Solution
2.3.8 The Flight Envelope
2.3.8.2 Flight Envelope Examples
In this section, the flight envelopes of several different types of aircraft are presented, including a general aviation airplane, a commercial airliner, a supersonic military jet fighter, and a very high altitude, very high Mach number airplane. The wide variations in flight envelopes are demonstrated by these different aircraft types. A comparison of flight envelopes is also provided at the end of this section.
Example 2.5 General Aviation Airplane Flight Envelope: Beechcraft A36 The Beechcraft A36 Bonanza is a six-place high-performance single-engine aircraft designed and manufactured by the Beechcraft Aircraft Corporation, Wichita, Kansas (Figure 2.23). The A36 has a conventional
Figure 2.23 Beechcraft A36 Bonanza general aviation aircraft. (Source: Alan Lebeda, “Beechcraft A36 Bonanza” https://commons.wikimedia.org/wiki/File:Beech_A36_Bonanza_36_AN1890204.jpg, GFDL-1.2.
License at https://commons.wikimedia.org/wiki/Commons:GNU_Free_Documentation_License,_version_1 .2.)
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Figure 2.24 Beechcraft A36 Bonanza flight envelope.
configuration with a low-mounted main wing, straight horizontal stabilizers, single vertical tail, and retractable tricycle landing gear. The Bonanza has a wingspan of 33.5 ft (10.2 m), height of 8.58 ft (2.62 m), and length of 27.5 ft (8.38 m). The aircraft is powered by a Continental IO-550-B horizontally opposed six-cylinder fuel injected air-cooled piston engine with approximately 330 hp (246 kW), turning an 84.0 inch (2.13 m) diameter propeller. The aircraft has a maximum takeoff weight of approximately 3650 lb (1660 kg). The Beechcraft A36 Bonanza was introduced in 1970.
The flight envelope of the Beechcraft A36 Bonanza is shown in Figure 2.24, plotted as true airspeed (in units of knots true airspeed or KTAS) versus altitude. The flight envelope is for the A36 at its maximum gross weight of 3650 lb. Similar to most piston-powered, general aviation aircraft, the A36 has a simple flight envelope, bounded only by an aerodynamic lift limit, maximum altitude, and maximum airspeed. Starting at the lower left-hand corner of the flight envelope, the 1 g, sea level stall speed of the A36 is 52 KTAS (60 mph, 96 km/h), increasing to about 69 KTAS (79 mph, 128 km/h) at the maximum altitude of 18,500 ft (5640 m). The maximum airspeed at sea level is 237 KTAS (273 mph, 439 km/h). As with many general aviation aircraft, the A36 flight envelope is not very large, relative to other types of aircraft.
Example 2.6 Commercial Airliner Airplane Flight Envelope: Boeing 767 The Boeing 767 is a wide-body twin-engine jet airliner, designed and manufactured by Boeing Commercial Air-planes, Everett, Washington (Figure 2.25). The airliner has a conventional configuration with a low-mounted wing, straight horizontal stabilizers, single vertical tail, and retractable tricycle landing gear. The Boeing 767 has a wingspan of 156.1 ft (47.6 m), height of 52.0 ft (15.8 m) and
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Figure 2.25 Boeing 767 prototype airliner flying over Mount Rainier, Washington. (Source: Seattle Munici-pal Archives, “Boeing 767 Over Mount Rainier, circa 1980s” https://en.wikipedia.org/wiki/File:Boeing_767_
over_Mount_Rainier,_circa_1980s.jpg, CC-BY-2.0. License at https://creativecommons.org/licenses/by-sa/2 .0/legalcode.)
length of 180.25 ft (54.9 m). The aircraft is powered by two Pratt & Whitney PW4056 high bypass ratio turbofan engines, with the engines mounted in nacelles hung from pylons underneath the wings. Each engine provides an uninstalled, sea level, static thrust of 63,300 lb (282 kN). The air-craft has a maximum takeoff weight of approximately 412,000 lb (186,900 kg). The first flight of the Boeing 767 was on 26 September 1981.
The flight envelope of the Boeing 767 is shown in Figure 2.26, plotted as true airspeed (in units of knots true airspeed or KTAS) versus altitude. The flight envelope is for the Boeing 767 with two Pratt
& Whitney PW4056 turbofan engines and a gross weight of 412,000 lb. As might be expected, the flight envelope of a subsonic, commercial airliner covers a broader range of altitudes and airspeeds than a general aviation aircraft. The flight envelope has aerodynamic lift limit, maximum altitude, maximum Mach number, and maximum airspeed boundaries.
The 1 g, sea level stall speed is 133 KTAS (153 mph, 246 km/h), increasing to about 280 KTAS (322 mph, 519 km/h) at the maximum altitude of 43,000 ft (13,100 m). The passenger cabin pressur-ization limits the maximum altitude. The Boeing 767 has a maximum operating airspeed, VMO, of 360 KTAS (414 mph, 667 km/h) at sea level, increasing to about 518 KTAS (596 mph, 959 km/h) at an altitude of 26,000 ft (7900 m). Although not obvious in Figure 2.26, the flight envelope is limited to a maximum operating Mach number, MMO, of 0.86 from 26,000 ft up to its maximum altitude.
The maximum cruise airspeed of the Boeing 767 is less than the MMO, to provide a safety margin.
Example 2.7 Supersonic Military jet Flight Envelope: McDonnell Douglas F-15 The F-15 Eagle is an air-superiority military jet fighter aircraft designed and built by McDonnell Douglas Aircraft Company (now The Boeing Company), St Louis, Missouri (Figure 2.27). The aircraft has a high-mounted, swept main wing with a modified delta shape, twin vertical tails, all-moving hor-izontal stabilators, and twin turbofan jet engines. The F-15 airplane has a wingspan of 42.8 ft
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Figure 2.26 Boeing 767-300 flight envelope.
(13.0 m), height of 18.7 ft (5.7 m), and length of 63.7 ft (19.4 m). The aircraft is powered by two Pratt
& Whitney F100-PW-100 turbofan engines. Each engine produces an uninstalled, sea level static thrust of approximately 25,000 lb (111 kN) in full afterburner. The aircraft has a fully fueled take-off weight of approximately 42,000 lb (19,000 kg) and a landing weight of approximately 32,000 lb (14,500 kg). The aircraft has aerial refueling capability for extended duration flight. The first flight of the McDonnell Douglas F-15A was on 27 July 1972.
The flight envelope of the F-15 is shown in Figure 2.28, on a Mach number versus altitude plot.
Often, two power settings are shown on a flight envelope for a military jet with an afterburning jet engine, that of military thrust (maximum thrust without use of the afterburner) and maximum thrust (maximum thrust with afterburner operating). This is shown in Figure 2.28, where the smaller flight envelope boundary (dotted line) is for military thrust and the larger, complete flight envelope boundary (solid line) is for maximum thrust. The military thrust flight envelope indicates that the aircraft is barely able to exceed Mach 1 without afterburner, and has a ceiling of about 50,000 ft (15,000 m). When afterburner is used, the maximum thrust flight envelope gives a standard day, maximum Mach number of about 2.2 at an altitude of 36,000 ft (11,000 m) and a ceiling of about 60,000 ft (18,000 m). The low speed portion of the F-15 flight envelope is bounded by a lift limit boundary, where the lift boundary minimum Mach number increases with increasing altitude as shown, reaching high Mach numbers at high altitudes.
Example 2.8 High Mach Number, High Altitude Aircraft Flight Envelope: Lockheed SR-71 The SR-71Blackbird, designed and manufactured by the Lockheed Advanced Development
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Figure 2.27 Mcdonnell douglas F-15 Eagle supersonic jet fighter aircraft (F-15B two-seat version shown).
(Source: NASA.)
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Figure 2.28 McDonnell Douglas F-15A Eagle flight envelope. (Source: Adapted from Vachon, M.J., Moes, T.R, and Corda, S., “Local Flow Conditions for Propulsion Experiments on the F-15B Propulsion Flight Test Fixture,” NASA TM-2005-213670, November 2005, Fig. 3.)
Company (commonly called the “Skunk Works”), Palmdale, California, is an ultra-high-altitude, supersonic reconnaissance aircraft (Figure 2.29). The SR-71 has a wingspan of 55.6 ft (16.9 m), height of 18.5 ft (5.64 m), and length of 107.4 ft (32.74 m). The aircraft has a long narrow fuselage, a large delta wing, two large engine nacelles mounted in the wings, and twin canted all-moving rudders. Lifting surfaces called “chines” extend along the sides of the fuselage, from the aircraft nose to the intersection of the wing and fuselage. The aircraft has a tandem, two-place cockpit configuration with flight controls in the forward cockpit only. The SR-71 has titanium construction and is painted black to increase radiative heat transfer for flight at the high temperatures
k k Figure 2.29 Lockheed SR-71 Blackbird reconnaissance aircraft flying near Mt Whitney, California.
(Source: NASA.)
associated with high Mach number supersonic flight: hence its designation as the Blackbird. The aircraft is powered by two Pratt & Whitney PW J58 turbojet engines. A prominent feature of the propulsion system is the cone-shaped spikes at the entrance of each nacelle. Each engine produces an uninstalled, sea level static thrust of approximately 34,000 lb (151 kN) in full afterburner. The aircraft has a fully fueled takeoff weight of approximately 143,000 lb (65,000 kg). The aircraft has aerial refueling capability for extended duration flight. The first flight of the Lockheed SR-71 Blackbird was on 22 December 1964.
The flight envelope of the Lockheed SR-71 is shown in Figure 2.30, on a Mach number versus altitude plot. Even though the SR-71 was a supersonic aircraft, its flight envelope is markedly different from the F-15A. The SR-71 flight envelope looks narrow in contrast to the more full flight envelope of the F-15. The SR-71 design was very focused on its mission to fly at triple-sonic Mach numbers at high altitude. In this sense, the aircraft was somewhat point designed for this specific flight condition, rather than being designed to fly in a broader flight envelope.
The minimum airspeed boundary on the left side of the flight envelope is specified in KEAS, for knots equivalent airspeed. (This is yet another type of airspeed, which is typically used in very high speed aircraft. The structural loads correlate with the square of the equivalent airspeed, which is an important consideration for very high Mach number aircraft, such as the SR-71.) The minimum airspeed below 25,000 ft (7600 m) is 145 KEAS and increases to 300 KEAS above 25,000 ft and below Mach 1. Above Mach 1, the minimum airspeed increases to 310 KEAS. The maximum altitude is above 80,000 ft (24,000 m), but this can only be reached when flying at the maximum Mach number of 3.2. Unlike some flight envelopes where flight on the Mach limit boundary may not be advisable, the SR-71 was designed for sustained cruise at its limit Mach number and altitude.
The Mach number limit decreases with decreasing altitude as shown, with a sea-level maximum
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Figure 2.30 The SR-71 Blackbird flight envelope. (Source: S. Corda, et al., “The SR-71 Test Bed Aircraft:
A Facility for High-Speed Flight Research,” NASA TP-2000-209023, June 2000, Fig. 3.)
Mach number of about 0.76. In actuality, this maximum Mach number boundary corresponds to a maximum equivalent airspeed limit of 500 KEAS (575 mph, 926 km/h), a limit set by aircraft structural considerations.