ME 408 Aircraft Design Final Report for Team FSLAP Four-Seat Light Airplane

Transcription

1 ME 408 Aircraft Design Final Report for Team FSLAP Four-Seat Light Airplane Matt Mayo Chris Hayes Bryant Ramon

2 Designed in 1956 more Cessna 172 Skyhawk s have been built than any other aircraft in history, this is greatly due to their legendary formula of affordability, reliability and ease of flying. Despite their legacy the design is aging and competitors such as the Cirrus SR22 boast faster cruise speeds sleek designs. The main objective of this aircraft design is to breathe new life into the Cessna 172 Skyhawk, updating the aircraft while retaining the ubiquitous brand. Our hard design goals were simple, a range of 800 nautical miles with one pilot and 3 passengers in a 192 ft 2 cabin; other secondary performance goals such as improved climb rate and take off /landing field length were also considered during the design process. The most significant design changes are the removal of wing braces, the enlargement of the wing and the introduction on a turboprop engine. These changes allowed us to decrease the drag and increase the thrust of the aircraft, bringing it more in line with the performance characteristics of modern four seaters. Overall we are content with the final design of the airplane. Our suggestion to management is not to replace the Skyhawk but to dub this aircraft the Super Skyhawk and offer alongside the Skyhawk as an option for buyers who are interested in more performance at an increased cost. Performance Quote Requirements/ Proposed Performance Item Targets Design Delta% Cessna 172 Cirrus SR 22 -Design Payload (Non-Expendable) 1 Pilot / 3 pax 4 n/a 4 4 -Passenger Allowance 250 lbs/pax 250lbs/pax n/a Cabin Length/Width/Height 12 /4 /4 (192 ft^3) 194 ft^3 1% 158 ft^3 184 ft^3 -Design Payload (Expendable) 0 0 n/a 0 0 -Design Range w/max Payload 800 nm 800 nm 0% 640 nm 400 nm -Design Time-on-Station w/ Payload 0 0 n/a 0 0 -Stall Speed <45 nm/hr 47.6 ktas -5.7% 48 ktas 60 ktas -Max Cruise Speed = Max Mach >160 nm/hr ktas -0.9% 124 ktas 183 ktas -AEO Takeoff Field Length <1,800 ft ft 1630 ft 1756 ft -OEI Takeoff Field Length (BFL) n/a n/a n/a n/a n/a -Landing Field Length <1,500 ft ft 11.7% 1335 ft 1178 ft -AEO Rate-of-Climb >900 ft/min 704 ft/min 730 ft/min 1270 ft/min -OEI Rate-of-Climb n/a n/a n/a n/a n/a -Glide Slope <3 deg 2.49 deg 17% 6.34 deg 5.95 deg -Max Sustained Turn Rate >2 deg/s 5.64 deg/s 182% 22.2 deg/s 17.6 deg/s -Max Instantaneous Turn Rate >2.5 deg/s 7.27 deg/s 190.8% 13.8 deg/s deg/s -Service Ceiling >20,000 ft 36,900 ft 84.5% 14,000 ft 17,500 ft -Unit Cost <$350,000 $689, % $364,000 $664,900 -Development Cost <$11M $113,900, % $68,200,000 $141,800,000

3 Chapter 2 Take-off Weight Estimate Mission Analysis Summary (W/Wo) Weight Parameter Symbol Value Fraction Empty Weight (lb) We 2, Payload (lb) Wp 1, Expendable Wpe Non-expendable Wpne 1, Fuel Load (lb) Wf Mission Fuel Burned Wfb Reserves Fuel Wr Trapped Fuel Wtf Design Takeoff Gross Weight (lb) Wo 3, Surplus Empty Wt. (lbs) 0.00 Table 1: Mission Analysis Summary for Chapter 2 The spreadsheet itertow.xls was used for the analysis of the takeoff weight. For our Cessna redesign, the design drivers that affected the spreadsheet the most were Operating Range, Cruise Altitude, Cruise Mach number, Specific Fuel Consumption, and Aspect Ratio. One of our hard requirements was our design range with max payload. The specified range was 800 nm (400nm operating radius). Our initial desire was to come up with a design that would make extensive use of composite materials which would thus give us a structure factor, SFACT, of around 0.5. Our design SFACT resulted in a value of after many iterations. Also resulting from countless iteration of our spreadsheets is our L/D ratio. The L/D ratio used in our design is 14 which is smaller than the initial value of 17. This L/D is obtained from the aero sheet in chapter 7. Another hard requirement for our design was our passenger allowance (i.e. our nonexpendable payload). The specified payload included a pilot and three passengers weighing 250 lbs each. The cruise altitude (although not an explicitly specified design driver) was determined from our max cruise speed requirement of >160. A decided cruise altitude of 10,000 feet results in a cruise Mach number of 0.25 (subsonic). This Mach number results in a cruise speed of or Although the soft requirement was not met entirely it was close enough to proceed with our other calculations. Our goal in this design is to meet as many of our soft requirements as possible or come relatively close to each. Since there is no combat time for our design, the TSFC and engine thrust are not used in the takeoff weight estimate. The engine SFC is , which comes from our engine analysis in

4 chapter 7. Our team allotted a 15 minute loiter time to account for the necessary time for lessexperienced pilots to position the aircraft prior to the landing approach. For the estimate of the fuel-weight fraction used in cruise and loiter, the governing equations were modified to account for the propeller efficiency. Our propeller efficiency calculated from the engine spreadsheet in Chapter 7 was 0.72 (for our turboprop design). The 0.72 propeller efficiency value replaced the original typical value of 0.8. Given all of these values and assumptions our resulting spreadsheet is shown in our appendix under Figure A.1. Our final takeoff weight was 3,967 lbs. Of this, 1000 lbs is payload, lbs is fuel, and 2,094.6 lbs is the empty or structure weight. Chapter 3 Wing Loading Selection Wing Loading Selection Summary Design Wing Loading W/S (lb/f^2) No. Flight Regime Parameter Value Target Del% 1 AEO Take-off S_TO (f) % 2 Landing S_L (f) 1, % 3 Cruise Start S (f^2) Cruise End H (f) 10, AEO Climb dh/dt (f/min) % 6 Acceleration n Turn - Instantaneous psi_dot (deg/s) % 8 Turn - Sustained psi_dot_act (deg/s) % 9 Ceiling H (f) 51, % 10 Glide Gamma (deg) % 11 Stall Speed Vstall (ktas) % Table 2: Wing Loading Selection Summary for Chapter 3 The spreadsheet wingld.xls was used for the analysis of the wing loading selection. The wing loading spreadsheet was used to obtain many of the soft requirements for our design. Although design range is one of our hard requirements the optimum wing loading in cruise was not used as the design wing loading. The reasoning for this was that a smaller wing loading was needed in order to meet or come close to a lot of our other soft requirements. Furthermore, the specified operating radius would allow the aircraft to make cross-country flights without the frequent refueling. By using a smaller wing loading we were able to meet our landing and takeoff field lengths, instantaneous and sustained turn rates, and AEO climb rate requirements. Our resulting takeoff and landing field lengths are ft and ft respectively. The resulting instantaneous and sustained turn rates are 7.27 and 2.5 respectively. Our AEO climb rate was

5 The value used in the takeoff and landing portion of the spreadsheet came from our chapter 9 analysis for plain flaps. The parasite drag value is the clean parasite drag which comes from our key outputs in the aero sheet from chapter 7. The Oswald s efficiency value used is one supplied by Professor Geiger which is an accepted value for e. Lastly our calculation of thrust stemmed from our desire to reach our soft requirement for climb. In order to get the desired climb rate we had to iterate through a number of T/W values which caused our thrust value to change until it reached a value that allowed our climb rate to be met. Other soft requirements met from the wing loading spreadsheet are glide slope, service ceiling, and stall speed. All the analysis is shown in our chapter 3 spreadsheet in our appendix under Figure A.2 Chapter 4 Main Wing Design Calculations b ft M eff c r 5.45 ft c t 5.45 ft m.a.c. 5.4 ft b C La /deg C Lo a trim 0.54 deg C Ltrim k C D L/D Total Drag lbf Table 3: Key outputs values from Chapter 4 The spreadsheet wingd.xls was used for the analysis of the main wing design. Because our aircraft is a subsonic design with a low Mach number our main wing did not require a leading-edge sweep. Our aircraft is designed to be homebuilt therefore our taper ratio input is 1. This results in a conventional rectangular design for our wing. With an aspect ratio of 7.5 (taken from chapter 2) and a surface area of ft^2 (from chapter 3) we end up with a wing span of feet. The wing section selected for the design is the NACA 2412 which is the same airfoil the Cessna 172S uses. The reasoning behind that airfoil was mainly our attempt to remain under the Cessna brand by simply redesigning the Skyhawk and not making a completely new design.

6 Lift Coefficient, CL, (-) Wing Half Span, b/2, (ft) Furthermore, the current model Cessna uses an interference factor of above 1 to account for wing braces. Our design will have an interference factor equal to 1 by getting rid of the wing bracers. The large aspect ratio and no leading edge sweep makes our wing act almost twodimensional. The following figures are outputs from the chapter 4 spreadsheet as well as the airfoil data from Theory of Wing Sections. The chapter 4 figures show the wing half span vs. axial position in one graph and the lift coefficient vs. angle of attack on the other. The airfoil data figures are taken straight from the Theory of Wing sections book. Wing Lift Curve Angle of Attack, a, (deg) 2D Lift 3D Lift Wing Planform Figure 1: Wing Lift Curve from Chapter 4 Figure 2: Wing planform from Chapter Axial Position, (ft) Figure 3.a and 3.b: Wing Section data for the NACA 2412

7 Fuselage Perimeter, (ft) All the analysis is shown in our chapter 4 spreadsheet in our appendix under Figure A.3 Chapter 5 Fuselage Design Viscous Drag Calculations: Elliptic Cylinder Fuselage Shape x/l x (ft) H (ft) W (ft) P (ft) Sw(ft^2) Re x C F Drag (lbf) Volume (ft3) E E E E E E E E E E E E E E E E E E E E Totals: Table 4: Fuselage output calculations for Chapter 5 The fuselage shape is constructed as a series of ellipses that are blended and tapered to allow enough room for the crew of 4 and to provide space for the engine. A fineness ratio of was selected to minimize the total drag on the fuselage. The overall fuselage length is 32 ft. with a diameter of 4.35 ft. Because our design is subsonic our aircraft does not experience wave drag. Therefore, based on our inputs our calculated viscous drag for our aircraft is 61.3 lbf. The equivalent drag coefficient, normalized by the wing area, is The following figure shows the fuselage design of our aircraft. Fuselage Perimeter Axial Position, (ft) Figure 4: Fuselage perimeter graph from Chapter 5

8 All the analysis is shown in our chapter 5 spreadsheet in our appendix under Figure A.4 Chapter 6 Tail Design Tail Design Summary Total VT TE Drag (lbf) Del% Sweep (deg) Conventional 56.9 Base 10.6 T-Tail % 10.6 Cruciform % 10.6 H-Tail % 10.6 V-Tail % 10.6 Inverted V-Tail % 10.6 Y-Tail % 10.6 Twin Tail % 10.6 Control Canard % 10.6 Lifting Canard % 10.6 Main Vertical Horizontal Wing Tail Tail Airfoil Section NACA NACA Max Thickness, % LE Sweep, deg Aspect Ratio, dcl/da, 1/deg Table 5: Tail Design summary from Chapter 6 The airfoil used for our horizontal and vertical tail is the same as the one by the Cessna 172 Skyhawk (NACA ). With this airfoil we have a thickness-to-chord ratio of The CVT and CHT values for the vertical and horizontal tail were and respectively. These values are based on historic data for aircraft of this type. For LHT and LVT we took ~60% of the fuselage length based on Professor Geiger s advice and Corke page 126. That results in LHT and LVT values of 18.0 ft. Our taper ratios for the horizontal and vertical tail were the same at 0.5. The aspect ratios for the vertical and horizontal tail were 1.3 and 3 respectively based on Corke Table 6.5. Our aspect ratios fall within the range supplied by the table. The leading edge sweepback angles for the vertical and horizontal tail were 40 degs and 10 degs respectively. With all these values established and inputted into the spreadsheet we are able to calculate our tail drags. For the vertical tail the viscous drag was lbf. The viscous drag on the horizontal tail is lbf. The tail planforms for both the vertical and horizontal tail are shown in the following figures for chapter 6. All the analysis is shown in our chapter 6 spreadsheet in our appendix under Figure A.5

9 H-Tail Span, (ft) H-Tail Planform Figure 5.a and 5.b: V-Tail and H-Tail planform plots from Chapter 6 With the main wing, fuselage, and tail analyses done we can create a basic external shape of the aircraft. The following figure depicts just that Axial Position, (ft) Figure 6: Basic External Shape based on our main wing, fuselage, and tail analysis

10 Chapter 7 Propulsion System Design Engine Selection Summary Value Units Number of Engines 1 - Uninstalled Engine Power, SLS ISA Max shp/eng Reference Engine PT6A-50 - Engine Scale Factor Type of Engine Turboprop - Ave. Design Cruise lbm/hr/shp Engine Weight lbf/eng Engine Length 39.6 in Engine Max Diameter 19.6 in Propeller Diameter 7 ft # of Blades 2 - Table 6: Engine Selection Summary from Chapter 7 The engine we selected was the PWC PT6A-50 turboprop engine. The PT6A turboprop engine is a powerhouse that offers unmatched performance, reliability and value in its class of 500 2,000 shaft horsepower for a wide range of applications. From our engine selection summary you can see that the uninstalled engine power is 945 shp. Our aircraft incorporates a 7- foot diameter, two-bladed propeller system based on the airframe size and comparison aircraft. With these inputs we have a propeller tip Mach of which is below the threshold of This chapter 7 spreadsheet is used to determine the amount of thrust tour engine-propeller system can produce. The total drag on our aircraft is a combination of the drag forcers on the wing, fuselage, and tail. Based on our previous spreadsheets our total drag is lbs. Our engine-propeller system can produce pounds of thrust with a power scale factor of 1. Initially we decided on a reciprocating propeller system without a super charger but that failed to give us the values we seek. The reciprocating propeller system with the super charger also proved to be inefficient. Ultimately we settled on the turboprop as the happy medium. The following figure from Chapter 7 shows the relationship between the various propeller systems and drag as a function of Mach number.

11 Thrust and Drag (lbf) Cruise Thrust and Drag 1800 Drag Recip w/o S/C Recip with S/C Turboprop Mach Number, (-) Figure 6: Relationship between the various propeller systems and drag as a function of Mach number The corrected static thrust value that will be used in the next chapter is 2749 lbs. All the analysis is shown in our chapter 7 spreadsheet in our appendix under Figure A.6 Chapter 8 Takeoff and Landing Analysis Takeoff and Landing Summary Design Gross Weight lbf 3967 Altitude ft 0 Engine Thrust lbf/eng 906 Stall Speed nm/hr 47.7 Field Lengths AEO Takeoff ft 2,021 OEI Takeoff ft #NAME? Landing ft 2,231 Regulatory Compliance AEO, Gear Up Vy ft/min 704 OEI, Gear Up Vy ft/min 0 OEI, Gear Up G % 0.0% OEI, Gear Down G ft/min 0.0% Table 7: Takeoff and Landing Summary from Chapter 8

12 The purpose of the Chapter 8 spreadsheet is to get accurate updated values for takeoff and landing field lengths. Apart from just updating the values obtained from Chapter 3, the chapter 8 spreadsheet introduces new parasite and lift coefficients due to flaps. A further understanding of the flap calculation will be done in the next section. The inputs necessary for this spreadsheet are wing aspect ratio, wing area, takeoff and landing weights, and static engine thrust. The overall drag coefficient was taken as the sum of the coefficients for wing, fuselage, and tail obtained in previous spreadsheets. The increase in drags due to flaps was specified to be The rolling friction coefficient corresponds to a grass field which is consistent with our recreational aircraft. For takeoff, a climb angle of 5 degrees was used with an obstacle of 50 feet to meet FAR Part 25 regulatory compliances. Our calculated takeoff field length was ft which doesn t meet our soft requirement but it pretty close. We would have to consider a higher climb angle of around 8 degrees in order to reach our desired field length. The change in climb angle will affect our thrust which we will need to adjust. For landing, a descent angle of 8 degrees was used with all other parameters remaining the same except for the updated weight for landing. Our final landing field length resulted in 1819 ft. although our field length for landing is larger than what we expected it is still lower than our take off length which we like. The following figures show the breakdown for both takeoff and landing. All analysis was done using the Chapter 8 spreadsheet which can be found in our appendix under Figure A.7 Take-off Breakdown Landing Breakdown 4 14% 1 19% 3 12% 2 14% 1 60% 4 50% 3 18% 2 13% Figure 7: Take-off and Landing Breakdowns from Chapter 8

13 Wing Half Span, b/2, (ft) Lift Coefficient, CL, (-) Chapter 9 Enhanced Lift Design Flap Design Summary Design Units Type of TE Flaps plain - LE Flaps No - Flap Area / Wing Area, Swf/Sw Flap Deflection Angle, df deg Flap Chord / Wing Chord, cf/c Flap Span / Wing Span, bf/b CL,max DCDo, flaps Table 8: Flap design summary for Chapter 9 For our aircraft, plain tailing-edge flaps were used. Our flaps have an angle of deflection of 40 degrees with a length of 40% the wing chord covering 50% of the wing span. Most of the vital inputs in this spreadsheet were taken from the wing design spreadsheet (chapter 4). The aspect criterion designated for the wing to be in the high category. That meant the low aspect ratio basic wing results are to be ignored. All relevant analysis can be seen in the spreadsheet corresponding to this chapter found in our appendix under Figure A.8. The following figures are taken from that spreadsheet and show the wing planform and wing lift curve for the flaps. Wing Planform Wing Lift Curve w/o Flaps Axial Position, (ft) Figure 8: Wing Planform for flaps Angle of Attack, a, (deg) Figure 9: Wing Lift Curve of main wing w/ and w/o flaps

14 Chapter 10 Material Selection Results Parameter Symbol Units Value Max Maneuver Load Factor n max maneuver Max Gust Load factor n max gusts Design Load Factor n design Table 9: Load Factor summary for Chapter 10 The material selection spreadsheet mainly focused on load factor, shear forces, and bending moment distribution on the wing and fuselage. The calculation of the load factor for the turning phase (both instantaneous and sustained) rely on the input Mach number and turn rate. Because our turn rates were a soft requirement we focused on that load factor calculation. The acceleration and intercept phase load calculations don't correspond to our aircraft. We added a safety factor of 1.5 to our load calculation and used that as our design load. We set our ranges for min and max load factors to -2 and 4 based on the Corke table. In the following figure you will see how our maneuver loads and gust loads fall within those ranges. Figure 10: V-n diagram for maneuvering and gust for Chapter 10 The inputs for the wing loads and fuselage loads sheets were taken directly from previous worksheets in order to calculate the moments and shear on the wing and fuselage. The following figures show the loads, shear, and moment graphs for both the wing and fuselage.

15 Figure 11a, 11b, 11c: Wing Load, Wing Shear, and Wing Moment for Chapter 10 Figure 12a, 12b, 12c: Fuselage Load, Fuselage Shear, and Fuselage Moment for Chapter 10

16 For the material selection of the wing spar and fuselage and longeron, the width, height, thickness, and material used were inputs. After much iteration, our design will incorporate a wing spar of width 2.06 in, height 7.00 in, and 0.51 in thickness. Our fuselage longeron will be 4 in. in width, 2 in. in height, and 1 in thickness. The skin material for both will be 2024-T3 aluminum alloy. The core material for the spar and longeron is 4130 normalized steel alloy and 2024-T3 aluminum alloy respectively. The following figures show the cross sectional area of our spar and longeron. Figure 13 a, 13 b: Cross section for the Wing Spar and Fuselage Longeron Chapter 11 Stability and Control Weight Summary General Component Symbol Fighter Transport Aviation Wing Wwing Horizontal Tail Wh-stab Vertical Tail Wv-stab Fuselage Wfuse Main Gear Wmain lg Nose Gear Wnose lg Engine(s) Weng Remaining Components Wrem Empty Weight We 2,910 2,793 2,204 Design Gross Weight Wo 3,967 3,967 3,967 Empty Weight Fraction We/Wo Table 10: Weignt summary for Chapter 11 For all of the component weights, general aviation was considered the appropriate category for the weight estimate. All relevant inputs such as design load factor were all taken from previous spreadsheets In our initial refined weight estimate we saw that our refine weight was too big. The main components of the weight were the wing, fuselage, and landing gear. We decided to go back and change our wing loading which is why we were unable to meet our vstall requirement. By taking into consideration the use of composite materials in our wing

17 we were able to reach a target weight that we were okay with. The weight summary above shows the breakdown of all the weight estimates for general aviation for our aircraft. Static Stability & Control Summary Static Margin Value Comments -Center of Lift xcl/l -Center of Gravity xcg/l -Static Wcr, start 9.0% stable -Dtrim / Dtotal Dtrim high, See Corke Page 279 Stability Coefficients -Longitudinal, Cm,a stable Corke: -1.5<Cm,a< Lateral, CL,b stable -Directional, Cn,b stable Corke: 0.08<Cn,b<0.28 Rudder Area 2.3 ft2 Table 11: Stability & Control summary for Chapter 11 The stability section of this spreadsheet proved to be the most difficult. We assumed our fuel was in our wing and our payload was distributed over and slightly forward of the main wing. All of these parameters and more were used to determine the center of gravity of our aircraft. What we found to be frustrating was that either the wing or fuselage would be destabilizing at any given time in the sections for S&C. Ultimately we went through the Corke book and spoke with Cody and came out with and acceptable aircraft that achieved stability. Our stability and control summary can be seen above. It shows our center of lift, our center of gravity, the change in trim, etc. The following figures show the vertical stabilizer planform and trim drag vs. static margin. Figure 14: V-Stabilizer planform from Chapter 11 Figure 15: Trim drag vs. static margin for Chapter 11

18 Chapter 12 Cost Estimate Cost Estimate Summary Year 2013 Number of Development Aircraft 2 Number of Production Aircraft 5300 Production Rate (per month) 50 Amortization Period (# of ac) 4000 Initial Unit Cost (1986 Model) $689,852 Final Unit Cost (1986 Model) $661,368 Initial Price Markup 4% Profit (%) 10

19 Range (nautical miles) Range (nautical Miles) Chapter 13 Trade Summary Specific Fuel Consumption vs Range (nm) Range (nm) Specific Fuel Consumption (lb/(lbf h)) Cruise Mach vs Range (nm) Cruise Mach

20 Jane s Style Datasheet Overall Length 32 ft Height 7 ft Wings Span 40.5 ft Root Cord 5.5 ft Tip Cord 5.5 ft Aspect Ratio 7.5 Engines Prop Diameter 7 ft Wheels Wheel Base 3.12 ft Internal Dimensions Cabin Length 12.5 ft Width 4 ft Height 4 ft Areas Wing area ft^2 Flaps Area 44.5 ft^2 V-Tail 15.2 ft^2 Rudder Area 2.3 ft^2 H-Tail 20.2 ft^2 Weights Empty lb Take Off 3967 lb Landing lb Fuel lb Payload 1000 lb Wing Loading Wing Loading lb/ft^2 Performance S_TO ft S_L ft Rate of Climb 704 ft/min Sevice Celing 36,900 ft Cruise Speed ktas Stall Speed 47.6 ktas Range 800 nm

21 3-D Solid Model

22 Sources for Competitor Data Cessna.com Cirrus.com Jane s All the World s Aircrafts Wikipedia Cirrus SR22 Pilot s Manual (cirrus glide slope) Airliners.net (cirrus glide slope) Excel Sheets (Development Costs)