AAE 451, SENIOR DESIGN

AAE 451, SENIOR DESIGN CONCEPTUAL DESIGN REVIEW TEAM 3: GOLDJET DIANE BARNEY DONALD BARRETT MICHAEL COFFEY JON COUGHLIN MARK GLOVER KEVIN LINCOLN ANDREW MIZENER JARED SCHEID ERIC SMITH

1 Table of Contents I. Mission Statement 2 II. Outline of NASA Competition 2 III. Key Assumptions 3 IV. Executive Summary 4 V. System Requirements Definition 5 Market Research / Business Plan 5 Design and Economic Mission 6 Requirements Development 7 VI. System Definition 8 Constraint Analysis 8 Morphological Matrices 9 Pugh s Method 11 Final Concept Refinement 12 VII. Conceptual Design 19 Aircraft Walk-around 19 Key Design Parameters 20 Aircraft Performance 20 Sizing 23 Aerodynamics 30 Propulsion 43 Weights and Balance 61 Structures 68 Stability and Control 76 Applications 79 VIII. Concept Summary 86 Requirements Compliance 86 Plausibility 88 Detailed Design Work Remaining 88 IX. References 89 X. Appix 91

2 I. Mission Statement To design a profitable supersonic aircraft capable of Trans-Pacific travel to meet the needs of airlines and their passengers around the world. II. Outline of NASA Competition The NASA Aeronautics Research Mission Directorate s (ARMD) 2008-2009 University Competition calls for the design of an N+2 generation supersonic aircraft which would have initial operational capability (IOC) in 2020. More specific goals for the aircraft as outlined by the competition guidelines include: Cruise speed of Mach 1.6 to 1.8 Design Range of 4000 nautical miles Payload of 35-70 passengers, mixed class Fuel Efficiency of 3 passenger-miles per pound of fuel Takeoff field length < 10,000 feet for airport compatibility Supersonic cruise efficiency Low sonic boom (<70 PldB) In addition, entries to the competition are to identify the possible market for a small supersonic airliner, develop design and economic missions for the aircraft (including likely routes), identify technologies that might enable the aircraft design, and complete a conceptual sizing. These guidelines proved to be a starting point for our aircraft. Deviations occurred as a result of assumptions made, a market study, and sizing based on historical data.

3 III. Key Assumptions Our aircraft, the GoldJet FAST, is designed to have initial operational capability in 2020, with entry into service by 2023. In order for the FAST to be successful, there are several precedents, both technological and political, that must be met. 1. There must be a change to the FAR regulations that prohibit supersonic flight over land. Supersonic flight over land has been prohibited in the United States since March 1972. Changes to these regulations must come in the form of a complete repeal, or a modification to allow certain supersonic corridors for flight over areas of low population density. According to a statement released by Carl Burleson, Director of Environment and Energy on October 16, 2008, it is anticipated that future regulations would propose any future supersonic airplane produce no greater noise impact on a community than a subsonic airplane. [1] A design with a sonic boom overpressure less than 0.3 lb/ft 2 is a target of GoldJet in order to meet these new anticipated regulations. 2. A number of Supersonic Business Jet (SSBJ) concepts are currently in design and study phases of development. A change in supersonic flight regulations would pave the way for the success of SSBJ s over the next 10-15 years, fueling technological innovation. Our aircraft will dep on this field of research for products like more efficient supersonic engines, and possibly composite materials with better temperature resistance. IV. Executive Summary The GoldJet FAST is the first trans-pacific supersonic airliner capable of linking the United States with Asia. Our aircraft s design mission flies from Los Angeles International Airport (LAX) to Narita International Airport (NRT) in Tokyo, Japan. With a cruise Mach number of 1.8 the FAST cuts 46% off the 10 hour 45 minute subsonic flight, dropping it to 5 hours and 45 minutes. The FAST has a double-delta cranked arrow wing planform with 4 low-bypass turbofan engines podded under

4 its wings. The FAST uses control canards for pitch control, a vertical tail and rudder for lateral stability, and ailerons for roll control. Wing space has been budgeted for high-lift devices, which allow for takeoff on runways smaller than 10,000 ft. The maximum range for the FAST is 4,800 nm and an extra 240 nm has been factored in for a missed approach and diversion to another airport. 40-Passenger 2x2 luxury cabin Canards for Pitch Control and Low Boom Vertical tail (no horizontal tail) Cranked-Arrow wing planform Under-Nose Cameras for Landing Assistance Two Emergency Exits per side All fuel storage in fuselage 4 Low-bypass turbofans under wing Figure 1 Exterior aircraft walk-around

5 Gold Jet Requirements Compliance Matrix Requirement Units Target Threshold Design TO Field Length ft 10,000 12,000 11,380 Boom Overpressure lb/ft2 0.3 0.5 0.36 TO Gross Weight lb 300,000 400,000 329,000 Landing Field Length ft 10,000 12,000 9,000 Range nmi 5,650 4,707 4,800 Turnaround Time min 30 45 27 Number of Pasengers pax 40 40 40 Crew # 3 3 3 Cruise Speed Mach 2.1 1.75 1.8 Max Speed Mach 2.2 1.8 1.9 Trip Time min 380 415 345 Cabin Volume ft3/pax 60 55 75.8 Cruise Altitude ft 50000 45000 45,000 Cruise Efficiency paxmi/lb fuel 3.5 3 1.2 Second Segment Climb Gradient % 5.0 3.0 3.0 Seat Pitch in 40 38 50 Seat Width in 26 22 26 Aisle Width in 22 20 22 Aisle Height in 76 72 76 Figure 2 Requirements compliance matrix Figures 1 and 2 show our aircraft walk-around chart and requirements compliance matrix, respectively. V. System Requirements Definition Market Research / Business Plan In determining the requirements our aircraft needs to fulfill, it is crucial to have an accurate image of the market in order to ensure our aircraft s profitability. Two important factors for consideration resulted from market research: Percentage of travelers to which our supersonic transport jet will appeal Routes on which our supersonic transport jet will best be utilized (ie. selection of most profitable city-pairs) These two factors guide our decision for aircraft capacity, and allow a reasonable estimate for total aircraft sold and profitability.

6 We determined that the FAST will have a higher operating cost than subsonic transport jets and, subsequently, a higher average ticket price. Our aircraft ticket price was assumed to be comparable to a typical first class subsonic ticket price and further research revealed approximately 2% of current airline travelers pay these higher fares. We also made the assumption that an additional 1% of the total market will be willing to purchase our higher priced-tickets for the added convenience of shorter trip times and the novelty of flying in a supersonic jet. With these assumptions we estimate that our supersonic transport has the potential of capturing 3% of the market share. We next needed to determine routes that our aircraft would be most profitable to operate on. City pairs were chosen based on the following criteria: Sufficient distance so as to have significant reduction in trip time when flying at supersonic speeds (approximately 1000 nmi and above) Large volume of passengers to provide a market foothold Transoceanic flight or easy access to supersonic corridors Connection of large economic, social and cultural centers Based on these criteria a collection of city-pairs were chosen and historical data on traffic between them were used to estimate the volume of passengers our jet could expect to carry on an average day. The above market research yielded two significant conclusions: 1. The optimum capacity for our jet in order to minimize the number of empty seats is 40 passengers 2. We project to sell at least 120 aircraft over its lifetime Design and Economic Mission Having determined the size of our market, we then selected specific missions to define our aircraft requirements. The following section will highlight the details of our economic and design missions.

7 Our economic mission is the most profitable route for the FAST, combining both high potential passenger volume and sufficient range for supersonic flight to provide appreciable time savings. Based on market research, our economic mission is John F. Kennedy International Airport (JFK, in New York) to Los Angeles International Airport (LAX). This mission connects the two largest population centers in the United States, both large and powerful economic and social centers. This mission has a range of 2,520 nmi (great circle distance) with an estimated extra 400 nmi required for diversion to supersonic corridors, as outlined in the SRR. This mission will be important during the design phase of our aircraft, as performance will need to be such to maximize profitability. Our design mission is the longest and furthest we would ever expect to travel, which is crucial to sizing our aircraft. Our original design mission was from Los Angeles International Airport (LAX) to Pudong International Airport (PVG) in Shanghai, China. However, after completing more detailed sizing, and accounting for headwinds, we decided that this range capability was not feasible at maximum payload. In order to meet our threshold design range, we chose our design mission to be from LAX to Narita International Airport (NRT) in Tokyo, Japan. This range enables our aircraft to link Asia to North America, North America to Europe, and the Middle East to most destinations. The design range is 4800 nmi. This mission ultimately determines the requirements for our design as the range will determine the required fuel and the gross takeoff weight of the aircraft. Requirements Development Our primary aircraft requirements are based on the range and capacity dictated by the market research and design mission stated above. Our aircraft will need to carry 40 passengers a distance of 4800 nmi (plus necessary reserve fuel). Additional requirements were developed to account for those customer needs and wants not exclusively depent on range. A House of Quality (HoQ) was constructed in which we determined customer wants and needs and ranked them according to their importance relative to each

8 other. We found our most important customer needs to be profitable operations, low trip time, long range, and marketability. The engineering requirements we determined to be most important in satisfying our customers needs are cruise speed, block time, and cruise efficiency. Hence it is clear that our cruise conditions are crucial to meeting the customer needs. Based on this we decided to design the FAST for a cruise Mach number of 1.8, allowing our aircraft to cruise at twice the speed of most subsonic carriers. Other important requirements to consider are takeoff and landing field lengths for airport compatibility. All of the airports considered in our business plan have a minimum field length of 10,000 feet or longer (many have field lengths greater than 12,000 feet). Hence, we have set a target field length of 10,000 feet with 12,000 feet as our design threshold. VI. System Definition Constraint Analysis and Sizing To begin analysis of our aircraft concepts, we begun with a constraint analysis, using 5 main performance constraints: Steady, level flight at Mach 1.8 and 45,000 ft Subsonic 2g maneuver at 250 knots and 10,000 ft (such as would be executed inside a landing pattern) Takeoff ground roll of 6,000 ft at an altitude of 1,000ft on a +15 hot day Landing ground roll of 6,000 ft at an altitude of 1,000ft on a +15 hot day 3% Second Segment Climb Gradient above an altitude of 1,000 ft on a +15 hot day The takeoff and landing distances come from a desired usable field length of 10,000 ft, and include an additional 2/3 of the takeoff distance (i.e. s TO 2 sto s 3 desired ). Using the equations provided by Professor Crossley, and modifying the spreadsheet he provided, we generate the constraint diagram shown in Figure 3. Each of these constraints required assumptions about the aircraft, which were generated indepent of the aircraft configuration. Not having done any substantive analysis

9 at this point, some assumptions were generic, and not based on any detailed understanding of our aircraft. However, we had already determined that we would have four engines. After investigating the available design space for two-, three-, and four-engined designs, only four engines gave us practical values of T SL /W 0 and wing loading. Once we chose a concept and further developed our design (and engine model), our constraints would become more defined and would give way to carpet plots, which would allow us to choose a solid design point. GoldJet Constraint Diagram 1 0.8 0.6 T SL /W 0 0.4 0.2 0 50 60 70 80 90 100 110 120 130 140 150-0.2 Steady, Level Flight (1g), M = 1.8 @ h = 45K ft Subsonic 2g Manuever, 250kts @ h =10K ft Takeoff Ground Roll 5400 ft @ h = 1K ft, +15 Hot Day Landing Ground Roll 5400 ft @ h = 1K ft, +15 Hot Day Second Segment Climb Gradient Above h = 1K ft, +15 Hot Day Landing Ground Roll 5400 ft @ h = 1K ft, +15 Hot Day, No TR -0.4 W/S [lb/ft 2 ] Figure 3: Constraint Diagram Morphological Matrices To begin defining our concepts, we used a two step approach. First, to better get an idea of the options available to us, we broke down our design into eight categories: wing planform, wingtips, engine location, canards, tail configuration, wing location, fuselage type, and landing gear. We omitted low-boom technologies, high-lift devices (flaps, slats, etc.) and spoilers, on the grounds that choosing one doesn t preclude the use of any of the others: flaps and slaps can be used on the same wing,

10 but you cannot choose both a conventional tail and T-tail or low and high wing on the same concept. We then listed all of the possible choices for each category in a Morphological Matrix (Figure 4). Figure 4: Morphological Matrix Then, splitting up into four teams, we each chose a concept design one choice from each of the categories in the Morphological Matrix. In addition, we chose a datum for Pugh s Method: Concorde. Concorde was chosen because it is the only commercial supersonic transport to achieve large-scale commercial success. The concepts are summarized in Figure 5. Figure 5: Initial Concepts From these, we can note an immediate narrowing of the design choices it can be plainly seen that some choices are not feasible for a supersonic transport. Among the four concepts, there are two wing platforms, two fuselage types, and one landing gear style.

11 Pugh s Method Following Pugh s Method, we took a first round of comparisons, shown in Figure 6. Note that these comparisons were based off the team s engineering experience and expertise, and had not been verified by any quantitative engineering analyses. Figure 6: Pugh's Method, Round 1 At first, it seems that Concepts 1, 3, and 4 clearly distinguish themselves, but at a second glance, none of the designs have very many negatives, and there is little to distinguish them. We determined that this was due to our choice of datum: Concorde. Attempting to compare a concept to come to market in 2020 to one designed in the 1960s didn t allow for proper analysis or meaningful comparisons. To rectify this disparity, we switched datums from Concorde to our Concept 2, which was the concept most similar to the Concorde in the first round of Pugh s Method. This allowed us to compare our design on a level plane. In addition, several categories were deemed either too difficult to judge or irrelevant, and were eliminated in the second round. The second round of Pugh s Method compared our concepts 1, 3, and 4 against the new datum, Concept 2 (Figure 7).

12 Figure 7: Pugh's Method, Round 2 Final Concept Refinement After the second round, we noticed that Concepts 1 and 3 were the most outstanding, and more so, were fundamentally different: Concept 1 was based around a double-delta wing, and Concept 3 a joined wing. We determined then to finish with two concepts for further study: A double-delta concept, and a joined wing concept (Figure 8). The joined wing concept is Concept 3, and the double delta concept is a result of taking the best double delta concept (Concept 1), and bling it with the other double delta concepts (2 and 4) to create the best possible design. Figure 8: Final Concepts

13 These two concepts are illustrated here: Figures 9, 10, and 11 show our joined wing design, and Figure 12 shows a sample double-delta configuration (please note that this is simply an example, further analysis was done to refine it). Figure 9: Joined Wing Concept, Front View Figure 10: Joined Wing Concept, Side View

14 Figure 11: Joined Wing Concept, Top View Figure 12: Example Double-Delta Configuration

15 These two concepts have very different needs and areas for further analysis, as well as different benefits. The double-delta is relatively simple structurally and aerodynamically, but is fundamentally a compromise, and requires further analysis to choose the engine placement, canard choice, and tail configuration. The joined wing is complicated structurally and aerodynamically, but has the potential for some extremely attractive benefits (especially in aerodynamics). However, choosing a joined wing planform would allow for fewer variations in layout and configuration, simply by the nature of the planform. For example, the choices left to make for the double delta design were engine placement and longitudinal control surface (i.e. horizontal tail or canards. For a joined wing, mounting the engines on the wing and forcing them to bear their weight would make the wing structure enormously heavy and complex further exacerbating an already complex optimization routine, mounting them on the fuselage precludes this. In addition, a joined wing does not need an additional longitudinal control surface, as the wing structure provides both pitch and roll control already. A canard would have been employed to improve the aerodynamic properties of the design, as stated in Wolkovitch (1985) [2]. Wing Planform The first step in narrowing our concept choices down to one single design was to select the wing planform from this selection would flow many of our other design decisions. The first design presented was the joined wing planform. The benefits of this planform were largely in the areas of aerodynamics, and the difficulties mostly in structures (Wolkovitch, 1985 and Gallman and Kroo, 1993) [3]. The double-delta, on the other hand, is a compromise between high- and low-speed flight aerodynamically, and has distinct structural benefits. After some initial analysis of the joined wing design using lifting-line theory and a much more detailed investigation on the magnitude of analysis required for a joined wing, it was determined that the structural concerns of the joined wing outweighed

16 the aerodynamic benefits, which proved to be difficult to quantify. In addition, the double delta proved to be simple structurally, have good efficiency at high and low speeds, have large internal volume for fuel, and provide weight savings. For these reasons, the double-delta design was chosen. After some further analysis and the discovery of a paper on the optimization of cruise speed impact on supersonic aircraft planform (Hermann, 2004) [4], the final design chosen is technically a Cranked Arrow, which is similar to a double-delta in that the leading edge has two distinct sections an area of high sweep closer to the root, and an area of lower sweep closer to the tip, but differs from it in that the wing root is not straight, but rather kinked towards the leading edge in planform view, forming a rough arrowhead shape. Figure 13 - Cranked Arrow Planform (Hermann, 2004)

17 Engine Placement Once the double delta design had been chosen, it remained to choose where the engines would be placed: under the wings, in the manner of Concorde, or podded and aft on the fuselage similar to the Embraer ERJ 145 (but with two engines per pod). To assist in making this decision, we evaluated the two options against each other for eight design considerations: weight, noise, complexity, ease of maintenance, airflow into the engine, dynamics, ground clearance, and crash safety. We indicated a + if the design is superior and a if it we deemed it to be inferior. This resulted in the following table: Table 1: Engine Placement Comparison Table The designs broke even at with 4 positives and 4 negatives apiece. To add an additional level of distinction, we then determined that the most important considerations to us were weight, noise, and ease of maintenance. The under-wing design won two of those three considerations, and was therefore chosen. It is important to note that these comparisons were all qualitative and not based on any real calculations. Longitudinal Control Surface

18 The longitudinal control surface was the final major layout decision. As the design choices hitherto made placed a large percentage of our weight at the back of the aircraft, the double-delta wing and under-wing engines would both be far aft, we would be required to have a large moment to trim the aircraft. To achieve this moment with a horizontal tail would have resulted in a much longer aircraft to yield the desired moment arm, or an excessively large control surface to attain the desired moment magnitude. A canard would allow us to have the correct moment arm and magnitude without increasing the length of the aircraft, and as a result was the design we chose. In addition, canards give a second benefit of reducing sonic boom (Yoshimoto, 2004) [5]. Figure 14: Canard Design for Low Boom (Yoshimoto, 2004)

19 VII. Conceptual Design Aircraft Walk-around A brief overview of the GoldJet FAST is given in the following walk-around, listing some key features of its exterior design and cabin layout: 40-Passenger 2x2 luxury cabin Canards for Pitch Control and Low Boom Vertical tail (no horizontal tail) Cranked-Arrow wing planform Under-Nose Cameras for Landing Assistance Two Emergency Exits per side All fuel storage in fuselage 4 Low-bypass turbofans under wing Figure 15 Exterior aircraft walk-around Luxury Lavatory Galley Overhead bins for carryon storage 40-Passenger 2x2 Luxury Cabin

20 Cargo Loading Door Two fuel tanks under fuselage Canard Box Figure 16 Interior and cabin layout Key Design and Performance Parameters A brief summary of aircraft s key design and performance parameters follows: General Performance Wing o Range: 4800 nautical miles o Wing Loading: 130 lb/ft 2 o Passengers: 40 o Area: 2541.5 ft 2 o Length: 190 ft o Sweep: 60 57 o Takeoff Distance: 11,400 ft o Span: 80.26 ft o Landing Distance: 7,380 ft o Aspect Ratio: 1.851 Weight Canard o W0 = 329,000 lb o Area: 500 ft 2 o We = 135,000 lb o Sweep: 45 o Wf = 185,000 lb o Span: 40 ft Engine o Aspect Ratio: 3.2 o Number: 4 Sonic Boom o Diameter: 4.7 feet o Overpressure: 0.36 lb/ft 2 o TSL: 35,400 lbs o T/W: 0.425 Aircraft Performance The V-n diagram for an aircraft shows the different load factors that the aircraft will experience for a full envelope of equivalent velocities, which are scaled by

21 atmospheric conditions. According to Raymer, the highest positive load factor for a transport should be three to four [6]. This would cause the structural components of the aircraft to experience three to four times the load they bear under normal straight and level flight conditions. The highest acceptable negative loads on a transport are between negative one to negative two. The V-n diagram is made up of two different factors, maneuvering loads and gust loads. Maneuvering loads are loads caused by the flight path of the aircraft. If the plane were to suddenly pull up the load factor would increase, this also happens in high banked and fast turns. Some of these maneuvering load factors are set by the aerodynamic capabilities of the aircraft. Others are set by the structural capabilities. Fig. 17 FAST maneuver loads V-n diagram Figure 17 shows the maneuvering load factor as equivalent velocity is varied. The curved portions beginning at a velocity of zero and continuing to the horizontal lines at the top and bottom of the plot represent the maximum load factor our aircraft can sustain at stall speed. These limits are set aerodynamically, as the airplane cannot function any slower than is represented on the plot. The horizontal lines at the top and bottom of the plot, positive three and negative 1, represent the load factor our structure will be designed to. These numbers are within the range

22 given by Raymer and will increase slightly when gust loads are factored in. The vertical line at maximum equivalent velocity is dive speed, which is caped at 1.2Vcruise. Gust loads account for times when there are strong wind forces that increase the effective angle of attack of the aircraft. This creates sudden lift which causes the aircraft to experience higher load factors, as if it were pulling up. The gust loads are based on the aerodynamic properties of the aircraft such as C l max, C l alp ha, and the mean chord length. These loads are also based on the atmospheric conditions like gust velocity and air density. Fig. 18 FAST gust loads V-n diagram Figure 18 shows the maximum gust loads expected to be applied to our aircraft. The peak gust load occurs at our aircraft s cruise speed, and is only slightly higher than the load experienced during our aircraft s maximum allowable speed in turbulence. This collection of gust loads is combined with the maneuvering loads calculated earlier to form a total load envelope for all flight conditions. The highest aerodynamically feasible load is recorded for each equivalent velocity to create the envelope seen below in Figure 19.

23 Fig. 19 FAST total loads V-n Diagram The maximum load reached is 3.12 and the minimum reached is negative 1.12. These are within the envelope set out by Raymer for transport aircraft. Sizing Summary The purpose of the sizing code was to find the MGTOW of an aircraft meeting the design range of 4800 nmi. The algorithm was based on Raymer Ch. 19 and programmed using MATLAB. The algorithm is similar to that used for earlier sizing (in the SRR and SDR), but uses more accurate equations based on actual FAST performance, and smaller step sizes during mission segments, most notably in cruise. The sizing code uses inputs from aerodynamics (for lift and drag), an engine model (for thrust available and specific fuel consumption), and statistical weight equations as described in Raymer Ch. 15.

24 The gross weight is the sum of the payload weight, crew weight, empty weight, and fuel weight. For a configuration of three crew, each at 200 pounds, the crew weight is 600 pounds. Each passenger is estimated to have a total weight of 220 pounds, based on an average person weighing 180 pounds with 40 pounds of baggage. For 40 passengers, the payload weight is 8800 pounds. Based on an initial guess for gross weight, and fixed values for payload and crew weight, the fuel weight and empty weight could be determined, and the sum could be compared to the guess for gross weight. Iteration continued until the gross weight guess and calculated gross weight converged. AR 1.85 T/W 0.425 W0/S 130 lb/ft2 S 2541.5 ft2 M cruise 1.8 Mach number of Crew 3 number of Pax 40 weight per Crew 200 lb weight per Pax 220 lb Design Range 4800 nmi cruise altitude 45000 ft wind speed 100 kts stall speed 168 kts t/c 0.03 Λ LE 62 CL max 1.2 Number of Engines 4 Table 2 Design Parameters Finding Fuel Weight In order to find fuel weight, we split the design mission into six segments: engine start/taxi/takeoff, climb, cruise, descent, loiter, and reserve. Each segment, including key equations and necessary assumptions, will be described.

25 Engine start, taxi, takeoff To account for the fuel used during this segment, Raymer suggests to calculate fuel consumed for 14 min at ground idle and 1 min at takeoff thrust. The design parameters chosen sized the engine at takeoff. The rubber engine model, discussed in more detail later, was then used to find the specific fuel consumption at each condition. Then we found the fuel fraction for each by the equation: Climb W i W i 1 = 1 Cd T W i The climb segment consists of two parts: a linearly increasing velocity climb to 10,000 ft, and an accelerating climb to cruise altitude, 45,000 ft. The climb to 10,000 ft was done in 1,000 ft increments, calculating lift, drag, and thrust required at each point. We assumed a flight path angle of 14 based on suggestions from Raymer, as well as on trial and error from engine performance. Due to difficulties in plotting a trajectory and calculating drag through the transonic regime, an approximate equation from Raymer Ch. 6 was used, which is: where M is the cruise Mach number. Range credit was given to the climb segment based on average horizontal velocity. Time credit was also given to the climb segment based on average vertical velocity, obtained from climb rate. Cruise The equations of motion for steady, level, un-accelerated flight, as well as a modified form of the Breguet range equation, were used to calculate the fuel fraction for cruise. The Breguet range equation used was

26 where R is the range, c is the specific fuel consumption, v is the velocity, and is the lift-to-drag ratio. The range accounted for a headwind of 100 kts. During cruise, the step size was 50 nmi, and L/D and SFC were calculated at each point to account for weight loss due to fuel throughout the flight. Descent/Landing Raymer points out that the historical fraction for descent, used in Ch. 6, is a good approximation even for detailed sizing. This is because very little fuel is used. No range credit was given during descent. The result of this approximation is that fuel use is slightly overestimated, but time of flight is slightly underestimated. Loiter The urance equation of the form where E is the time in hours, was used to calculate the fuel weight fraction. For the purposes of sizing, 45 min of loiter time was used. L/D was estimated from an approximation in Corke [7], but compared to the cruise L/D calculated to ensure it was reasonable. Reserve To account for diversions to alternate airport, as well as trapped fuel, 6% was added to the fuel from the previous segments. Any diversion to an alternate airport would be done at subsonic speeds. W 1 /W 0 0.973 Takeoff W 2 /W 1 0.952 Climb W 3 /W 2 0.55 Cruise W 4 /W 3 0.995 Land

27 Finding Empty Weight W 5 /W 4 0.926 Loiter W f /W 0 0.562 Total Fuel Fraction Table 3 Weight fractions After one iteration of the fuel fraction, key parameters (such as engine weight, engine thrust, fuel weight, and cruise L/D) are passed to a statistical component weights function. Other inputs to the component weights function include wing and control surface area, fuselage data, and landing gear. The method for calculating component weights from these data will be discussed in a later section. A summary of the results of the sizing code are presented in Table 4. W 0 (approx) 329,000 lb W e (approx) 135,000 lb W f (approx) 185,000 lb Range 4800 nmi L/D cruise 8.85 Engine Diameter 4.7 ft Engine Thrust 35,400 lb Total Thrust 141,600 lb Cruise time 5:03 Flight time (no diversions or loiter, estimate) 5:45 Flight time (includes diversions and loiter, estimate) 7:16 Table 4 Sizing code results As mentioned before, the range of 4800 nmi represents a flight from LAX-NRT (Tokyo, Japan). The estimated flight time for subsonic transports is 10 hr, 44 min. The FAST s estimated flight time of 5:45 then gives a savings of about 5 hours, or 46%. Carpet Plots

28 For the conceptual sizing, the design parameters chosen were based on a generated constraint diagram (featured in the SDR report). The values were then refined through structural and aerodynamic constraints, and actual engine performance. This constraint diagram, however, was based on a more general supersonic aircraft, not specifically for the FAST. The next stage of design would use the carpet plots to re-center the baseline around the optimal thrust-to-weight and wing loading values for our aircraft. Performance Parameters The sizing code, as it stands, ensures that the FAST will be able to meet the required mission range. After sizing the engine, the code also ensures that the aircraft is capable of sustaining a supersonic cruise by comparing drag to available thrust. To further test our aircraft, the carpet plots introduce five other parameters: fuel efficiency, takeoff distance, landing distance, subsonic 2g maneuver, and second segment climb gradient. The equations listed below are from Raymer, Chapters 5 and 17. Fuel Efficiency: FE = n pax R W f Takeoff Distance: BFL = 0.863 1 + 2.3G W S ρgc Lclimb + obstacle 1 655 + 2.7 + T av W U ρ ρ SL Landing Distance: S G = 1 2g V f d(v 2 ) V i K T + K A V 2 2g Maneuver:

29 Second segment climb gradient: P s = V T W qc D0 W S K W n2 q S T SL W 0 = β α N N 1 CGR + 1 L D After finding the constraints on thrust-to-weight and wing loading using these equations, we determined that the fuel efficiency requirement set by NASA of 3 pax-mi/lb of fuel was not feasible for our aircraft. Achieving this fuel efficiency would require extensive aerodynamics work beyond the scope of this project. Therefore, fuel efficiency was removed from the carpet plot constraints. Figure 20 shows the resulting carpet plot. Figure 20 Carpet plot

30 The plot shows that our current design point is very close to the optimal, and meets all of the required constraints. Takeoff distance and required climb gradient appear to be the constraining performance parameters for the FAST. Changing our baseline design point to the lowest weight (T/W = 0.417, W 0 /S = 132 lb/ft 2 ) would achieve a weight savings of approximately 10,000 lb, according to rough estimates. Aerodynamics In order for us to compute the thrust required at cruise, we performed an analysis of the drag polar for free stream conditions (Figure 21) of standard atmosphere at 45,000 feet and Mach 1.8. The sizing code provided the weight at various points during cruise. By equating lift to weight, we could find drag and therefore thrust required. Figure 21 Drag polar at cruise

31 The initial and final weights for the cruise mission segment provide upper and lower limits for the lift required for level flight. This gives the range for cruise angle of attack, which is at its maximum at the beginning of cruise and diminishes as fuel is burned off and less lift is needed as shown in Figure 22. Figure 22 Lift vs angle of attack at cruise The maximum and minimum angles of attack show the maximum and minimum drag demonstrated in Figure 23.

32 Figure 23 Drag vs angle of attack at cruise This lift and drag data was then input to the cruise mission segment of the sizing code. Also of importance were the takeoff conditions. We studied the drag polars of takeoff conditions (Figure 24) to ensure the aircraft could hypothetically lift off at the initial weight of 329,000 lbf.

33 Figure 24 Takeoff drag polar For standard sea level conditions with 60% effective plain flaps (Raymer), Figure 25 shows that the aircraft requires an eight degree angle of attack at 150 knots to lift off the ground, which is reasonable.

34 Figure 25 Lift vs angle of attack at takeoff The approach configuration varies from the take-off configuration in speed, weight and flap effectiveness. Figure 26 gives the drag polar on normal approach with no high-lift devices employed. In Figure 27, the flaps are assumed to be 100% deployed, as suggested in Raymer. We computed the effect of the flaps on coefficient of lift using estimated values of C L and the flapped area as given in Raymer.

35 Figure 26 Drag polar on approach with no high-lift devices Figure 27 Drag polar on approach with high-lift devices

36 Wing Planform Our wing planform was chosen from Herrmann, CISAP: Cruise Speed impact on Supersonic Aircraft Planform; a Project Overview. [4] In the CISAP project, Airbus created three datum wing body configurations, chosen for three Mach numbers, and they were then optimized by multiple organizations. The key performance parameters for each aircraft design were mission range, the lift to drag ratio, and the mass of the wing. They also made sure that the wings would perform at low speeds, to guarantee a feasible planform. We chose the wing optimized by DLR for Mach 1.6 because that is closest to our design space and it has the best performance. Their optimal design, improved range by 25.4%, lift to drag ratio by 13.2% and reduced weight by 11%. These improvements in performance made it the logical choice for our aircraft. They also presented the optimized structural layout for the wing that facilitated the weight reduction. Figure 28 The wing planform optimized for Mach 1.6 by DLR.

37 Drag prediction We predicted the drag of the aircraft using a MATLAB function as a superposition of three components induced, wave, and parasite - with an addition of three percent of this total to account for miscellaneous factors. However, after receiving feedback during the CoDR presentation to Lockheed Martin, we discovered that a higher percentage, approximately fifteen percent, would have been more reasonable to account for miscellaneous factors. The method for evaluating induced drag used is a function of lift and angle of attack of the lifting surfaces completely indepent of Mach number [8]. All calculations were performed assuming the canard was fixed at the same angle of attack as the wing. Wave drag is only non-zero at supersonic conditions. The method for finding wave drag we used is based on an approximate area profile of the aircraft found with basic geometric representations of the nose, engines, fuselage, wings, tail, and canards. From this area profile, a code generated points on the surface of an equivalent body of revolution. The code then found the boundary of the intersection of the body of revolution with a plane rotated from the vertical by the Mach angle of the free stream at many positions along the length of the body.

38 Figure 29 Equivalent body of Revolution Figure 29 illustrates the body of revolution (blue) with an example of a Mach cut (green) at Mach 1.8. The area of each boundary projected onto the plane perpicular to the longitudinal axis was then used to form a new area profile. The second derivative of this new area profile, depent on Mach number, was used in a formula along with a reference area to find the coefficient of wave drag [9]. Parasite drag was found by summing the contributions of the nose, engines, fuselage, wings, tail, and canards. For supersonic conditions, only the wetted area and coefficient of friction under turbulent conditions were relevant for finding parasite drag. Subsonic conditions required the estimation of an interference factor, the wetted area, the friction factor and coefficient of friction with estimates for percent length of turbulent flow along each component (Raymer).

39 Lift Prediction Whole wing lift prediction model is given in Lee, An Analytical Representation of Delta Wing Aerodynamics. [8] The model is designed to be accurate in the range of aspect ratios between 1 and 3, where lifting line theory and thin wing theory are inaccurate. Figure 30 The regions of aspect ratio where lifting line theory and thin wing theory are accurate. The model in Lee fills in the area around an Aspect Ratio of 2 for delta wings. [10] To accurately predict the lift, Lee derived the equations for the normal force on the delta wing with no approximation assumptions. The equations were simplified to get the coefficient of lift in terms of a linear and non-linear factor. When simplified, these functions are factors of only angle of attack, leading edge sweep, and aspect ratio. With this model, airfoil section and thickness are irrelevant.

40 Figure 31 Theory compared to experiments on a wing with an aspect ratio of 2. While not completely accurate, it is much closer than lifting line or thin with theory. Due to this theory s accuracy for the aspect ratio of our wing, we approximated the wing of the Gold Jet FAST as a delta wing of identical aspect ratio, using the average leading edge sweep. The resulting lift curve for the planform of the Gold Jet FAST can be seen in Figure 32. Figure 32 The lift curve slope for the Gold Jet FAST planform

41 Based upon some of the more complete experimental data presented in Lee, a C LMAX of 1.2 was chosen at an angle of attack of 27 degrees. While approximate, experimental of computational validation is required. For further work a higher fidelity, most likely CFD based model should be used, or at the very least experimental verification that the assumptions made to use this model are accurate. Sonic Boom Prediction Sonic-boom prediction was carried out using a simple N-wave prediction. The method is based on Carlson s Simple Sonic-Boom Prediction method. [11] It uses a series of non-linear factors to estimate the effects of shape, and altitude on the propagation of the sonic boom. The non-linear factors were determined from charts and graphs in the paper. To improve the generality of the code and simplicity of the input file, the non-linear factors were interpolated in Microsoft Excel. This change made it so the input file only requires data about the aircraft shape, Mach number, and altitude. The shape can be accounted for, either from the effective area distribution or based on the weight, Mach number, altitude, curve fit to historical data. Test cases were run against the examples given in the paper to verify accuracy. Initial prediction of the sonic-boom signature was calculated based upon the cross sectional area, Mach number and altitude. Fidelity is improved over the last estimate by calculating shape factor based on the cross sectional area instead of basing it off of Concorde [11]. The resulting sonic boom signature is lower but not substantially.

42 Figure 33 The predicted sonic-boom signature, modified in both Experimentally changing the area distribution had little effect upon the resulting sonic boom signature. The baseline signature had an overpressure of 1.5 lb/ft 2 which is far above the acceptable level of 0.5 lb/ft 2 and nowhere near the target of 0.3 lb/ft 2. To improve the overpressure, shaping of the aircraft is required. Aircraft shaping reduces the overpressure by making the shockwaves parallel to prevent them from coalescing into a stronger shockwave. Since doing so requires quite a bit of CFD and experimentation, it is infeasible for this level of design. To simulate the effects of aircraft shaping, reduction factors were created based upon the NASA F-5 Shaped Sonic Boom Demonstrator(SSBD), and the SAI Quiet Supersonic Transport. NASA successfully demonstrated that shaping of the aircraft body can reduce the sonic boom overpressure at the ground. They did this by modifying the nose of an F-5 based upon CFD optimization. They managed to reduce the sonic boom overpressure when compared to an unmodified F-5 by almost 40 percent [12]. Comparing their experimental results to the ones predicted

43 using Carlson s method, a shaping factor of 0.63 was used. This resulted in a reduction of boom overpressure to 0.9 lb/ft 2. This is still well above the threshold. To see the effects of shaping the whole aircraft, another shaping factor was created based upon the SAI QSST. The QSST boasts an overpressure of 0.3 lb/ft 2 which is our target value [13]. This is accomplished by shaping of the nose, use of canards at a high dihedral angle, and a gull wing [14]. Comparing the predicted overpressure with the number given on the website resulted in a shaping factor of 0.37. When this is applied to the Gold Jet FAST, the overpressure is reduced to 0.36 lb/ft 2 with a duration of 0.14 seconds. This is within our threshold and means that the Gold Jet FAST will require substantial CFD and shaping to reduce the overpressure to an acceptable amount. This will be a large focus of the aerodynamics team during preliminary design. Propulsion Engine Configuration and Performance Summary The propulsion system on FAST has been designed with 4 Low bypass turbofan engines contained in two nacelles. It may have been possible to achieve the necessary thrust with fewer engines, however the size of such engines would have required an unreasonable increase in noise and drag. Each nacelle is designed to hold two engines (as depicted in the Figure below) with one nacelle placed underneath each wing.

44 Figure 34: Engine Nacelles Since there is currently no other supersonic commercial jet, and considering the Olympus engines of Concorde were designed with 1960s hardware, it seemed unreasonable to expect any currently operating engine to be optimal for FAST. For this reason we are proposing a new engine program which will be more suited for FAST s design goals and optimized to achieve the best possible performance. The Table below details the primary design parameters for this engine: Inlet Type 2D Ramp inlet with variable geometry Nozzle Type Converging-Diverging, Variable exit area Fan Face Diameter 4.7 ft 2 Engine Length 17.5 ft Inlet and Duct Length 22.2 ft Bypass Ratio 0.5 Overall Compressor Pressure Ratio 20 Table 5: Engine Specifications

45 From this chosen engine configuration and with the use of a rubber engine model, which will be discussed in the following section, we generated the following performance curves. Figure 35: Max Power Thrust TSFC at multiple flight conditions

46 Figure 36: Max Power Thrust at multiple flight conditions To summarize the results depicted in the charts shown above, each single engine has the following important performance characteristics: Max Sea Level, Static Thrust Max Cruise (45k, Mach 1.8) Thrust Cruise TSFC 35,361 lbf 9,102 lbf 0.9492 (lbm/hr)/lbf Table 6: Performance characteristics for each engine To ensure that these engines are producing the necessary thrust at various flight conditions, the total thrust of all 4 engines is plotted against the required thrust (ie. Drag) as functions of Mach number at important altitudes.

Thrust (lbs) Team GoldJet 47 140000 120000 100000 Thrust Required (Drag) and Thrust Available vs Mach # for Important Altitudes Assuming Steady level flight at Max Cruise Weight (307,000 lb) T req - 0 ft Treq - 10k ft Treq - 45k ft Tavail - 0 ft Tavail - 10k ft Tavail - 45k ft 80000 60000 40000 20000 0 0 0.5 1 1.5 2 2.5 Mach # Figure 37: Thrust available, required as function of Mach # varying altitude The above chart shows that there is more than sufficient thrust at low altitudes for slow speeds. From this chart it is clear that the crucial condition is in fact the cruise point. At 45,000 ft the thrust available drops below the thrust required at Mach 1.85. Hence there is sufficient power to operate at the desired cruise point of 1.8, however nearly full power will be required. It should also be noted that there is a minimum speed at which FAST can operate at 45,000 ft as the required thrust (Drag) increases when slowing down to the transonic region. This has been taken into account when considering the climbing and acceleration pattern used to reach cruise. Engine Model As already discussed, we at Gold Jet are proposing a new engine that will be optimized specifically for FAST s design point. For this reason, during the design of FAST a rubber engine model was needed in order to perform optimization

48 studies as well as to create a final engine model which could be implemented along with our sizing code to determine engine size and compute engine performance. We created a thermodynamic model based on Hill & Peterson s text for a turbofan engine [15]. The engine model accounts for varying flow conditions deping on the operating conditions of the aircraft (ie. flow through aircraft mach cone, compression shocks across inlet etc.). Inlet Design For FAST we have decided to use a 2D ramp inlet with variable geometry to allow for optimal capture area in both subsonic and supersonic flight conditions. The figure below shows the inlet design in both the supersonic and the subsonic configuration. Standard relations for normal and oblique shocks were used to calculate inlet conditions.

49 Figure 38: 2D Ramp variable inlet geometry The geometry depicted above was designed specifically so that the shown capture areas would be met for two conditions: (1) The supersonic capture area sized for required engine airflow at design cruise conditions (Mach 1.8 at 45000 ft), (2) The subsonic capture area sized for required engine flow at takeoff (Mach 0.32 at Sea Level). These two capture areas were computed from (10.19) in Raymer s text: A capture = m e 1+ m s m e ρ u 1 + A b A capture Where, m e is the airflow required by the engine, m s is the secondary flow requirement, A b is the boundary layer bleed port area, and ρ and u represent the

50 ambient density and flow velocity (note: for supersonic flight, u represents the flow velocity inside the aircraft s Mach cone). Based on typical values given in Raymer s text, the secondary bleed fraction was assumed to be m s m e = 0.20 (Table 10.2 in Raymer for fighter) and the boundary layer bleed area was assumed to be Bleed at M=1.8). A b A capture = 0.04 (Fig. 10.19 in Raymer, Slot Having arrived at an inlet geometry design, this inlet then needed to be included in the engine model. The shock angles depicted in the Figure above are computed for the design condition of Mach 1.8 at 45,000 feet. However, the engine model must be capable of computing Inlet performance at virtually any given flight condition. Figure 39: Shock pattern across inlet For supersonic flow, assuming the conditions are known at Station 1 (M 1, P 1, T 1 ) and for the known turning angle, δ 1, the shock angle, σ 1, and the conditions at 1a can be computed using the oblique shock relations. Likewise from the conditions at 1a, the conditions at 1b can be computed and then from which the conditions at 1c can be computed using the Normal Shock relations. This flow in 1c is then passed into a subsonic diffuser, which continues to decelerate the flow to a Mach number of 0.4 or less at the fan face (Station 2).

51 From this setup the stagnation pressure loss across all the shocks through the inlet can be computed: P 01 P 01c = P 01 P 01a P 01a P 01b P 01b P 01c Nozzle Geometry We have designed the exit nozzle to be a converging-diverging nozzle to create supersonic flow out the exit in order to maximize the thrust output of the engine. Furthermore we have chosen a variable exit area design to allow for perfect expansion to ambient conditions. The Figure below shows the conceptual design for the nozzle. Figure 40: Converging-Diverging Variable Nozzle Design We recognize that a variable exit geometry adds significant complexity to the engine design, increasing production and maintenance cost. However, considering that FAST will have to perform well over such a wide range of conditions, we believe the performance benefit of a variable nozzle design will outweigh the extra complexity of the design. Engine Required Airflow

Required Airflow (lbm/hr) Team GoldJet 52 Total thrust and fuel consumption of a jet engine are depent on airflow through the engine, which is a function of altitude and mach number. For the purpose of this analysis, the total airflow required by the engine will be assumed based on data from Raymer s text in Appix E.1 for an afterburning turbofan. While our engine does not have an afterburner, this approximation is considered close enough for the conceptual design stage. 700 Total Required Airflow 600 500 400 300 200 100 0 0 0.5 1 1.5 2 2.5 3 Mach Number SL 10k 20k 30k 36k 40k 50k 60k Figure 41: Total Required Airflow from Engine in Raymer s Appix E.1 Data from the Raymer s plots for required engine airflow (m ee1) were tabulated as functions of Mach number and altitude, however it is recognized that this airflow value is for an engine of a specific size (Fan-face diameter, D fe1 44 inches). Hence this airflow needs to be scaled to match our engine diameter, D f. Assuming that mass flow is proportional to fan-face area, the total airflow required by our engine is then: m e = m ee1 D f 2 D2 fe 1

53 This total engine airflow will then be split into two airflows, bypass flow, m b, and the core flow, m a. Hence for a given Bypass ratio, B pr = m b m a then the core and bypass flows can be computed: m a = m e B pr +1, m b = m e m a Thermodynamic Modeling 8 9 1c 2 3 4 5 6 7 [citation e-2] Figure 42: Thermodynamic Model and Stations of Turbofan engine Let the numbers depicted in the Figure above be the station definitions throughout the engine. Station 1c being the flow entering the subsonic diffuser (after external compression from the shocks). Station 2 is then the condition at the fan face, Station 3 is the exit of the compressor and the inlet of the combustor/burner, Station 4 is the combustor exit and the inlet to the turbine, Station 5 is the exit of the turbine and the inlet of the afterburner, Station 6 is the entrance to the Nozzle and Station 7 is the core nozzle exit position. For the bypass flow, Station 8 is the flow exiting the fan in the bypass duct, and station 9 is the bypass duct exit.

54 At this point, in order to thermodynamically model the engine, several assumptions must be made. The Table below lists these assumptions. Diffuser Efficiency η d = 0.97 Fan Efficiency η f = 0.85 Fan Pressure Ratio P 08 P02 = P rf = 1.6 Compressor Efficiency η c = 0.85 Burner Pressure Drop P 04 P03 = P rb = 0.99 Max Turbine Inlet Temperature T 04max = 1500 K Turbine Efficiency η c = 0.90 Core Nozzle Efficiency η nc = 0.98 Fan Nozzle Efficiency η nf = 0.98 Fuel Heating Value Q r = 45,000 kj/kg Specific Heat Ratio prior to combustion γ 1 = 1.4 Constant Press Spec heat prior to combustion C p1 = 1005 J/kgK Specific Heat Ratio after combustion γ 2 = 1.31 Constant Press Spec heat after combustion C p2 = 1240 J/kgK 1) Conditions inside Mach cone Table 7: Engine Assumptions Let the ambient conditions be designated as Station a. If the aircraft is flying at supersonic speeds, then there will be a Mach cone generated with an angle: μ = sin 1 1 M If the flow conditions inside the Mach cone are designated as Station 1, then Mach number, Temperature and Pressure (M 1, T 1, P 1 ) can be computed using the oblique shock equations for a shock angle μ. If the aircraft is flying at subsonic speeds then the conditions at Station 1 are equivalent to the ambient conditions. 2) External Compression across inlet

55 For the computed flow conditions at Station 1 (M 1, T 1, P 1 ) and for the given inlet geometry, the flow through the inlet can be computed up to Station 1c as described in the Inlet Design section. If M 1 < 1 then condition at 1c are assumed equivalent to conditions at Station 1. 3) Compressor Inlet Conditions For inlet conditions, T 1c and M 1c and assuming adiabatic flow through the subsonic diffuser, the stagnation temperature and Pressure are computed: T 02 = T 1c 1 + γ 1 1 2 M 2 1c P 02 = P 1c 1 + η d T 02 T 1c 1 γ 1 γ1 1 4) Compressor outlet conditions For a known compressor pressure ratio, P rc, the conditions at the compressor exit can be computed: T 03 = T 02 1 + 1 η c P rc γ 1 1 γ1 1 5) Fan outlet conditions P 03 = P 02 P rc Similar to the compressor, for an assumed fan pressure ratio, P rf, the fan outlet conditions can be computed: T 08 = T 02 1 + 1 η f P rf γ 1 1 γ1 1 P 08 = P 02 P rf 6) Burner fuel-air ratio

56 For a specified Power setting, Pwr, given in percent (ie Max throttle: Pwr = 100) the turbine inlet temperature (burner outlet temperature) can be defined as follows: T 04 = T 04max T03 100 Pwr + T03 Hence, the fuel-air ratio which will achieve this turbine inlet temperature is: m f m a = f = T 04 T03 1 Q r Cp 1 T 03 T 04 T03 Where m f is the total fuel flow and m a is the total core air flow. 7) Turbine inlet pressure Assuming a value for the burner pressure drop, P rb, the stagnation pressure at the turbine inlet can be computed: 8) Turbine outlet conditions P 04 = P 03 P rb For the power balance in the engine, the total power output by the turbine must equal the power required for the compressor and the fan. Hence in this case the power balance is: m a + m f C p2 T 04 T 05 = m ac p1 T 03 T 02 + B pr m ac p1 T 08 T 02 Where B pr is the Bypass ratio. Hence, solving this balance for T 05 gives: T 05 = T 04 m ac p1 T 03 T 02 + B pr m ac p1 T 08 T 02 m a + m f C p2 And the turbine exit stagnation pressure can then be computed:

57 P 05 = P 04 1 1 η t 1 T 05 T 04 γ 2 γ2 1 9) Core Nozzle Inlet conditions Assuming no afterburner, then T 06 = T 05, P 06 = P 05 10) Core Nozzle Exit Velocity For variable nozzle geometry which perfectly expands the exit gas to ambient pressure (P 1 ) the core nozzle exit velocity can be computed: u ec = 2η nc γ 2 γ 2 1 R 2T 06 1 P 1 P 06 γ 2 1 γ2 Where, R 2 = C p2 1 1 γ 2. 11) Fan Nozzle Exit Velocity Similarly to the core nozzle, if the fan nozzle perfectly expands the gas to ambient pressure then: u ef = 2η nf γ 1 γ 1 1 R 1T 06 1 P 1 P 08 γ 1 1 γ1 Where, R 1 = C p1 1 1 γ 1. 12) Thrust and TSFC

58 Hence, having calculated the nozzle exit velocities, and knowing the mass flows in the engine, the total installed thrust of the engine can be computed: F = m a + m f u ec + m bu ef ρ 1 u 1 A capture u 1 The Thrust Specific Fuel Consumption (TSFC) is then simply the total fuel flow, divided by this thrust value: TSFC = m f F With the above equations, an engine model was created (in MATLAB) which computes Thrust and TSFC with flight Mach number, altitude, power setting, bypass ratio and compressor ratio as inputs. This rubber engine model then allowed for multiple combinations of bypass ratio and overall compressor pressure ratio to be checked during the engine optimization. Engine Optimization results Two parameters which can have a significant impact on engine performance are bypass ratio, and overall compressor pressure ratio. For this reason, after developing an engine model, we performed an optimization analysis to determine what values would best suite the design goals for FAST.

Specific Thrust [lbf/(lbm/s)] TSFC [(lbm/hr)/lbf] Team GoldJet 59 2 1.8 1.6 1.4 TSFC vs Compressor Pressure Ratio T04 = 1500 K, BPR = 0 M = 0, Alt = 0 M = 0.8, Alt = 30k M = 1.8, Alt = 45k 1.2 1 0.8 0.6 0.4 0.2 0 0 20 40 60 80 100 Compressor Pressure Ratio Figure 43: TSFC as it deps on Compressor Pressure Ratio The Figure above shows how TSFC deps on compressor pressure ratio for different flight conditions, the most important of which is the design cruise point shown by the green line. This plot clearly shows the TSFC is minimized for a very high pressure ratio of nearly 70. 0.03 0.025 0.02 Specific Thrust vs Compressor Pressure Ratio T04 = 1500 K, BPR = 0 M = 0, Alt = 0 M = 0.8, Alt = 30k M = 1.8, Alt = 45k 0.015 0.01 0.005 0 0 20 40 60 80 100 Compressor Pressure Ratio

TSFC [(lbm/hr)/lbf] Team GoldJet 60 Figure 44: Specific Thrust as it deps on Compressor Pressure Ratio While a high value of pressure ratio optimize TSFC, this plot shows that specific thrust ( F/m a ) is optimized for a relatively low compressor pressure ratio of approximately 5. Some tradeoff must be made between optimization of fuel consumption, and optimization of thrust. Based on these two plots, a compressor pressure ratio of 20 appears to be the optimum compressor pressure ratio. 1.2 1 TSFC vs Bypass Ratio T04 = 1500 K, CPR = 20, FPR = 1.6 M = 0, Alt = 0 M = 0.8, Alt = 30k M = 1.8, Alt = 45k 0.8 0.6 0.4 0.2 0 0 1 2 3 4 5 Bypass Ratio Figure 45 TSFC vs. bypass ratio This plot shows how TSFC deps on Bypass Ratio. High bypass ratios have a beneficial impact on fuel consumption. Based on this chart alone, a fairly high bypass ratio would seem optimum. However, a high bypass ratio, while it would produce a lower TSFC would require a larger fan area in order to meet thrust demands. This would increase drag which would hurt overall aircraft performance. A high bypass ratio engine, while initially temping, would not be beneficial in the for a supersonic transport.

61 There is, however, some benefits to having a relatively small bypass ratio. A bypass ratio of 0.5 would give a benefit of 0.04 (lbm/hr)/lbf in TSFC with relatively little increase in engine size needed. While this number seems small, for 4 engines producing a total of approximately 36,000 lbs of thrust at cruise during a six hour flight, this improvement in TSFC leads to a total fuel reduction of 10,000 lbs. Our optimization study lead us to an overall compressor pressure ratio of 20 and a bypass ratio of 0.5. Weights and Balance Component Weights As discussed earlier, our sizing code calculates the empty weight of FAST by estimating the weight of each individual component and then summing the weights to create a total composite weight. Raymer gives statistical models of each component based on the type of aircraft being modeled. There are three different types of component equations: fighter, transport and general aviation. Based on mission profile, FAST does not fit entirely in any of the groups of equations. To solve this problem, a logical, intuitive approach was used to model each component with the most appropriate equation. Because of the high cruise speed, the wings and vertical tail have to be built stronger than ordinary transport aircraft in order to withstand increased stresses at supersonic speed. This includes the higher drag, as well as the effects of increased temperature due to skin friction. We felt that the fighter equations would more accurately reflect the weight of these components. The canard was modeled using the transport equation because it would never have to achieve the maneuverability required of fighter aircraft, and thus would not have to be built as tough as the fighter canard. FAST's engines are low bypass turbofans that are mounted flush with the wings, and utilize converging/diverging nozzles and a ramp inlet. This configuration is the most common one for fighter aircraft, so the fighter equations were used for the entire engine group. The remainder of the component equations used were from the transport section, because they are not affected by the increased speed of the aircraft. Use of advanced materials on the

62 FAST is also reflected in the component weight codes. Because of the use of GLARE panels for the skin of FAST, a materials weight factor of.95 was used for the fuselage. This number was not higher because the interior structure extensively used traditional aluminum alloys. For the wings, canard and vertical tail, a factor of 0.90 was used, due to the combination of GLARE for the skin and Al-Li alloy 2090 for the leading edges. To account for the total increase of weight during the final design phases, the entire empty weight was multiplied by a factor of 1.02. Raymer describes this 2% increase as reasonable for modern computer aided design techniques. The weight statements of the individual components are shown in Tables 8-10.

Table 11 shows the various payloads that are carried. For the purposes of this early design, the passengers are assumed to be 180 pounds, including carry-on luggage. Checked baggage is represented by the cargo weight. The overall FAST weight statements are compiled in Table 12. The empty weight is the weight of the components that cannot be removed from the aircraft, including structures and systems. OWE is the empty weight plus the weight of the crew and their baggage and equipment. MZFW is the zero fuel weight, and includes the crew and the maximum possible payload. MFW is the zero fuel weight, plus the reserve fuel. Finally, MTOGW is the maximum takeoff weight for the aircraft. In this case, it was assumed that taxiing the aircraft resulted in negligible fuel loss. Figures 46-48 show the statistical breakdown of the weight empty, at MZFW and at MTOGW, respectively. Figure 46 MTOGW Figure 47 Zero Fuel Weight

64 Figure 48 Empty Weight Landing Gear When sizing the landing gear, we used Raymer s equations for transports and bombers. These equations give the diameter and the width of the landing gear tires based on the amount of weight each carries. The equation for both diameter and width is A W B w, where W w is the weight on each wheel, and the coefficients A and B dep on the parameter being calculated. For the diameter equation, A = 1.63 and B =.315, giving a tire diameter of 44.35 inches for the main landing gear wheels. This also gives the nose wheel diameter of 39.74 inches. For the width equation the coefficients change to A =.1043 and B =.48, according to Raymer s sizing for transports. This gives the widths of the tires to be 16.01 inches and 13.54 inches for the main and nose wheels, respectively. Since there are no real-world tires that fit those specifications exactly, we used a database of 100 actual tires and passed into the tire sizing code. The program then selected the lightest tire that met both the diameter and width criteria. These tires also have properties that lead to the calculation of tire pressure and the stroke distance of the oleo cylinder. We deemed those calculations to be too detailed at this point in the design process, so they were not used. The main landing gear had to be placed first on the structure in order to maintain static stability. The main landing gear must be aft of the center of gravity so that the aircraft does not tip on its tail. Since the FAST s engines are mounted under the wings, the

65 main landing gear had to be behind the nozzle inlets. This is to avoid debris being kicked into the engine, and also to eliminate turbulent air from being ingested by the engine. After placing the main landing gear, the nose landing gear was then placed to take 15 percent of the static load of the aircraft. According to Raymer, the nose gear is supposed to be smaller than the main gear, but it must take at least 8 percent of the load to allow for steering. This dictates that the main landing gear be much closer to the CG than the nose gear. Once the main and nose landing gear were placed, their length was calculated. It is important to make the main landing gear long enough so that the tail does not hit the ground during rotation for takeoff. Figure 49 FAST dimensions The angle between the main landing gear and the tip of the tail must be greater than the takeoff angle. We designed the FAST for a maximum takeoff angle of 15, which means that the length of the gear from ground to bottom of fuselage would need to be at least 6.5 feet. Center of Gravity Another important reason for using component based weight prediction is center of gravity (CG) predictions. CG prediction and management is an important part of the design process, as it is necessary for ensuring the aircraft is stable. To calculate the CG, we simply treated the aircraft as a static beam and found the location where the moments balance. This is shown in the following simple equation.

66 W Aircraft x CG = W component x distance to nose Components The weight of each component was found as described earlier using the component weight equations. The weight of the aircraft fluctuates in flight, based on the fuel consumption. This results in a shift in the CG during flight, which affects the static margin. Stability is compromised when the static margin is no longer positive, and would require an expensive stability augmentation control system to correct. The goal of CG management is to ensure that the aircraft CG remains between forward and aft limits. To do this, components are placed so that the CG is maintained in the proper location at all times. The majority of the components must be located based on other factors, such as the wing for aerodynamics and the vertical tail and canard for pitch and yaw control. The cockpit is at the tip of the fuselage, and the cabin is constrained by operating restrictions. The cargo and fuel tank placement took potential CG impact into consideration, but were treated as fixed at this point in the design. The remainder of the components were placed in order to achieve the necessary balance. The main segments that were moved were the avionics and APU. The final location for the APU is directly behind the aft fuel tank, and above the wing box. This is shown in blue in Figure 60. The avionics were kept in the nose, as shown later in Figure 62. After final placement, the CG is calculated for all points of the mission. These include the design weights shown in Table 12, as well as the different stages where the fuel tanks are emptied. From this information, the most forward and aft CGs are found. These numbers are 111 and 128 feet from the nose, respectively, and this is shown graphically in Figure 50.

67 Figure 50 Fore and aft CG The CG for each point are also plotted as a function of the gross weight in Figure 51, and this was used heavily to fine tune the locations of components. Important to note is the different forward CG limits. This occurs because the aerodynamic center moves back during supersonic flight. Based on fuel consumption calculations from the sizing code, FAST will weigh approximately 310,000 pounds when it enters supersonic flight, which is represented in the graph by the horizontal dashed red line.

68 Figure 51 CG travel During the first stages of design, the forward fuel tanks were modeled as one, but during CG travel calculation it was found that this produced a CG that was ahead of the supersonic forward limit when the aircraft weighed 310,000 pounds. To correct this, the forward fuel tanks were split in two, and the forward-most tank would be emptied first. This served to move the CG back fast enough so that the CG remained in between the limits at all times. Structures At this stage of design, the structure is approached at a very basic level. The goal of the team is to ensure that the concept chosen is structurally feasible, and that there is adequate space allocated for all necessary structural components. Figure 52 highlights the initial structural design of FAST modeled in CATIA. Figure 52 Structural layout One of the most important structural considerations is the load path. FAST utilizes a keel beam that is located directly underneath the cabin, as shown in Figure 53. This nonstandard location was chosen to simplify the structure in the fuselage. Locating the keel beam directly beneath the cabin reduces the distance between the deck and the load path, eliminating the need for intervening structure and reducing weight. The

69 position of the keel beam also allows the landing gear and canard box to integrate directly to the load path, further simplifying the structure. Figure 53 Keel beam connection The keel beam is connected to the fuselage via the deck and reinforced deck stringers, shown in blue in Figure 54. This figure also shows the forward fuel tanks susped from the keel beam, shaded in brown. Figure 54 Keel beam and fuselage

70 The fuselage itself is designed using traditional stringers and frames. The actual sizing of structural members would be accomplished after preliminary design, but a few important concepts are highlighted here. First, both the stringers and frames are spaced such that they reinforce the areas around the windows. The window edges form areas of stress concentration due to the joining of dissimilar materials, so the structure must be reinforced at these locations. This is also true for the door, which is larger and has increased weight from opening and closing mechanisms. Another important design choice was the reinforcement of the stringers that attach the deck to the fuselage. As stated earlier, these stringers serve to connect the main load path (the keel beam), with the fuselage, and do so along the length of the fuselage. This means that they are larger than the typical stringer. Figure 55 shows the area under the fuselage where the nose landing gear attaches to the keel beam (highlighted in green). Figure 55 Nose gear and keel beam The location of the wings presented special structural challenges. FAST's wings are located aft and vertically central, and not on the keel's axis. This means that we had to account for a mechanism to transfer the loads from the keel beam to the wing box. This is shown in Figure 56.

71 Figure 56 Wing structure The junction box then transfers the load to a pair of longerons that form the main load path in the wing. These are significant because they are responsible for carrying a large portion of FAST's loads, including the weight and thrust of the engines, the main landing gear loads, and the lift generated by the wings. Figure 57 Landing gear and engine nacelle Figure 57 shows a cutaway of the main landing gear and engine nacelle locations. Because of the size of the main landing gear trucks, they could not fit inside the tapered fuselage or the thin wing, necessitating the outer structure. The landing gear box, shown in green, is designed to act as a fairing to reduce its impact on drag. The final shape of these landing gear housings would be depent on more in-depth aerodynamic design. The next major layout decision was the location of the cargo section. In most conventional airliners, cargo is located under the cabin. This works well with cabins with large diameters, but FAST was designed specifically to reduce cabin diameter.

72 Consequently, the area underneath the cabin is only 28 inches tall at its largest point. We decided that this would make it difficult to store cargo in this space, as this is approximately the same size as some checked luggage. The small size would also make it difficult to access areas that were not directly adjacent to a cargo door, increasing the amount of time needed to load and unload the aircraft. Based on the total number of bags, and the maximum volume of a typical checked bag (approximately 6 ft 3 ), we determined that adding a 9 ft section of cabin aft of the main cabin would account for all of the necessary cargo, with a 150% margin of tolerance. The added length was deemed acceptable due to the minimal structural increase and the improved fineness ratio. This cargo section is shown in Figure 58, and is shown separate from the main cabin for clarity. Note the large cargo door that allows easy and rapid loading. The door next to the cargo section is an emergency exit. Figure 58 Fuselage structure The next large complication for the FAST was finding room for the fuel. Due to the long range required for transpacific flight, FAST carries over 180,000 pounds of fuel. This works out to be over 3,600 cubic feet. In many typical transports fuel is carried in the wings. However, for FAST this represented problems in balance and volume. In most conventional aircraft, the wings are located at or near the longitudinal center of the aircraft. This means that any fuel carried in this location does not significantly affect the center of gravity. However, FAST has wings located at the most aft section of the fuselage, like a typical supersonic fighter. This also dictated that the engines and landing gear were located extremely far aft. This combination resulted in a very rearward empty weight CG. Adding large amounts of fuel in the wings would serve to

73 further move the CG aft, resulting in control issues. The FAST s wings also have a t/c of 3%, making them very thin, and reducing potential volume available for fuel. As a result of these complications, we decided to forgo placing fuel tanks in the wings. Instead of putting fuel in the wings, we decided to place them under the fuselage and in the aft fuselage section. As previously stated, the area under the fuselage was eliminated as a location for cargo. However, it is an ideal location for fuel tanks, as they could be molded around structural elements such as the canard box, landing gear and keel beam. The two forward fuel tanks are shown in Figure 59. Figure 59 Fuselage and canard box Volume was made available in the aft fuselage section due to the aerodynamic shaping of the fuselage, which needed a rapidly tapering shape to approximate a Sears-Haack body and reduce wave drag. The increasingly small diameter proved to be of little use for cargo and passengers, but is adequate for fuel storage. Its location ahead of the aerodynamic center also helped with balance. One complicated factor for this location is the internal structure running through this section of fuselage. We would prefer not to encase the load path structures in fuel, as this can cause corrosion and other fatigue related issues. However, for preliminary structural design, we are not making detailed plans for this fuel tank. As an approximation, we modeled the fuel tank occupying the entire available volume as shown in light brown in Figure 60, and then applied a factor of 0.80 to the volume to account for losses due to structural losses resulting from further design work.

74 Figure 60 Aft fuel tank structure The last major structural component considered in our preliminary design was the cockpit and nose. The exterior nose fuselage is shown in Figure 61, and shows the continuation of the frame and stringer system used in the main fuselage. Figure 61 Nose structure The nose was shaped primarily for aerodynamic reasons. This works well to reduce overpressure and drag, but also reduces visibility for the cockpit. To increase visibility,

75 we decided to make a raised cockpit section. This is shown in Figure 62. This section also includes an extra seat for the third crewmember. Figure 62 Cockpit interior With all of the major structural components placed, the next step was to choose materials. The primary requirements for material choice are set by the high temperatures created during supersonic flight. FAST cruises at Mach 1.8, but to be safe we chose materials based on conditions at Mach 2.2. Based on Raymer Figures 14.18 and 14.19, the leading edge temperatures will reach 270 ºF, while the nose will reach 300 ºF. This presents problems for most conventional Al alloys, which cannot operate above 250 ºF. In aerospace, materials ranging from titanium to advanced alloys of rare materials are used for operation at very high temperatures. FAST employs Al-Li 2090, an advanced alloy that that combines aluminum with lithium and copper to produce sheets that are lighter and stronger than traditional alloys. Alcoa claims that 2090 has 8% less density and 10% higher elastic modulus than 7075 Al, along with operating temperatures that allow supersonic flight. This material is used in the leading edges of the Eurofighter Typhoon, a fighter that according to the German Luftwaffe, can cruise at Mach 1.5 and reach top speeds of Mach 2+. FAST uses Al-Li 2090 in the wing leading edges as well as the nose cone.

76 The skin panels of FAST are made with GLARE (GLAss REinforced fiber metal laminate). GLARE is made up of bonded layers of aluminum and glass fibers, a combination that gives excellent strength and durability. GLARE panels are 10% less dense than conventional Al, and as a result give excellent weight savings. Also, GLARE has shown excellent fatigue properties, with a large critical crack length. GLARE is currently utilized extensively on the Airbus A380, and as such will be fully certified for use prior to FAST. Despite the advantages of composites and advanced alloys, most of FAST's structure is made up of traditional aerospace aluminum. This is done to reduce cost, in terms of purchase cost as well as certification cost. The purchase cost is easy to quantify, as Alloy 2090 (for example) costs approximately five times as much as traditional Al. FAST reduces cost by balancing the light weight of the advanced materials in critical components with the cheaper price of traditional materials. Traditional materials also save on maintenance cost. Airlines already have maintenance procedures in place for conventional aluminum. This includes specific inspection procedures, tools and training to handle problems. Introducing new materials can require new techniques. For example, composites do not respond well to magnetic inspection, as most composites are not magnetic, and they also are not receptive to dye penetrant, because their flaws are usually subsurface. Titanium requires special tools to repair, including harder drill bits and special coatings that do not etch the material. Using materials that are familiar to the airline maintenance systems allows for more seamless integration of FAST into existing airline procedures. Stability and Control The canard and vertical tail provide the longitudinal and lateral stability necessary for controlled flight. The size of the canard determines the aircraft s available pitching moments as well as the aircraft s ability to trim in pitch. The vertical tail provides lateral stability and the rudder, attached to the rear of the tail, provides the aircraft s yaw moment and lateral trim ability. Vertical tail and rudder size are constrained by the requirement to land in a strong crosswind and fly with one engine inoperative.

77 Estimates for vertical tail and canard sizes (Table 13) were obtained with parameters from the sizing code, wing data, and estimates of aircraft center of gravity. Planform Area Estimates Canard 500 ft 2 Vertical Tail 282 ft 2 Table 13 Planform Area Estimates These estimates are fed into the canard and vertical tail functions, which iterate along with the sizing code outputs, to converge on the minimum allowable control surface sizes. Canard Canard size is constrained by supersonic and subsonic trim conditions, as well as takeoff performance. The supersonic trim constraint considers the aft-moving aerodynamic center (AC) during supersonic cruise. This aft AC creates a larger moment to be countered by the canard, which must remain at relatively low deflection to reduce trim drag. The takeoff constraint requires the canard to be sized to provide enough moment to rotate the plane to the required takeoff angle of attack. Each constraint will require a different planform area, and the canard function selects the more demanding of the two for final size. The aircraft CG position moves during the flight, changing the moment arm of the canard and affecting its ability to trim. With our canard being in the front of the aircraft, its shortest moment arm occurs with the CG at its forward-most point. The canard function converges on canard size while using the forward-most, and most demanding, CG for the aircraft. The remaining function inputs were determined from preliminary aircraft layout. Within the canard function, assumptions were made for canard sweep and coefficients of aerodynamic performance said to be typical of control canards in Roskam. [16]

78 The canard function iterates canard size for both subsonic and supersonic trim conditions with takeoff condition as a minimum constraint. The canard function outputs a planform size for each trim condition once all of the moments are appropriately balanced. The subsonic trim condition was determined to be the limiting factor in canard size for our final aircraft weight and a final planform area of approximately 500 ft 2. Vertical Tail Vertical tail and rudder size are constrained by the aircraft s ability to land in a crosswind and fly stable with one engine inoperative. The ability to trim in each of these conditions is largely determined by rudder size, which is measured in percent chord of vertical tail. Figure 2.23 in Roskam shows a plot of rudder effectiveness vs. rudder percent chord. We decided to use a rudder that was 30% chord in order to achieve a rudder effectiveness of 50%. For the landing in a crosswind condition, we used maximum crosswind velocity of 20% of the takeoff speed. Using equations from Roskam, the code finds the various yawing moment coefficients applied to the aircraft while in sideslip. With a maximum rudder deflection of 20 o, the code finds the yawing moment coefficient due to rudder deflection. When the size of the vertical tail becomes large enough, the loop stops and the tail area is saved. The next step is to find the tail area required to trim with one engine out. The same steps are taken as in the crosswind condition, except the actual moments are used, not the coefficients. The loop iterates until the vertical tail and rudder are large enough to provide lateral stability with one engine inoperative. The one engine inoperative condition is the limiting factor in our design, and it corresponds to a tail area of approximately 282 ft 2. Aircraft Trim Aircraft trim diagrams (Figure 63) were created to show longitudinal trim capability for subsonic and supersonic flight. These diagrams were created using methods found in Roskam chapter 4. The diagrams show that the aircraft can be trimmed at any required flight condition. The black lines on the left and right of the diagrams show the center of gravity limits, fore and aft, respectively. The upper black line shows the limit on angle

79 of attack, and the colored lines represent the corresponding angles of incidence of the canard. Figure 63 Trim Diagrams The lateral trim conditions require a rudder deflection of 20 o for one engine inoperative and 10.5 o for a crosswind landing. Applications Gate Compatibility Airport compatibility was a major consideration when looking at design tradeoffs for the FAST. Our aircraft s canard and wing positions were the limiting factors when pulling up to the gate and placing the service equipment required for turnaround. Our aircraft is expected to require one passenger bridge, two fuel trucks, one potable water/lavatory service truck, one galley/cabin service truck, and a maximum of two bulk cargo carriers. Figure 64 shows an example arrangement of aircraft servicing equipment during a typical turnaround.

80 Figure 64 Gate compatibility diagram Our wing and canard placement allow for maximum service equipment access to the aircraft. The leading edge of our canard is located 10 feet aft of our main passenger door, which allows for plenty of space to maneuver a passenger bridge without any significant threat of damaging the canard. Had the canard been placed forward of the main door there would be an increased concern with the bridge operator s ability to maneuver in and around the canard without causing damage. The FAST s wing is located aft of the cabin and cargo service doors, allowing easy access by ground crews for loading and unloading cargo, cleaning the cabin, and refreshing the galley. The two forward fuel tanks for the fast are located in the belly of the fuselage and are expected to be serviced by the same fuel truck, while the rear fuel compartment will be serviced by the second truck. Turnaround Analysis We modeled the FAST s turnaround procedures after a combination of the Embraer ERJ 145 and the Boeing 777 procedures. The ERJ 145 is a short to mid-range commercial aircraft with a cabin size of 50 passengers. The passenger load and unload times are expected to remain similar between the two aircraft, however the FAST s trans-pacific range along with its luxury market require significantly larger galleys for

81 full meals and beverages. The ERJ 145 was also used for modeling the cabin cleaning, potable water, and lavatory servicing times. The FAST s long range requires a large fuel volume and high refueling rates, which were modeled after the Boeing 777. The gate servicing procedures for both the 777 and ERJ 145 were found in the airport planning manuals supplied on their manufacturers websites. [17][18] The planning manuals contain the technical specifications for baggage, fuel, and passenger loads, as well as the total time required for ground crews to perform each service. Table 14 shows the specifications for each plane, as well as a passengers/minute (pax/min) bulk rate for each service performed. Turn Time Stat Table Measurement Units FAST ERJ 145 777 Passenger Capacity pax 40 50 375 Pax Bridges # 1 1 2 Pax Unload Time min 5.0 4.0 7.5 Pax Unload Rate pax/min 8.0 12.5 50.0 Pax Load Time min 9.0 5.0 12.5 Pax Load Rate pax/min 4.4 10.0 30.0 Baggage Doors # 1 1 3 Bag Load Time (Total) min 8.0 8.0 52.5 Bag Unload Time (Total) min 8.0 6.0 52.5 Baggage rate pax/min 5.0 6.3 7.1 Cabin Cleaning Time min 8.0 6.0 26.5 Cabin Cleaning Rate pax/min 5.0 8.3 14.2 Fuel Capacity gal 27,612 1,690 31800 Fuel Trucks # 2.0 2.0 2.0 Fuel Ports # 4.0 2.0 4.0 Fuel Time min 20.3 14.0 23.0 Fuel Rate gal/min 303.0 125.0 303.0 Lav Time min 10.0 5.0 15.0 Water Time min 10.0 5.0 17.0 Galley Time (Total) min 12.0 7.0 56.5 Galley Rate pax/min 3.3 7.1 6.6 Table 14 Fast Turn Time We used conservative estimates for every service rate with the exception of fueling rate, which we set equal to the Boeing 777 with 303 gallons/minute. The fueling rate assumes 2,985 gallons remaining in the fuel tanks for our missed approach reserves.

82 We added a considerable amount to galley, water, and lavatory service times to account for the additional capacity of our long-range flights. Figure 65 shows the complete FAST turnaround procedure for a full load of 40 passengers. Figure 65 FAST turnaround procedure The dark blue bars represent actual service time, while the light blue bars represent equipment placement time. With these assumptions, the total turnaround time for our aircraft is 27 minutes. Cost Model Cost estimation and analysis for the GoldJet FAST was broken down into two parts: Research, Development, Tooling, and Engineering (RDT&E) and Production Costs