The Aerus DecaJet AA241B: Final Report Due on March 20, 2013
Christopher Pepper
1 Christopher Pepper The Aerus DecaJet AA241B: Final Report
Contents
1 Introduction 4 1.1 Very Light Jets ...... 4 1.2 Project Motivation ...... 4
2 Fuselage Design 5 2.1 Diameter Choice and Cross Sectional Layout ...... 5 2.2 Layout ...... 5
3 Wing Design 7 3.1 Airfoil ...... 7 3.2 Planform ...... 9 3.2.1 Thickness to Chord Ratio and Sweep ...... 9 3.2.2 Wing Lift Distribution ...... 9 3.3 Wing Placement ...... 10
4 High-Lift Systems 12
4.1 Determining cl,max for Cruise, Take-off, and Landing ...... 12 4.2 Adjusting cl,max to CL,max ...... 12
5 Empennage Design 13 5.1 Vertical Tail Sizing and Location ...... 13 5.2 Horizontal Tail Sizing and Location ...... 13 5.3 Static Margin Calculation ...... 14
6 Propulsion 15 6.1 Engine Selection ...... 15 6.2 Nacelle and Engine Placement ...... 16
7 Drag Polar and 3-View Drawing 17
8 Structure 19 8.1 Loads Estimation ...... 19 8.2 Component Weight Estimation ...... 20 8.2.1 Wing Weight ...... 20 8.2.2 Horizontal Tail Weight ...... 20 8.2.3 Vertical Tail Weight ...... 21 8.2.4 Propulsion System Weight ...... 21 8.2.5 Fuselage Weight ...... 21 8.2.6 Landing Gear Weight ...... 22 8.2.7 Surface Controls Weight ...... 22 8.2.8 Auxiliary Power Unity Weight ...... 22 8.2.9 Computer Systems Weight ...... 22 8.2.10 Hydraulics Weight ...... 22 8.2.11 Electrical Weight ...... 22 8.2.12 Electronics Weight ...... 22 8.2.13 Furnishings Weight ...... 22 8.2.14 Air Conditioning Weight ...... 23 8.2.15 Operating Items Weight ...... 23 8.2.16 Flight Crew Weight ...... 23
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8.2.17 Flight Attendant Weight ...... 23 8.2.18 Payload Weight ...... 23 8.3 Total Weights ...... 23
9 Baseline Performance Estimation 24 9.1 Take-off Performance ...... 24 9.2 Landing Performance ...... 24 9.3 Second Segment Climb Performance ...... 25 9.4 Cruise Performance ...... 25 9.5 Baseline Summary Sizing Plot ...... 26
10 Optimizing the Design 28
11 Environmental Characteristics 31 11.1 Noise ...... 31 11.2 Emissions ...... 31
12 Future Work 33 12.1 Engine ...... 33 12.2 Materials ...... 33 12.3 Cabin Design ...... 33 12.4 Airfoil ...... 33 12.5 The Business End ...... 33
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1 Introduction
The aircraft we selected to develop is the very light jet, or Air Taxi. We selected this mission to explore an aircraft design that may help make air travel a more personal experience. Current business jets are not well suited for the mission of an air taxi because they may be over designed for this role, having expensive capabilities that would be unused on this type of service. An air taxi would likely serve some of the more popular routes in the United States such as JFK to MIA. We should then design the vehicle to be capable of a range near 1000nm, to carry about four passengers, to need less than 3000ft runway, and to cruise in the range of Mach 0.6 to 0.8. Our goal therefore is to meet and not greatly exceed all of these requirements so to hopefully find a competitive niche in the market.
1.1 Very Light Jets The highest selling personal jet at this point is the Cessna Citation Mustang, which has delivered over 300 units. This is an important aircraft to consider due to its popularity and strong brand recognition. A new air taxi company would certainly consider this aircraft when in the acquisition phase. Another important aircraft is the newly developed and about to be released is the Honda Jet. This aircraft is currently undergoing certification and is expected to be delivered to customers within a couple years. This aircraft is an important analog to the DecaJet because it is Hondas first aircraft, and it is almost 10 years newer than the Cessna. The new technology used in the Honda Jet will make it a competitor in terms of operational cost. The Cirrus Vision SF50 is another good airplane, but this aircraft is not specifically intended to compete for commercial use. This airplane, and the Diamond D-Jet, is intended for the personal use market and as such is not specifically considered in this project.
1.2 Project Motivation The Aerus DecaJet is particularly well suited for a few commercial roles, which includes air taxi and rental. Currently, many companies offer the ability to charter an aircraft, and clients chose it for its convenience. Chartering an aircraft allows clients to fly into one of the thousands of smaller regional airports which are often nearer to their destinations. Trips are shorter, there is much less lead time in embarking on the journey, and the chosen aircraft are often more comfortable. A smaller aircraft reduces weight and operating cost, and the very light jet is more suited for small group travel. Because the aircraft has a range over 1000nm and can cruse at higher speeds, its unlikely to be the favored aircraft for short trips, such as perhaps from a business meeting in San Jose from San Francisco (less than 30nm) or even Philadelphia to NYC (85nm). Air travel over shorter distance like this is would probably be done with a helicopter since our aircraft would hardly get to cruise altitude at such a short distance. Some of the most popular routes in the US include San Francisco to Las Angeles (300nm) and New York to Miami (950nm). These are the likely routes best handled by an air taxi, which can provide comparable times with added convenience. An airplane designed to service routes will need an onboard bathroom.
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2 Fuselage Design
2.1 Diameter Choice and Cross Sectional Layout Given that the average American male is 5’10” (70”) tall, a good inner diameter for the aircraft fuselage will be 72”. A larger fuselage would be more luxurious and allow for easier movement about the cabin, but this would come at the cost of additional weight and performance. We use the estimated 8% thickness to predict an outer diameter of 78”. This gives a structural thickness of 3”.
Figure 1: Fuselage Cross Section
The fuselage diameter allows for comfortable seat width of 20” and a reasonable aisle width of 15”. All together, the majority of customers will be able to move about the cabin in full comfort.
2.2 Layout Lower Mach numbers constrain typical transport aircrafts to have a nose fineness ratio of 1.5 as a result of fuselage pressure gradients. Similarly, the tail cone is generally within the range of 1.8 to 2.0, and we choose 1.8 for our conceptual design. The nosecone is therefore 117” and the tail cone is 140”. The aircraft will be furnished by the purchasing airlines, but a sample layout is included below. Among very light jet manufacturers, there are various opinions as to the necessity of an onboard lavatory. As this aircraft is intended for medium length flights, it is clear that installing one is a necessity. We however chose not to include a full galley or space for a flight attendant. A small refrigerator and some cabinet space should be more than sufficient for our chosen mission. To fit a lavatory, emergency exits, and seating for four, the cabin length will be 100”.
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Figure 2: Fuselage Layout
Two exits, one emergency and one standard, meet the FAA safety regulations. The layout will accom- modate five passengers, with two on the sofa-like seat in the rear of the aircraft. We have chosen to make the aircraft single-pilot certified.
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3 Wing Design
Since the configuration of our aircraft is similar enough to the Cessna Citation Mustang and the Honda Jet, we can look to these aircraft to choose reasonable preliminary values for various wing parameters. The first parameter to consider is wing area. The Cessna has a wing area of 210ft2. Using this as a benchmark, the wing area is chosen to be 150 ft2 or 13.9 m2. We next consider wing span, which we choose to be 37’ where the Cessna uses a 43’ span and the Honda Jet uses a 40’ span. These two choices give an aspect ratio of 9.1. Knowing that the lift in cruise is equal to the weight of the aircraft, we can approximate this as 97% of the maximum take off weight for the start of cruise. The maximum take off weight we are designing for is
8600lbs or 3900kg. The equation for CL is
L .97 · mg .97 · 3900kg · 9.81m/s2 C = = = = .33 (1) L 1 2 1 −4 3 2 2 q∞Sref 2 ρv · Sref 2 · 3804 × 10 kg/m · (205m/s) · 13.9m
3.1 Airfoil The design altitude of the aircraft is FL350, where the atmospheric density is taken to be 3804×10−4kg/m3, and the dynamic viscosity is 142.2 × 10−7N · s/m2. The airspeed will be 400 knots or 205 m/s. For a wing area of 150 ft2 and a wing span of 37 ft, the average chord length will be approximately 4 feet or 1.25m. The Reynolds number at the cruise condition is therefore given by the following calculation.
ρ · v · l 3804 × 10−4kg/m3 · 205m/s · 1.25m R = = = 6.85 × 106 (2) e µ 142.2 × 10−7N · s/m2
In anticipation of three-dimensional air flow effects, we choose a Cl that is about 20% higher than the expected need. This is a reasonable approximation for an aspect ratio of 9.11. For our intended whole wing
CL of .33 our goal sectional airfoil is therefore cl is 0.4. Through the use of the airfoil design tool PANDA, the first design developed is shown in Figure 3. This ∗ ∗ design meets or exceeds the given constraints that |Cp,min| < 1.2 · Cp and |Cp,crest| < 1.05 · Cp . Some slight modification to the tail was necessary to keep the airfoil from having separated flow at the angle of attack that gives a cl of zero. This is for the constraint that |Cmo| < .15. The final design is shown in Figure 4.
1This approximation is from the Wikipedia article on lifing-line theory.
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Figure 3: Airfoil Design and Pressure Distribution at Cruise Condition
Figure 4: Zero Lift Pressure Distribution at Cruise Speed and Altitude
The analysis for developing the airfoil was done with an assumed x/c transition of 0.4. The final airfoil is a 50/50 blend of super critical airfoil and the traditional peaky airfoil. This was done to flatten the pressure distribution while still reducing Cm. Thickness was removed from the upper surface where necessary to keep ∗ Cp from approaching Cp.
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3.2 Planform 3.2.1 Thickness to Chord Ratio and Sweep For the air taxi, reasonable values for sweep are from 0o to 20o, so this is the range of possible sweep angles that we will explore. Using the cruise Mach number of M=.68, we should expect an Mcc=0.68 and an Mdiv=0.7. We can now compute the maximum thickness to chord ratio of the airfoil for each value of sweep given Mcc and the cruise CL. The results are tabulated below in Table 2.
2 Λ M∞⊥ CL/cos Λ (t/c)⊥ t/c 0o .680 .33 .152 .152 5o .677 .33 .154 .153 10o .670 .34 .161 .159 15o .657 .354 .176 .17 20o .639 .374 .195 .183
Table 1: Maximum Thickness to Chord Ratio vs. Sweep Angle
The conclusion we draw from this table is that either 0o or 5o of sweep and a thickness ratio of 15% are
good choices for this application. This will achieve our intended CL without too thick of an airfoil.
3.2.2 Wing Lift Distribution With the use of the wing design program, we selected a planform to provide a relatively uniform lift distri- bution while still having a near minimized induced drag. The optimum induced drag occurs for an elliptical
wing loading where the Oswald efficiency factor, einviscid, equals one. Our goal is to have ours within the range of 1.0 to .98. Figure 5 shows the results from the wing design tool.
Figure 5: Results of Wing Design Tool
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In this analysis, the wing area, wing aspect ratio, and sweep have been decided, and we are choosing the taper, extensions, and twist angles that provide our designed CL and desired Oswald efficiency factor. The parameters that satisfied the requirements are a taper ratio of .3, a root chord leading edge subtraction of .1 · c which extends 40% of the span, and a sweep of 5o. The twist angles are 1.37o at the root, 1.07o at 40% of the span, and .07o at the wing tip. Trailing edge extensions were not used. The wing planform generated in the wing geometry tool is shown below in Figure 6, where the nose of the aircraft would be at the top of the figure and the tail at the bottom.
Figure 6: Wing Geometry
3.3 Wing Placement From the geometry of the wing, we can develop an equation for the chord as a function of the spanwise location. This function is: ( 6.37 · (.9 − .18 · y/.4), if 0 < y < .4 c(y) = (3) 6.37 · (1 − .7 · y), if .4 < y < 1 We can use this equation to calculate the mean aerodynamic chord which is defined as:
b/2 2 Z MAC = c(y)2dy = 4.280 (4) Sref 0 This calculation result was confirmed with the wing geometry tool result, and the MAC is found at a spanwise location of .356. As an initial placement, we will choose to put the wing such that the quarter- chord location at the mean aerodynamic chord is located at 60% of the cargo area. The cargo and passenger area is approximately 180” long, 60% of which is 108”. The quarter-chord length at the mean aerodynamic chord is 12.75”. Placing the mean aerodynamic chord quarter chord at 60% is equivalent to placing the mean aerodynamic chord leading edge at 95.25” from the beginning of the cargo area. This is 45.25” from the reference plane we’ve chosen which is the seam between the nose cone and constant cross section area. Figure 7 shows this location.
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Figure 7: Wing Placement
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4 High-Lift Systems
Inspired by the Honda Jet which has a 30% chord, double-slotted flap, a 35% chord, double-slotted flap is what we will use as our preliminary high-lift system. We will not need slats and decided therefore to not include them for the sake of saving on weight and complexity. The Honda Jet design required a maximum lift coefficient of 2.5, and deflects the flaps to 0o in cruise, 15.7o for take-off, and 50o for landing. We will have similar deflections of 0o in cruise, 15o for take-off, and 50o for landing. Based on a three-view drawing the Honda Jet flap appears to be 60% of the wing span, so this is also what we will use.
4.1 Determining cl,max for Cruise, Take-off, and Landing Using the airfoil design tool, we can increase the angle of attack of the airfoil until there is turbulent separation. This will allow us to determine the cl,max of the various configurations. The inputs to the tool are the airfoil, Mach number, and Reynolds number. Our cruise condition Mach is .7, and we will design for a take-off and landing Mach of 0.2. The chord length at 75% semi-span is 4.46ft or 1.36m. At sea level, atmospheric density is 1.225 kg/m3, dynamic viscosity is 1.983 ×10−5N · s/m2, and we expect a take-off and landing speed of 125 knots or 65 m/s.
ρ · v · l 3804 × 10−4kg/m3 · 205m/s · 1.36m R = = = 7.46 × 106 (5) e,cruise µ 142.2 × 10−7N · s/m2
ρ · v · l 1.225kg/m3 · 65m/s · 1.36m R = = = 5.46 × 106 (6) e,T OL µ 1.983 × 10−5N · s/m2 With the inputs to the tool resolved, we find that in cruise the airfoil has leading edge separation at 5.5o. o Just prior to this, the cl,max is 1.96. At take-off and landing, we similarly find separation at 5.4 which has a cl,max of 1.12.
4.2 Adjusting cl,max to CL,max To adjust the sectional coefficient of lift to a three-dimensional wing coefficient of lift, we will use a series of correlations based on the performance of finished aircraft. This should work well in our case as the design is similar enough in configuration to the aircraft which these correlations were based upon. Were we creating a design of an unconventional aircraft, this would not be a reasonable approach. With consideration for aspect ratio, Mach number, wing area, sweep angle, and flap deployment, the maximum wing lifts are as follows:
CL,maxcruise = 1.01, CL,maxtake−off = 1.53, CL,maxlanding = 2.30.
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5 Empennage Design
To develop the design of the vertical tail and the horizontal tail, we will use a fuselage based index. This will be useful in comparison with other aircraft as it will allow us to determine an estimate for the horizontal tail volume and vertical tail volume. This is accurate enough for conceptual design.
5.1 Vertical Tail Sizing and Location
To calculate the index, we know the height of the fuselage (hf ) is 6.5ft, the length of the fuselage (lf ) is 29.78ft, the wing area (Sw) is 150ft, and the wingspan (b) is 37ft.
2 h · lf f = .227 (7) Sw · b Though this is beond the range of the graph, we can extrapolate from the linear function given for conven- tional jet aircraft. This gives us a vertical tail volume of .1086. Assuming the center of gravity to be at 60% of the cabin space, which is 180” long, the center of gravity is approximately 50” behind the reference plane. The aerodynamic center of the tail is approximately going to be around 250” behind the reference plane,
meaning the value of lh is 200”. Using the vertical tail volume equation, we can calculate the vertical area of the tail. Vv · b · Sw 2 Sv = = 36.5ft (8) lv The shape of the vertical tail will be a trapezoid with 37ft2 area. To do this, a 6.2ft height is chosen with a 7.5ft root chord with a 4.5ft tip chord. This is given a sweep of 50o for better stall characteristics.
5.2 Horizontal Tail Sizing and Location The horizontal tail volume can be calculated more directly with some knowledge of the aircraft. We do this by calculating the pitching moment coefficient without the effects of the aerodynamic term. This is sufficient for conceptual design, but a more detailed design should include the aerodynamic effects.
−Cm,wheels Vh = (9) Cl,h
The largest tail authority is required at landing, so we will use atmospheric conditions at sea level. Knowing
that the distance from the main landing gear to the nose landing gears (lh) is approximately -10ft, Cm,wheels can be calculated as follows. .08 · lg · W Cm,wheels = = −.194 (10) q∞ · Sw · MAC
We can assume the value of CL,H,max is one, and using equation 9, we find that the tail volume is .194. With the same approximations as the vertical tail, the aerodynamic center of the tail is approximately going to be
around 250” behind the reference plane, and thus the value of lv is 200”. Using the horizontal tail volume equation, we can calculate the horizontal area of the tail.
Vh · b · Sw 2 Sh = = 65.5ft (11) lh
The shape of the horizontal tail will be two trapezoids, each of 33ft2 area. To do this, a 5.5ft span is chosen o with a 7.7ft root chord with a 4.3ft tip chord. This is given a sweep (Λh) of 50 for better stall characteristics. The aspect ratio of the horizontal tail (Ah)is 1.8. With an assumed value of .9 for the tail efficiency (ηh) we can use the Datcom formula to calculate Clα,h. The following is for a Mach number of .2 representing
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landing or take-off. 2π · Ah Clαh = = 2 (12) p 2 2 2 2 + (Ah/ηh) · (1 + tan Λh − M ) + 4
5.3 Static Margin Calculation The static margin is useful for determining aircraft longitudinal static stability. It represents the distance between the aircraft neutral stability point and the location of the center of gravity. Without a detailed design, we must make simplifying approximations and assumptions to come up with a rough estimate of the static margin. We will begin by assuming that the location of the center of gravity is at 60% of the cabin length. This is, not coincidentally, the location where we placed the quarter chord of the mean aerodynamic
chord. This gives us a center of gravity directly upon the center of pressure, and the value of xc.g. is zero.
−x l · S · C ∂C Static Margin = c.g. + h h lαh − m,fuse (13) c c · Sw · Clαw ∂CL The contribution of the last term is as a result of the fuselage and can be calculated with the empirical
formula from Gilruth. For a wing placement at 60% of the cabin space, the empirical factor Kf is .888.
2 ∂C Kf · w · Lf m,fuse = f = .350 (14) ∂CL Sw · c¯ · CLαw
The last remaining value to calculate is Clαw. We once again use the Datcom formula where the wing efficiency (η) is taken to be .97 and the Mach number is once again .2.
2π · Aw Clαw = = 5 (15) p 2 2 2 2 + (Aw/η) · (1 + tan Λ − M ) + 4
We can now enter these values into equation 13 where we find that the static margin is .323. A positive static margin in our equation indicates that the horizontal tail has sufficient authority to overcome the destabilizing effect of the fuselage.
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6 Propulsion
6.1 Engine Selection The Honda Jet uses two GE Honda HF120 turbofan engines, and the Cessna Citation Mustang uses two Pratt & Whitney Canada PW615F turbofan engines. We will similarly use a turbofan engine. Executive jets have historically had a thrust to maximum take-off weight ratio of about .4. Because this aircraft is similar to those aircraft, this is a good starting point for our design. With an expected maximum take-off weight of 8600lbs or 3900kg, the required thrust per engine can be calculated as follows.
.4 · m · g .4 · 3900kg · 9.81m/s2 T = = = 7.6kN or 1700lbf (16) 2 2 The engine we’ve chosen is the Pratt & Whitney PW617-E. This engine has 1780lbf, a 29.6” max diameter, is 52.6” long, and has a dry weight of 380kg.
Figure 8: PW617-E
This engine is specifically designed for very light jets and is intended to be reliable with low operation and maintenance costs. It is currently in use on the Embraer Phenom 100, and since the thrust is nearly the exact thrust needed for our application, no adjustments will be necessary. Though the specific fuel consumption(SFC) has not yet been released, Jane’s indicates that it should be ”20% below today’s engines”. We can however come up with an estimate of the SFC for cruise, assuming an efficiency of around 38% at a cruise speed of 672.5ft/s. V 672.5 SFC = = = .44 (17) cruise 4000 · η 4000 · 0.38
Take-off Thrust 8.096kN Normal Take-off Thrust 7.495kN Max. Continuous Thrust 7.108kN
Table 2: Engine Specifications
As stated in the EASA certificate for the PW617 engines:
“The engine ratings are based on dry sea level static ICAO standard atmospheric conditions, no external accessory loads and no air bleed. The quoted ratings are obtainable on a test stand with the specified fuel and oil, and using the exhaust duct and intake bellmouth specified in the Installation Manual.”
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6.2 Nacelle and Engine Placement For both style and to not disturb the wing design, we will use an aft-mounted twin engine setup. We expect the maximum nacelle diameter to be ten percent larger than the maximum engine diameter. Since the maximum engine diameter is 29.6”, our maximum nacelle diameter will be 32.6”. The inlet cowl length ahead of the engine fan face is approximately sixty percent of the maximum nacelle diameter, or 19.5”. Similarly, the nozzle cowl length behind the turbine exit is expected to be approximately sixty-five percent of the nacelle diameter at the turbine. With an estimated 30” nacelle diameter at the turbine, we have the nozzle cowl length end 19.5” behind the turbine exit. The total length of the nacelle then is 91.6”. To ensure proper spacing, the fuselage pylon length is at least fifteen percent of the nacelle diameter, which in our case is about 5”. Vertically, we place our engines to avoid interference with the wing and empennage.
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7 Drag Polar and 3-View Drawing
With the propulsion system placed, all systems have been sized and located. The drag polar of the aircraft is calculated for three configurations, take-off, landing, and cruise. Figure 10 is the 3-view drawing that depicts all of the design choices. This includes a full drag buildup for the effect of nacelles, gaps, trim, etc, the code for which is included at the end of this paper.
Figure 9: Drag Polar
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Figure 10: 3-View of Completed Conceptual Design
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8 Structure
8.1 Loads Estimation To visualize the speeds and the maximum loads the aircraft can be subject to at various operating conditions, we make use of the placard diagram and the V-n diagram. The placard diagram shows the limits on the structural design airspeeds as they change with altitude, while the V-n diagram shows the maximum wing loading as a function of speed. In calculating the Placard diagram, a Vc altitude of 26,000ft was chosen. This is within the typical values of 25,000ft to 28,000ft.
Figure 11: Placard Diagram
In the following V-n diagram, we only show the maximum positive loads. It was determined in the analysis that the aircraft is not gust-critically loaded, so the loads depicted below are created in maneuvering.
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Figure 12: V-N Diagram
By federal aviation regulations our maximum load that we must consider is 3.4g. This is the limiting load factor up to our maximum speeds of 205m/s in level flight and 215m/s in dive.
8.2 Component Weight Estimation To estimate the various component weights of the DecaJet, we will once again use a series of statistical correlations with similar aircraft. Some of the calculations depend on the zero fuel weight of the aircraft, so we will choose a starting guess of seventy-six percent of the maximum take-off weight. Once we develop an initial estimate of each component, we can recalculate the zero fuel weight and iterate the calculations until convergence. For the design of maximum take-off weight(MTOW) at 8600lbs, the first estimate of zero fuel weight(ZFW) is 6536lbs. This converged to 6867lbs.
8.2.1 Wing Weight The weight of the wing can be accurately estimated from calculating a wing weight index and comparing that with wing weights of various other similar aircraft. The index is intended to represent the bending stresses on the wing box. The values we used include the taper ratio(λ) of .3, average thickness to chord o ratio((t/c)avg) of .15, span (b) of 37ft, the ultimate load factor (Nult) of 3.4, sweep (Λ) of 5 , and gross wing 2 area (Swg) of 150ft . √ 3 −6 Nult · b MTOW · ZFW(1 + 2λ) Wwing = 4.22 · Swg + 1.642 × 10 · 2 = 753lbs (18) (t/c)avg · cos Λ · Swg(1 + λ)
8.2.2 Horizontal Tail Weight The horizontal tail weight is similarly estimated with the assumption that the elevator is roughly 25% of the horizontal tail area. The elevator is included in the weight estimate. New values used in this calculation are 2 2 55ft of exposed horizontal tail area (She), 65.5ft of exposed horizontal tail area (She), 11ft of span (bh),
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16ft between wing horizontal tail aerodynamic center and aircraft center of gravity (lh), a thickness to chord o ratio ((t/c)avg) of 5%, a sweep angle (Λ) of 40 , and a wing mean aerodynamic chord (MACw) of 4.3 ft. √ 3 −6 Nult · bH MTOW · MACw She WH.T ail = 5.25 · She + .8 × 10 · 2 1.5 = 293lbs (19) (t/c)avg · cos Λ · lh · She
8.2.3 Vertical Tail Weight The vertical tail weight is estimated with the assumption that the rudder is roughly 25% of the vertical tail area. The rudder is not included in the weight estimate, and so it must be included separately. New values 2 used in this calculation are 36.5ft of vertical tail area (Sv), 5.5ft of span (bv), a thickness to chord ratio o ((t/c)avg) of 5%, and a sweep angle (Λ) of 40 .
3 MTOW Nult · b (.8 + .44 ) −5 v Swg WH.T ail = 2.62 · Sv + 1.5 × 10 · 2 = 105lbs (20) (t/c)avg · cos Λ
2 The surface area of the rudder (Srudder) is roughly 25% of the vertical tail area, which is 9.125ft . The rudder weighs approximately 60% more per unit area and can be calculated as follows.
WH.T ail · Srudder Wrudder = 1.6 · = 42lbs (21) Sv
8.2.4 Propulsion System Weight This is the total weight of the propulsion system, which includes the nacelles, pylons, engine, exhaust, starter, controls, and other closed system weights. The PW617F-E has a dry weight (Wdry) of 380lbs.
Wprop = 1.6 · (2 × Wdry) = 1216lbs (22)
8.2.5 Fuselage Weight The fuselage weight is estimated in multiple steps. The first step is to determine whether the structure is pressure-dominated or not, which is done by calculating the pressure index and the bending index. We find in our case that the fuselage is pressure dominated, which means that the fuselage weight index will be equal to the pressure index. The fuselage index is then used in the same manner as in the several previous calculations. New values used in this calculation are a maximum pressure differential (P),fuselage width (B) of 6.5ft, a fuselage height (H) of 6.5ft, fuselage length (L) of 30ft, limit load factor at zero fuel weight (N) 2 of 3.4, fuselage area (Sarea) of 425ft . The maximum pressure differential is at the cruise altitude of 35000ft where the cabin will be pressurized to 6000ft altitude. This pressure differential is 1201 lb/ft2. We will also use a weight W which is calculated as the zero fuel weight less the weight of the wing and propulsion system installation. This weight W is 4570lbs.
−3 IP = 1.5 × 10 · P · B = 11.7 (23)
−4 2 IB = 1.9 × 10 · N · W · L/H = .14 (24)
This tells us that the pressure is the dominating force on our aircraft. Because of this, Ifuse is set equal to IP . Wfuse = (1.051 + 102 · Ifuse) · Sfuse = 954.3lbs (25)
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8.2.6 Landing Gear Weight The landing gear weight is taken to be approximately 4% of the take off weight. This is the full landing gear system which includes wheels, brakes, tires, structure, and actuation.
Wgear = .04 · MTOW = 344lbs (26)
8.2.7 Surface Controls Weight The calculation of the surface weight controls, not the control surfaces, depends primarily on the area of the horizontal and vertical tail. The index used depends on whether fully-powered, part-powered, or fully aerodynamic controls are installed. We have chosen fully-powered controls, which has a surface controls index of 3.5.
Wsc = Isc · (Sv + SH ) = 357lbs (27)
8.2.8 Auxiliary Power Unity Weight With only six seats in the aircraft, an auxiliary power unit is unnecessary.
WAP U = 0lbs (28)
8.2.9 Computer Systems Weight A good estimate for the weight of computer systems in a business jet is 100lbs. This will work well for the DecaJet.
Wcomputers = 100lbs (29)
8.2.10 Hydraulics Weight The hydraulic system is most closely correlated with the wing reference area.
Whydraulics = .65 · Sw = 97.5lbs (30)
8.2.11 Electrical Weight The electrical weight is for the wiring and harnesses throughout the aircraft. This correlation is poor for smaller aircraft and should be replaced for a more representative value.
Whydraulics = 13 · Nseats = 78lbs (31)
8.2.12 Electronics Weight The amount of electronics is fairly consistent among aircraft types, and for a business jet 300lbs is the average weight.
Whydraulics = 300lbs (32)
8.2.13 Furnishings Weight
The furnishing is typically proportional with the number of seats on the aircraft (Nseats). The estimation below includes 23lbs for overwater necessities such as lifevests.
Wfurnish = (43.7 − .037 · Nseats + 46 + 23) · Nseats = 675lbs (33)
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8.2.14 Air Conditioning Weight The air conditioning system is also proportional with the number of seats on the aircraft.
WAirCon = 15 · Nseats = 90lbs (34)
8.2.15 Operating Items Weight
The amount of operating items is related to the number of passengers (Npassengers), where for business jets we expect 28lbs per passenger.
Woperating = 28 · Npassengers = 140lbs (35)
8.2.16 Flight Crew Weight We will have a single crew member who we estimate to be 190lbs with 50lbs of personal cargo.
Wcew = (190 + 50) · Ncrew = 240lbs (36)
8.2.17 Flight Attendant Weight The size of the DecaJet does not require a flight attendant, so no additional weight for considering one is necessary.
Wattendant = 0lbs (37)
8.2.18 Payload Weight We estimate a passenger weight of 170lbs, 10lbs for winter clothing, and 15lbs of carry-on bags. The passengers will also likely have about 30lbs of checked bags, leading to 225lbs per passenger. The airline may also include additional cargo of roughly 20lbs per passenger.
Wpayload = (225 + 20) · Npassengers = 1225lbs (38)
8.3 Total Weights With all of the components estimated, we can calculate the various total weights of the aircraft. The zero fuel weight is the sum of all of these components, the total of which is 6867lbs. The manufacturers empty weight is the dry weight only including closed fluid systems, which is 5262lbs. Using an estimated of 8% of the zero fuel weight to calculate the reserves, we would expect the aircraft to carry 549lbs of fuel in excess of mission requirements. The landing weight is 7447lbs, and the fuel weight allowance 1183lbs.
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9 Baseline Performance Estimation
9.1 Take-off Performance Take-off field length is the required length of runway that the aircraft will use when loaded to maximum take- off weight. We compute this with another index based equation. The take-off speed will at least be twenty percent more than the stall speed, and knowing the maximum lift coefficient in the take-off configuration, we can calculate both. s 2 · W VLO = 1.2 · Vstall = 1.2 · = 23m/s or 45kt (39) ρ · Sref · CLmax
The engine model shows that at seventy percent of this speed the thrust produced by the engine is ninety percent of the sea level static thrust. The twin PW617s can thererfore be expected to produce 3204lbs at take-off. The field length required for a two engine aircraft is calculated with the following equations.
W 2 ITOFL = = 120 (40) σ · CLmax · Sref · T.7VLO
σ is the ratio of the lowest pressure at take-off to the highest pressure at take-off, and in this calculation we use a value of .84. 2 TOFL = 857.4 + 28.43 · ITOFL + .0185 · ITOFL = 4535ft (41) This is outside of the mission constraint of 3000ft, which will need to be addressed through design refinement.
9.2 Landing Performance To calculate the landing distance, we split up the problem into two parts. The first part is the distance covered in the air, and the second is the distance covered on the ground during braking. First we determine the landing speed, which is taken to be twenty-five percent more than stall. s 2 · W VLand = 1.25 · Vstall = 1.2 · = 19m/s (42) ρ · Sref · CLmax
Vs0 is thirty percent more than stall, which comes to a value of 20m/s. The maximum landing weight is taken to be eight percent more than the zero-fuel weight, 3400kg. The distance covered in the air is calculated with the following equation, where the lift/drag was determined with the drag polar plot to be 7.7.
L L/D d = 50 · ( ) + · (V 2 − V 2 ) = 396m (43) air D 2 · g s0 land
The distance on the ground requires yet more assumptions. Assuming a dry runway the coefficient of friction is taken to be .7. We also assume that the lift at touchdown becomes zero, a favorable assumption, and that the aerodynamic drag is also zero, a worst case assumption. With these simplifying assumptions the distance to come to stop on the ground is calculated in the following equations.
R = µ · Wmax land = 2380kg (44)
V 2 · W d = Land = 26m (45) ground 2 · g · R
dtotal = 1.67 · (dair + dground) = 705m or 2311ft (46)
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9.3 Second Segment Climb Performance Calculating the second segment climb gradient requires some knowledge of the drag during climb. Using the
drag polar, we find that the CD is 1.3 for the CL of 1.53 in take-off configuration. 1 D = ρV 2 · C · S = 5754N (47) 2 D ref The climb gradient is then a trigonometric relation, which simplifies greatly with the assumption that the
climb is performed at a constant velocity. For this calculation, we assume climb is performed at 1.2·Vs, or 45kt. T −D T − D sinγ = W = = 0.046 (48) V dV W 1 + g · dh
sinγ ≈ h/V˙ =⇒ h˙ ≈ V · sinγ = 210ft/min (49)
9.4 Cruise Performance The metrics for cruise performance we will investigate are range and cruise climb gradient.
W CL = = 0.344 (50) q∞ · Sref
Using the drag polar generated earlier, we find that the drag coefficient, CD, is 0.0317 and the lift to drag ratio is therefore 10.9. Next we must estimate the weight at the beginning and end of cruise.
Wmaneuver = 0.007 · MTOW = 60.2lbs (51)
Wclimb = 0.016 · MTOW = 137.6lbs (52)
1 W = MTOW − · W − W = 8432lbs (53) i 2 maneuver climb
Wreserves = 0.08 · ZFW = 549lbs (54)
1 W = ZFW + · W + W = 7446lbs (55) f 2 maneuver reserves With the previously calculated thrust specific fuel consumption at cruise of .44, we now have all the values needed to use the Breguet Range Equation. V L Wi Cruise Range = · · ln = 1221nm (56) C D cruise Wf The range of the aircraft exceeds the design goal considerably. This is not necessarily a good thing as the airplane could be potentially less efficient for the actual missions for which it will be flown. Next we investigate the climbing capability of the aircraft. The drag of the airplane at the beginning of cruise is easily obtained from the coefficient of drag found in the drag polar.
D = CD · q∞ · Sref = 3522N (57) To calculate inital drag to thrust ratio we use the engine model to determine that at cruise conditions we can expect between 25% to 30% of the sea level static thrust. This comes out to 3877N, which gives a D/T of .91. Assuming a constant Mach number climb, the climb is described by the following equations.
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V dV · = −0.133 · M 2 = −.06517 (58) g dh
T −D W sinγ = V dV = 0.0101 (59) 1 + g · dh
sinγ ≈ h/V˙ =⇒ h˙ ≈ V · sinγ = 407.5ft/min (60) This is well above our required 300ft/min, which, again, may not result in the best aircraft for the mission
9.5 Baseline Summary Sizing Plot Repeating the calculations for different weights and wing reference areas, we can develop a parametric plot and illustrate the design constraints in a clear way. The design constraints that we are working with are summarized in Table 3.
Constraint Value Take-off Field Length Less than 3000ft Landing Field Length Less than 3000ft Range Greater than 1000nm Second Segment Climb Greater than .024 Drag to Thrust Ratio Less than 0.93
Table 3: Design Contstraints
The drag to thrust ratio was found to not be a constraining value for the range of take-off weights we can consider. Because of this, it is not reflected in this the Figure 13. The shaded areas reflect the regions of the plot where a constraint is violated. The range constraint, for example, indicates that for the given reference area, the take-off weight must be greater than the line such that sufficient fuel is carried to complete a 1000nm flight. The unshaded region is the area of the plot which all of the constraints are satisfied. Because this is for values of take-off weight above the structural maximum take-off weight, the design is not closed and does not satisfy all of its design requirements. We will need to perform an optimization to modify our parameters and meet all of the constraints.
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Figure 13: Summary Sizing Plot
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10 Optimizing the Design
The key design variables we choose to modify are MTOW, ZFW, A, Sref , wing position, and Sh. These are the most important variables for impacting range, field lengths, and the stability of the aircraft. The
MTOW and ZFW determine the component weights, A and Sref effect the lift and drag characteristics of the wing, and the wing position and horizontal tail area. This should be sufficient to allow the optimizer to find a feasible design. Using the Matlab version of PASS, we setup an optimization to modify some aircraft parameters such that all constraints are satisfied and the ticket price is minimized. The parameters that were available to the optimization to change, the design variables, as well as their corresponding maximum and minimum bounds are summarized in Table 4. These values can of course only be modified in such a way that the mission of the airplane is satisfied. These restrictions are accounted for with the optimization constraints, which are shown in Table 5. With the optimization problem formulated, it’s very simple to enter the data into an XML file and have matlab FMINCON solve the optimization through PASS. We do exactly this, giving us the optimal aircraft for our mission. The initial and final values for each parameter are also included in both tables below. The optimization takes the airplane from costing $770 per ticket to $478 per ticket while also satisfying all of the constraints.
Design Variable Min Max Before After Maximum Take-Off Weight, MTOW 8,000 10,000 8,600 8,366
Wing Reference Area, Sref 140 210 150 187 Sea Level Static Thrust 1700 2000 1700 1700
Wing Aspect Ratio, Aw 8.0 12.0 9.1 11.5 Initial Cruise Altitude FL300 FL400 FL300 FL300 Final Cruise Altitude FL300 FL400 FL350 FL300 Wing Position 0.4 0.6 0.53 0.5
Horizontal Tail Area, Sh/Sref 0.2 0.5 .44 0.25 Wing Sweep Angle 0.0 20.0 5.0 5.6
Wing Thickness/Chord Ratio, (t/c)w 0.1 0.15 0.15 0.15 Take-Off Mach Number 0.1 0.25 0.1 0.13 Landing Mach Number 0.1 0.25 0.1 0.11 Maximum Zero Fuel Weight, MZFW/MTOW 0.6 0.9 0.798 0.86
Table 4: Design Variables for Optimization
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Constraints Min Max Before After Cruise Range, nm 1000 1500 1221∗ 1000 Take-off Field Length, ft 1000 3000 4535∗ 3000 Landing Field Length, ft 1000 3000 2311∗ 3000 Minimum Stability Margin 0.20 0.50 -0.30 0.20
Vertical Tail CL with Engine Out -1.0 1.0 0.65 0.29 Second Segment Climb Gradient 0.024 0.1 .019 0.075 Landing Gear Location 0.3 0.8 0.87 0.39 Initial Cruise Drag/Thrust 0.0 0.92 0.64 0.73 Final Cruise Drag/Thrust 0.0 0.92 0.64 0.72
Horizontal Tail Take-off CL Margin 0.0 2.0 0.77 0.43 Horizontal Tail Rotation CL Margin 0.0 2.0 0.23 0.55 Horizontal Tail Climb CL Margin 0.0 2.0 0.93 0.57 Horizontal Tail Initial Cruise CL Margin 0.0 2.0 1.16 0.98 Horizontal Tail Final Cruise CL Margin 0.0 2.0 1.17 0.98 Horizontal Tail Landing CL Margin 0.0 2.0 0.90 1.98 Wing Climb CL Margin 0.0 2.0 -0.68 0.59 Wing Initial Cruise CL Margin 0.0 2.0 0.75 0.76 Wing Final Cruise CL Margin 0.0 2.0 0.71 0.78 Wing Take-off CL Margin 0.0 2.0 0.0 0.0 Wing Landing CL Margin 0.0 2.0 0.18 0.18 Payload Margin, lbs 250 1000 129 250
Table 5: Optimization Constraints
The result of the optimization then is a larger and longer wing, a lighter aircraft, and a smaller horizontal tail. The updated 3-view is shown below, as well as the updated sizing summary chart.
∗ These numbers are based on the baseline hand calculations
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Figure 14: Updated 3-View
Figure 15: Updated Summary Sizing Plot
Second segment climb and cruise thrust were also examined but found to not be constraining factors in this range.
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11 Environmental Characteristics
11.1 Noise The noise generated by an airplane is one of the most important factors for airports and their surrounding communities. Because of this, strict regulations have been developed to protect the interests of neighboring communities. Stage three noise regulations for the takeoff weight of the aircraft limit the takeoff EPNL to 89dB, sideline EPNL to 94dB, and approach EPNL to 98dB. Stage four requires a total improvement beyond this of 10dB, with no less than a 2dB sum in any two categories. Using the noise calculator, we can determine the expected noise at the three observer locations.
Figure 16: Noise Estimate
The noise produced by the airplane is under the limits for all of the microphone positions. The take-off EPNL is -20dB lower, sideline EPNL is -12dB lower, and the approach EPNL is -14dB lower. This meets both stage three and stage four requirements for noise.
11.2 Emissions The engine we have chosen for our aircraft was certified in 2008 and produces 3590N SLST. Because it is newer and smaller, the regulations for gaseus emissions do not apply; however, the regulations on smoke,
Page 31 of 33 Christopher Pepper The Aerus DecaJet AA241B: Final Report hydrocarbons, carbon monoxide, and nitrous oxides do still apply. When certified with the EASA, the engine was found to satisfy the emissions constraints.
Figure 17: Emissions Calculation
As we can see from the results of the analysis, we have far less than maximum amount of NOx. For conceptual design, this will be enough to ensure that emissions regulations are satisfied.
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12 Future Work
12.1 Engine The engine we chose was the PW617F-E, for which very little technical data is available. To ensure that this engine meets all of the specifications on thrust and specific fuel consumption throughout the mission envelope, we should get more information from Pratt and Whitney. Useful information would include engine thrust lapse rate, bypass ratio, and thrust specific fuel consumption at various conditions. This would eliminate some of the coarser approximations used in the engine model and in some of the performance estimations.
12.2 Materials We would like to use carbon fiber composite technology in building the aircraft, which was not taken into account during the weight estimation. This is common practice to treat carbon-fiber as ”black aluminum,” but there is an unnecessary overdesign as a result. Future work could include a more representative weight estimate either by discounting the weight by a certain amount or by developing a comparison with similar carbon-fiber composite aircraft. We could also begin to use finite element analysis to come up with more detailed structure and therefore more detailed weight estimates.
12.3 Cabin Design At the onset of this design, we decided to make this aircraft smaller than the Honda Jet and Cessna Citation Mustang. It would be interesting to explore the design space of having a slightly larger aircraft and see if we could potentially make a more direct competitor.
12.4 Airfoil The airfoil we developed in this conceptual design was a mix of the traditional peaky airfoil and the newer supercritical airfoil. Many of the calculations are based on the assumption that we have a peaky airfoil. A good next step would be to use more sophisticated tools, like CFD, to reach conclusions more accurate for our specific airfoil.
12.5 The Business End Finally, one of the most important aspects of developing a new product is to understand the customer and the potential market. Since the profit margins in aviation are rather slim, it is critically important to ensure that the product is viable prior to continuing development. It would be most prudent to conduct surveys and interviews to determine whether there is truly a market for this aircraft.
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