Aircraft Design: Synthesis and Analysis - part 8 docx

Materials Choice of materials emphasizes not only strength/weight ratio but also: ● Fracture toughness ● Crack propagation rate ● Notch sensitivity ● 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. Miscellaneous Numbers Although the yield stress of 7075 or 2024 Aluminum is higher, a typical value for design stress at limit load is 54,000 psi. The density of aluminum is .101 lb / in 3 Minimum usable material thickness is about 0.06 inches for high speed transport wings. This is set by lightning strike requirements. (Minimum skin gauge on other portions of the aircraft, such as the fuselage, is about 0.05 inches to permit countersinking for flush rivets. 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. > 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: Wing Horizontal Tail Vertical Tail Fuselage Landing Gear Surface Controls Propulsion System APU Instruments and Navigation Hydraulics and Pneumatics Electrical System Electronics Furnishings Air Conditioning and Anti-Ice Crew Flight Attendants Operating Items Payload Fuel 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, N ult ), span (b), average airfoil thickness (t/c), taper (λ), sweep of the structural axis (Λ ea ), and gross wing area (S wg ). 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 S V 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 S v 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: I p = 1.5E-3 * P * B The bending index is: I b = 1.91E-4 N * W * L / H 2 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 = ZFW max - weight of wing and wing-mounted engines, nacelles and pylons. The fuselage is pressure-dominated when: I p > I b . When fuselage is pressure dominated: I fuse = I p When fuselage is not pressure-dominated: I fuse = (I p 2 + I b 2 ) / (2 I b ) 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: W fuse = (1.051 + .102 * I fuse ) * S fuse 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: W gear = 0.04 TOW 6. Surface Controls [...]... of a fully-stressed beam A derivation is given here Wing Weight Breakdown DC- 8- 5 5 DC-1 0-1 0 STOL Study Wing Bending Material 13,115 21 ,83 0 5, 983 Wing Spars, Webs, Stiffeners 2,301 2 ,82 2 1,136 Bending, Spars, Webs, Stiffners 15,416 24,652 7,119 Ribs 1,463 2,333 82 5 Wing Box Weight 22,7 18 33,623 10, 387 Total Wing Weight 33,604 49,2 98 20 ,86 1 Bending / Total 387 443 287 Box / Total 676 682 4 98 Detailed... 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... runway length is too long, the aircraft cannot take-off with full fuel or full payload and the aircraft economics are compromised For example, In some cases aircraft take-off from San Jose and fly all the way to San Francisco (about 40 miles) before making their first refueling stop This is because the field length is insufficient to take-off with full fuel in San Jose and the tanks are topped off at... is the aircraft maximum lift coefficient in the take-off configuration T is the total installed thrust (all engines running) It varies with speed and must be evaluated at 70% of the lift-off speed which we take as 1.2 Vs The variation of thrust with speed shown here may be used for this calculation if detailed engine data is not available For 2 engine aircraft: TOFL = 85 7.4 + 28. 43 Index + 0 185 Index2... seats installed, and furnishings-other, which is a function of the total cabin size and is found as a function of the number of all-coach passengers that can be fit into the fuselage 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... Wzfw-(Wpayload+Wcrew+Wattend+Wopitems) Wreserv = 08* Wzfw Wfuel = TOW-Wzfw-Wreserv Wnopay = Wmt+Wfuel+Wreserv+Wcrew+Wattend+Wopitems Landing weight includes 1/2 maneuver fuel Wland = Wzfw+Wreserv+.0035*TOW Wowe = Wzfw-Wpayload 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: Cruise Mach:... calculations with statistical data from actual aircraft Each of these performance measures will be used as a constraint in the airplane optimization process and are among many constraints imposed by the FARs q q q q Take-off field length Landing field length Climb performance Cruise performance and range Take-Off Field Length Introduction Although the take-off field length may seem like a performance... estimate 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 q q q q q q Maximum Taxi Weight Maximum Brake Release Weight Maximum Landing Weight... is not desirable, the aircraft is designed to meet take-off field length requirements for selected airports with full payload and fuel This constraint often sets the aircraft wing area, engine size, or high lift system design To compute the required take-off distance, we consider the take-off profile shown below Important Speeds The following speeds are of importance in the take-off field length calculation:... performance If the all-engines runway length multiplied by 1.15 exceeds the 1-engine-out field length, the larger value is used For four-engine aircraft the all engines operating condition times 1.15 is usually critical Fits have been made to the FAR field length requirements of 2,3 ,and 4 engine jet aircraft vs the parameter: W is the take-off gross weight (lbs) Sref is the reference wing area (sq ft) σ is . a fully-stressed beam. A derivation is given here. Wing Weight Breakdown DC- 8- 5 5 DC-1 0-1 0 STOL Study Wing Bending Material 13,115 21 ,83 0 5, 983 Wing Spars, Webs, Stiffeners 2,301 2 ,82 2 1,136 Bending,. 24,652 7,119 Ribs 1,463 2,333 82 5 Wing Box Weight 22,7 18 33,623 10, 387 Total Wing Weight 33,604 49,2 98 20 ,86 1 Bending / Total . 387 .443 . 287 Box / Total .676 . 682 .4 98 Detailed Wing Weight Buildup. S fuse 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