Final Report Aircraft Design ME 4770, C'08 Prof. D. Olinger
Dustin Bradway '08 Kyle Miller '09
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Contents Introduction ................................................... ...................................................... .............................................................................. ........................ 5 Specifications Table ............................................... ..................................................... ..................................................................... ................ 5 Dimensions and Detailed Specifications .................................................................................... 6 Background ................................................................................................................................. 7 Mission Profile .............................................. ...................................................... .............................................................................. ........................ 8 Initial Weight (W0) Estimation ................................................ ................................................... 9 Trade Studies ............................................................................................................................ 10 Detailed Drawings .................................................................................................................... 12 Interior....................................................................................................................................... 13 Airfoil Selection ..................................................... .......................................................................................................... ................................................................... .............. 14 Airfoil Performance .................................................................................................................. 15 Wing Area ................................................. ...................................................... ............................................................................ ...................... 16 Aspect Ratio .............................................. ...................................................... ............................................................................ ...................... 16 Wingspan .............................................................................................................................. 16 Wing Sweep .......................................................................................................................... 16 Wing Taper Ratio and Root Chord ....................................................................................... 17 Mean Chord Length .............................................................................................................. 17 Stall Behavior........................................................................................................................ 17 W/S Calculations ...................................................................................................................... 18 Cruise .................................................................................................................................... 19 Loiter ................................................ ...................................................... ..................................................................................... ............................... 19 Landing/Stall ............................................. .................................................... ............................................................................ ........................ 19 Takeoff ...................................................... ............................................................................................................ ............................................................................ ...................... 19 Refined Weight (W0) Estimation ...................................................... .............................................................................................. ........................................ 20 "Newton's Equations of Takeoff" ............................................................................................. 21 T/W Ratio and Fixed Engine Design ........................................................................................ 22 Updated Wing Characteristics .................................................................................................. 23 Wing Area ................................................. ...................................................... ............................................................................ ...................... 23 Wingspan .............................................................................................................................. 23 Wing Taper Ratio and Root Chord ....................................................................................... 23 Mean Chord Length .............................................................................................................. 24 Tail Geometry ........................................................................................................................... 24 Horizontal Tail Geometry ..................................................... ..................................................................................................... ................................................ 24 Horizontal Tail Area ............................................................................................................. 24 Horizontal Tailspan ...................................................... .......................................................................................................... ......................................................... ..... 25 Horizontal Tail Root Chord C hord and Tip Chord Ch ord .................................................... .......................................................................... ...................... 25 Vertical Tail Geometry ......................................................................................................... 25 Vertical Tail Area ................................................................................................................. 25 Vertical Tail Height .............................................................................................................. 25 Wing and Tail Geometry Geometr y Summary .................................................. ........................................ 26 Winglets .................................................................................................................................... 26 Structural Analysis ................................................. ..................................................... ................................................................... .............. 27 Landing Gear ............................................................................................................................ 29
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Contents Introduction ................................................... ...................................................... .............................................................................. ........................ 5 Specifications Table ............................................... ..................................................... ..................................................................... ................ 5 Dimensions and Detailed Specifications .................................................................................... 6 Background ................................................................................................................................. 7 Mission Profile .............................................. ...................................................... .............................................................................. ........................ 8 Initial Weight (W0) Estimation ................................................ ................................................... 9 Trade Studies ............................................................................................................................ 10 Detailed Drawings .................................................................................................................... 12 Interior....................................................................................................................................... 13 Airfoil Selection ..................................................... .......................................................................................................... ................................................................... .............. 14 Airfoil Performance .................................................................................................................. 15 Wing Area ................................................. ...................................................... ............................................................................ ...................... 16 Aspect Ratio .............................................. ...................................................... ............................................................................ ...................... 16 Wingspan .............................................................................................................................. 16 Wing Sweep .......................................................................................................................... 16 Wing Taper Ratio and Root Chord ....................................................................................... 17 Mean Chord Length .............................................................................................................. 17 Stall Behavior........................................................................................................................ 17 W/S Calculations ...................................................................................................................... 18 Cruise .................................................................................................................................... 19 Loiter ................................................ ...................................................... ..................................................................................... ............................... 19 Landing/Stall ............................................. .................................................... ............................................................................ ........................ 19 Takeoff ...................................................... ............................................................................................................ ............................................................................ ...................... 19 Refined Weight (W0) Estimation ...................................................... .............................................................................................. ........................................ 20 "Newton's Equations of Takeoff" ............................................................................................. 21 T/W Ratio and Fixed Engine Design ........................................................................................ 22 Updated Wing Characteristics .................................................................................................. 23 Wing Area ................................................. ...................................................... ............................................................................ ...................... 23 Wingspan .............................................................................................................................. 23 Wing Taper Ratio and Root Chord ....................................................................................... 23 Mean Chord Length .............................................................................................................. 24 Tail Geometry ........................................................................................................................... 24 Horizontal Tail Geometry ..................................................... ..................................................................................................... ................................................ 24 Horizontal Tail Area ............................................................................................................. 24 Horizontal Tailspan ...................................................... .......................................................................................................... ......................................................... ..... 25 Horizontal Tail Root Chord C hord and Tip Chord Ch ord .................................................... .......................................................................... ...................... 25 Vertical Tail Geometry ......................................................................................................... 25 Vertical Tail Area ................................................................................................................. 25 Vertical Tail Height .............................................................................................................. 25 Wing and Tail Geometry Geometr y Summary .................................................. ........................................ 26 Winglets .................................................................................................................................... 26 Structural Analysis ................................................. ..................................................... ................................................................... .............. 27 Landing Gear ............................................................................................................................ 29
3 Fuel Tanks ..................................................... ........................................................................................................... ............................................................................ ...................... 30 Thrust-Drag Analysis ............................................. ..................................................... ................................................................... .............. 30 Stability Analysis ................................................... ..................................................... ................................................................... .............. 32 Maneuvers ..................................................... ........................................................................................................... ............................................................................ ...................... 34 Climb..................................................................................................................................... 34 Turn .................................................. ...................................................... ..................................................................................... ............................... 35 Logo and Name ............................................. .................................................... ............................................................................ ........................ 35 Conclusion and Summary ......................................................................................................... 36 Appendix A: Historical Comparison Data ................................................. ............................... 37 Appendix B1: Initial Weight Estimate Iteration ................................................. ...................... 38 Appendix B2: Initial Weight Estimate Iteration ................................................. ...................... 39 Appendix C: Initial Weight Trade Studies ................................................. ............................... 40 Appendix D: Artwork ............................................................................................................... 41 Appendix E: Airfoil Geometry Data ................................................. ........................................ 47 Appendix F: XFOIL Analysis .................................................. ................................................. 48 Appendix H: Calculated Drag .................................................. ................................................. 50 Appendix I: Center of Gravity ................................................. ................................................. 51 Appendix J: Final Presentation Slides ...................................................................................... 52 Note: "Creativity" is denoted throughout by an asterisk (*) in the margin of the text.
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Table of Figures Figure 1: Range Map ...................................................................................................................... 5 Figure 2: Historical design trends .............................................................................................. ..... 8 Figure 3: Mission profile ................................................................................................................ 9 Figure 4: Trade studies.................................................................................................................. 11 Figure 5: ProEngineer CAD model............................................................................................... model............................................................................................... 12 Figure 6: Concept art .................................................................................................................... 13 Figure 7: Interior layout ............................................. ..................................................... ................................................................... .............. 13 Figure 8: Cross-section of our NACA 64008a airfoil ....................................................... ................................................................... ............ 14 Figure 9: Airfoil performance plots .............................................................................................. 15 Figure 10: Wing sweep trends ...................................................................................................... 17 Figure 11: Leading edge flow separation at stall .................................................... .......................................................................... ...................... 18 Figure 12: Moment coefficient about quarter-chord point ........................................................... 18 Figure 13: Fuel allocation ............................................................................................................. 21 Figure 14: Takeoff capability........................................................................................................ 22 Figure 15: Installed PW308B engines .......................................................................................... 23 Figure 16: T-tail ............................................................................................................................ 24 Figure 17: Winglets....................................................................................................................... 27 Figure 18: Box spar .................................................... ......................................................................................................... ................................................................... .............. 27 Figure 19: Plot of shear force (N) and bending moment (N-m) throughout the wing .................. 28 Figure 20: Shear force (left) and bending moment (right) distributions in the wing .................... 28 Figure 21: Wing deflection ........................................................................................................... 29 Figure 22: Fuel tank location and size .................................................. ........................................ 30 Figure 23: Coefficients of drag ..................................................................................................... 30 Figure 24: Thrust-drag plot .................................................. .................................................... ......................................................... ..... 32 Figure 25: Stability diagram ......................................................................................................... 34 Figure 26: Turn rate ...................................................................................................................... 35 Figure 27: Logo............................................................................................................................. 36
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Introduction We have designed a two-pilot business b usiness jet, capable of transporting eight to ten passengers and their baggage on routes on the order of Halifax-to-London and Los Angeles-to-Honolulu (see range map below, showing capabilities c apabilities from three major world cities). Our aircraft has a range of 2,500 nautical miles, a cruise speed of 560 mph, and a cruise altitude of 45,000 feet. We have planned for special situations and contingencies by building in a generous loiter time (one hour), designing for use on short runways (< 5 ,000 ft), and specifying a modular m odular interior so that our aircraft can be used for other o ther purposes (e.g., high-altitude photography). Our aircraft employs composite materials in an effort both to keep weight down and to help examine the feasibility of designing future aircraft in a similar manner. Our aircraft will be designed for high reliability – reliability – to to executives and companies, wasted time is wasted money – money – and and 24-hour readiness and operability. Twin engines allow for high safety margins, and the aircraft will be able to fly and climb safely on a single engine. Our jet features a generous fuel supply stored in the win gs, air conditioning, soundproofing, and a full glass cockpit. Following are the specifications for our new business jet.
Specifications Table Aircraft type Aircraft purpose Crew number Estimated payload Range Propulsion system type Cruise speed and altitude Mission Loiter time Maneuverability Takeoff distance and speed Stall speed
Small business jet Intercontinental passenger travel Two pilots 2,000 kg (6-8 passengers and luggage) 2,500 nautical miles Turbofan (2 x Pratt & Whitney 308B) 485 kts at 45,000 feet (Mach 0.726) Takeoff – Takeoff – cruise – cruise – loiter – loiter – land land 1 hour Basic (climb, descend, turn) ~ 4,000 feet at 135 kts 120 kts
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Figure 1: Range Map
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Dimensions and Detailed Specifications Specification General Crew Wcrew Passengers Payload Range SFCcruise SFCloiter Loiter time Maximum speed Cruise speed Stall speed Cruise altitude W0 T/W L/D Oswald efficiency, e Wing loading, W/S Wing Airfoil type Aspect ratio Win s an Area, Swin Win ta er, λ Dihedral Wing incidence angle Wing sweep Airfoil thickness Mean chord, c Chordroot Chordti Winglets Tails Tail type Horizontal Tail sweep Tail taper Aspect ratio Tail span Shtail Mean chord, c Vertical Tail sweep Tail taper Aspect ratio Tail span Shtail Mean chord, c Stabilit Anal sis Fuselage length Length overall Height Fuselage diameter X Neutral Position XMost Forward XCenter of Gravit
Preliminary
Interim
Final
Historical
2 200 kg 8 2,000 kg 2,500 nm 0.5 0.4 1 hour 485 kts 45,000 ft 13,730 kg .0917 10.9 -
2 200 kg 8 2,000 kg 2,500 nm 0.5 0.4 1 hour 485 kts 120 kts 45,000 ft 14,543 kg .0967 10.34 0.8258 82.09 lb/ft2
2 200 kg 8 2,000 kg 2,500 nm 0.5 0.4 1 hour 524 kts (Mach 0.91) 485 kts (Mach 0.84) 120 kts 45,000 ft 14,543 kg .0967 10.34 0.8258 82.09 lb/ft2
~2 6 to 12 ~ 1,080 kg 1,500 to 3,000 nm 0.5 0.4 ~480 to 500 kts 120 to 140 kts 39,000 to 43,000 ft ~ 16,000 kg 0.625 to 0.1 60 to 95 lb/ft2
NACA 64008a 7.461 19.96 m 2 53.416 m 0.45 5˚ 1˚ 20˚ 0.179m 2.804 m 3.7 m 1.66 m Yes
NACA 64008a 7.461 15.98 m 2 34.26 m 0.45 5˚ 1˚ 20˚ 0.179 m 2.25 m 2.95 m 1.33 m Yes
NACA 64008a 7.461 15.98 m 2 34.26 m 0.45 5˚ 1˚ 20˚ 0.179 m 2.25 m 2.95 m 1.33 m Yes
7.25 to 9.10 12.2-17 m 2 24 to 48 m 0.4 to 0.5 3-7˚ 14˚ to 31˚ -
T-tail
T-tail
T-tail
-
25˚ 0.85 4 -
25˚ 0.85 4 4.64 m 2 5.37 m -
25˚ 0.85 4 4.64 m 2 5.37 m 1.16 m
15˚ to 30˚ -
30˚ 0.7 1.0 -
30˚ 0.7 1.0 2.71 m 7.37 m2 -
30˚ 0.7 1.0 2.71 m 7.37 m2 2.71 m
35˚ to 55˚ -
-
17.69 m -
17.69 m 18.61 m 6.60 m 2.35 m 10.14 m 9.09 m 9.58 m
~ 20 m ~ 18 to 20 m ~5.5 to 7.5 m -
Background We considered four aircraft as a basis for our own d esign. Examined in detail were the following aircraft, with a summary of their major specifications:
Range Cruise speed Cruise altitude Max. ramp weight Max. payload
Engines
Length Wingspan Wing area Height
*
Gulfstream G200
Learjet 60XR
Cessna Sovereign
3400 nm 459 kt 39,000 ft 35,600 lb 4,050 lb 2 Pratt & Whitney Canada 306A (6040lb each) 62.25 ft 58 ft 369 ft 21.5 ft
2365 nm 466 kt 41,000 ft 23,750 lb 1,820 lb 2 Pratt & Whitney 305A (4600lb each)
2664 nm 431 kt 41,000 ft 30,550 lb 2,500 lb 2 Pratt & Whitney Canada PW306C (5690lb each) 61.1 ft 63.3 ft 510 ft 19.1 ft
58.7 ft 43.8 ft 264.5 ft 14.5 ft
Cessna Citation X
3250 nm 595 kt 41,000 ft 36,400 lb 1,200 lb 2 Allison AE 3007C (6400lb each) 72.1 ft 63.9 ft 527 ft 18.9 ft
Each is an 8-12 passenger aircraft with two pilots. The overall design of the reference aircraft also matched what we envisioned for our plane: low wing, high tail out of the way of wing turbulence, two aft fuselage-mounted engines, and so on. Averages of the above values have been computed and are used in some early calculations later in this report. In addition to the four reference aircraft, we also examined a larger pool of business jets of various sizes, from 5-passenger very light jets (VLJs) to large planes capable of transporting 25 people distances exceeding 3700 nautical miles. Our goal with this study was to determine whether trends can be discerned in aircraft development and characteristics, to help us envision the "business jet of the future" and to ensure that our work produces a realistic aircraft. Some of our successful attempts at finding correlations can be seen below. Our aircraft's final specifications are also presciently indicated in red, demonstrating that ours is a design that successfully follows contemporary and historical design trends. It should be n oted that our adherence to trends is a result of following the tried-and-tested design process, not from an attempt to "not deviate from the line."
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Empty Weight (lb, X) vs. Wingspan (ft, Y)
Length (ft, X) vs. Wingspan (ft, Y)
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100
100
80
80
60
60
40
40
20
20
0
0 0
50
100
150
0
20000
Passengers (X) vs. Empty Weight (lb, Y)
40000
60000
Length (X) vs. Engine Power (Y)
60000
16000 14000
50000
12000 40000
10000
30000
8000 6000
20000
4000 10000
2000
0
0 0
10
20
30
0
50
100
150
Figure 2: Historical design trends
Interestingly, when we attempted studies comparing changes ov er time, we found no correlations – wingspan, passenger capacity, engine power, and other factors have not changed markedly or predictably since the first business jets were produced in the 1960s. The historical data used for these studies can be found in Appendix A: Historical Comparison Data.
Mission Profile Our aircraft's mission profile is very simple, consisting only of takeoff, climb, cruise (with altitude variations as required by ATC), descent and landin g. Our aircraft is also capable of loiter for up to one hour (not pictured).
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40000 ) t e 30000 e f ( e d u t i 20000 t l A
10000
0 0
250
750
1250
1750
2250
2500
Distance (nautical miles)
Figure 3: Mission profile
Initial Weight (W0) Estimation The four reference aircraft matching our design requirements were examined in detail to help prepare our estimate for W0; more information on these aircraft and other research can be found in the Background section previous. We averaged maximum ramp weights for the four aircraft, found it to be 14,322 kilograms, and used that as our starting point for estimating W 0. The following values were used in our initial weight e stimate, most derived by rounding off average values from the four reference planes:
*
Range: 2,500 nm (allowing Halifax-to-London, NYC-to-LAX, and LAX-to-Honolulu) Cruise speed : 485 kts (250 m/s) Ccruise: 0.5 / hr (textbook) Cloiter: 0.4 / hr (textbook) L/D: 10.9 (textbook) Wcrew: 200 kg (two pilots and gear) Wpayload: 2000 kg (eight 220-lb passengers and 1,200 kg of cargo, baggage, gear, etc.) Loiter endurance : 1 hour (to allow flexibility in CEO schedules) Wingspan : 17.1 m (reference aircraft) 2 Swetted: 510.6 m (preliminary sketches; see below)
Swetted was computed with the aid of our preliminary sketches (tails, wings, winglets) and by calculating the surface areas of tubes (the main fuselage and two engines), a cone (fuselage tail), and a hemisphere (the fuselage nose): Swetted = Stails + Swings + S body tube + Snose + Stail cone + Swinglets + Sengines
10 To obtain an initial estimate of the weights in the different mission stages, historical trends and equations were used as follows:
W1 = 0.97 W0
W2 = 0.985 W1
W5 = 0.995 W4
(where W1 = weight after take-off, W2 = weight after climb, W3 = weight after cruise, W4 = weight after loiter, W5 = weight after landing). Wf / W0 was then calculated with a 6% safety margin:
We / W0 could then be computed using the formula provided in the textbook in Table 3.1:
And finally our initial weight estimate was updated:
Three iterations were necessary to bring our estimate to within a successive iterative error of less than 0.5%. Our updated estimate for W0, using conventional construction materials, is 16,080 kilograms. For details, see Appendix B1: Initial Weight Estimate Iteration. We have decided, however, to use a composite material construction, the details of which are discussed in the Trade Studies section to follow. As a result, our final W0 estimate is actually 13,730 kilograms .
*
Trade Studies We conducted several studies to determine the weight tradeoffs that would be required if we changed our aircraft's specified range, pa yload capacity, and loiter time. Values were computed with the use of our iteration algorithm, allowing for the quick and eas y creation of several data points in each study. The results are as follows, and details can be found in Appendix C: Initial Weight Trade Studies.
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W0 vs. increasing range
W0 vs. increasing loiter
45000
25000
40000 20000
35000 30000
15000
25000 20000
10000
15000 10000
5000
5000 0
0 0
1000
2000
3000
4000
5000
0
0.5
1
1.5
2
2.5
W0 vs. increasing payload
30000 25000 20000 15000
10000 5000 0 0
1000
2000
3000
4000
5000
Figure 4: Trade studies
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We reduced our specified payload early in the design process as a result of conducting trade studies; our initial specification of 2,500 kg caused ou r aircraft to exceed our reference aircraft average by too large a margin, and we now feel 2,000 kg is perfectly adequate given the passenger capacity of our jet (and whatever luggage those passengers could possibly need to bring). We are satisfied by where we sit on the range and loiter curves, feeling no need to increase either specification; however, we note that loiter could be increased beyond its alread y above-average value without incurring too much of a penalty. We have also decided to use composite materials in our aircraft construction, in an effort to keep rising weights down and to add an element of "futurism" to our design. As an example, the Learjet 85, introduced in October of 2007, will feature an all-composite structure designed b y Grob Aerospace. We are of the opinion that composite aircraft, with declining material prices and ever-advancing manufacturing processes, will become more common in the future. To account for a composite structure, the We / W0 ratio is adjusted to 95% of its original value with the following formula:
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W0 is then calculated as before. Our early estimate for an initial weight using composite materials is 13,730 kilograms. This is 85% of the weight of a conventional aluminum structure. Because of this, we have decided to use composite construction in our b usiness jet.
Detailed Drawings Full sets of detailed drawings are located in Appen dix D: Artwork. A CAD model of our aircraft was created with PTC's ProEngineer software. The dimensions used in the model are, of course, the same as the final specifications we provide in this report. Here is one view of our model:
Figure 5: ProEngineer CAD model
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In the spirit of the design process (and simulating the role of an Art Department), we have also produced "concept art" for our aircraft, to better illustrate our proposed aircraft's shape and details. These graphics are entirely of our own creation, having been steadily modified throughout the design process to represent our ev olving design. For all the drawings one could possibly desire, including a visual depiction of the evolution of our aircraft, see Appendix D. Depicting details can be difficult in ProEngineer, but is quite simple with illustration software (here, Adobe Flash). It should be noted, too, that these drawings are made exactly to scale.
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Figure 6: Concept art
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Interior Our aircraft's modular interior can be configured in a variety of seating arrangements, two of which are depicted here. The red areas indicate exits. The rear of the cabin contains luggage, loaded externally. An optional head is located directly behind the pilots. Six seats:
Eight seats:
Figure 7: Interior layout
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Airfoil Selection Our background research indicates that smaller-to-midsize business jets use a variety of airfoil shapes for their wing cross sections, including the IAI Sigma 2, Cessna 7500 and the NACA 64008a shown below. The NACA 64008a airfoil was chosen for our plane because of its favorable characteristics when used in our type o f aircraft – a thin airfoil is important when flying at high subsonic Mach numbers, because it increases critical Mach and allows for lower drag at higher flight speeds. A list of non-dimensional geometry data for a NACA 64008a airfoil can be found in Appendix E: Airfoil Geometry Data.
Figure 8: Cross-section of our NACA 64008a airfoil
Typical flying conditions for our aircraft will be a cruise altitude of 45,000 ft (13,720 m) and a velocity of 560 mph (250 m/s). To obtain realistic data for the NACA 64008a airfoil and aircraft wing, we conducted analysis at those c ruise conditions. The atmospheric conditions at cruise altitude are shown here: Properties at Cruise Altitude
Property Temperature Pressure Density Dynamic Viscosity Gamma Gas Constant
SI Units 216.6 K 15,327 N/m 0.24646 kg/m 1.42x10 kg/m-s
287 J/Kg-K
English Units 390°R 3095 psf 0.4623 slug/ft .2969 sl/ft-s 1.4 1717.23 ftlbf/slug°R
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*
Airfoil Performance The performance of the NACA 64008a airfoil was evaluated with XFOIL; details are provided in Appendix F: XFOIL Analysis. Plots of the lift coefficient (Cl) and drag coefficient (Cd) versus angle of attack are shown below. 0.8 0.6 l
C t f i l f o t n e i -4.5 c i f f e o C
0.4 0.2 -2.5
0 -0.5 -0.2
1.5
3.5
5.5
7.5
5.5
7.5
-0.4 -0.6 -0.8 Angle of Attack
d
C g a r D f o t n e i c i f f e o C
-4.5
-2.5
0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 -0.5
1.5
3.5
Angle of Attack Figure 9: Airfoil performance plots
These graphs are excellent references for deciding and confirming a wing's fixed angle of attack. Historical data specifies that the typical angle of attack for a commercial aircraft is 1˚. Referring to the table in Appendix F: XFOIL Analysis, our airfoil provides a lift coefficient of 0.1623 at α = 1˚. We verified that this value would be sufficient to overcome the weight of the aircraft with the following equation:
where W0 = initial weight and
,
. We calculated the minimum required lift coefficient
to be 0.04467, indicating that our jet will have no problem becoming airborne from the runway.
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Wing Area To calculate the initial size of the wing, the following equation was used:
,
where Swing = area of wing, W 0 =initial weight of aircraft, and
= wing loading.
The number we used for wing loading was the average of our reference planes: 70.475 2 2 lb/ft (344.087 kg/m ). A (non-final) value of 53.42 m resulted for our wing area. 2
Aspect Ratio To calculate the aspect ratio of the wing the following equation was used:
,
where AR = aspect ratio, b = wingspan, and c = chord length. Since the wingspan, b, and chord length, c, were not yet known, historical data was needed for initial aspect ratio estimation. This can be found in the course textbook, in table 4.1. A provided formula, C AR = aMmax allows the calculation of aspect ratio. Values of 7 and -0.02 were used for a and c respectively, and a Mach number of 0.7267 was used (this Mach number was obtained by dividing the aircraft's cruise velocity by the speed of sound at 45,000 feet). The resulting final aspect ratio is 7.46, very close to those of our reference aircraft. This is a value close to that of historical reference aircraft, and while it may be slightly high on an absolute scale, our aircraft is nonetheless able to e asily support the resulting increased wing root structural forces (see Structural Analysis section later).
Wingspan To calculate the wingspan, we used the following formula:
Our values for aspect ratio and wing yielded a (non-final ) wingspan, b, of 19.96 m. This value is consistent with and close to the wingspans of the reference planes.
Wing Sweep Our aircraft will have a wing sweep of 20 degrees , based on historical trends. This value was obtained from the textbook. The following is the plot used to estimate this value:
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Figure 10: Wing sweep trends
Wing Taper Ratio and Root Chord A taper ratio, 0.45, chosen based on historical data, allows the root chord to be calculated with the following equation:
where S is the wing reference area, b is the wingspan, and λ is the wing taper. The resulting (non-final ) root chord was 3.69 m. With this value, the wing's tip chord can be calculated by manipulating the taper ratio formula and solving for Ctip:
The resulting (non-final ) chord for the wingtip was 1.66 m.
Mean Chord Length To calculate a mean chord length for our wing, we used the following equation:
̅ Our (non-final ) mean wing chord length, c, was 2.804 m.
Stall Behavior The NACA 64008a has a maximum thickness of 8% of its chord. This value is less than 14% and falls in the moderate airfoil thickness category. Because of its thickness, this airfoil stalls at the leading edge, as shown below.
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Figure 11: Leading edge flow separation at stall
This airfoil's stall characteristics require a professional pilot familiar with leading-edge stall behavior; in particular, during stall, the moment about the quarter-chord point changes drastically, as shown here, and amateur pilots would likely be unable to maintain control of the aircraft:
Figure 12: Moment coefficient about quarter-chord point
W/S Calculations To size the aircraft wing accurately and safely, estimates must be made for the ratio of W/S (weight to wing area). This value depend s on the flight condition, and can vary substantially during the flight. As a result, four values are c alculated and compared, and the lowest (i.e., the lowest wing loading) is selected for safety. Wing loading is important to determining an aircraft's takeoff, stall and landing speeds, its cruise speed a nd, of course, its wing size.
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Cruise
⁄ Cruise values for ρ and V were used. CD0 was estimated at 0.015 for a streamlined jet, and e0, the Oswald efficiency factor, was estimated using equation 12.50 in the textbook:
2
A value of 60.975 lb/ft resulted.
Loiter
⁄
The same values for ρ and V were used as in the cruise calculation. A value of 105.61 lb/ft resulted. 2
Landing/Stall
⁄
New values for ρ and V were used, assuming a generous landing altitude of 4,000 ft and a stall speed of 120 kts, a good approximation of the stall speeds of our reference aircraft and general trends. CLmax was approximated with Figure 5.3 from the textbook, assuming doubleslotted flaps, and was found to be around 2.5. 2 A value of 109.18 lb/ft resulted.
Takeoff
⁄
We have used the "alternative" (non-iterative) method to determine W/S for takeoff; the iteration method produced contradictory values that would not allow us to complete the process. In the above equation, SG is the takeoff distance (4,000 ft), g is acceleration due to gravity, and the thrust-to-weight ratio was calculated (from Table 5.3) to be 0.23865 for our aircraft. 2 A value of 133.64 lb/ft resulted. Each value was then corrected back to the "takeoff condition," i.e., in terms of the aircraft's initial weight. The corrected values are presented below for ease of comparison.
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Takeoff 133.64 lb/ft
Cruise 82.09 lb/ft
Loiter 145.22 lb/ft
Landing 150.50 lb/ft
Our takeoff W/S is very close to the historical trends given in the textbook in Table 5.5 – for jet 2 transports, 120 lb/ft is the norm. Our lowest wing loading value is the W/S for the cruise condition. Using it to calculate our aircraft's wing area, we obtained the following:
(⁄)
This value is in perfect alignment with those of our reference aircraft; the Gulfstream G200 has a 2 wing area of 369 ft , and the others are spread to both sides of our value.
Refined Weight (W0) Estimation Having pinned down some of our aircraft's specifications, we repeated our algorithm to estimate its W0, this time with a few changes and updates. To summarize:
*
-
The starting value for W0 was set to the final value from the first estimate. L/D was calculated based on power sizing estimates, as the inverse of T/Wcruise. Wingspan was updated to our new value, 15.98m.
-
An additional weight segment was added, Wdescent, where
-
We/W0 was improved with the formula in Table 6.1 Composite construction was still used, resulting in the usual weight reduction.
The final value for W0 is now 14543.4 kg, a weight increase of 5.92% over our first estimate. This difference is small enough that it does not warrant redoing calculations elsewhere in the design process. Details from this iterative process can be seen in Appendix B2, following the initial estimates. The following chart gives an idea of how fuel use is distributed over the course of an average mission for our aircraft:
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* Cruise 76%
Loiter 11% Taxi & Takeoff 5% Climb 5%
Descent 2% Landing 1%
Figure 13: Fuel allocation
*
"Newton's Equations of Takeoff" Simple equations of motion can be used to compute basic takeoff properties for our aircraft. Both engines together produce 61,385 N of takeoff thrust (see the Engine Design section that follows for details). For a takeoff weight of 15453 kg,
The resulting time to reach takeoff speed is
This translates to a takeoff roll of:
Thus, our aircraft can theoretically become airborne in 2 ,300 feet, although of course friction and drag have been ignored here. Prevailing winds, runway conditions and other factors would alter this somewhat, too. The following graphic depicts our aircraft's theoretical minimum takeoff roll compared to the lengths of the shortest runways at some of the world's major (and not so major) airports.
22
Shortest runways Hong Kong Heathrow Denver LAX Charles de Gaulle Frankfurt Honolulu Newark T.F. Green Worcester Logan 0
2000
4000 6000 8000 Runway length (feet)
10000
12000
Figure 14: Takeoff capability
It is apparent, then, that our aircraft will have no problem serving any destination required by our customer base. While we have not analyzed braking and deceleration, it is a safe assumption that, if our aircraft can be landed at an airport, it will be able to take off from that airport, too.
T/W Ratio and Fixed Engine Design With the completion of the initial weight estimate, the T/W ratio was calculated using the following equation:
Our cruise thrust-to-weight ratio is 0.0967. Multiplication of this fraction by the initial weight yields the minimum thrust needed for our aircraft to fly at c ruise conditions. Our resultant minimum thrust is 1,400 kg, or 4,100 lbf. Basing our work on data from similar business jets, we have selected a fixed engine design that uses two Pratt & Whitney 308B high bypass turbofans. Each engine produces comfortably more thrust than our minimum specification for cruise, an impo rtant consideration for engine-out maneuverability and other emergency conditions. The following table contains the specifications for the 308B model (per engine): P&W 308B Take-off thrust (per engine) 8242 lb 3738 kg Cruise thrust (per engine) 7400 lb 3356 kg Dry weight 1043 lb 473 kg 1.92 m Length 6.3 ft 0.914 m Width 3 ft
23 Below, a depiction of our engines positioned inside the nacelles:
Figure 15: Installed PW308B engines
Updated Wing Characteristics The slight increase in our initial weight estimate and the change in the wing loading characteristics resulted in changes in the values for some of our wing geometries. Following are the recalculated values.
Wing Area
A new, final value of 34.26 m2 resulted for our wing area.
Wingspan
Our values for aspect ratio and wing area yield a new, final wingspan, b, of 15.98 m. This value is still consistent with wingspans of our reference planes.
Wing Taper Ratio and Root Chord Our taper ratio remained the same, at 0.45. It allow calculation of the wing root chord:
24
The resulting, final root chord is 2.95 m. With this value, the final wingtip chord can be calculated: 1.33 m.
Mean Chord Length Our new, final mean aerodynamic chord length, c, is 2.25 m.
Tail Geometry Our aircraft has a T-tail configuration, chosen for several reasons. Despite the T-tail's typical disadvantage of adding to aircraft weight (due to required extra structural strengthening), its advantages of the T-tail outweigh the disadvantages. One such advantage is that the T-tail puts the horizontal tail clear of wing wake and engine exhaust. Another is its aesthetically pleasing design. Overall, however, the T-tail results in higher efficiency and a smaller tail than would be possible if it were of a different design. Depicted below is our T-tail design:
Figure 16: T-tail
Horizontal Tail Geometry The sweep of the horizontal tail's leading edge has been set to 25 degrees. This value was obtained from historical data; a trend in past aircraft has been to sweep the horizontal tail 5˚ further than the wings. This increase in sweep ang le ensures that the tail stalls later than the wing, important to maintaining control and maneuv erability in adverse conditions. An increase in tail sweep angle also increases its critical Mach numbe r relative to the wing; this prevents the loss of elevator effectiveness in case of shock formation. The taper ratio of the horizontal tail has been set to 0.85, based on historical data for Ttails.
Horizontal Tail Area To calculate the initial size of the horizontal tail, the following equation was used:
25
̅
̅
,
where Swing = area of wing, =mean chord length of wing, =tail volume coefficient and LHT = length between wing and horizontal tail. Our value for the tail volume coefficient was take n from historical data; this value is 0.085. The length between the wing and horizontal tail was estimated to be 6.34 m. A value of 2 5.37 m resulted for our horizontal tail area.
Horizontal Tailspan To calculate the horizontal tailspan, we used the following formula:
Our values for aspect ratio and wing yield a tailspan, b, of 4.64 m. This value is consistent with and close to the tailspans of reference aircraft.
Horizontal Tail Root Chord and Tip Chord The root chord can be calculated as before, and results in a horizontal tail root chord of 1.25 m. The corresponding tailtip chord is 1.07 m.
Vertical Tail Geometry The sweep of the vertical tail has been set to 30 degrees, again obtained using historical data that indicates that vertical tails are swept 5-10 degrees further than the horizontal tail. The increase in the sweep angle once again also increases the tail's critical Mach number relative to the wing, preventing loss of critical yaw control d uring turbulence. The taper ratio of the vertical tail has been set to 0.7, based on historical data for T-tails; T-tail vertical surface taper ratios are in the range of 0.5 to 1.0, to provide adequate chord for the attachment of the horizontal tail and associated control linkages.
Vertical Tail Area Using a vertical tail volume coefficient taken from historical data (0.95), and an 2 estimated length from the wing to vertical tail of 6 .34 m, we have assigned a value of 7.37 m for the vertical tail area.
Vertical Tail Height To calculate the height of our vertical tail, we used the following formula:
Our values for aspect ratio and wing yield a height, b/2, of 2.71 m.
26
Vertical Tail Chords The horizontal tail base chord is 3.19 m. The corresponding top chord is 2.23 m.
Wing and Tail Geometry Summary Property Wingspan, b Mean chord length, c Wing area, S Aspect ratio, AR Wing sweep angle Taper ratio, λ Root chord length, Croot Tip chord length, CTip Airfoil thickness
SI Units 15.98 m 2.25 m 34.26 m
English Units 53.46 ft 7.37 ft 368.80 ft 7.461 20˚ 0.45 2.95 m 9.70 ft 1.33 m 4.36 ft 0.08
Tails Vertical Height Wing area, S Root chord length, Croot Tip chord length, CTip Vertical taper ratio, λ Tail A.R., vertical Vertical tail sweep Horizontal Span, b Wing area, S Root chord length, Croot Tip chord length, CTip Vertical taper ratio, λ Tail A.R. Horizontal tail sweep
*
2.71m 7.37m 3.19m 2.23m
8.91ft 79.43ft 10.49ft 7.34ft 0.7 1.0 30˚
4.64m 5.37m 1.25m 1.07m
15.21ft 57.85ft 4.91ft 3.49ft .85 4 25˚
Winglets Our aircraft will employ winglets, as is common in modern business jets. While we will not do detailed analysis on the benefits winglets impart, a few effects can be quantified in a basic manner. Winglets improve cruise speed, somewhere on the order of 5 %. Maximum speed is not increased by much, however. Rate of climb increases (see discussion in Maneuvers section) by around 6%. Stall speed remains unaffected, and handling is improved.
27 Winglets improve aerodynamic efficiency by reducing drag (they h elp to dissipate wingtip vortices, a contributor to induced drag at wingtips, and increase Oswald efficiency by around 10%). Only zero-lift drag increases marginally, because o f a small increase in wetted area (we account for this when required in this report). The handling benefits offered by winglets are num erous, too: rudder yaw control improves, heading overshoot is reduced, and stall speeds are lower. Our winglets are depicted below: Front:
Side:
Top:
Figure 17: Winglets
Structural Analysis
*
Research into the nature of composite (carbon fiber) materials in aviation yielded the discovery that composite wings support loads in a markedly different manner than conventional aluminum construction. The skin of a carbon fiber aircraft is much more capable of supporting loads than an aluminum skin would be, and so the interior structure is very different. Without the tools at our disposal to completely alter the way we conduct structural analysis, we have elected to use a box spar, which, to a limited degree, simulates the skin effect and also the h H tube spars used in some carbon fiber aircraft. Our composite spar is depicted here. b The area of the spar Properties of carbon fiber is BH – bh. Its moment of 275 GPa λ inertia is: 1.75 g/cm ρ B 3.5 GPa Tensile strength 1.25 GPa Compressive strength Figure 18: Box spar 0.69 Poisson's ratio 15.15 GPa Shear modulus 55.15 MPa Shear strength For structural analysis, we used an elliptic 234.4 GPa Young's modulus loading, which is characterized by a distribution as
[ ]
follows:
With a total aircraft weight of 14,543 kg, the load supported by each wing at cruise is (14543 / 2) * 9.81 = 71,262 newtons. A safety factor of 3.5 is used henceforth.
28 Integration of the distributed elliptic load results in the total reaction force that the airframe must exert on the wing at the root. This value is 31,725 newtons . Integration of the load multiplied by the distance at which it acts results in the total reaction moment exerted on the wing at the root. This value is 675,977 newton-meters . Integration of the distributed load with respect to the wingtip results in an equation for the shear force acting at any point on the wing. The equation is as follows:
Integration of the load multiplied by the distance at which it acts, with respect to the wingtip, results in an equation for the moment acting at any point on the wing:
Plots and graphical depictions of these functions can be seen below. Original data is available in Appendix G: Structural Analysis Data.
Figure 19: Plot of shear force (N) and bending moment (N-m) throughout the wing
*
Figure 20: Shear force (left) and bending moment (right) distributions in the wing
29 Our spar is symmetrical about its center, so the cross-sectional centroid is easily located. The spar's moment of inertia is calculated by subtracting that of the small rectangle from that of the large rectangle. Compressive and tensile stresses are easily determined. One simply multiplies the moment at the wing root by a vertical distance within the beam, y, and divides by the moment of inertia. The result can be used to determine the stresses at the points of greatest tension and compression (along the vertical axis, not longitudinally). Along the top surface of the wing, the stress is
| |
. Along the bottom, the stress is
.
The values are the same because the spar is symmetrical about the longitudinal axis. Needless to say, these values are well within the limits of our material, even accounting for ver y large safety factors. Finally, deflection analysis can be conducted. Integrating the moment equation twice yields an expression for deflection, too complicated to include here. The wing deflection looks like this:
Figure 21: Wing deflection
The maximum deflection occurs at the wingtip, an d has a value of 6.603 mm. This is certainly reasonable. In non-dimensional form:
*
or 0.08%
Landing Gear As with virtually every other business jet in existence, our aircraft will employ tricycle landing gear. This permits ease of entry, ex cellent ground handling, good pilot visibility, and the ability to land "crabbed" in adverse crosswind conditions. The nosewheel will have two tires, to allow some degree of steering control should one be punctured. Using Table 11.1 in the textbook as a reference, we have sized our aircraft tires as follows: Diameter Width Rear tires 67 cm 19 cm Front tires 60 cm 17 cm Tires: 6 total Pressure: 120 psi
30
*
Fuel Tanks Based on a Wf /W0 of 0.3037 from our refined W0 estimate, our aircraft's fuel weight is 3 4416.8 kilograms. With a density of Jet A-1 fuel of approximately 800 kg/m , our fuel tanks 3 must have a volume of 5.521 m . Making some broad assumptions (like a uniform wing thickness of 0.179 m, based on our airfoil characteristics), the tanks would need to have an area 2 (when seen from above) of 30.84 m . This is under our aircraft's wing area, which is around 34 2 m . As a result, our aircraft should be able to comply with FAA regulations for passengercarrying aircraft by storing all of its fuel in the wings. The following is an approximate sketch of the fuel tanks' area and location. Of course, real aircraft fuel tanks would be compartmentalized to pe rmit pumping of fuel as ballast and to maintain proper wing loading distributions.
Figure 22: Fuel tank location and size
Thrust-Drag Analysis Drag is a function of two components that act at different speeds. Induced drag increases in proportion to the square of the aircraft's velocity, while parasitic drag increases in proportion to the inverse of the square of the aircraft's velocity. That is, induced drag goes to infinity as the aircraft travels faster, while parasitic drag goes to zero: 0.03
0.0014
0.025
0.0012 d e c u d n I D
0.02
0.001
0.0008
o D
0.015
C
C0.0006
0.01
0.0004
0.005
0.0002
0
0 0
100
200
300
0
Velocity (m/s) Figure 23: Coefficients of drag
100
200
Velocity (m/s)
300
31 Induced drag is drag due to the lifting forces of the aircraft wing. According to one explanation, lift is caused by a pressure differential between the top and bottom o f the wing. At the tips of the wing, however, air can move freely from the high pressure bottom to the low pressure top of the wing. This movement induces drag through the creation of vortices (which generate no lift). Two-dimensional induced drag coefficients can be calculated with the following equation:
However, a better lift coefficient can be c alculated for a 3D wing as follows:
() ,
where
, AR = aspect ratio, M = Mach number,
. The complete list of
calculations for induced drag are listed in Appendix H Parasitic drag, as the name implies, is caused b y friction between the air and components that make up the aircraft's external structure. It can be approximated to any desired or required degree using the "component build-up" method, which finds individual parasitic drags for each part of the aircraft and sums them. For our aircraft, we found drags for the following compon ents: fuselage, tails (vertical and horizontal), wings, winglets, and engines. We used the most recent version of our aircraft drawings to ensure the most accurate dimensions for each component. We used the following parameters, representing our aircraft's cruise conditions, in determining its parasitic drag (V∞ and Mach number are variables). Altitude 45,000 ft
Temp. 216 K
ρ 0.2371 kg/m
Vsound 295.06 m/s
The following are sample values taken at our cruise velocity of 485 kts:
*
Component Fuselage Vertical tail Horizontal tail Wing Winglets Engines
Length 18 m 2.4 m 1.35 m 2.25 m 0.6 m 2.7 m
Reynolds #
C f
FF
74,703,141 9,960,418 5,602,735 9,337,892 2,490,104 11,205,471
0.00208 0.00281 0.00309 0.00284 0.00355 0.00276
1.2 1.449 1.530 1.458 1.505 1.162
Swetted 169.9 m 18.0 m 18.0 m 54.0 m 0.7 m 21.2 m
To produce our final thrust-drag plot, we pe rformed the above calculations for velocities from 10 m/s to 290 m/s in increments of 10 m/s. Formulas used are as follows:
32 Form factor calculations depend on the component being considered. Wings, tails and winglets have a form factor determined by airfoil thickness and sweep, while the fuselage and engine nacelles have a form factor determined by fineness ratios. To calculate the total drag that of the plane the following equation is used.
A list of calculated values for total drag can be found in Appendix H. Our aircraft's cruise speed can be confirmed with the following thrust-drag plot, indicating that cruise thrust and drag intersect slightly above our specified cruise velocity of 250 m/s. 12000 10000 g 8000 a r D & 6000 t s u r h T 4000
Drag Thrust
2000 0 0
50
100
150
200
250
300
Velocity (m/s)
Figure 24: Thrust-drag plot
It should be noted that, as a result of thrust-drag analysis, we realized that our original engine specification, the Pratt & Whitney 306A, was not powerful enough. The 306A was therefore discarded in favor of the better-suited 308B. Using maximum thrust instead of cruise thrust results in our aircraft's maximum speed: 524 kts (Mach 0.91). Our cruise speed is therefore 92.5% of our maximum speed.
Stability Analysis The stability of an aircraft is a very important design consideration when conceptualizing an aircraft. Pilot type becomes irrelevant if the plane cannot be made to fly in a stable, predictable manner (whether by design or by complicated computer tricks). Complete stability analysis typically considers pitch, roll and yaw moments and displacements within six degrees of freedom. Due to time constraints, however, we will focus only on static pitch stability. The first step of the stability analysis is to calculate the aircraft's neutral point, X np. This location is significant because, if the center of gravity were to travel further aft, the aircraft becomes unstable. As such, knowledge of its location is important to loading and weight
33 distribution, factors that are determined by pilots and computer weight management systems before and during flight. The value of Xnp can be calculated as follows:
̅ ̅ ̅
A value of 10.15 m from the aircraft nose results for our plane's neutral point. The next step is to calculate the aircraft's most forward point, Xmf . The most forward point, like the neutral point, represents a plane beyond which the center of gravity cannot pass if stability and proper control are to be maintained. A center of gravity forward of the most forward point results in control sluggishness and potentially dangerous flight conditions. The following equation was used to calculate the most forward point:
̅ ̅ ̅
Our aircraft's most forward point is located 9.09 m beh ind the nose. The final step is to calculate the aircraft's center of gravity. As long as the center of gravity lies between the neutral and most forward points, the aircraft will be stable and will respond properly to control inputs. Our aircraft's center of gravity was determined, like parasitic drag, using a component method. A simple statics equation was used:
̅ ∑∑
Centers of gravity for the following components were used in the calculation:
*
Component Wings Horizontal tail Vertical tail Engines (both) Nose gear Main gear Avionics Fuel tanks (full) Baggage Fuselage Passengers Pilots Bathroom
Weight 2467 kg 389 kg 388 kg 728 kg 100 kg 407 kg 225 kg 4416 kg 425 kg 3690 kg 800 kg 200 kg 300 kg
x CG 9.2 m 16.7 m 15.8 m 13.5 m 3.1 m 10.5 m 1.2 m 10 m 13.8 m 7.8 m 10 m 3.6 m 5.7 m
34 The total weight for the above components is 14535 kg, very close to our W0 estimate of 14543 kg. This yields a CG location of 9.58 m. Details are in Appendix I: Center of Gravity. The simplest assessment of stability can be conducted: Does
̅ ̅ ̅
?
Our values satisfy this relation, and our aircraft is therefore stable in its pitch axis. A graphical representation of the above relation is presented h ere (to avoid cluttering up our drawings elsewhere):
Figure 25: Stability diagram
The distance between xnp and xmf is 1.06 m, or 37.8% of our aircraft's mean aerodynamic chord. The static margin,
̅
works out to 0.253, which is greater than zero, again indicating a stable design.
Maneuvers Climb We used the following equations to determine ou r aircraft's climb characteristics:
Climb angle: Climb rate:
*
Our aircraft's resulting climb angle is 3.54˚. This corresponds to a climb rate of 15.4 2 m/s or 3030 fpm. At this climb rate, our aircraft reaches its cruising altitude of 45,000 ft in approximately 15 minutes, assuming a takeoff at sea level. Research performed by NASA indicates that winglets, as used on our aircraft, can dramatically improve rate of climb. Below 5,000 ft, winglets can raise ROC by 6%, and above
35 that altitude the improvement increases to roughly 15% ("Flight Evaluatio n of the Effect of Winglets…", Holmes et al., 1980). Theoretically, then, our aircraft could be capable of a climb rate of up to 3485 fpm (above 5,000 ft), and thus could reach cruise altitude in the vicinity of 13 minutes, shaving two minutes off the non-winglet time. The corresponding improved climb angle would be roughly 4˚.
Turn We used the following equations to determine ou r aircraft’s turn characteristics: Turn Rate:
̇ √
Turn Radius:
Our aircraft’s calculated turn rate is 0.1316 rad/s or 7.54 deg/s. This results in a turn o radius of 1899 m (6230 ft or 1.18 miles). At this turn rate, our aircraft can complete an 180 turn in roughly 24 seconds. This is a good value for our aircraft, providing a low response time if it were necessary to turn the aircraft around and make an emergency landing. The load factor, n, was set at 3.5 as in the structural analysis section. An idea of the range of the turn radius values for our jet can be obtained from the following graph.
*
3.5 3 ) s 2.5 / d a r ( 2 e t a R1.5 n r u T 1
0.5 0 0
50
100
150
200
250
300
350
Velocity (m/s)
Figure 26: Turn rate
*
Logo and Name More for fun than anything else, we also named our aircraft company and model, as well as creating simple logos for the same:
36
Figure 27: Logo
Vulcan was, of course, the Roman god of fire, metallurgy and technology. He produced thunderbolts for Jupiter, the king of the Roman gods. Were Vulcan Aircraft to produce other, perhaps larger jet models in the future, the naming theme lends itself to other logical (and agreeable) names like "Jupiter" and "Lightning."
Conclusion and Summary We present the Vulcan Thunderbolt, a new business jet capable of transporting six to eight passengers on trans-Atlantic and inter-continental routes in complete comfort and luxury. Featuring composite construction, a large fuel suppl y, and high safety margins, our aircraft is well on its way through the design process. No major pitfalls were encountered in our design process. Virtually every dimension, weight and specification is in alignment with historical trends, although our aircraft does "push the envelope" in a few areas like its composite construction. It checks out, structurally and in maneuvers, and offers short-field capability and a rapid rate of climb. As such, not much revision of existing work is necessary. Looking forward, however, complete stability (in all three axes) would need to be conducted, the design would need to be laid out and refined (detailed lofting), and scale -model testing and CFD analysis would need to be conducted. Electrical, hydraulic, mechanical and aeronautical engineering expertise would be required for these phases of design. Because our aircraft is a business jet, comfort is of high priority to our customers. Our interior has been laid out in a basic manner, but individual orders would ha ve specific requests for customization. Our large payload capacity wo uld permit any number of interior appointments to be installed. Once design work ends, engineers perform cost a nalysis. Passing that, our aircraft would be prototyped and would undergo rigorous testing by the FAA before receiving its flight certification. If we were to go ahead with the design process immediately, we wouldn't expect our aircraft to fly before sometime in 2010 or 2011. Reserve your Vulcan Thunderbolt today!
37
*
Appendix A: Historical Comparison Data
Hawker 800 Hawker 1000 Cessna S550 Citation Cessna Citation X Cessna Citation Excel Learjet 45 Gulfstream G100 Hawker 400 Sabreliner Learjet 35 Learjet 28 Learjet 40 Learjet 55 Learjet 23 Gulfstream IV Gulfstream III Gulfstream G200 Embraer Phenom 300 Embraer Legacy 600 Bombardier Global Express XR Bombardier Challenger 500 Dassault Falcon 10 McDonnell 119 Eclipse 500
Pax.
Length (ft)
Wingspan
Height
Empty weight
Power
Year
8 8 8 8 8 9 ? 7 6 8 8 6 7 6 15 25 8 6 13 12 14 6 10 5
51.1 51.1 47.25 72.3 63.6 57.5 55.6 48.4 44 48.6 47.5 55.5 55.1 35.6 88.3 88.3 62.25 52 85.4 99.4 68.4 45.4 66.5 33
54.3 54.3 52.25 63.6 63.2 47.8 54.6 43.5 44.5 39.5 43.8 47.8 42.75 43.25 77.9 77.9 58 53.1 68.9 94 64.3 42.9 57.6 37.2
18 18 15 19 20.4 14 18.1 13.9 16 12.25 12.23 14.1 14.6 12.25 24.4 24.5 21.4 16.3 22.1 24.9 20.6 15.1 23.6 11
15670 15670 8060 21700 17700 13695 14400 10550 9257 10119 ? ? 12860 6151 35500 38000 19200 ? 30000 49750 20485 10760 41000 3550
4660 4660 2500 6764 5686 3500 4250 2965 3000 3500 2944 3500 3750 3000 13850 11400 6040 3200 8810 14750 9140 3230 2980 900
1963 1962 1978 1996 1996 1995 1986 1996 1962 1973 1977 2002 1977 1963 1985 1979 2000 2008 2000 1993 1978 1970 1955 2006
The following formulas, applying to business jets in gen eral, can be derived: 0.012 (length)
Wingspan = 25.16e
Wingspan = – 7*10 (empty weight) + 0.001 (empty weight) + 32.88
Empty weight = 25896 ln (number of passengers) – 36903
Engine power = 196.4 (length) – 6264
-9
2
38
Appendix B1: Initial Weight Estimate Iteration Initial parameters SFC – cruise 0.5 / hour
W0 14322 kg
Range 2500 nm
Speed 250 m/s
Wcrew 200 kg
Wpayload 2000 kg
Loiter endurance 1 hour
SFC – loiter 0.4 / hour
Wingspan 17.1 m
First iteration W0 – Initial 14322 kg
W1 – Taxi, takeoff 13892 kg
W4 – Loiter 10418 kg
W5 – Landing 10365 kg
W2 – Climb 13683 kg W5 / W0 0.7237
We / W0 0.5744
W0 – new 16569 kg
Second iteration We / W0 0.5694
W0 – new 15968 kg
Third iteration We / W0 0.5707
W0 – new 16116 kg
Fourth iteration We / W0 0.5704
W0 – new 16078 kg
W3 – Cruise 10807 kg Wf / W0 0.2928
L/D 10.9
39
Appendix B2: Initial Weight Estimate Iteration Initial parameters SFC – cruise 0.5 / hour
W0 16078 kg
Range 2500 nm
Speed 250 m/s
Wcrew 200 kg
Wpayload 2000 kg
Loiter endurance 1 hour
SFC – loiter 0.4 / hour
L/D 10.34
Wingspan 15.98 m
First iteration W0 – Initial 16078 kg
*
W4 – Loiter 11616 kg
W1 – Taxi, takeoff 15756 kg W5 – Descent 11529 kg
W2 – Climb 14881 kg
W6 – Landing 11471 kg We / W0 0.5539
W6 / W0 0.71345
W0 – new 15453 kg
Second iteration We / W0 0.5539
W0 – new 15453 kg
Only two iterations were necessary to converge the result.
W3 – Cruise 12074 kg Wf / W0 0.3037
40
*
Appendix C: Initial Weight Trade Studies Range (nm) W0 (kg) 1500 12100 2000 14200 2500 16920 3000 20560 3500 25520 4000 32150 4500 38280 2
Weight = 0.002 (range) – 3.308 (range) + 12582
Loiter (hr) 0.5 0.75 1 1.25 1.5 1.75 2
W0 (kg) 15819 16380 16980 17600 18280 18980 19740
Weight = 2609 (loiter) + 14421
Payload (kg) W0 (kg) 1000 9130 1500 12060 2000 14860 2500 17570 3000 20210 3500 22800 4000 25330
Weight = 5.387 (payload) + 3953
41
*
Appendix D: Artwork Dimensioned drawings:
42
43
44
Side Concept art:
Front Concept art:
Top Concept art:
45
Design evolution:
Preliminary:
Interim:
Final:
Color schemes:
Yellow
Blue
"WPI"
Green
46
CAD drawing:
47
Appendix E: Airfoil Geometry Data Non-dimensional, normalized coordinates for a NACA 64008a airfoil: X
Yu
X
Yl
1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.075 0.05 0.025 0.0125 0.0075 0.005 0
0.00018 0.00438 0.00858 0.01278 0.01698 0.02117 0.02521 0.02897 0.03234 0.03524 0.03757 0.03921 0.03998 0.03972 0.03866 0.03681 0.03414 0.03047 0.02559 0.02245 0.01863 0.01353 0.00983 0.00778 0.00646 0
0 0.005 0.0075 0.0125 0.025 0.05 0.075 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
0 -0.00646 -0.00778 -0.00983 -0.01353 -0.01863 -0.02245 -0.02559 -0.03047 -0.03414 -0.03681 -0.03866 -0.03972 -0.03998 -0.03921 -0.03757 -0.03524 -0.03234 -0.02897 -0.02521 -0.02117 -0.01698 -0.01278 -0.00858 -0.00438 -0.00018
48
*
Appendix F: XFOIL Analysis α -4 -3.9 -3.8 -3.7 -3.6 -3.5 -3.4 -3.3 -3.2 -3.1 -3 -2.9 -2.8 -2.7 -2.4 -2.3 -2.2 -2.1 -2 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1 2.2
CL -0.5911 -0.5788 -0.5693 -0.5585 -0.5464 -0.5334 -0.5198 -0.5061 -0.4914 -0.4767 -0.4623 -0.4482 -0.4413 -0.4265 -0.3825 -0.3678 -0.3529 -0.3379 -0.3226 -0.3072 -0.2915 -0.2756 -0.2596 -0.2435 -0.2273 -0.211 -0.1948 -0.1785 -0.1622 -0.146 -0.1297 -0.1134 -0.0972 -0.081 -0.0648 -0.0486 -0.0324 -0.0162 0 0.0162 0.0324 0.0486 0.0648 0.081 0.0972 0.1134 0.1297 0.146 0.1623 0.1785 0.1948 0.2111 0.2274 0.2436 0.2598 0.2758 0.2917 0.3075 0.323 0.3383 0.3534
CD 0.01868 0.01789 0.0167 0.01566 0.0147 0.01381 0.01301 0.01237 0.01173 0.01118 0.01075 0.01038 0.01114 0.01073 0.00971 0.00944 0.0092 0.00899 0.0088 0.00865 0.00851 0.0084 0.00831 0.00823 0.00817 0.00812 0.00808 0.00805 0.00802 0.008 0.00798 0.00796 0.00794 0.00793 0.00791 0.0079 0.0079 0.00789 0.00789 0.00789 0.0079 0.0079 0.00791 0.00793 0.00794 0.00796 0.00798 0.008 0.00802 0.00805 0.00808 0.00812 0.00817 0.00823 0.00831 0.0084 0.00851 0.00865 0.00881 0.00899 0.0092
CDp 0.01569 0.0148 0.01345 0.01225 0.01114 0.01013 0.0092 0.00839 0.00763 0.00695 0.00635 0.00581 0.00557 0.00508 0.0039 0.00358 0.00328 0.00302 0.00278 0.00258 0.0024 0.00224 0.00211 0.002 0.0019 0.00182 0.00175 0.0017 0.00165 0.00161 0.00157 0.00154 0.00152 0.0015 0.00149 0.00147 0.00147 0.00146 0.00146 0.00146 0.00147 0.00147 0.00148 0.0015 0.00152 0.00154 0.00157 0.00161 0.00165 0.0017 0.00175 0.00182 0.0019 0.002 0.00211 0.00224 0.0024 0.00258 0.00279 0.00302 0.00328
CM -0.0214 -0.0206 -0.0197 -0.0187 -0.0178 -0.0169 -0.016 -0.0151 -0.0143 -0.0134 -0.0126 -0.0117 -0.0104 -0.0095 -0.0071 -0.0063 -0.0056 -0.0049 -0.0043 -0.0038 -0.0033 -0.0029 -0.0025 -0.0022 -0.0019 -0.0017 -0.0015 -0.0013 -0.0011 -0.0009 -0.0008 -0.0007 -0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0001 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0009 0.0011 0.0013 0.0015 0.0017 0.0019 0.0022 0.0025 0.0029 0.0033 0.0037 0.0043 0.0049 0.0055
2.3 2.4 2.5 2.6 2.7 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8
0.3683 0.3831 0.3978 0.4126 0.4274 0.4494 0.4636 0.4781 0.4929 0.5076 0.5214 0.5351 0.5481 0.5602 0.571 0.5804 0.5935 0.6096 0.6211 0.6299 0.637 0.6428 0.6477 0.6515 0.654 0.6553 0.6557 0.6555 0.6547 0.6522 0.6488 0.6454 0.6421 0.6383 0.6349 0.6324 0.632 0.6324 0.6324 0.6322 0.6314 0.6307 0.6299 0.6287 0.6263 0.6274 0.6278 0.6284 0.6291 0.63 0.6309 0.6319 0.6332 0.6348 0.6365 0.638 0.639
0.00944 0.00972 0.01002 0.01037 0.01074 0.0104 0.01076 0.01121 0.01176 0.0124 0.01305 0.01385 0.01475 0.01572 0.01677 0.01798 0.01868 0.01915 0.02016 0.02148 0.02294 0.02451 0.02616 0.02785 0.02955 0.03126 0.03301 0.03479 0.03663 0.03839 0.0402 0.04217 0.04426 0.04636 0.04862 0.05105 0.05349 0.05617 0.05881 0.06118 0.06336 0.06548 0.06752 0.06938 0.07104 0.07315 0.07519 0.07722 0.07922 0.0812 0.08314 0.08504 0.0869 0.08873 0.0905 0.09221 0.09391
0.00358 0.00391 0.00426 0.00466 0.00509 0.00583 0.00637 0.00698 0.00766 0.00842 0.00925 0.01017 0.0112 0.01232 0.01353 0.0149 0.0157 0.01622 0.01736 0.01883 0.02042 0.0221 0.02385 0.02565 0.02745 0.02927 0.03111 0.03297 0.03487 0.03668 0.03853 0.04056 0.04271 0.04486 0.04716 0.04963 0.0521 0.05479 0.05745 0.05986 0.06209 0.06424 0.06632 0.06829 0.07007 0.07224 0.07428 0.0763 0.0783 0.08028 0.08222 0.08411 0.08598 0.0878 0.08957 0.09128 0.09298
0.0062 0.007 0.0077 0.0085 0.0094 0.0115 0.0123 0.0132 0.014 0.0148 0.0157 0.0166 0.0175 0.0184 0.0193 0.0202 0.021 0.0217 0.0226 0.0234 0.024 0.0246 0.0251 0.0254 0.0256 0.0256 0.0255 0.0253 0.0248 0.0244 0.0238 0.0225 0.0207 0.0189 0.0167 0.0141 0.0115 0.0084 0.0056 0.0034 0.0018 0.0002 -0.001 -0.0019 -0.0022 -0.0039 -0.0052 -0.0064 -0.0076 -0.0087 -0.0098 -0.0108 -0.0117 -0.0127 -0.0135 -0.0143 -0.0149
Appendix G: Structural Analysis z
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 4.5 4.75 5 5.25 5.5 5.75 6 6.25 6.5 6.75 7 7.25 7.5 7.75
V -20309 -19500.5 -18692.7 -17886.6 -17082.8 -16282.2 -15485.7 -14693.9 -13907.9 -13128.3 -12356.2 -11592.4 -10837.9 -10093.6 -9360.61 -8639.91 -7932.65 -7240.01 -6563.25 -5903.73 -5262.89 -4642.34 -4043.83 -3469.31 -2921 -2401.45 -1913.67 -1461.27 -1048.85 -682.492 -370.997 -129.303
ω M 103360.5 0 96949.47 1.37E-05 90657.66 5.35E-05 84501.9 0.000118 78497.73 0.000205 72659.4 0.000313 67000 0.000441 61531.43 0.000587 56264.5 0.00075 51208.95 0.000927 46373.44 0.001119 41765.66 0.001323 37392.24 0.001539 33258.87 0.001764 29370.2 0.001999 25729.95 0.002241 22340.81 0.00249 19204.49 0.002746 16321.69 0.003006 13692.05 0.003271 11314.15 0.00354 9185.437 0.003812 7302.174 0.004086 5659.363 0.004362 4250.638 0.00464 3068.129 0.004919 2102.279 0.005199 1341.585 0.005479 772.2251 0.00576 377.486 0.006041 136.7789 0.006322 23.67364 0.006603
50
Appendix H: Calculated Drag V (m/s)
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 295
Mach
Cl afla
Cd ind
0.03389 0.082457 0.000351 0.067781 0.082464 0.000351 0.101671 0.082484 0.000351 0.135561 0.082523 0.000352 0.169452 0.082588 0.000352 0.203342 0.082685 0.000353 0.237232 0.082821 0.000354 0.271123 0.083004 0.000356 0.305013
0.08324
0.000358
0.338903 0.083537 0.000361 0.372793 0.083906 0.000364 0.406684 0.084355 0.000368 0.440574 0.084896 0.000372 0.474464 0.085541 0.000378 0.508355 0.086305 0.000385 0.542245 0.087207 0.000393 0.576135 0.088266 0.000402 0.610026
0.08951
0.000414
0.643916 0.090971 0.000428 0.677806
0.09269
0.000444
0.711697
0.09472
0.000463
0.745587 0.097132 0.000487 0.779477 0.100023 0.000517 0.813368 0.103529 0.000554 0.847258
0.10785
0.000601
0.881148 0.113295 0.000663 0.915038 0.120377 0.000749 0.948929 0.130023 0.000873 0.982819
0.14418
0.001074
0.999764
0.15428
0.00123
C_d_o
0.0244 0.0224 0.0214 0.0208 0.0203 0.0199 0.0196 0.0193 0.0191 0.0188 0.0186 0.0185 0.0183 0.0181 0.018 0.0178 0.0177 0.0175 0.0174 0.0173 0.0171 0.017 0.0169 0.0167 0.0166 0.0165 0.0163 0.0162 0.0161 0.016
Cd
Drag
Thrust
0.024743
16.28712
7476.00
0.022765
59.94061
7476.00
0.021761
128.9195
7476.00
0.021105
222.2743
7476.00
0.020621
339.3479
7476.00
0.020239
479.6047
7476.00
0.019924
642.6405
7476.00
0.019654
827.9743
7476.00
0.019416
1035.217
7476.00
0.019203
1263.996
7476.00
0.019009
1513.999
7476.00
0.018829
1784.713
7476.00
0.018661
2075.95
7476.00
0.018503
2387.185
7476.00
0.018354
2718.292
7476.00
0.018211
3068.729
7476.00
0.018073
3438.17
7476.00
0.017943
3826.71
7476.00
0.017817
4233.679
7476.00
0.017696
4659.278
7476.00
0.01758
5103.371
7476.00
0.017471
5566.222
7476.00
0.017369
6048.031
7476.00
0.017275
6549.689
7476.00
0.017192
7072.798
7476.00
0.017124
7619.774
7476.00
0.017082
8196.78
7476.00
0.017078
8813.531
7476.00
0.017151
9494.465
7476.00
0.017243
9877.23
7476.00
51
Appendix I: Center of Gravity Component Wings Horizontal tail Vertical tail Engines (both) Nose gear Main gear Avionics Fuel tanks Baggage Fuselage People Pilots Bathroom Total
Weight (kg) 2467 389 388 728 100 407 225 4416 425 3690 800 200 300 14535
x CG (m) 9.2 16.7 15.8 13.5 3.1 10.5 1.2 10 13.8 7.8 10 3.6 5.7
Moment (N*kg) 22696.4 6496.3 6130.4 9828 310 4273.5 270 44160 5865 28782 8000 720 1710 139241.6
52
Appendix J: Final Presentation Slides SPECIFICATIONS DUSTIN BRADWAY & K YLE MILLER •
Two-crew small business jet (pax: 6 to 8)
•
485 kts cruise @ 45,000 feet –
•
Business Jet
•
•
•
•
DRAWINGS
2 x PW308A
2,500 nm range, 1 hr loiter 2,000 kg payload including passengers Composite materials Quiet, efficient, comfortable Airborne at 135 kts, stalls at 120 kts
DESIGN P ARAMETER SUMMARY •
Payload: 2,200 kg (2 crew, 8 passengers and baggage)
•
Stall : 120 kts; Cruise: 485 kts (M 0.84); VNE: 524 kts (M 0.91)
•
•
W0: 14,543 kg; We: 8,559 kg L/D: 10.34; T/W: 0.0967
•
Airfoil: NACA 64008a; AR: 7.46; Wingspan: 15.98 m
•
T-tail; tailspan: 4.64 m; tail AR: 4.0
–
•
•
Wing loading: 82.09 lb/ft 2 Dimensions: 18.61 m long; 6.60 m tall; 2.35 m fuselage diameter –
•
5˚ dihedral; 8% thickness; 1˚ incidence angle, 45% taper, 20˚ sweep
Fuselage fineness ratio: 6.67
Fuel tank volume : 5.52 m3 (4417 kg of Jet A-1)
STRUCTURAL ANALYSIS SUMMARY
AERODYNAMIC ANALYSIS SUMMARY
•
Box spar, carbon fiber
Cruise Thrust from engine > Cruise Thrust Calculated
•
Moment and shear diagrams
•
Deflection
12000
10000
8000 g a r D & t s u r h T
6000 Drag Thrust 4000
2000
0 0
50
100
150 Velocity (m/s)
200
250
300