, and

(2) Must vary linearly with speed from the value at Vc to zero at V&

(d) Maneuvering load factors lower than those specified in this section may be used if the airplane, has design features that make it impossible to exceed these values in flight.

In these regulations, Vc is referred to as the design cruising speed. It need not exceed VH, the maximum speed in level flight at maximum con­tinuous power. Otherwise, it must not be less than VB plus 43 knots where VB is the lowest speed that can produce a load factor of 2.5. VD is the design dive speed, and for the transport category it need not be greater than VH-

Gust Load Factors

A wing suddenly penetrating a “sharp-edged” gust is pictured in Figure 7.29. The gust velocity is denoted by Udc in accordance with FAR notation. After penetrating the gust and before the wing begins to move upward, the angle-of-attack increment rdsulting from the gust, Да, equals

Да=-^ (7.58)

The increase in the wing’s lift then becomes

Д L = PV2Sa^

Before encountering the gust, in level flight,

.W = ^pV2Saa

The load factor, rt, resulting from the gust encounter therefore becomes

L

W

W + AL
W

Ude

Va

^rT777////////777T^,_______________ v_

Figure 7.29 A wing penetrating a sharp-edged gust.

In practice, one never encounters a truly sharp-edged gust. Therefore Udc is multiplied by an alleviation factor less than unity, again based on experience, which lessens the acceleration due to the gust. The final result, given in FAR Part 23, for the load factor resulting from a gust is expressed as follows. ‘ 1 iJ >

where

Positive and negative values of t/de up to 50 fps must be considered at Vc at altitudes between sea level and 20,000 ft. The gust velocity may be reduced linearly from 50 fps at 20,000 ft to 25 fps at 50,000 ft. Positive and negative gusts of 25 fps at VD must be considered at altitudes between sea level and

20,0 ft. This velocity can be reduced linearly to 12.5 fps at 50,000 ft.

For FAR Part 23, the foregoing criteria for the maneuvering and gust loads results in the type of V-n diagram pictured in Figure 7.30 In certifying an airplane, one must demonstrate the structural integrity of the airplane subjected to the aerodynamic loadings that can exist throughout the V-n diagram.