Aircraft Design: Synthesis and Analysis - part 9 pot

Operational Climb Normal climb to cruise altitude is carried out at the speed for best overall economy high speed climb which is considerably faster than the speed for maximum rate of cl

yengine is the distance from fuselage centerline to critical engine

T is the take-off thrust for the critical engine

lv is the vertical tail length (distance from c.g to vertical tail a.c.)

The total drag increment is the sum of the windmilling term and the trim drag.

These climb gradients are determined for all applicable weights, altitudes, and temperatures From this data, the maximum permissible weight for a given condition are established.

Operational Climb

Normal climb to cruise altitude is carried out at the speed for best overall economy (high speed climb) which is considerably faster than the speed for maximum rate of climb, which, in turn, is much faster than the speed for maximum climb gradient If fuel quantity is limiting, climb may be performed at the speed for best fuel economy (long range climb speed), a speed between the best overall economy climb speed and the best gradient climb speed Speed schedules are selected to be easily followed by the pilot with available instrumentation Recent introduction of automatic flight directors, makes this task easier The computed climb rates are integrated to produce time, fuel, and distance to climb to any altitude.

For approximate calculations, the additional fuel to climb to altitude (as compared with cruising the same distance at the cruise altitude) can be approximated by adding an increment to the total cruise fuel This increment has been determined for a wide range of weights for the DC-9-30, the DC-8-62, and the DC- 10-10 The results, expressed as a percentage of take-off weight are summarized in the following figure.

For different aircraft such as SST's we might think more fundamentally about the cause of this fuel

increment With a rough estimate of the overall propulsion efficiency, we can express the extra fuel used

in terms of the change in kinetic and potential energy The net result, expressed as a percentage of off weight, is:

take-Wclimb_fuel_inc / Wto (%) = h(kft) / 31.6 + [V(kts) / 844] 2

This agrees with the plot above, indicating a 1.3% increment for flight at M = 8 and 30,000 ft, while for

an SST that climbs to 60,000 ft and Mach 2.4, the increment is over 4.5%

Cruise Performance and Range

Introduction

The calculation of aircraft range requires that we describe the entire "mission" or flight profile A typical mission is illustrated below Altitude is shown as the vertical coordinate and distance on the horizontal axis Note that the altitude is greatly exaggerated: even on a short trip, the maximum altitude is only 1%

to 2% of the distance flown.

The mission profile consists of two portions: the nominal mission and the reserves Each of these is divided into several segments.

Taxi and take-off

A certain period of time is assumed for taxi and take-off This time varies depending on traffic and airport layout, but a period of about 15 minutes is a reasonable average, used in cost estimates The take- off segment also includes acceleration to the initial climb speed.

Initial Climb and Maneuver

The initial climb and air maneuvering involves airport-specific noise alleviation procedures and is

constrained by other regulations such as a 250 kt CAS speed limit below 10,000 ft in the U.S and some other countries This segment also involves acceleration to the enroute climb speed.

Climb

The climb segment of the mission is discussed in the previous section of these notes Detailed

calculations of time and fuel burned during climb may include several climb segments flown at different speeds Climb computations for supersonic aircraft are especially important, with several subsonic and supersonic segments computed separately For very short range missions the optimum cruise altitude is not reached and the climb may constititute half of the flight.

One cannot continue climbing for long because as the altitude increases at a given speed the CL

increases Speeding up would reduce CL, but this is limited by Mach number constraints or engine

power Thus, there is a best altitude for cruise and this optimum altitude increases as the aircraft weight decreases (as fuel is burned) For long range missions, the initial and final cruise altitudes are quite

different since the airplane weight changes substantially.

We could compute the altitude that leads to lowest drag at a given Mach number, but the optimum

altitude is usually a bit lower since it results in higher true speeds, smaller engines, reduced pressure loads on the fuselage, and more margin against buffet Thus, we will consider both initial and final cruise altitudes as design variables in the aircraft optimization Except in a few lightly-travelled regions,

variable altitude, or climbing cruise is not practical from a traffic control standpoint Thus the true

optimum is not generally attainable In the U.S ATC rules specify that aircraft be flown at specific flight altitudes so that the aircraft must cruise at constant altitude, and request clearance to climb to the next highest available altitude when sufficient fuel is consumed This leads to "step cruise" profiles shown on the previous page, with 1 to 3 steps of 4000 ft in altitude due to airway requirements Such stepped

profiles lead to reductions in cruise range by 1%-2% if the altitudes are chosen to be optimal for the weight at the beginning of the step.

Descent, Approach, and Landing

Like the climb segment, the descent is performed according to a specified airspeed schedule with speed limit restrictions below 10,000 ft and extra fuel associated with maneuvers on approach.

There are also other "reserve" requirements such as those associated with "ETOPS" (extended twin

engine operations) ETOPS rules currently require that the airplane be capable of flying with one engine inoperative to the nearest "suitable" airport Some operators are certified for 180 minute ETOPS Some are allowed 120 minutes, some 90, some only 75 Some aren't allowed to fly ETOPS under any

circumstances (Typically this is an economic decision made by the airline - not a reflection of relative safety - because of the onerous bookkeeping requirements.)

Domestic Reserves:

1 Climb from sea level to cruise altitude

2 Cruise to alternate airport at best speed and altitude (typ 250 n.mi.)

3 Descend to sea level

4 Cruise for 45 minutes at long range cruise speed and altitude

International Reserves:

1 Fuel to fly 10% of planned block time at long range cruise speed

2 Climb from sea level to cruise altitude

3 Cruise to alternate

4 Descend to 1500 ft and hold for 30 minutes

5 Descend to sea level

Estimating the Aircraft Range

For the purposes of this course, we compute an equivalent still-air range (no wind) using a simplified mission profile.

The fuel required for warm-up, taxi, take-off, approach, and landing segments is sometimes taken as a single item called maneuver fuel For our purposes, we estimate this as 0.7% of the take-off weight.

The fuel consumed in the climb segment is estimated in the previous section as a certain percentage of take-off weight above that needed to cruise the same distance at initial cruise altitude.

The descent segment of the mission requires slightly less fuel than would be required to cruise the same distance at the final cruise speed and altitude, so in the simplified computation the cruise extends to the destination airport and the mission is completed at the final cruise altitude.

The simplified mission is shown in the figure that follows.

In order to compute the cruise range, we estimate the weight at the beginning and end of the cruise segment:

Wi = Wtow - 5 Wmaneuver - Wclimb

Wf = Wzfw + Wreserves + 5 Wmaneuver

Where:

Wmaneuver is estimated (roughly) as 0.7% of the take-off weight

Wreserves is estimated even more roughly as 8% of the zero fuel weight

and Wclimb is estimated from the plot in the climb section of these notes.

The difference between initial and final cruise weights is the amount of fuel available for cruise This is related to the cruise range as follows

The specific range is the distance flown per unit weight of fuel burned, often in n.mi / lb It can be

related directly to the engine specific fuel consumption:

Specific Range = V / cT

where V is the true speed, c is the thrust specific fuel consumption, and T is the thrust.

In level flight (or approximately when the climb angle is very small):

T = D = W / (L/D),

so, Specific Range = V/c L/D 1/W

V/c L/D is sometimes called the range factor It is related to the aerodynamic (L/D) and propulsion

system (V/c) efficiencies.

The cruise range is then computed by integrating the specific range:

If the airplane is flown at a constant angle of attack (constant CL) and Mdiv in the isothermal atmosphere (above 36,089 ft) where the speed of sound is constant, then V, L/D, and c are nearly constant and:

This is known as the Breguet Range Equation When the altitude variation is such that L/D, V, or c is not constant, the integral may be evaluated numerically

When the value of brake power specific fuel consumption is assumed constant (propeller aircraft), the range equation becomes:

where η is the propeller efficiency and BSFC is the power specific fuel consumption in consistent units.

Range / Payload Diagram

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

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 V1 and greater than 1.05 Vmc

V lo Lift-off Speed Must be greater than 1.1 Vmu with all engines, or 1.05 Vmu with engine out

V 2 Take-off climb speed is the demonstrated airspeed at the 35 ft height Must be greater than 1.1 Vmcand 1.2 Vs, the stalling speed in the take-off configuration

Aircraft Performance FARs

● Take-off

● Landing

● Climb

I Kroo 4/20/96

Sec 25.115 Takeoff flight path.

(a) The takeoff flight path begins 35 feet above the takeoff surface at the end of the takeoff distance determined in accordance with Sec 25.113(a) (b) The net takeoff flight path data must be determined so that they

represent the actual takeoff flight paths (determined in accordance with Sec 25.111 and with paragraph (a) of this section) reduced at each point by a gradient of climb equal to

(1) 0.8 percent for two-engine airplanes;

(2) 0.9 percent for three-engine airplanes; and

(3) 1.0 percent for four-engine airplanes.

(c) The prescribed reduction in climb gradient may be applied as an

equivalent reduction in acceleration along that part of the takeoff flight path at which the airplane is accelerated in level flight.

Sec 25.117 Climb: general.

Compliance with the requirements of Secs 25.119 and 25.121 must be shown

at each weight, altitude, and ambient temperature within the operational

limits established for the airplane and with the most unfavorable center of gravity for each configuration.

Sec 25.119 Landing climb: All-engine-operating.

In the landing configuration, the steady gradient of climb may not be less than 3.2 percent, with

(a) The engines at the power or thrust that is available eight seconds

after initiation of movement of the power or thrust controls from the minimum flight idle to the takeoff position; and

(b) A climb speed of not more than 1.3 VS.

Sec 25.121 Climb: One-engine-inoperative.

(1) The critical engine inoperative and the remaining engines at the power

or thrust available when retraction of the landing gear is begun in

accordance with Sec 25.111 unless there is a more critical power operating condition existing later along the flight path but before the point at which

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 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 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.

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 fans were placed on the aircraft wings This is one reason why many prop-fan aircraft were designed as aft-mounted pusher configurations.

prop-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 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 log10 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.

Contours of equal loudness, plotted against intensity and frequency for the average ear.

The db(A) Scale

In an attempt to develop a noise measuring scale more responsive to these characteristics of the ear, the "A" scale was defined to weight noise at frequencies above 1000 Hz more heavily Noise measured on this scale is given in units of db(A).

Frequency response weighting for the "A" scale (From Peterson and Gross, 1967, p.9).

The Perceived Noise Level Scale PNdb and EPNdb

The scale most often used for aircraft noise measurement is the Perceived Noise Level (PNL) scale The scale requires that the SPL be measured in each of nine contiguous frequency ranges and combined according to a special

prescription, not too different from the A-weighting method, to provide a noise indication level The units are PNdb The effective perceived noise level, EPNL, accounts for duration and presence of discrete frequency tones It involves a correction factor that adds to the PNL when there are discrete tones in the noise spectrum It also includes a correction obtained by integrating the PNL over a 10 second time interval (Details are given in the full text of FAR Part 36.) The effective perceived noise level correlates with people's perceived noisiness as shown in the figures below.

Subjective Reactions to Various Noise Levels

The fact that people's perception of noise varies logarithmically with sound intensity results in some interesting

relations Note that as intensity is reduced by 50% the SPL changes by 10 log I1/I2 = -3db From the plot above this reduction would be only barely perceptible This is why noise reduction is a challenge To make something seem about half as noisy requires a reduction in SPL by about 10 db This is a reduction in I of about 90%!.

People's reactions also depend on how often such noises occur and a variety of methods for averaging noisiness have been used Sound exposure levels (SEL), noise exposure forecasts (NEF), and Day-Night-Levels all involve some kind

of averaging of multiple noise events, usually with higher weightings (e.g 10-20 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 metric known

as DNL as a method for predicting the effects on a population of the long term exposure to environmental noise The DNL metric is legislated to be the single system for measuring aircraft noise impact and for determining land use compatibility.

Noise maps typically depict the DNL 65dB contour as this is identified by federal guidelines as the threshold level of aviation and community noise that is "significant" In general, most land uses are considered to be compatible with DNLs less than 65 dB.

Sample of Estimated Noise Footprints Atlanta Airport in Jan 2000

Contours of constant DNL or EPNdB are often plotted to determine the areas affected at a given levels 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 noise has grown, but engine noise still accounts for most of the aircraft external noise The relative importance of various noise sources is shown in the figure below.

Propulsion-Related Noise Sources

Engine noise includes that generated at the fan inlet and exit, the combustor core, the turbine, and that caused by jet mixing While jet noise, caused by the turbulent mixing of the high speed exhaust with the ambient air, is a broad band noise source, with most of the energy directed aft of the engine at a 45 degree angle from the engine axis, the

turbomachinery noise often includes discrete tones associated with blade passage frequencies and their harmonics.

Jet noise levels vary as the sixth to eighth power of the jet exhaust velocity as shown in the figure below Early turbojet engines had exhaust velocities of nearly 2000 ft/sec and noise suppressors were used to try to obtain better mixing and

lower the noise associated with the strong shear Such suppressors were effective in reducing the low frequency noise, but often not the high frequencies and added weight and cost to the design.

The jet velocity was reduced considerably as the bypass ratio increased This is indicated by the figure below that applies to older engines, but is still representative of the trend observed for larger modern engines.

The net result is a substantial reduction in the noise due to jet mixing At the same time, though, the larger fan noise become more significant as seen from the figure below.

Computational aerodynamics is getting to the point of predicting such effects in a practical way, but it is a very complex problem, involving internal unsteady flows and propagation estimates.

Without such CFD tools, one can still estimate the effects of engine thrust levels, separation distances, and number of engines by scaling experimental results according to the fundamental physics of the problem as described in the following sections.

Non-propulsive noise

In addition to the engine noise, the shear of the boundary layer and unsteady vortex shedding from landing gear, landing gear doors, and other separated flows as well as flap edge flows contribute a significant part of the acoustic energy, especially for large aircraft on approach.