Aircraft Design: Synthesis and Analysis - part 8 docx

Aircraft Weight EstimationOverview The multitude of considerations affecting structural design, the complexity of the load distribution through a redundant structure, and the large numbe

● Stress corrosion resistance

● Exfoliation corrosion resistance

Acoustic fatigue testing is important in affected portions of structure.

Doublers are used to reduce stress concentrations around splices, cut-outs, doors, windows, access panels, etc., and

to serve as tear-stoppers at frames and longerons.

Generally DC-10 uses 2024-T3 aluminum for tension structure such as lower wing skins, pressure critical fuselage skins and minimum gage applications This material has excellent fatigue strength, fracture toughness and notch sensitivity 7075-T6 aluminum has the highest strength with acceptable toughness It is used for strength critical structures such as fuselage floor beams, stabilizers and spar caps in control surfaces It is also used for upper wing skins.

For those parts in which residual stresses could possibly be present, 7075-T73 material is used 7075-T73 material has superior stress corrosion resistance and exfoliation corrosion resistance, and good fracture toughness Typical applications are fittings that can have detrimental preloads induced during assembly or that are subjected to

sustained operational loads Thick-section forgings are 7075-T73, due to the possible residual stresses induced during heat treatment The integral ends of 7075-T6 stringers and spar caps are overaged to T73 locally This unique use of the T73 temper virtually eliminates possibility of stress corrosion cracking in critical joint areas

On the Cessna Citation, a small high speed airplane, 0.04 inches is the minimum gauge on the inner portion of the wing, but 0.05 inches is preferred Ribs may be as thin as 0.025 inches Spar webs are about 0.06 inches at the tip For low speed aircraft where flush rivets are not a requirement and loads are low, minimum skin gauge is as low as 0.016 inches where little handling is likely, such as on outer wings and tail cones Around fuel tanks (inboard wings) 0.03 inches is minimum On light aircraft, the spar or spars carry almost all of the bending and shear loads Wing skins are generally stiffened Skins contribute to compression load only near the spars (which serve as

stiffeners in a limited area) Lower skins do contribute to tension capability but the main function of the skin in these cases is to carry torsion loads and define the section shape.

In transport wings, skin thicknesses usually are large enough, when designed for bending, to handle torsion loads Fuel density is 6.7 lb/gallon.

Structural Optimization and Design

Structures are often analyzed using complex finite element analysis methods These tools have evolved over the past decades to be the basis of most structural design tasks A candidate structure is analyzed subject to the

predicted loads and the finite element program predicts deflections, stresses, strains, and even buckling of the many elements The designed can then resize components to reduce weight or prevent failure In recent years, structural optimization has been combined with finite element analysis to determine component gauges that may minimize weight subject to a number of constraints Such tools are becoming very useful and there are many examples of substantial weight reduction using these methods Surprisingly, however, it appears that modern methods do not do

a better job of predicting failure of the resulting designs, as shown by the figure below, constructed from recent Air Force data.

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Aircraft Weight Estimation

Overview

The multitude of considerations affecting structural design, the complexity of the load distribution

through a redundant structure, and the large number of intricate systems required in an airplane, make weight estimation a difficult and precarious career When the detail design drawings are complete, the weight engineer can calculate the weight of each and every part thousands of them and add them all up and indeed this is eventually done But in the advanced design phase, this cannot be done because there are no drawings of details In the beginning, the advanced design engineer creates only a 3-view and some approximate specifications The rest of the design remains undefined

One may start the design process with only very simple estimates of the overall empty weight of the aircraft based purely on statistical results Some of these correlations are not bad, such as the observation that the ratio of empty weight to gross weight of most airplanes is about 50% Of course, this is a very rough estimate and does not apply at all to aircraft such as the Voyager or other special purpose designs

One of the interesting aspects of this data is that it does not seem to follow the expected "square-cube" law We might expect that the stress in similar structures increases with the linear dimensions if the imposed load is proportional to the structural weight because the latter grows as the cube of the linear dimension while the material cross-section carrying the load grows as the square There are several

reasons that the relationship is not so simple:

1 Some aircraft components are not affected very much by the square-cube law

2 New and better materials and techniques have helped empty weight

3 Higher wing loadings are used for larger aircraft

4 Some portions of airplanes have material size fixed by minimum "handling" thickness

The figures below show some of this effect They are from a classic paper by F.A Cleveland entitled,

"Size Effects in Conventional Aircraft Design" (J of Aircraft, Nov 1970)

" As might be expected there is a considerable diversity of scaling among components This is

particularly apparent between the airframe components where the square-cube law has a strong influence,

as on the lifting surfaces, and those where it has little effect, as on the fuselage The landing gear,

powerplant, and air-conditioning system, tend to increases gross weight, but the electrical system,

electronics, instruments ice-protection and furnishings are affected more by mission requirements than

by aircraft size On balance, the overall factor of about 2.1 reflects the tendency of the square/cube law to project a modestly increasing structural weight fraction with size."

The next step in weight estimation involves a component build-up, in much the same fashion as we

considered aircraft drag This is the approach described here It involves a combination of structural analysis and statistical comparisons, with the complexity of the analysis dependent on the available

information and computational resources

If the analysis is too simple or the statistical parameters are not chosen properly, these correlations have dubious validity In some cases such correlations can be expected to hold for a very restricted class of aircraft, or to hold with accuracy sufficient for presentation only on log-log plots It is very important that the method be based on the fundamental physics of the design rather than on a ad-hoc correlation

parameter One must also be cautious of the self-fulfilling nature of such correlations If one expects, based on historical precedent that a wing should weigh 20,000 lbs, one may work hard to reduce the weight if the original design weighs 25,000 lbs When the design is finally brought down to the initial estimate the project leader may be satisfied, and the new design appears as a point on the next edition of the plot

The following sections provide methods for estimating the component weights for advanced design

purposes Some of the sections (e.g wing weight estimation) provide a more in-depth discussion of the derivation of the method and comparisons with several aircraft The correlations vary from fair to very good, and provide a reasonable basis for estimating weights They are based on a variety of sources, from published methods of aircraft manufacturers to methods developed by NASA and some developed

originally here We do not use Boeing's method or Douglas' method because these methods constitute some of the most proprietary parts of the preliminary design systems in use at these companies

Component Weight Methods

In the following sections, aircraft weights are divided into the following components Each company divides the weight into different categories, so it is sometime difficult to compare various components

from different manufacturers Here we divide the system into the following categories:

Instruments and Navigation

Hydraulics and Pneumatics

Sample Weight Statements

Companies typically present a summary of these items in an airplane weight statement Some examples are available from this link

Total Weights

The component weights are grouped together to form a number of total weights that are routinely used in aircraft design This section lists some of the typical weights and their definitions

Component Weights

1 Wing

The wing weights index is related to the fully-stressed bending weight of the wing box It includes the effect of total wing load (at the ultimate load factor, Nult), span (b), average airfoil thickness (t/c), taper (λ), sweep of the structural axis (Λea), and gross wing area (Swg) The total wing weight is based on this bending index and actual data from 15 transport aircraft Additional information on the wing weight

computation is provided from this link

2 Horizontal Tail

The horizontal tail weight, including elevator, is determined similarly, but the weight index introduces both exposed and gross horizontal tail areas as well as the tail length (distance from airplane c.g to aerodynamic center of the horizontal tail) The method assumes that the elevator is about 25% of the horizontal tail area Several sources suggest treating V-tails as conventional horizontal tails with the area and span that would be obtained if the v-tail dihedral were removed

3 Vertical Tail and Rudder

This graph shows the vertical fin (vertical tail less rudder) weight The rudder itself may be assumed to occupy about 25% of SV and weighs 60% more per unit area The weight of the vertical portion of a T-tail is about 25% greater than that of a conventional tail; a penalty of 5% to 35% is assessed for vertical tails with center engines (The formula below does not include the rudder weight, but Sv is the area of the vertical tail with rudder.)

4 Fuselage

Fuselage weight is based on gross fuselage wetted area (without cutouts for fillets or surface intersections and upon a pressure-bending load parameter

The pressure index is: Ip = 1.5E-3 * P * B

The bending index is: Ib = 1.91E-4 N * W * L / H2

where: P = maximum pressure differential (lb / sq ft)

B = fuselage width (ft)

H = fuselage height (ft)

L = fuselage length (ft)

N = limit load factor at ZFW

W = ZFWmax - weight of wing and wing-mounted engines, nacelles and pylons

The fuselage is pressure-dominated when: Ip > Ib

When fuselage is pressure dominated: Ifuse = Ip

When fuselage is not pressure-dominated: Ifuse = (Ip2 + Ib2) / (2 Ib)

To better represent the distributed support provided by the wing, the effective fuselage length is taken to

be the actual fuselage length minus the wing root chord / 2

The fuselage weight is then:

Wfuse = (1.051 + 102 * Ifuse) * Sfuse

Subtract 8.5% for all-cargo aircraft.

5 Landing Gear

Gear weight is about 4.0% of the take-off weight This is the total landing gear weight including

structure, actuating system, and the rolling assembly consisting of wheels, brakes, and tires The rolling assembly is approximately 39% of the total gear weight:

Wgear = 0.04 TOW

6 Surface Controls

Surface controls are the systems associated with control surface actuation, not the control surfaces

themselves This system weight depends primarily on the area of the horizontal and vertical tails

Wsc = Isc * (SH + SV)

where:

Isc = 3.5 (lb / sq ft) for fully-powered controls

2.5 for part-power systems

1.7 for full aerodynamic controls

7 Propulsion System

The propulsion system weight is about 60% greater than that of the dry engine alone The engine

structural section, or nacelle group, and the propulsion group which includes the engines, engine exhaust, reverser, starting, controls, lubricating, and fuel systems are handled together as the total propulsion weight This weight, which includes nacelle and pylon weight, may be estimated as:

Wpropulsion = 1.6 Wengine dry weight

The correlation below may be used if engine dry weight is not available

8 Auxiliary Power Unit (APU)

Smaller airplanes may not have an APU, but if it is there, its weight may be estimated by:

Wapu (lbs) = 7 * Nseats

We will assume that there is no APU for airplanes with fewer than 9 seats

9 Instruments and Navigational Equipment

WInst&Nav = 100 lbs for business jet, 800 lb for domestic transport, 1200 lb for long range or overwater operation

10 Hydraulics and pneumatics

Here we will not distinguish between the actual number of seats and the maximum number Similarly, a more accurate furnishings weight is based on the actual division of seats between first class and coach, and the maximum number of seats that can be installed on the aircraft For our purposes we simply use:

Wfurnish (lbs) (43.7 -.037*Nseats)*Nseats + 46.*Nseats

When the number of seats exceeds 300, we use:

Wfurnish (43.7 -.037*300)*Nseats + 46.*Nseats

For overwater or long range aircraft, we add another 23 lbs per seat For business jets, most anything is possible

14 Air conditioning and anti-ice

Data on these systems suggest a very large scatter We use:

Waircond (lbs)= 15 * Nseats

although this is probably too high for very large aircraft

15 Operating Items Less Crew

Woperitems (lbs) = 17 * Npax, Short range, austere

28 * Npax, medium range, coach or business jet

40 * Npax, long range, first class

Wattend = 130 + 20 lbs per attendant

18 Payload

Typically 205 lbs / passenger (165 per person + 40 lbs baggage) is used by major U.S airlines 210

lbs/passenger is sometimes assumed for international operations One generally allocates 4.5 ft3 per passenger for baggage volume or 5.2 ft3 for international operations

The aircraft may also carry cargo as desired An added cargo weight of 20lbs / pax is reasonable in the determination of maximum zero fuel weight if no other guidelines are available Typical passenger load factors (actual / maximum) range from 60% to 70%

For cargo aircraft 8.9 lbs/ft3 is typical of containerized cargo, while bulk cargo occupies about 7.7 lb /

ft3 Typical cargo laod factors are 40% for containerized and 25% for bulk cargo

Wing Weight

The wing weight is taken as the sum of two terms, a portion that varies directly with the wing area and a part that varies in proportion to the amount of material required to resist the applied bending loads This estimate is done statistically, but is based on an index that is related to the weight of a fully-stressed beam A derivation is given here

Wing Weight Breakdown

Wing Spars, Webs,

Bending, Spars, Webs,

Spoilers and Supports 650Ailerons and Supports 1,305Flaps and Supports 5,960Wing/Fuselage Fairing 960Wing Fuselage Attach 1,000

Primer and Sealant 30

Derivation of the Wing Weight Index

Consider a section of a wing structural box assumed symmetrical about a neutral axis If we consider only the bending stress in the wing upper and lower skins, then, the bending moment is related to the normal stress by:

Mb = 2 σA

2

t 2

= σA

t 2

where Mb is the bending moment at the spanwise section under consideration, t is the section thickness, and A is the total cross sectional area of the stressed material If the skins are carrying a given allowable stress then:

σallow =

2 Mb(y) tA

where an average value of t/c is used If the wing has a linear chord distribution then:

c(y) =

S b(

2 1+λ ) (1-η(1 - λ))

where η is the dimensionless span statio, 2y/b The wing bending moment is related to the lift by:

Sample Aircraft Weight Statements

Small Commercial Aircraft

Larger Commercial Aircraft

Military Aircraft

* Estimated

Total Weights

The component weights are grouped together to form a number of total weights that are routinely used in aircraft design This section lists some of the typical weights and their definitions

● Maximum Taxi Weight

● Maximum Brake Release Weight

● Maximum Landing Weight

● Maximum Zero-Fuel Weight

● Operational Empty Weight

● Manufacturer's Empty Weight

The weights are defined as follows:

MAXIMUM TAXI WEIGHT

The certified maximum allowable weight of the airplane when it is on the ground This limit is

determined by the structural loading on the landing gear under a specified set of conditions and/or wing bending loads

MAXIMUM BRAKE RELEASE WEIGHT

The certified maximum weight of the airplane at the start of takeoff roll Maximum Brake Release

Weight will always be less than Maximum Taxi Weight to allow for fuel burned during taxi Brake release weight, in operation, may be limited to values less than Maximum Brake Release Weight by airplane performance, and/or airfield characteristics

MAXIMUM LANDING WEIGHT

The certified maximum weight of the airplane at touch-down This limit is determined by the structural loads on the landing gear, but not under the same conditions that determine maximum taxi weight

Landing weight, in operation, may also be limited to values less than Maximum Landing Weight by airplane performance and/or airfield characteristics

MAXIMUM ZERO FUEL WEIGHT

The maximum weight of the airplane without usable fuel

OPERATIONAL EMPTY WEIGHT

Manufacturer's empty weight plus standard and operational items Standard items include unusable fuel, engine oil, emergency equipment, toilet fluid and chemicals, galley, buffet and bar structure, etc

Operational items include crew and baggage, manuals and navigational equipment, removable service equipment for cabin, galley and bar, food and beverages, life vests, life rafts, etc

MANUFACTURER'S EMPTY WEIGHT

Weight of the structure, powerplant, furnishings, systems, and other items of equipment that are

considered an integral part of a particular airplane configuration It is essentially a "dry" weight,

including only those fluids contained in a closed system (such as hydraulic fluid)

Other totals that are commonly used include:

Actual take-off weight

Maximum take-off weight

Landing weight

Zero payload weight

The airplane zero fuel weight is the sum of each of the components as shown below Note that the actual zero fuel weight is generally less than the maximum zero fuel weight The maximum zero fuel weight, may in fact exceed the zero fuel weight that is possible for this particular aircraft, but the structure is designed to handle the larger values to accommodate future growth

Wzfw = Wwing + Whoriz + Wvert + Wrud + Wfuse

+ Wcrew + Wopitems + Waircond + WElectn + WElectc

+ Wsurfc + Wgear + Whydpnu + Wpropul + WAttend

+ Wpax + Wbags + Wcargo + WOther

+ Winst + Wapu + Wfurnish

Interactive Placard Diagram

The placard diagram for your aircraft is shown above The input parameters may be specified here and are defined as follows:

Init Cruise Altitude: Initial cruise altitude (ft)

Cruise Mach: Design cruise Mach number

Altitude at Vc: Altitude for which the airplane is to be capable

of operating at the design Mach number (ft)

Note that the Vc altitude (also known as the "knee" of the placard) determines the maximum dynamic pressure for which the aircraft is to be designed Typical values for transonic aircraft are in the 26,000 - 28,000 ft range

For SST's, the placard is often more complex, but one should choose the Vc altitude here to produce a reasonable low altitude maximum speed The Concorde, for example, has a Vc speed of about 400 kts EAS up to 30,000 ft A cruise Mach number of 2.0 and a Vc altitude of 57,000 ft leads to this value of

Vc The Concorde actually allows higher q's above 32,000 ft, but for our calculations of gust loads, this simpler placard will suffice

Interactive V-n Diagram

The V-n diagram for your aircraft is shown above based on parameters specified elsewhere See the placard diagram for calculation of the design airspeeds Vc and Vd

Balance, the proper placement of the center of gravity (c.g.) with respect to the aerodynamic center of the wing, is a vital element of a proper, and safe, flying airplane In order to attain proper stability the c.g must never,under any condition of fuel loading, passenger loading, cargo loading or landing gear retraction or extension, be aft of the aft stability limit For proper control, usually trim in the landing approach configuration or nose wheel lift off, the c.g must never be forward of the most forward aerodynamic limit.

After completing the first weight estimate of a configuration, the center of gravity of the airplane should be estimated

A moment schedule should be constructed listing each element of the airplane, its weight and the location of its center

of gravity The c.g.'s are located by their distances from two mutually perpendicular axes These axes may be arbitrarily chosen but the horizontal axis is usually taken parallel to the fuselage floor and the vertical axis is best selected near the estimated airplane c.g The moments of each element about the origin are then determined and the total used to

establish the empty airplane c.g If the wing is not suitably located, it must be shifted forward or aft and the moment calculation readjusted Note that relocating the wing also may move engines and landing gear as well as requiring tail size changes because the tail length (moment arm) is altered.

Having determined the empty center of gravity, a loading diagram showing the effect of the most forward likely

loading and the most aft likely loading of passengers and cargo is drawn To this is added the effect of fuel loading.

An example of a loading diagram, often called a "potato" curve, is shown in Fig 1.

Figure

1 Balance Study showing changes in C.G with loading.