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An aircraft does not have a single number that represents its range. Even the maximum range is subject to interpretation, since the maximum range is generally not very useful as it is achieved with no payload. To represent the available trade-off between payload and range, a range-payload diagram may be constructed as shown in the figure below. At the maximum payload weight is often constrained by the aircraft structure, which has been designed to handle a certain maximum zero fuel weight. (Sometimes the maximum payload weight is limited by volume, but this is rather rare. It has been noted that the MD-11 would exceed its maximum zero fuel weight if the fuselage were filled with ping pong balls.) So, the airplane take-off weight can be increased from the zero fuel weight by adding fuel with a corresponding increase in range. This is the initial flat portion of the payload-range diagram. At some point, the airplane could reach a limit on maximum landing weight. This usually happens only when the required reserve fuel is very large. Usually we can increase the weight until the airplane reaches its maximum take-off weight, with the full payload. If we want to continue to add fuel (and range) from this point on, we must trade payload for fuel so as not to exceed the maximum take-off weight. At some point, the fuel tanks will be full. We could increase the range further only by reducing the payload weight and saving on drag with a fixed fuel load. This is the final very steep portion of the payload range diagram. Usually we are most interested in the range with maximum take-off weight and here we will focus on the range of the aircraft with a full compliment of passengers and baggage. This point is somewhere on the portion of the curve labeled maximum take-off weight, but often at a point considerably lower than that associated with maximum zero fuel weight (since the maximum zero fuel weight may be chosen to accommodate revnue cargo on shorter routes and to provide some growth capability.) Take-Off Field Length Computation Inputs The following speeds are of importance in the take-off field length calculation: V mu Minimum Unstick Speed. Minimum airspeed at which airplane can safely lift off ground and continue take-off. V mc Minimum Control Speed. Minimum airspeed at which when critical engine is made inoperative, it is still possible to recover control of the airplane and maintain straight flight. V mcg Minimum control speed on the ground. At this speed the aircraft must be able to continue a straight path down the runway with a failed engine, without relying on nose gear reactions. V 1 Decision speed, a short time after critical engine failure speed. Above this speed, aerodynamic controls alone must be adequate to proceed safely with takeoff. V R Rotation Speed. Must be greater than V 1 and greater than 1.05 V mc V lo Lift-off Speed. Must be greater than 1.1 V mu with all engines, or 1.05 V mu with engine out. V 2 Take-off climb speed is the demonstrated airspeed at the 35 ft height. Must be greater than 1.1 V mc and 1.2 V s , the stalling speed in the take-off configuration. Aircraft Performance FARs ● Take-off ● Landing ● Climb I. Kroo 4/20/96 the landing gear is fully retracted; and (2) The weight equal to the weight existing when retraction of the landing gear is begun, determined under Sec. 25.111. (b) Takeoff; landing gear retracted. In the takeoff configuration existing at the point of the flight path at which the landing gear is fully retracted, and in the configuration used in Sec. 25.111 but without ground effect, the steady gradient of climb may not be less than 2.4 percent for two-engine airplanes, 2.7 percent for three-engine airplanes, and 3.0 percent for four- engine airplanes, at V2 and with (1) The critical engine inoperative, the remaining engines at the takeoff power or thrust available at the time the landing gear is fully retracted, determined under Sec. 25.111, unless there is a more critical power operating condition existing later along the flight path but before the point where the airplane reaches a height of 400 feet above the takeoff surface; and (2) The weight equal to the weight existing when the airplane's landing gear is fully retracted, determined under Sec. 25.111. (c) Final takeoff. In the en route configuration at the end of the takeoff path determined in accordance with Sec. 25.111, the steady gradient of climb may not be less than 1.2 percent for two-engine airplanes, 1.5 percent for three-engine airplanes, and 1.7 percent for four-engine airplanes, at not less than 1.25 VS and with (1) The critical engine inoperative and the remaining engines at the available maximum continuous power or thrust; and (2) The weight equal to the weight existing at the end of the takeoff path, determined under Sec. 25.111. (d) Approach. In the approach configuration corresponding to the normal all-engines-operating procedure in which VS for this configuration does not exceed 110 percent of the VS for the related landing configuration, the steady gradient of climb may not be less than 2.1 percent for two-engine airplanes, 2.4 percent for three-engine airplanes, and 2.7 percent for four- engine airplanes, with (1) The critical engine inoperative, the remaining engines at the available takeoff power or thrust; (2) The maximum landing weight; and (3) A climb speed established in connection with normal landing procedures, but not exceeding 1.5 VS. Sec. 25.123 En route flight paths. (a) For the en route configuration, the flight paths prescribed in paragraphs (b) and (c) of this section must be determined at each weight, altitude, and ambient temperature, within the operating limits established for the airplane. The variation of weight along the flight path, accounting for the progressive consumption of fuel and oil by the operating engines, may be included in the computation. The flight paths must be determined at any selected speed, with (1) The most unfavorable center of gravity; (2) The critical engines inoperative; (3) The remaining engines at the available maximum continuous power or thrust; and (4) The means for controlling the engine-cooling air supply in the position that provides adequate cooling in the hot-day condition. (b) The one-engine-inoperative net flight path data must represent the actual climb performance diminished by a gradient of climb of 1.1 percent for two-engine airplanes, 1.4 percent for three-engine airplanes, and 1.6 percent for four-engine airplanes. (c) For three- or four-engine airplanes, the two-engine-inoperative net flight path data must represent the actual climb performance diminished by a gradient of climb of 0.3 percent for three-engine airplanes and 0.5 percent for four-engine airplanes. Noise Introduction Aircraft noise is hardly a new subject as evidenced by the following note received by a predecessor of United Airlines in about 1927. Although internal noise was the major preoccupation of aircraft acoustic engineers for many years and still is important, the noise produced by the aircraft engine and experienced on the ground has become a dominant factor in the acceptability of the airplane. With the development of high bypass ratio engines, noise due to other sources has become important as well. Internal noise is treated by placing the engines to minimize the noise directly radiated to the cabin, (e.g. using the wing as a shield) and by providing insulating material over the entire surface of the flight and passenger compartments. If the engines are mounted on the fuselage, vibration isolation is an important feature. In the late 1980's when prop-fans were being developed, internal noise become an important consideration again. It was, at one point, estimated that 2000 lbs of additional acoustic insulation would be required to reduce cabin noise levels to those of conventional jets if prop- fans were placed on the aircraft wings. This is one reason why many prop-fan aircraft were designed as aft-mounted pusher configurations. External noise is affected by the location of the source and observer, the engine thrust, and a number of factors that influence the overall configuration design. These will be discussed in detail later in this chapter, but first we must understand the origins of noise and its measurement. The Nature of Noise A sound wave carries with it a certain energy in the direction of propagation. The sound becomes audible because of energy which originates at the source of the sound vibrations and which is transported by the sound waves. The changes in air pressure which reach the eardrum set it vibrating; the greater these changes, the louder is the sound. The intensity of sound, I, is the quantity of energy transferred by a sound wave in 1 sec through an area of 1 cm. For a plane sine wave: I = p 2 / 2 ρ c where: p = the amplitude of the varying acoustic excess pressure ρ = air density c = speed of sound I is usually expressed in ergs per cm 2 per sec. (mW/m 2 ) The human ear responds to a frequency range of about 10 octaves. It responds to air vibrations whose amplitude is hardly more than molecular size; it also responds without damage to sounds of intensity 10 13 to 10 14 times greater without damage. The response of the ear is not proportional to the intensity, however. It is more nearly proportional to the logarithm of the intensity. If sound intensity is increased in steps of what seem to be equal increments of loudness, we find that the intensities form a sequence of the sort 1, 2, 4, 8, 16, or 1, 10, 100, 1000 not 1, 2, 3, 4, or 1, 10, 19, 28, . Since the ear responds differently to different frequencies, the logarithmic relation of intensity to loudness is not generally perfect, but it is easier to handle than the enormous numbers involved in the audible intensity range. Therefore, the intensity level of sound is defined in decibels as 10 times the logarithm of the ratio of the intensity of a sound, I, to a reference level defined as 10 -9 erg/cm 2 /sec. Thus: Sound intensity level (SPL), decibels = 10 log 10 I / 10 -9 The response of the ear is not exactly proportional to the decibel scale. In addition to the physical quantities, intensity and frequency, the psycho-physiological quantities of loudness and pitch must be considered. The loudness of a sound depends both on intensity level and frequency; pitch depends chiefly on frequency but to some extent on intensity. Contours of equal loudness for the average person are plotted in the following figure from Ref. 2. The actual contour values are the values of SPL at 1 kHz. [...]... and applicable only on approach, but usually is not the major part of the noise contribution Example Computations (DC-10) Take-off: Base = 101 PNdb, 25,000 lb thrust, 1 engine, 1000ft + 4.8 for 3 engines + 1.9 for 40,000 lb SLS thrust engines - 4.0 for 1500 ft altitude at 6500m from start of take-off - 4.0 correction to EPNdb on take-off -Total: 99.7 EPNdb (Flight measurement shows 98 db) Sideline:... the base case with which we start the analysis The order of magnitude of the D.O.C sensitivity factors is usually quite similar for different aircraft, however, so a good impression of the effect of design changes on D.O.C can be obtained from the following table (Fig 7) developed for the DC-l0-l0 trijet DIRECT OPERATING COST SENSITIVITY FACTORS (Based on DC-1 0-1 0, 1967 ATA Method) DOC 1.1 10% INCREASE... engines - 6.5 for 1476 ft (450m) from centerline (effective distance = 1476*1.25 = 1845ft) - 4.0 correction to EPNdb on take-off -Total: 97.2 EPNdb (Flight measurement shows 96 db) Approach: Base = 101 PNdb, 25,000 lb thrust, 1 engine, 1000ft + 4.8 for 3 engines + 1.9 for 40,000 lb SLS thrust engines + 9.1 for 370 ft altitude at 6562 ft (2000m) from runway - 7.0 correction for 45% throttle - 5.0... of 300,000 lbs -Total (add I's): 105.2 EPNdb (Flight measurement shows 106 db) Operating Costs (based on a summary by R.S Shevell) The figure of merit used to evaluate competitive airplane designs is always based on a cost-benefit analysis The minimum cost per unit of work performed must be the criterion, here the work is performed equally well by the competing designs If one design excels in some... continuing to improve nacelle treatments, and operating the aircraft with take-off power cutbacks and 2-segment approaches The picture below shows a large acoustic test facility used by NASA Lewis as part of their work on engine noise reduction The Regulations Noise regulations in FAR Part 36 Stage 3 include restrictions on noise in 3 conditions The take-off noise is defined as the noise measured at a distance... Different aircraft may have very different footprints, this is especially obvious when comparing 2 vs 4 engine aircraft, because of different climb rates Sources of Noise Aircraft noise is generally divided into two sources: that due to the engines, and that associated with the airframe itself As higher bypass ratio engines have become more common and aircraft have become larger, interest in airframe-related... and is attached to these notes Direct operating costs can be expressed in terms of $/hour, $/mile, ¢/seat-mile, or for cargo aircraft, ¢/ton-mile Costs in terms of $/mile indicate the maximum loss to an operator with an empty airplane, while costs per unit productivity such as ¢/seat-mile, or ¢/ton-mile are indicative of the fare that must be charged with reasonable load factors Current practice usually... consumption of ink on the pages of a 4-color brochure — — Examples of justified modification of the ATA equations by aircraft manufacturers are 1) Maximum engine parts replacement cost per hour is guaranteed by the engine manufacturer Then this value may be safely used in lieu of the equation 2) The design uses significantly lower numbers of components than previous designs, e.g., fewer actuators, fewer... forecasts (NEF), and Day-Night-Levels all involve some kind of averaging of multiple noise events, usually with higher weightings (e.g 1 0-2 0 times) for night flights These are intended to capture the community response in a statistical way (See figure below.) Community Response to Different Noise Levels Footprints The U.S Environmental Protection Agency (EPA) uses a Day-Night Average A-Weighted Sound Level... 19% 16% 13% 12% 13% 11% 9% 8% 100% 100% 100% 100% NOTE: BASED ON DC-1O TWIN 500 N Mi RANGE Figure 8 It is common to estimate aircraft manufacturing cost in terms of $ /lb of airframe weight empty plus the engine cost Actually each portion of the airframe has a different cost per pound The table in Figure 9 shows the distribution of airplane costs between basic structure and the various aircraft . percent for two-engine airplanes, 1.4 percent for three-engine airplanes, and 1.6 percent for four-engine airplanes. (c) For three- or four-engine airplanes, the two-engine-inoperative net . levels to those of conventional jets if prop- fans were placed on the aircraft wings. This is one reason why many prop-fan aircraft were designed as aft-mounted pusher configurations. External. (4) The means for controlling the engine-cooling air supply in the position that provides adequate cooling in the hot-day condition. (b) The one-engine-inoperative net flight path data must