Preliminary Design Review

Transcription

1 Preliminary Design Review A&AE 451 Senior Design Spring 2006

2 Table of Contents 1. Executive Summary....pg.3 2. Introduction pg Product and Market Review...pg Initial Design Requirements...pg Design Missions pg.5 3. Design Concept pg Wing...pg Fuselage...pg Tail.....pg Landing Gear...pg Cabin Layouts...pg Sizing...pg Rough Sizing...pg Constraint Sizing...pg Constraint Diagram.pg Carpet Plots. pg Detailed Sizing...pg Compliance with Design Requirements...pg Structures...pg Wing and Tail...pg Fuselage...pg Landing Gear...pg Material Selection...pg Aerodynamics...pg Airfoil...pg Drag Polar...pg Lift Estimation...pg Drag Estimation...pg Weight and Stability...pg Weight Breakdown...pg Structural Weight...pg Propulsion Weight...pg Systems and Equipment Weight...pg Operating Weight...pg Payload Weight...pg Stability and Balance...pg Weight Locations...pg Center of Gravity and Static Margin...pg Tail Configuration...pg Vertical Tail...pg Horizontal Tail...pg Longitudinal Trim...pg Performance...pg Performance Values...pg V-n Diagram...pg.47 AAE 451 Group 1 page 1 of 79

3 Table of Contents (continued) 9.3 Operating Envelope...pg Propulsion...pg Engine Selection...pg Propeller Design...pg Fuel Selection...pg Fischer-Tropsch-based Jet Fuel...pg Soy-Methyl-Ester-based Jet Fuel...pg Conclusion...pg Cost...pg Acquisition Cost...pg Research, Development, Testing, Evaluation and Flyaway Cost...pg Direct Operating Cost...pg Conclusion...pg Feasibility...pg Open Issues...pg References...pg Appendix...pg.60 Design Team Members Miguel Alanis Tim Block Becca Dale Sarah Weise Aaron Mayne Jason Olmstead Joseph Fallon AAE 451 Group 1 page 2 of 79

4 1. Executive Summary Author: Miguel A. Alanis The design team has conceptually created a rugged, versatile aircraft fueled by a nonpetroleum-based alternative fuel that will mainly serve the international markets such as Australia and South America. The motivation for this design was the lack of affordable petroleum-based fuels that are crippling the aviation industry. Possible markets for the proposed aircraft include the European Union and Australia, who have expressed concern over emissions and would find a cleaner-burning fuel beneficial. Fischer-Tropsch kerosene and biodiesel, among other fuels, have been explored as possibilities to replace Avgas and diesel for their compatibility to current storage and power plant technology, as well as their environmentfriendly makeup. The aircraft will be powered by a Pratt & Whitney Canada PT6A-67D turboprop engine. A four-bladed, variable pitch Hamilton standard propeller with a diameter of 110 in has been selected to convert the power of the engine into thrust. Several trade studies were preformed to develop initial sizing values for the aircraft. Among these were GTOW and range trade studies. A performance constraint diagram was also created based on a specified design mission. This design mission is a one-way, 1200 nm trip for combination payload of 2000 lbs. There were many sections to the analysis, including structures, aerodynamics, stability, performance, propulsion, and cost. Several aluminum alloys will be used to manufacture the plane. A NACA 4412 airfoil was chosen for the wing of the plane. The aircraft designed is never in an unstable position. The cruise speed is 170 knots, and the stall speed is 61 knots. The airplane s engine has 1248 hp to power it. The current acquisition cost estimate for the plane is $3.24 million (US 2006), which is considerably more than the cost of the Cessna Grand Caravan ($1.75 million) but comparable to the cost of the PC-12 ($3.4 million), both planes which are in the same class as the designed plane. Per hour, the designed plane has an operating cost of about $425 (US 2006), which is higher than both the Grand Caravan and the PC-12. When petroleum fuels are more expensive, it the DOC of the Grand Caravan and the PC-12 will increase to comparable or higher levels than the DOC of the designed plane. The team decided after analysis that the design was feasible. There were, however, several open issues, such as performance analysis at landing and takeoff, detailed wing design, and dynamic stability analysis. AAE 451 Group 1 page 3 of 79

5 2. Introduction Author: Miguel A. Alanis 2.1 Product and Market Review The aircraft being designed is described as follows: a rugged, dependable, versatile airplane powered by non-petroleum based fuel that would serve as a transport vehicle in underdeveloped and rural areas of the world. Possible customers could be air charters, governments (land surveying, mail), medical transport, and supply delivery companies that operate in these rural, developing areas of the world such as Australia, South America, or even rural parts of Canada. There are many markets around the world that offer the potential for a successful business case. Australia and the European Union, for example, have expressed concern over the environment and thus would be interested in green transportation. There are many international markets that are also in need of an alternative fuel-based aircraft to replace their existing fleet or to meet a growing demand. Australia is one of the countries with expressed interest in replacing aging fleets. In a 2003 paper written by S.J. Swift 1 it is pointed out that as a result of the population distribution of their country; regional airlines are of significant importance to their economy. As Figure 1 depicts, most of the population is concentrated in the coastal regions, with 84% of Australians living on 1% of the continent; the other 16% scattered in rural regions. Because of these demographics, air transportation is vital to the general welfare of Australia. Figure 1: Population Density of Australia, taken from Swift 1 AAE 451 Group 1 page 4 of 79

6 The Canadian airline industry also faces many problems, including rapid consolidation, inconsistent service and rising costs. It is apparent that Canada needs smaller aircraft to service smaller markets around the country. Between major cities lies vast rural terrain that is not serviced regularly by the monopolistic national airline Air Canada. According to Dadgostar and Poulin 2, a significant change in the regulation of the Canadian aircraft industry is needed. The existing market includes several successful regional airlines, including Pacific Coastal Airlines and Bearskin Airlines. Both of these airlines use existing aircraft that are comparable to the capabilities and requirements used in developing the current design. The need for a small, general aviation replacement aircraft is evident in the Latin American region as well. A very successful aircraft in this market is the Cessna Grand Caravan. It is ideal for military transport, air rescue, border patrol, surveillance and supply operations. Cessna Grand Caravans are used extensively by Chile, Brazil, and Colombian government organizations. Additionally, these aircraft are utilized by airlines in Brazil, Venezuela, and Mexico. Often serving as an airline transport from remote locations to major airports, these aircraft offer spacious cabins, room for cargo, and are versatile. An aircraft similar in function and capacity to the Cessna Grand Caravan is ideal for this region s needs and has the potential to compete in a highly successful market. 2.2 Initial Design Requirements Based on market analysis, collected costumer attributes, and an extensive Quality Function Development (QFD) matrix, the following design requirements were initially considered: Passenger range: 9-12 Max Range: 1200 nm Max Cruise speed: 200 kn Max Service Ceiling: ft Take Off Distance: <2000 ft GTOW: 10,000 lbs Acquisition Cost: $2.0 million (US2006) 2.3 Design Missions In order to begin designing an aircraft, initial design missions were established. All of the design missions have taken into account the rural routes targeted as well as the lack of infrastructure needed to refuel in underdeveloped areas. Figure 2 shows a mission profile for a 1200 nm design range, with mission reserves in the event of a landing being unavailable at the AAE 451 Group 1 page 5 of 79

7 scheduled airport. This mission would also be used in the event of unfavorable weather conditions or other extenuating circumstances at the location of the planned landing. The steps of this mission are as follows: 0-1: Take-off (<2000 ft) 1-2: Climb to <10,000ft 2-3: Cruise climb <1200nm 3-4: Descend 4: Loiter <45min 4-5: Approach 5-6: Attempt to land 6-7: Climb 7-8: Divert to a neighboring airport 8-9: Descend 9: Loiter <45min 9-10: Approach 10-11: Land Figure 2: Design Mission for Full Range Flight For the above mission, the airplane would attempt to land at the prescribed location. The design mission includes a reserve segment that meets FAR part 23 requirements, which is expected to be compatible with requirements elsewhere in international markets. From here, the aircraft must descend and loiter again around the airport to which it has been diverted. The mission profile shown in Figure 3 represents a flight from one airport, to a destination, and back to the original airport. The distance from origin to destination is approximately 475 nm. This is an important mission, because the aircraft will be using alternative fuels, thus refueling stations may not be available at all airports. Thus, the aircraft AAE 451 Group 1 page 6 of 79

8 will need to return to the original airport in order to refuel for the next mission. The steps of this mission are as follows: 0-1: Take-off (<2,000 ft) 1-2: Climb to <10,000ft 2-3: Cruise climb <475nm 3-4: Descend 4: Loiter <45min 4-5: Approach 5-6: Land 6-7: Take-off (<2000 ft) 7-8: Climb to <10,000ft 8-9: Cruise climb <475nm 9-10: Descend 10: Loiter <45min 10-11: Approach 11-12: Land Figure 3: Design Mission for a Round trip Flight without Refueling The design mission in Figure 3 was taken into account when creating a preliminary constraint diagram. AAE 451 Group 1 page 7 of 79

9 3. Design Concept Author: Aaron Mayne In order to fulfill the requirements set forth by the design team, a concept was generated. This concept was generated to be qualitatively rugged, durable, and simple. In addition, the aircraft had to be versatile and able to hold combinations of cargo and passengers. The concept for this aircraft is shown in Figure 4. Figure 4: Isometric view of the Design Concept The main features were developed for the concept by splitting the aircraft components into four categories: Wing, Fuselage, Tail, and Landing Gear. AAE 451 Group 1 page 8 of 79

10 3.1 Wing The wing of this concept airplane was designed with features that compromise between a high performance and low structural weight. The concept features a high tapered wing with a strut. The wing was placed in a high configuration for considerations of ground clearance. With the market this aircraft is being designed to serve, there will be times when unimproved or dirt runways will have to be used. In these instances there may be small obstacles or tall plants that may cause damage to the wing and its structure. With the wing elevated it is possible to avoid many of these hazards. The taper on the shape of the wing was put there in order to help produce an elliptical load distribution. The wing s elliptical loading provides the most efficient performance. Also, a loading assumption was needed in order to complete structural calculations. The discussion of structural needs led to the final major feature of the wing. The conceptual wing was designed to be supported by struts. Strut support is an option to consider when a high wing is present. This option reduces the structural weight inside the wing while actually reducing the aerodynamic performance, since the struts add drag to the aircraft. The simplicity and structural weight reduction of the wing justifies the placement of a strut on the wing. 3.2 Fuselage The features present on the fuselage of this concept were selected in order to help aide in the ability to carry both passengers and cargo for the specific market presented for this aircraft. In order to complete these missions the aircraft should be simple and flexible. The first feature is a non-pressurized cabin. The non-pressurized cabin was selected to keep the conceptual aircraft lightweight and to reduce the necessary systems. Also without needing to pressurize the cabin, a square cross section is possible. A square cross section is the easiest way to wrap the fuselage around a standard LD3 shipping container. The ability to carry these cargo containers was a key design point for this concept. The second fuselage feature also enables the ability to use the standard shipping containers, the cargo door. A large sliding cargo door is present on the side of the fuselage. Placed behind the wing this 66 wide sliding door was designed in order to be able to fit the 62 wide LD3 shipping containers through with small clearance around the edges. This is a key feature that made this AAE 451 Group 1 page 9 of 79

11 design concept a good choice for the market that the team is trying to reach. 3.3 Tail The tail section of the selected concept as shown in Figure 4 is a T style tail. This tail configuration was selected for this concept primarily for the aerodynamic advantages. A specific quality of a T-tail configuration is a reduction in necessary tail surface area. This is due to the horizontal stabilizer acting as a tip device on the tail section, reducing the tip effects and increasing the percentage of the area that is effective to create a stabilizing force on the aircraft. Also the Horizontal stabilizer can have a smaller exposed area, as compared to the area for a conventional tail configuration. This is due to the fact that in this configuration the moment arm from the aerodynamic center of the wing to the horizontal stabilizer is longer. A smaller area is then needed because a smaller force is necessary to produce the needed force on the aircraft. This information on the effect of tail configuration comes from the text by Dan Raymer Landing Gear The final feature that was considered an integral part of this design concept is the landing gear. The design team decided that a fixed landing gear would be used for the design concept. The reasoning behind this decision was the durability issue for landings on unimproved runways. It can be seen from many existing aircraft that are capable of using rough runways and airfields that a fixed landing gear system is a feasible design choice. This choice of fixed landing gear was weighed between the structural advantages and the aerodynamic performance reductions. The final choice was made for the sake of simplicity. A simple fixed gear design allows for two major advantages: an ease of manufacture and repair, and landing gear that are always available. It is more important for the concept aircraft to always be able to land than to have the aerodynamic advantages. The layout and features of the design concept presented are shown in the fully dimensioned representation of Figure 5. AAE 451 Group 1 page 10 of 79

12 Figure 5: Dimension 3-view representation of the concept aircraft As stated previously, this concept was chosen in order to service the market presented in Section 2. This market is made up of many, small, unimproved, rough, or otherwise challenging airfields and runways that will be used. Also the ability to carry a flexible combination of payload or passengers is a key to the specified market. The design concept presented here was created to be capable of performing these specific tasks set about by the market requirements and the design mission. 3.5 Cabin Layouts Author: Sarah Weise The layout of the cabin interior is essential for sizing an aircraft. This aircraft will be used not only as a passenger transport, but also as a cargo transport. For the cargo aspect of this aircraft s mission, the LD-3 industry standard shipping container was chosen. This container has dimensions of 5 1 by 5 4 by 5 1½. Because of the designated missions of the aircraft, the AAE 451 Group 1 page 11 of 79

13 dimensions of the cabin were dependent on three sizing factors. First, the shipping container size set the cabin height and width for all possible interior configurations. The third and final constraint on the cabin size was the volume per passenger aboard the aircraft. This constraint mainly affected the overall length of the cabin. A graph summarizing passenger comfort is shown in Figure 6. Figure 6: Passenger Comfort 4 This graph shows the relationship between passenger comforts, cubic feet per person, and trip length. The data in this graph was essential in sizing the length of the cabin for certain flights. For a flight of six hours, a goal of 55 ft 3 was set. For shorter flights, 30 ft 3 was acceptable. The pitch of the seats, or the distance between the seats, was also an important factor in designing the interior of the aircraft. However, this value was simply adjusted to meet the volume per person goals. In a few of the layouts that are to be described, a standard lavatory has been included in the floor plan, which is 2 10 by The chosen standard layout included five rows of two seats each. Figure 7 depicts the basic floor plan, including the passenger-only flight option. AAE 451 Group 1 page 12 of 79

14 Figure 7: Passenger Only Configuration Because this configuration does not include a lavatory, it is intended for shorter distance flights. The overall dimensions of the interior were 5 6 by 5 2½ by These dimensions were dependant on the cubic volume per person as described earlier. For a comfortable interior, the passengers had a 36 pitch, and 47.7 ft 3 per person. The cross-sectional area for this configuration is shown in Figure 8. Figure 8: Cabin Cross-Section The cross-section of the cabin interior was sized using the LD-3 shipping containers. Thus, the width and height were dependent on the dimensions of these containers. Because of this, the aisle was calculated to be 26 wide, since the seats were assumed to be 18 wide 3. There were several other configurations chosen for this aircraft. One such alteration to the original design was made so that an executive version could be created. This aircraft included a lavatory, but only had six seats instead of ten. For this case the pitch was 50 and the volume per person was 79.6 ft 3. This option is depicted in Figure 9. AAE 451 Group 1 page 13 of 79

15 Figure 9: Executive Cabin Layout This layout would be used as a more plush setting for high paying customers. This configuration, as with most of the configurations, could also include the lavatory in the back of the aircraft; however, this option has not been depicted here. The reason for the lavatory to be moved to the rear of the cabin is for the comfort of the passengers. Passengers would prefer not having a lavatory directly across from the entrance. Because this configuration included a lavatory, it will be used for longer distance flights such as a 1,200 nm trip. The next configuration for this aircraft was similar to the previous layout, except that it had eight seats instead of six. This configuration would be used as a comfortable flight option for longer trips since it included a 40 pitch and 59.7 ft 3 per person, and a lavatory. While this option was not as plush as the executive version, it was more comfortable than the original layout with ten seats, and would be acceptable as a long range transport aircraft. There were three options for this cabin size including shipping containers. All of the options for this cabin size including shipping containers did not include a lavatory. First, one LD-3 was placed onboard. This option can be viewed in Figure 10. Figure 10: One LD-3 Shipping Container AAE 451 Group 1 page 14 of 79

16 The interior included eight seats with a 34 pitch and 41.2 ft 3 per person, or it included six seats with a 40 pitch and 54.9 ft 3 per person. Another configuration included two LD-3 shipping containers. In this case the pitch was 36. There was enough space for fours seats with 45.4 ft 3 per person. The final configuration for this size of cabin included three LD-3 shipping containers. This configuration is depicted in Figure 11. In this case there was no room for extra passenger seating. 4. Sizing Figure 11: Three LD-3 Shipping Containers Author: Aaron Mayne Conceptual sizing of an aircraft can take into account as few or as many parameters as can be defined about the concept. Most sizing models are based off of historical data sets of existing aircraft. The stages of sizing for this design can be separated into three distinct phases. These phases will be called rough sizing, constraint sizing, and detailed sizing. Each section will be described in detail, and present with some significant findings. During the conceptual sizing process, the concept was defined quantitatively and became a design. 4.1 Rough Sizing During the early stages of this process a rough estimate of the gross weight, empty weight and fuel consumed for the design mission were necessary. For this rough sizing case a simple weight buildup model was created from historical data of existing aircraft used. For this initial sizing, the technique was taken from the text by Dan Raymer 3. This technique used equation (eq. 4.1), and forms of the Breguet Range (eq 4.3) and Endurance equations (eq. 4.3). These three equations made it possible to create a calculation routine to find a basic weight of the aircraft that was being designed. AAE 451 Group 1 page 15 of 79

17 The weight buildup was an iterative process that used several estimated values, approximated both by the design team and from previously designed aircraft. The weight of the aircraft was estimated as, where W 0 = GTOW W crew = weight of the total crew W W payload = weight of the payload or passengers 0 Wcrew + W = W f W 1 W W 0 payload W f = weight of the fuel necessary to complete the mission W e = empty weight of the aircraft. For this and all further sizing it was assumed that a 2 man flight crew would be present on every flight of the design mission. Also, it was determined that each crew member would be given a weight of 200 lbs. The payload weight was determined from the design requirements laid out for the concept. The empty weight was estimated by taking a database of similar mission aircraft and using simple design parameters to create a multivariate regression for this database. This empty weight equation was found by taking the values of range, cruise speed, payload, and takeoff weight from the database and using a least squares method to find an equation that would calculate the empty weight. This regression equation was, lnw = lnV R lnW AR where V cr = cruise velocity R = Range e 0 (4.1) e cr (4.2) AR = Aspect Ratio of the wing. The last piece of the weight breakdown was the weight of the fuel necessary to complete the design mission. The fuel weight was found using the Breguet equations for range and endurance. These equations find the weight change for each portion of the design mission. The design mission was simplified by having takeoff, climb, and landing sections of the design AAE 451 Group 1 page 16 of 79

18 mission use average weight fractions taken from Raymer 3 (Table 3.2, pg. 20). The range equation (eq. 4.3) was used to find the fuel consumption for the cruising section of the design mission. w w i i 1 = e V cr RC L D (4.3) where C = specific fuel consumption L D = Lift to drag Ratio wi w i 1 = weight fraction of before and after the cruise segment. The endurance equation (eq.4.4), used for the loiter sections of the design mission is the similar to the Range Equation, with one exception, E = Endurance time, w w i i 1 = e EC L D which is substituted for the Range over Velocity. The values that were estimated for those two equations were the L/D of 13.8, taken from diagrams in Raymer s 3 book, estimated values from the aircraft database, and the specific fuel consumption values for simple Kerosene turbine fuel. 4.2 Constraint Sizing This stage of the sizing process was completed in order to determine necessary values of parameters for the aircraft. The three major parameters determined from this process were the Wing Loading (W/S), the Power to Weight ratio (P/W) and the Aspect ratio of the wings (AR). These three parameters can describe many things about the size and performance of the airplane. These values effect whether or not the design mission is feasible within the design requirements. (4.4) AAE 451 Group 1 page 17 of 79

19 4.2.1 Constraint Diagram The first step in this process was to create a constraint diagram, which plots the required W/S and P/W necessary to perform mission requirements. This constraint diagram was created originally on general assumptions about the aircraft and its performance. Later on during the design process, it was able to be updated with numbers obtained for parameters such as maximum lift coefficient, climb rates, etc. Figure 12 is the final constraint diagram which gives the possible ranges of P/W and W/S Sealevel Takeoff 5000ft altitude Takeoff on a Hot Day 0.2 Sealevel Cruise Power to Weight Ratio (hp/lb) Wing Loading (lb/ft^2) ft altitude cruise Sealevel Climb ft altitude climb ft cruise Emergency Landing at 5000ft altitude on an Icy Runway Emergency Landing at 5000ft altitude on an Icy Runway With Fuel Dump Option Emergency Landing at 5000ft altitude on a Hot Day Comparison Aircraft Design Points Figure 12: Constraint Diagram The lines on this plot show the feasible design space. The final design point is shown on this constraint diagram, in red, as a comparison to the constraints and existing aircraft. The P/W values need to be above the horizontal curves in order to perform the maneuvers, and the wing loading needs to be below the vertical lines present. These constraints were then transferred to the next step of constraint sizing, carpet plots. From this initial sizing and constraint analysis, it was seen that the best design point had to have a wing loading below 58 lb/ft 2 and a power to weight ratio of at least 0.07 hp/lb. These constraints were then transferred to the next step of constraint sizing, carpet plots. AAE 451 Group 1 page 18 of 79

20 4.2.2 Carpet Plots A carpet plot is a method of comparing P/W, W/S, and AR and their effects on the GTOW. The comparisons made on the carpet plots make it possible to find a best aspect ratio for each wing loading and power to weight ratio. A sample of these carpet plots is shown in Figure 13. This carpet plot contains the final design point of the aircraft. From the constraint diagram, the limiting case for the aircraft being designed seemed to be the climb from sea level. This constraint along with a takeoff, stall, and maximum gross weight constraints were used in order to determine the best design point TOGW Stall FAR 23 GTOW max Sea level Takeoff W/S Climb Rate 5 Sea Level, Takeoff Flight Figure 13: Carpet plot of Aspect Ratio 9 From a series of carpet plots such as this, which are presented in the appendix at the end of this report, a set of minimum GTOW design points were obtained. From these design points the point producing the lowest weight was chosen as the design W/S, P/W, and AR. These design point values are as follows in Table 1. AAE 451 Group 1 page 19 of 79

21 Carpet Plot Design Points Summary AR W/S P/W T/W GTOW Table 1: Summary of least GTOW design points The chosen design point for the least weight is a P/W of and a W/S of These analyses gave the design parameters that were necessary to move forward with other portions of the analysis and a more detailed sizing model. 4.3 Detailed Sizing Detailed sizing for this design project was done using the FLOPS, Flight Optimization System, release With this tool, the aircraft was able to be sized with many separate and specific parameters that make this airplane operational. When using the FLOPS sizing code, the first consideration in the sizing process was that the model was designed to describe large commercial and/or military aircraft. In order to calibrate this sizing model, an input file based on the Cessna Grand Caravan was created to determine the best way the input parameters had to be set to get reliable and correct results from the sizing model. As shown in Table 2 after calibrating the FLOPS sizing model, it produced very reliable outputs for the sizing values. Cessna Grand Caravan Published FLOPS Error Passengers(#) 10 to Range 1 way (leg of Round Trip) (nm) Wing Span (ft) % Length (ft) Height (ft) Wing Area (ft 2 ) % Empty Weight (lbs) % Gross Weight (lbs) % Engine Power (hp) % Max Speed (kts) Normal Cruise (kts) % Stall Speed (kts) Table 2: FLOPS sizing code calibration results Some of the characteristics of the model that were changed were multiplication factors that controlled performance numbers, most importantly the L/D ratio and SFC. Also, some of the AAE 451 Group 1 page 20 of 79

22 weights such as the furnishings group were reduced because the amount of empty weight originally attributed to them didn t make sense for this rugged, simple class of aircraft. Taking this calibrated input file, an accurate sizing model of the design concept was able to be produced. After changing the design point parameters and the design requirements of the aircraft a size and weights estimate was made. Iterations were then made to the input file for the sizing model, as subsystems and parts of the aircraft were more defined. Finally, once all the areas of the aircraft: aerodynamics of the wing and tail, stability of the aircraft, performance of the design propeller, structural makeup of the concept, and performance; the final inputs were run through the sizing model to create up to date design characteristics. In Table 3 a summary of the aircraft design is given as it was finally sized. Design Concept Passengers/Payload 10 or 2000lbs Range 1 way (leg of Round Trip) (nm) 1200 (475) Wing Span (ft) Length (ft) 52 Height (ft) 19.7 Wing Area (ft 2 ) Empty Weight (lbs) 6113 Gross Weight (lbs) Engine Power (hp) 1248 Max Speed (kts) 245 Normal Cruise (kts) 170 Stall Speed (kts) 61 FAA TO Length (ft) 3295 Fuel Capacity (lbs) 3906 Table 3: Final Values of the aircraft sizing code These values represent the size of the aircraft designed around the design requirements laid out for this project. 5. Compliance with Design Requirements Author: Aaron Mayne The aircraft design was based around the accomplishment of specific requirements that would enable it to serve its target market. A comparison of the current characteristics of the design with the requirements points out where improvements still need to be made. Table 4 lists the design requirements as goals and thresholds, and then places where the current value stacks up against these goals. These design compliances are a simple way to judge what has been accomplished and what is still necessary. AAE 451 Group 1 page 21 of 79

23 Goal Threshold Value Payload (lbs) Range, Full Payload (nm) TO Field Length (ft) GTOW (lbs) 12,500 12,432 Max Speed (knots) Acq. Cost ($US2006 millions) $2.5 $3.5 $3.24 DOC ($US2006) $500/hr $424/hr Table 4: Chart displaying compliance with design requirements The majority of the design requirements have been fulfilled. There are a few areas, such as acquisition cost and takeoff performance, which have yet to meet the set goals, and require further work. 6. Structures Author: Jason Olmstead The preliminary structural analysis and design was done using several design resources and techniques. A comparison to existing aircraft, including the Cessna Grand Caravan, was also considered. A representative view of the main structural systems including the wing and tail, the fuselage, and the landing gear will be examined. Finally, the material selection for each structural member will be explained. 6.1 Wing and Tail Shown in Figure 14 is a representation of the interior wing structure and the very similar tail configuration. The tapered wing is modeled very closely to other aircraft of similar size, such as those in the database. The main load-bearing members in the wing are the spars. In this design, there is a main spar and a rear spar which are both shown in green. These members carry the force and moments due to the span-wise lift distribution. Further analysis can be done to decrease the weight of the spar by using a spar-cap and web combination instead of an I-beam or rectangular beam. The spar-cap and web would provide similar strength capabilities but would also reduce the cross-sectional area of the beam, therefore decreasing the weight. The chord-wise pressure and shear distributions on the NACA 4412 airfoil are carried to the spars by the thin wing skin and by the ribs which help to keep the airfoil s shape. These members are shown in yellow in the figure below. The design incorporates ten rib structures on each side for a total of twenty ribs which also help to resist the wing twisting and torsion effects. The stringers are the AAE 451 Group 1 page 22 of 79

24 longitudinal members shown in red. These rods help transmit the skin surface loads to the ribs and spars and stop the skin from bending under high loads. Also shown in the representative figure below are the two fuel tanks, shown in blue (not to scale), which are placed between the spar structures. Figure 14: Interior Wing and tail structures 6.2 Fuselage The fuselage structure (Figure 15) is a semi-monocoque design that consists of 12 rib frames, or bulkheads, which run perpendicular to the longitudinal axis. The fuselage beams, called longerons, along with the stringers, help to stiffen the fuselage skin. The main part of the fuselage includes a keel-type beam that is used to strengthen the fuselage floor for potentially heavy payloads. Initially, two beams were used in the design. The switch to a single beam was made to decrease the structural weight. The entire fuselage structure helps to increase the bending and torsion stiffness of the overall fuselage shape. Figure 15: Fuselage Structure AAE 451 Group 1 page 23 of 79

25 6.3 Landing Gear Figure 16 shows a representation of the aircraft s landing gear arrangement. The landing gear is non-retractable and is configured as a tricycle arrangement. Non-retractable landing gear was chosen for strength considerations for potential rough landings along with the simplicity of the design. Using Raymer s design book along with some online sources, the wheel base was computed to be 17 feet along with a tread length of feet. The main landing gear angle from the ground is close to 51 degrees. Figure 16: Landing Gear 6.4 Material Selection The material selection is a very important part of the structural design process. The aircraft s structural body is entirely comprised of aluminum alloy. The final selection was based on the use of the different alloys for a specific aircraft section or part. All of these aluminum alloys include high strength-to-weight characteristics, high resistance to corrosion, ease of fabrication and a relatively low cost. The materials selected for the structural components and their advantages are summarized in Table 5. AAE 451 Group 1 page 24 of 79

26 Aircraft Section Wing/Tail Structure (Spars, ribs, stringers) Fuselage Structure (Keel beams, ribs, longerons) Wing/tail Skin & Fuselage skin Landing Gear Material Selection Aluminum Alloy ~70, or psi 7150 Aluminum Alloy ~70, or psi 7075 Aluminum Alloy 2090-T83 Yield ApproximateAdvantages StrengthCost Strength, resists corrosion. ~77,000 psi $ /lb $ /lb Up to $10.00/lb Aluminum 60,000 Alloy 2024-T6 70,000 psi $3.00/lb commonly used, low cost Strength, resists corrosion. commonly used, low cost Very high strength, resist corrosion, weight reduction Strength, resists corrosion. commonly used, cheap Disadvantages Fatigue life Fatigue life relatively new material, more expensive Fatigue life Table 5: Materials (Data from Alcoa Inc. Aerospace Materials) For the Wing and Tail structural members alloy 7075-T6, an Al-Zn-Mg-Cu alloy, was used. Introduced in 1943, most aircraft structures have been specified in alloys of this type. A higher-strength alloy in the same series, 7150-T6 (78,000-psi yield strength), was developed in 1951; it has not generally displaced 7075-T6, which has superior fracture toughness. Alloy T6 is used primarily in structural members where performance is critical under compressive loading. Alloy 6061 was selected to create the main structure of the fuselage. Various tempers of this alloy are some of the most widely used alloys in the 6000 series. This standard structural alloy is on of the most versatile and heat-treatable alloys and is popular for medium to highstrength requirements also has good fracture toughness characteristics. This alloy also has excellent corrosion resistance to atmospheric conditions and sea water. This versatile alloy will be a perfect material used for a variety of parts for this aircraft. When making a decision on what material to use for the aircraft skin the following information was used to decide on. aluminum alloy 2090-T83. This sheet metal used for the wing and fuselage skin is a fully commercialized aluminum-lithium alloy developed for many high strength aerospace applications. The Al-Cu-Li alloy offers an 8 percent density savings when compared with other aerospace alloys. This alloy also has a 10 percent higher elastic AAE 451 Group 1 page 25 of 79

27 modulus then average aluminum sheets. When coupled with the low density feature, this provides for unique weight saving benefits. Alloy 2090-T83 has strengths comparable with other high strength aluminum alloys and superior corrosion resistance. This alloy is also one of the easiest aluminum products to weld that is available. The material selected for the landing gear arrangement is a 2024 series aluminum alloy which is a common choice for an aircraft of this size and function. Steel landing gear is also used, but would add to the overall structural weight. The landing gear tires should be selected carefully and should be based on the type of landing or runway conditions. Aluminum alloy 2024 was introduced by Alcoa in 1931 as a sheet in the T3 temper class. It was the first Al-Cu-Mg alloy to have a yield strength approaching 50,000-psi and generally replaced 2017-T4, or Duralumin, as the predominant 2000 series aircraft alloy. With its relatively good fatigue resistance, especially in thick plate forms, 2024 continues to be specified for many aerospace structural applications series alloys, such as higher purity 2124 and 2324, with improvements in strength and other specific characteristics, have also found application in critical aircraft structures. 7. Aerodynamics Author: Joseph Fallon 7.1 Airfoil A NACA 4412 airfoil was used for the wing of the plane. Data for this airfoil was taken from Abbot (p ) 14. From this data, the lift curve slope, clα, the stall angle, α stall angle of attack for zero lift, α L= 0, and the change in angle of attack due to the flap, Δ α flap, the, were estimated. The airfoil drag polar was needed as well. Since the wind tunnel testing was only performed for Reynolds numbers of three, six and nine million, X-Foil was used to estimate the drag polar for higher Reynolds numbers. These results were superimposed over the airfoil data; the results are located in the appendix. 7.2 Drag Polar In order to quantify the aerodynamic performance of the aircraft, a drag polar was needed. A NACA 4412 airfoil was chosen for the wing because it had the highest lift coefficient, c lα. The wing s taper ratio of 0.3 was chosen because it produces the minimum induced drag factor as illustrated in Anderson (p.376 fig 5.18) 6. Also, a twist angle of 3, a AAE 451 Group 1 page 26 of 79

28 typical initial guess (p. 66) 3, was chosen in order to cause the root of the wing to stall first. This twist angle allows control of the ailerons during stall. The stall conditions are the determining factor in the size of the wing. In order to meet FAA regulations, a stall speed of 61 knots was required. A simple slotted flap with a single hinge was decided upon due to its simplicity Lift Estimation A series of calculations was required in order to correctly estimate the lift produced by the wing. The process is outlined as follows. The lift curve slope of the wing was approximated by C Lα = clα 1+ (7.1) (p.100, eq. 4.14) 7 ( 57.3c / πear) The span efficiency factor, e, was estimated by where Λ t max lα 2 e = (7.2) (p.107, eq. 4.15) AR AR 2 ( 1+ tan Λ ) t max = the sweep angle of a line connecting the maximum thickness of the root and tip airfoils. Equation 7.2 produced a span efficiency factor of A similar analysis was performed for the tail with tail properties provided by the stability analysis. The effect of the tail on the lift curve slope was scaled in proportion to the ratio of planform areas of the wing and the horizontal tail. This effect is given in equation 7.3. The scaling factor by ε St ΔCLα = CLαt 1 (7.3) (p.111, eq. 4.22) 7 α S ε accounts for the downwash effect of the wing on the tail. This is given α where ε = α 21 C AR Lα c l h λ z h 1 7 b (7.4) (p.111, eq. 4.21) 7 c l h z h = mean chord of the wing, = horizontal distance between the quarter cord of the root of the wing and tail, and = height of the tail chord from the wing chord. AAE 451 Group 1 page 27 of 79

29 The effect of the flap is estimated by assuming a α L= 0 for the flapped airfoil, α stall for the clean airfoil and a C Lα from the sum of equations 7.1 and 7.3. The results of the lift estimation are shown in Figure 17. CL or cl α ( ) Airfoil Airfoil with Flap Wing Wing and Tail Dirty wing and Tail Figure 17: Lift Curve Slope The wing area required for cruise at 10,000 ft and 168 knots is only 250 ft 2. A wing area of 400 ft 2 was determined from constraint analysis. To allow for a stall speed of 61 knots, a flap area of 91% is required. This means that the flap must extend 25.1 ft from the fuselage. When this wing is evaluated at cruise conditions, a C L of 0.5 is required. This requires a root angle of attack of 1.9. Thus, the aircraft's wing root chord will be inclined by 1.9 from the chord of the fuselage. 7.3 Drag Estimation The drag polar for the airfoil was approximated by a second order polynomial, using two reference points from wind tunnel testing. The drag due to the wing was then estimated by C D 2 ( C / πear) = c + (7.5) d The drag polar of the entire aircraft is given by L 2 CD = CD0 + k1cl + k2 C L (7.6) (p.125, eq. 4.48) 7 where k 1 is given by k1 = 1/( πe0 AR) (7.7) (p.112, eq. 4.27) 7 e 0 is given by AAE 451 Group 1 page 28 of 79

30 ( 0.045AR )( cos Λ ) 3. 1 e 0 = LE (7.8) (p.114, eq. 4.30) 7 Λ LE is the sweep angle of the leading edge. k 2 was found by where k 2 2 1C L min D = k (7.9) (p.115, eq. 4.31) 7 2 ( S S ) k C C = C + (7.10) (p.115, eq. 4.34& 4.35) 7 D0 fe wet / 1 L min D C fe =correction factor to find parasitic drag normalized for wetted area. C values are determined from historical data. A of was used. This came from fe Table 4.1 of Brandt (p.114) 7. C fe The whole-body drag polar for the dirty configuration was determined by subtracting the clean-wing drag from the clean, whole-body drag and adding the dirty-wing drag; the results of this are given in Figure CL Clean (whole aircraft) Dirty (whole aircraft) Clean (just the wing) Dirty (just the wing) C D Figure 18: Drag Polar AAE 451 Group 1 page 29 of 79

31 8. Weight and Stability Author: Becca Dale 8.1 Weight Breakdown The weight of the aircraft as comprised of several different components both in the physical structure of the plane and the interior make up, as can be seen in Table 6. WEIGHT COMPONENT (lbs) WING 825 HORIZONTAL TAIL 48 VERTICAL TAIL 56 FUSELAGE 1244 LANDING GEAR 524 ENGINES 527 FUEL SYSTEM-TANKS AND PLUMBING 130 SURFACE CONTROLS 102 AUXILIARY POWER 338 INSTRUMENTS 107 HYDRAULICS 156 ELECTRICAL 626 AVIONICS 594 FURNISHINGS AND EQUIPMENT 700 AIR CONDITIONING 136 CREW AND BAGGAGE 410 UNUSABLE FUEL 75 ENGINE OIL 17 PASSENGER SERVICE 165 PASSENGERS, 1600 BAGGAGE 400 MISSION FUEL 3651 Table 6: Detailed Weights of the Aircraft All of these weights had varying affects on the balance of the aircraft. Figure 19 demonstrates a detailed description of all of the weights and what percentage of the total weight of the plane they each make up. In addition, Figure 20 shows each of these weights but in a much broader view: structural, propulsion, systems and equipment, operations, payload, and fuel. Both of these figures are shown on the page to follow. AAE 451 Group 1 page 30 of 79

32 Detailed Weight Breakdown 3.2% 29.4% 12.9% 1.3% 0.1% 0.6% 3.3% 1.1% 6.6% 5.6% 0.4% 0.4% 10.0% 4.2% 4.2% 1.0% 0.8% 2.7% 0.9% 1.3% 4.8% 5.0% WING HORIZONTAL TAIL VERTICAL TAIL FUSELAGE LANDING GEAR ENGINES FUEL SYSTEM-TANKS AND PLUMBING SURFACE CONTROLS AUXILIARY POWER INSTRUMENTS HYDRAULICS ELECTRICAL AVIONICS FURNISHINGS AND EQUIPMENT AIR CONDITIONING CREW AND BAGGAGE UNUSABLE FUEL ENGINE OIL PASSENGER SERVICE PASSENGERS, BAGGAGE MISSION FUEL Figure 19: Weight Distribution Overall Weight Breakdown 21.7% Structural Weight 29.4% Propulsion 'Weight Systems and Equipment Weight 5.3% Operating Weight Payload Weight 16.1% 22.2% Fuel Weight 5.4% Figure 20: Generalized Weight Distribution AAE 451 Group 1 page 31 of 79

33 8.1.1 Structural Weight The structural weight makes up 21.7% of the total gross takeoff weight of the aircraft when it is fully loaded with 2,000 lbs of payload. This group is comprised of the weights for the: wing, vertical tail, horizontal tail, fuselage, and landing gears. Figure 21 demonstrates a breakdown of all of these weights and how they play into the total 2,697 lbs of the plane. The structural weight was figured into the empty weight of the plane when calculating the center of gravity, neutral point, and static margin. Structural Weight Breakdown 46.1% 19.5% WING HORIZONTAL TAIL VERTICAL TAIL FUSELAGE LANDING GEAR 2.1% 1.8% 30.5% Figure 21: Detailed Structural Weight Distribution Since the fuselage is the largest portion of the structure of the plane, it naturally is the heaviest, weighing in around 1,244 lbs. The wing is the next heaviest, followed by the landing gear, vertical tail and horizontal tail. All of these weights were calculated using FLOPS, a sizing code for aircraft Propulsion Weight The propulsion weight does not make up a very major portion of the plane since the engine and fuel tanks only weight a total of 657 lbs combined. Of this weight, the majority of it, goes to the engine weight, as can be seen in Figure 22. AAE 451 Group 1 page 32 of 79

34 Propulsion Weight Breakdown 19.7% ENGINES FUEL SYSTEM-TANKS AND PLUMBING 80.3% Figure 22: Weights for the Propulsion System The fuel however, which will be stored in the fuel tanks, as well as running through the engine for power weighs 3,903 lbs, which plays a major role in the gross takeoff weight of the aircraft. The fuel is 29.4% of the overall weight of the plane at takeoff, as can be seen in Figure 20. As the fuel burns throughout the flight, the center of gravity and static margin of the plane both vary. This is all part of the balancing of the aircraft that is discussed later Systems and Equipment Weight The systems and equipment in the plane make up 22.2% of the total GTOW of the aircraft weighing in around 2,759 lbs. This portion of the weight breakdown of the plane is made up of various portions of the plane, with the three largest being furnishings, avionics and electrical wiring and systems. Figure 23 shows a more precise make-up for the systems and equipment portion of the weight estimation. These weights, too, help to determine the stability and balance of the aircraft. AAE 451 Group 1 page 33 of 79

35 Systems and Equipment Weight Breakdown 5.0% 3.7% 12.3% SURFACE CONTROLS AUXILIARY POWER 25.4% 3.9% INSTRUMENTS 5.7% HYDRAULICS ELECTRICAL AVIONICS 21.5% 22.7% FURNISHINGS AND EQUIPMENT AIR CONDITIONING Figure 23: Weights for the Systems and Equipment of the Aircraft Operating Weight For the aircraft to fly, certain additions must be made to the plane, such as a crew to operate the plane in flight. Oil must be added to the engine for it to run properly, as well as fuel. Some of the fuel will remain trapped in the engine after the flight; this is considered the unusable fuel, as it is trapped in the engine, the plumbing, or the fuel tanks. All of these portions of the plane s operating weight add up to a total of 668 lbs. This is not a very major portion of the GTOW, but it still does have an affect, as do all of the weights in the airplane, in the balance and total GTOW. Figure 24, shown below, demonstrates a weight breakdown of the operational weights. As can be seen the crew make up the largest portion of this weight at 61.5% of the operating weight. AAE 451 Group 1 page 34 of 79

36 Operating Weight Breakdown 11.4% 2.6% 24.6% CREW AND BAGGAGE UNUSABLE FUEL ENGINE OIL PASSENGER SERVICE 61.5% Figure 24: Airplane s Operational Weight Payload Weight The payload of the aircraft can range in size from 0 to 2,000 lbs. When the payload is at full capacity of 2,000 lbs it makes up 16.1% of the GTOW of the aircraft. In Figure 25 the payload is demonstrated assuming that there are 10 passengers on-board plus their luggage. A weight of 160 lbs was estimated for each passenger, with a total baggage weight of 400 lbs for all of the passengers combined. The plane is designed to carry storage containers as well, so instead of a passenger configuration, cargo would work as payload too as long as it did not exceed the 2,000 lb design limit. AAE 451 Group 1 page 35 of 79

37 Payload Weight Breakdown 80.0% 20.0% PASSENGERS, BAGGAGE Figure 25: Payload Weights for 10 Passengers plus Baggage 8.2 Stability and Balance The aircraft designed is never in an unstable position. No matter, if the plane is in the air or on the ground it cannot be put into an unstable position with how the weights are distributed. The plane can be loaded with a full load of 2,000 lbs or with out any payload and it will not ever have a negative static margin Weight Locations The weights discussed in the previous section are located throughout the length of the aircraft. Figure 26 shows where the major weights of the airplane are located in relation to each other. The locations of the weights as well as the amount of each weight were used to determine the center of gravity, neutral point, and static margin for the aircraft. AAE 451 Group 1 page 36 of 79

38 Figure 26 Weight Locations on the Aircraft With the weights located in the positions shown in the previous figure, the neutral point of the plane was determined to be ft from the nose of the plane. The neutral point was determined using the values for the aerodynamic center of the wing and the horizontal tail volume coefficient. For this particular plane the aerodynamic center of the wing is located 15 ft from the front of the plane and the volume coefficient for the horizontal tail is Center of Gravity and Static Margin The center of gravity of the aircraft was determined by using the weights diagramed in Figure 26 and their locations relative to the nose of the plane (the datum). The center of gravity of the plane moves throughout the flight as fuel is burned. Figures 27 and 28 demonstrate the distances the center of gravity travels throughout the flight. Figure 27 is for when there are two pilots, whereas, Figure 28 is when there is only one pilot operating the plane. The most the center of gravity ever moves throughout the flight is less than 0.25 inches, as can be seen in Table 7. AAE 451 Group 1 page 37 of 79

39 Center of Gravity Travel with 2 crew members Weight (lbs) lbs 1750 lbs 1500 lbs 1250 lbs 1000 lbs 750 lbs 500 lbs 250 lbs crew only CG Location (ft) Figure 27: Travel of the Center of Gravity with different payloads (2 crew) Center of Gravity Travel with 1 crew memeber Weight (lbs) lbs 1750 lbs 1500 lbs 1250 lbs 1000 lbs 750 lbs 500 lbs 250 lbs crew only CG Location (ft) Figure 28: Travel of the Center of Gravity with different payloads (1 crew) AAE 451 Group 1 page 38 of 79

40 Payload (lbs) CG travel (ft) 2 crew CG travel (ft) 1 crew Table 7: Distance Center of Gravity moves throughout Flight The center of gravity envelope shown in Figure 30 demonstrates that the aircraft never has a negative static margin (center of gravity location, % MAC from datum). The numbers used for the center of gravity envelope are shown in Figure 29 and Table 8. The static margin limits of 5% and 20% were determined from historical data stating that the majority of planes in this size range have a static margin around this point. With the C.G. limits at 5% and 20% this means the center of gravity cannot move forward farther than ft or aft beyond ft. The forward limit can probably be moved forward as much as to ft and the plane would still be stable around 40% static margin, but at this point the plane is becoming very stable and may be hard to control throughout flight. General Weight Breakdown 16.4% 3.4% 30.0% Empty Weight Payload Crew Fuel 50.2% Figure 29: Weights used for the Center of Gravity Envelope AAE 451 Group 1 page 39 of 79

41 Empty Weight 6113 lbs Payload 2000 lbs Crew 410 lbs Fuel 3903 lbs Table 8: Major Weights for C.G. Envelope A Empty airplane A-B fuel is added B-C crew is added C-D payload is added D Takeoff D-E fuel is burned E-F payload is taken off the plane F-A crew gets off the plane Figure 30: CG Envelope AAE 451 Group 1 page 40 of 79

42 The static margin of the plane varies throughout the flight depending on the amount of payload the plane is carrying. Assuming the plane starts off carrying approximately 3,900 lbs of fuel, the static margin of the plane will change up to 3.76% when there is one crew member flying the aircraft and up to 2.87% when there are two crew members operating the plane. These numbers as well as the change in static margin with varying payload weight can be viewed in Table 9. In addition, the static margin is plotted verses the total weight of the plane at varying payloads for both one and two crew members; Figures 31 and 32 demonstrate this. Payload (lbs) SM (%) 2 crew SM (%) 1 crew Table 9: Change in Static Margin for varying Payloads Static Margin Range During Flight with 2 crew Weight (lbs) lbs 1750 lbs 1500 lbs 1250 lbs 1000 lbs 750 lbs 500 lbs SM (%) Figure 31: Static Margin for various payloads (2 crew) AAE 451 Group 1 page 41 of 79

43 Static Margin Range During Flight with 1 crew Weight (lbs) lbs 1750 lbs 1500 lbs 1250 lbs 1000 lbs 750 lbs 500 lbs SM (%) Figure32: Static Margin for various payloads (1 crew) Tail Configuration The design of the tail is a very subjective process which involves often conflicting requirements of the weight, size, center of gravity, static margin, range, and designed aircraft handling properties. To determine the length of the plane first the volume coefficients for the vertical and horizontal tail needed to be decided upon. To determine these values historical data for aircrafts of similar size with a T-tail were investigated. Table 10 shows the values for the sizing of both the horizontal and vertical tails. Veritcal Tail Horizontal Tail distance from AC of v-tail to AC of wing 32 ft distance from AC of h-tail to AC of wing 34 ft v-tail volume coefficient h-tail volume coefficient 0.69 Area of vertical tail 49.4 ft 2 Area of horizontal tail 53.5 ft 2 Table 10: Tail Properties Vertical Tail The vertical tail moment arm (distance from the aerodynamic center of the wing to the aerodynamic center of the vertical tail) was determined by varying the length to obtain a suitable value that did not create a very large static margin as well as a very large wetted area. The larger the wetted area the heavier the tail will get. Figure 33 demonstrates the trend of the length of the moment arm compared to the wetted area required. In addition, Figure 34 shows the trend of the AAE 451 Group 1 page 42 of 79

44 static margin verses the moment arm of the vertical tail. These trends were created by varying the length of the vertical tail moment arm, while keeping the horizontal tail moment arm constant. Vertical Tail Moment Arm verses Area Area (ft 2 ) Moment Arm (ft) Figure 33: Vertical Tail Moment Arm verses Wetted Area AAE 451 Group 1 page 43 of 79

45 Vertical Tail Moment Arm verses Static Margin Static Margin (%) Moment Arm (ft) Figure 34: Vertical Tail Moment Arm verses Static Margin (%) As can be seen by the Figure 33, as the moment arm increases the wetted area required for control surfaces decreases, which creates a lighter tail that helps with stability. Also, in Figure 34 it is noted that as the moment arm increases the static margin for the aircraft decreases. Therefore the design point chosen for the vertical tail moment arm was 32 ft Horizontal Tail The horizontal tail is the determining factor in the length of the aircraft. With a larger moment arm for the horizontal tail, this in turn creates a longer aircraft. Once again, like the vertical tail, when the length of the moment arm is varied it affects the static margin, center of gravity, and wetted area required. Figure 35 shows the horizontal tail moment arm verses the static margin for the plane. Also, Figure 36 demonstrates the values required for the wetted areas for both the vertical tail and the horizontal tail as these values are increased simultaneously. AAE 451 Group 1 page 44 of 79

46 Airplane Length verses Static Margin Static Margin (%) Horizontal Tail Moment Arm (ft) Figure 35: Horizontal Tail Moment arm verses Static Margin (%) Tail Length verses Tail Area Tail Area (ft 2 ) Vertical Tail Horizontal Tail Tail Moment Arm (ft) Figure 36: Tail length verses Wetted Area Required AAE 451 Group 1 page 45 of 79

47 As was the case with the vertical tail, very similar trends take shape. The static margin increases as the tail gets shorter since the control surfaces are depleting. In addition, as the moment arms increase the amount of surface area required begins to decrease. Therefore, the moment arm length required for the horizontal tail was 34 ft. With the vertical tail moment arm length of 32 ft and a horizontal tail moment arm length of 34 ft, the overall length of the plane was determined to be ft Longitudinal Trim The longitudinal trim of the aircraft was determined to ensure the stability of the plane. The center of gravity, aerodynamic center, GTOW, and the distance from the aerodynamic center of the horizontal tail to the center of gravity were all used to determine the lift required by the wing and the horizontal tail. The lift required by the wing and the horizontal tail are 11,909 lbs and lbs respectively. 9. Performance Author: Miguel Alanis Performance analysis was made using equations and concepts from chapter 5 of Brandt 7. This section is comprised of three parts: important performance values, V-n diagram, and operating envelope. 9.1 Performance Values Several important velocities were calculated for the airplane. To reiterate, the aircraft will cruise at approximately 170 knots, as calculated by FLOPS for the design range of 1200 nm. The stall speed is 61 knots and is regulated by FAA regulations; the wing area had to be increased from initial estimates to meet this requirement. The velocity for the maximum glide range was found to be 148 knots, using equations from Brandt 7. The airplane has good climb performance as can be seen from Table 11. In addition to the values in Table 11, there were other values calculated that were not depicted. Among these were the design flight time of 7.10 hrs and 3213 lbs of fuel needed. AAE 451 Group 1 page 46 of 79

48 Parameter Value Units V cruise 170 knots V stall 61 knots V maxgliderange 148 knots γ maxclimb 16.3 deg Climb rate max 46 ft/s Table 11: Tail Properties 9.2 V-n diagram The V-n Diagram depicted in Figure 37 describes the structural limits of the aircraft to create lift for specific maneuvers. The design loading factors were n=3 and n=-1, which are the positive and negative structural limits, respectively. The point on the curved portion of the diagram is the stall speed of the airplane, where the loading factor is n=1. The V-n diagram was computed for a clean configuration at sea level. Figure 37: V-n Diagram, red=normal flight conditions, blue= gusty flight conditions AAE 451 Group 1 page 47 of 79

49 9.3 Operating Envelope Figure 38 shows four constraints that construct the envelope. The blue curves are constant energy heights, computed from equation (5.69) 7. The red line is the stall limit, as set by FAA regulations and equation (5.67) 7. The black curve is the curve defined at velocities and heights where there is no excess power available for acceleration. This was computed using equation (5.70) 7. The orange curve is defined by a structural limit (dynamic pressure tolerance). Finally, the green line is the altitude where the plane will be cruising. Figure 38: Operating envelope, red=stall limit, black=excess power limit, orange=q limit, green=cruise altitude AAE 451 Group 1 page 48 of 79

50 10. Propulsion Author: Tim Block The subject of propulsion as covered in this preliminary design review has three sections. First, the engine selection will be discussed followed by an analysis of the propeller that converts the engine power into thrust. Finally the alternate fuel choice and its impacts on the design will be discussed Engine Selection A single turbine power plant was chosen based on the rubber sized engine approach. Further detailed studies of the aircraft size, weight, and aerodynamics finalized the required power output at 1250 hp. The market for small turbines in the class of 1250 hp is dominated by the very successful PT6A series (see Figure 39) of turbines built by Pratt & Whitney Canada. Screening the PT6A product line narrowed the selection down to the PT6A-67D model that is capable of producing a max. rated power of 1271 shp. For more technical information refer to Table 12, which provides all information based on conventional jet fuel. Figure 39: PT6A Turbine AAE 451 Group 1 page 49 of 79

51 Pratt & Whitney Canada PT6A-67D mech. rated shp 1271 dry weight (lbs) 515 shaft rpm 1700 length (in) 74 Basic HSI (hr) 2000 envelope (in) 19 Basic TBO (hr) 6000 power (lb/hp/hr) overall pressure ratio 10.8 Table 12: Technical facts of the PT6A-67D Based on the selected propeller, and conventional Jet-A fuel in the selected engine, the calibrated FLOPS sizing code estimated the engine thrust specific fuel consumption at lb/lb/hr during cruise Propeller Design A four-bladed variable pitch Hamilton standard propeller with a diameter of 110 in has been selected to convert the power of the engine into thrust. The propeller is aluminium made for both cost and ease of maintenance reasons and will be full feathering and reversible. Detailed technical information including the generated thrust can be found in Tables 13 and 14. The propeller design has been performed in two steps. A preliminary design was carried out using fully empirical formulas 8 based solely on the engine power output. These preliminary design numbers were then compared to the baseline Pilatus PC-12 propeller, which is set to convert a maximum of 1200 shp into thrust. As the numbers corresponded well, these values were used for preliminary design and sizing purposes. The second step involved the use of the formulas from Raymer s textbook 3 and Hamilton Standard propeller efficiency charts. This final design was done in an iterative approach of first comparing different activity factors and blade numbers at the three most significant design points (take off, climb, and cruise) and afterwards comparing propeller dimensions and speeds in order to refine the design further. As all efficiency values from the propeller efficiency charts are for free propellers installation losses were taken into consideration by using assumptions from Raymer s textbook. Hamilton Standard propeller diameter [in] 110 activity factor 140 rpm [1/min] 1700 integrated design CL 0.5 blades [-] 4 max. tip speed [Ma] 0.78 material aluminum Table 13: technical details of propeller AAE 451 Group 1 page 50 of 79

52 flight condition velocity [kn] thrust available [lbf] thrust required [lbf] max. thrust req. thrust static take-off climb cruise Table 14: thrusts and propeller efficiencies 10.3 Fuel Selection After team 1 decided to use a single turbine as the power plant, two choices of alternative fuels were considered. Fischer-Tropsch-based jet fuel (FT fuel) and Soy-Methyl-Ester-based jet fuel (SMT fuel) which both have the capability of replacing current petroleum-based jet fuel. The general characteristics of both alternate fuel types have been described previously in the SDR. Thus emphasis is now put on the performance in the given engine Fischer-Tropsch-based Jet Fuel The impact of FT fuel on the performance of a jet engine is hard to estimate. As of now, there is only one FT fuel employed on a regular basis. This fuel is produced from coal by the Sasol Company in South Africa and has been approved for use in a blend with traditional Jet-A fuel. However, only scarce information on the actual performance of this fuel available. The properties of FT fuels are dependent on the process characteristics and the conventional or renewable resources used to produce the fuel. Conventional resources for this process have tended to be coal, while renewable resources include any of a number of types of biomass. The process characteristics are currently heavily under research and thus may alter fuel specifications until entry of service of the proposed aircraft. There are only very general statements on the impacts of FT fuel available. As a pure generic fuel, it is free of sulphur and has a lack of aromatics, reducing its lubricating quality, but improving emissions. Some sources 9 state that FT fuel has a slightly lower energy content, which if not offset by superior combustion characteristics, it will lead to higher fuel consumption. Tests of FT diesel in piston engines for heavy trucks 10 revealed no changes in fuel consumption, but significant improvements in emissions. The only available FT fuel today has been approved for use in current jet engines under the given regulations. Thus, the performance of FT fuel can be assumed to meet the minimum performance requirements of current Jet-A fuel. AAE 451 Group 1 page 51 of 79

53 Soy-Methyl-Ester-based Jet Fuel SMT fuel commonly known as Bio-Diesel is the second choice of alternate fuel for the proposed aircraft. Recent research conducted at the University of North Dakota 11 indicates significant improvements of the low temperature characteristics making SMT fuel a potential aviation fuel. As the low temperature characteristics of SMT fuel have yet prevented its application in the aviation sector there a no reliable numbers on its performance in gas turbines available. Figures from piston engines 12 indicate a specific fuel consumption penalty of about 15%. Comparing the gravimetric energy content 13 of regular SMT fuel available for piston engines with conventional Jet-A produces a 13.5% lower value for the SMT fuel. A comparison of these fuels can be found in Table 15. Gravimetric Energy Content (BTU/lb) Density (g/cm 3 ) Volumetric Energy content (BTU/gal) Jet A SMT fuel FT Fuel Comparable to Jet A Jet A Comparable to Jet A Table 15: Fuel Properties This leads to the assumption that the fuel consumption of a gas turbine running on SMT fuel will be about the magnitude of 15% higher similarly to the performance in piston engines Conclusion The numbers used in the design process were based on regular Jet-A fuel, which applies to FT fuel. For the case of SMT fuel, a later recalculation will be required as more accurate numbers for this kind of fuel are available. Seeing that it is not currently available for use in gas turbines, it is very likely that the aircraft will have a lower performance while using SMT fuel compared to FT fuel. 11. Cost Author: Sarah Weise Cost of any design is an important issue. The acquisition cost is driven by the development cost along with the manufacturing cost. This acquisition cost is a driving force in the sale of every aircraft. Besides the acquisition cost, other expenses such as direct operating costs are important to customers looking to purchase an airplane. AAE 451 Group 1 page 52 of 79

54 11.1 Acquisition Cost The total purchasing price of this aircraft was determined using a method based off of data from competing aircraft. A trend was found using a least squares method assuming the acquisition cost was a power series function which depended on several key factors. These variables were chosen because they were important factors in the overall cost of an aircraft. These variables were as follows: wing span, aspect ratio, gross take-off weight, shaft horsepower, cruise speed, and range. This power series was assumed to be of the following form: a b c d e f cost = S AR GTOW T V R g (11.1) Where cost = acquisition cost S = wing span AR =Aspect Ratio GTOW= gross take-off weight T = thrust in hp V = cruise velocity R = range a, b, c, d, e, f, and g are all constants solved for using a least squares method. To solve for these constants, the natural log of both side of this equation are found. A vector of all the competing aircraft acquisition costs made up the left hand side of this equation, and a matrix of all of other data made up the right hand side of the equation. When the natural log of the cost vector was divided by the natural log of the remaining data matrix in Matlab, the constants are found. This yielded the following constants: a = b = c = d = e = f = g = AAE 451 Group 1 page 53 of 79

55 From these constants and the values for aspect ratio, etc.; the acquisition cost of the aircraft was found to be $3.24 million (US 2006). This value seems a little bit high for the size and range of the aircraft, but within reasonable limits. This value is acceptable due to the experimental nature of the propulsion system Research, Development, Testing, Evaluation and Flyaway Cost The research, development, testing and evaluation costs, RDT&E, are the costs due to the initial creation of an aircraft. The amount of money spent to develop an aircraft is important to recover within a certain amount of time. For this aircraft a break even point was assumed to be after 200 aircraft would be sold. To estimate the research costs of this aircraft, the DAPCA 3 model outlined in Raymer s Text was used to calculate the acquisition cost, development cost, and flyaway cost. This model consisted of the following equations: This equation (11.2) is the calculation of the engineering hours required for the project. H 7 W V Q E =.07 e (11.2) This equation (11.3) is the calculation of the tooling hours required. H 8 W V Q T =.71 e (11.3) This equation (11.4) is the calculation of the manufacturing hours required. H M = 10.72W e V Q (11.4) This equation (11.5) is the calculation of the quality control hours required. H = (11.5) Q This equation (11.6) is the calculation of the development support costs. C D = 66.0W e V (11.6) This equation (11.7) is the calculation of the flight test costs. C F = W e V FTA (11.7) This equation (11.8) is the calculation of the manufacturing costs. C M = 16W e V Q (11.8) This equation (11.9) is the calculation of the engineering production costs C eng = [0.043T + M 0.969T _ 2228] (11.9) max max + turbine inlet where W e = empty weight AAE 451 Group 1 page 54 of 79

56 V = maximum velocity Q = number of aircraft produced in 5 years FTA = number of flight test aircraft N eng T max = total production quantity times number of engines per aircraft = engine max thrust M max = engine max Mach number T turbine inlet = turbine inlet temperature C avionics = avionics cost Several assumptions were made for these equations. First of all, the number of aircraft to break even was 200 aircraft in ten years. Thus, Q was 100, since that was the number of aircraft sold in five years. This number of aircraft to break even was a conservative estimate for the break even point for this aircraft. Many of the aircraft of this type and class broke even at approximately 200 aircraft as well. Next, two flight test aircraft were used, which was a low number of flight test aircraft; however, since this airplane was so similar to existing aircraft in its design, fewer testing aircraft are needed. Finally, the avionics costs were assumed to be 7% of the flyaway cost. This percentage was set based on the sophistication of the equipment. Since this aircraft did not need highly priced equipment like that of a military fighter, a low percentage was chosen. By combining the above hours with the following wages in US1999, R E R T R Q R M = $86 (Engineering) = $88 (Tooling) = $81 (Quality Control) = $73 (Manufacturing) the total acquisition cost can be calculated. This relation can be seen in the following equation: RDT & E + flyaway = H R + H R + H R + H E D E F T T M M eng M + C + C + C + C N + C (11.10) While this equation was used to calculate an acquisition cost for the aircraft, the results were less than favorable for the competing aircraft. The comparison of the calculated data from the DAPCA model and the actual acquisition costs can be seen in Table 16. eng Q R Q avionics AAE 451 Group 1 page 55 of 79

57 Calculated Cost Real Cost % error Cessna Grand Caravan $2,989, $1,750, % Explorer 500T $3,012, $1,035, % Pilatus PC-12 $4,670, $3,400, % Table 16: Real Cost, Calculated Cost, and Percent Error As can be seen from this table, the DAPCA model did not yield a consistent model for calculating the acquisition cost. This was the reason the model previously described in section 11.1 was used instead of the DAPCA model. This model was inaccurate due to its creation from military data. While the acquisition cost cannot be estimated from the DAPCA model, the research and flyaway costs may still be estimated from this model. These costs were calculated using specific parts of the DAPCA model. These costs were calculated by assuming the development cost was a combination of the engineering costs, tooling costs, development support costs, flight test costs, and engineering production costs. The flyaway cost was a combination of manufacturing costs, quality control costs, manufacturing materials costs, and avionics costs. From these summations, the manufacturing and flyaway costs were calculated. Again, these values were not accurate. However, the fraction of the acquisition cost that was the research cost and the flyaway cost was consistent for each of the competing aircraft. The summary of these fractions is given in Table 17. % Research % Flyaway Cessna Grand Caravan 64.68% 35.32% Explorer 500T 65.30% 34.70% Pilatus PC % 37.96% Table 17: Research and Flyaway Percentages From this the percent of the acquisition cost that was the research expenses was 64% and the flyaway percentage was 36%. From these values, the total research cost was calculated to be $415 million US2006 and the flyaway cost of each aircraft was $1.17 million (US 2006) Direct Operating Cost The direct operating cost, DOC, was again calculated using the DAPCA model. The DOC was a combination of the fuel costs, maintenance costs, material costs, depreciation and insurance. The fuel costs were calculated by assuming that there were 1000 flight hours per year of operation of the aircraft. This number was chosen from the assumption that this aircraft will be used as a commuter transport. The cost of FT kerosene was estimated to be $7.40 per gallon. By combining the SFC, cost of FT kerosene, and flight hours per year, the fuel costs per year AAE 451 Group 1 page 56 of 79

58 were calculated. From here, the maintenance man hours per flight hour was estimated as 1 MMH/FH. This value came from Table 18.1 in Raymer s text. The maintenance labor hourly rates were assumed to be the same as those of the manufacturing hourly rates from the acquisition cost model. The material costs were estimated using the following equation: where C a C e N e material cost FH = aircraft cost minus the engine = cost per engine = number of engines C C = a e N 6 6 e (11.11) The engine cost was assumed to be about $250,000. A rough estimate for this value was acceptable since the model was not exact. The engines for the competing aircraft were assumed to be about the same price. Depreciation was also calculated for this aircraft. This value was assumed to be 10% of the acquisition cost per year. This value is the decrease in value of the aircraft over time. Finally, the insurance costs were estimated as 1% of the total yearly costs. From all of these correlations, the yearly DOC and then the hourly DOC can be calculated. Like the acquisition cost, the calculated DOC was not the same as the real DOC from the competing aircraft data. However, for this case there was a correlation between the calculated value and the real value. This correlation was found to be approximately 64%. Therefore, the real DOC was 64% of the calculated DOC. This calculation was done for the current fuel cost of $2.40 per gallon. Thus, the DOC to be calculated for the aircraft which was designed must first be calculated with standard JetA fuel prices. From this calculation, the DOC for the aircraft was found with standard fuel, and then adjusted according to the increase in fuel prices. The final calculated value for the DOC was found to be $ per hour. This value seems high for a direct operating cost. However, the reason this value is so large is due to the fuel prices. With standard fuel the DOC would be $ per hour. Therefore the extra $ per hour was due to the use of expensive fuel. AAE 451 Group 1 page 57 of 79

59 12. Conclusion Author: Miguel A. Alanis 12.1 Feasibility The preliminary design of the aircraft proposed is feasible since there were no indications in any analysis that pointed to a serious flaw. There were many tools and techniques used in the analysis of the design, and they were all validated using existing information from the benchmark plane, the Cessna Grand Caravan. The rugged and versatile features will do well in markets wishing to reach a rural population. Also, the alternative fuel-based engine will be a key selling point in a society where petroleum is no longer an affordable commodity Open Issues Due to time and knowledge constraints, there were several issues that the team would have liked to explore further but did not get the chance. Among these are the stall characteristics of the T-tail that may be important to the safety of the vehicle in flight. Performance needs to be analyzed at landing and takeoff. Finally, more detail needs to go into the design of the control surfaces of the airplane. AAE 451 Group 1 page 58 of 79

60 13. References [1] Swift, S J. Big Challenges For Little Airliners. Australian International Aerospace Congress. Brisbane, Australia: AIAC, [2] Bahram Dadgostar and Bryan Poulin. Smaller Carriers in Small Markets Better for Customers. Canadian Business Economics. February, [3] Raymer, Daniel P. Aircraft Design : A Conceptual Approach, Third Edition [4] Class Notes, AAE 451, Professor Crossley, Spring 2006 [5] Stanford University. AA 241 A,B Aircraft Design: Synthesis and Analysis. 4 Jan [cited 9 February 2006] [6] Anderson, John D. Fundamentals of Aerodynamics, Third Edition. New York, NY: McGraw-Hill, [7] Steven A. Brandt, Randall J. Stiles, John J. Bertin, Ray Whitford. Introduction to Aeronautics: A Design Perspective AIAA, Inc., Reston, Virginia. [8] Howe, Dennis. Aircraft Conceptual Design Sythesis. London, UK: Professional Engineering Publishing Limited, [9] Bob Saynor, Ausilio Bauen, Matthew Leach. The Potential for Renewable Energy Sources in Aviation. Imperial College, London, UK, 2003, [cited 2 February 2006] [10] Various Authors, Fuel Property, Emission Test, and Operability Results from a Fleet of Class 6 Vehicles Operating on Gas-To-Liquid Fuel and Catalyzed Diesel Particle Filters. SAE International , 2004, [cited 2 February 2006] [11] David Dodds, UND scientists nearing test for new biojet fuel. The Grand Herald Folks, 2006, [cited 21 February 2006] [12] U.S. Bureau of Mines, Twin Cities Research Center, Emissions Characteristics of Soy Methyl Ester Fuels in an Underground Mining Diesel Engine with and without Diesel Oxidation Catalyst Aftertreatmen. National Biodiesel Board, 1994, [cited 24 January 2006] [13] National Biodiesel Board, Biodiesel fact sheets energy content, [cited 27 January 2006] [14] Abbot, Ira H., and Von Doenhoff, Albert E. Theory of Wing Sections. New York, NY: Dover Publications, Inc., AAE 451 Group 1 page 59 of 79

61 14. Appendix 14.1 Database AAE 451 Group 1 page 60 of 79

62 14.2 QFD Matrix AAE 451 Group 1 page 61 of 79

63 14.3 Sample Concepts for Pugh s Method AAE 451 Group 1 page 62 of 79

64 14.4 Tabulated Cabin Layout Specifications Length Width Height Seats Per Row Cabin Size 1 22'10" 5'2.5" 5'6" 2 Option Lavatory Containers Passengers Pitch Volume Per Person 1 yes " 56.8 ft^3 2 no " 47.3 ft^3 3 yes " 41.2 ft^3 4 yes " 54.9 ft^3 5 no " 42.0 ft^3 6 no " 52.5 ft^3 7 yes " 68.0 ft^3 8 no " 45.4 ft^3 9 yes no " 62.1 ft^3 Length Width Height Seats Per Row Cabin Size 2 19'8" 5'2.5" 5'6" 2 Option Lavatory Containers Passengers Pitch Volume Per Person 1 no " 47.7 ft^3 2 yes " 59.7 ft^3 3 yes " 79.6 ft^3 4 no " 41.2 ft^3 5 no " 54.9 ft^3 6 no " 45.4 ft^3 7 no AAE 451 Group 1 page 63 of 79

65 14.4 Tabulated Cabin Layout Specifications (cont.) Length Width Height Seats Per Row Cabin Size 3 16'10" 5'10" 5'6" 3 Option Lavatory Containers Passengers Pitch Volume Per Person 1 yes " 49.3 ft^3 2 yes " 49.3 ft^3 3 no " 37.0 ft^3 4 no " 37.0 ft^3 5 yes " 46.3 ft^3 6 no " 30.9 ft^3 7 yes no " 37.4 ft^3 Length Width Height Seats Per Row Cabin Size 4 18'5" 5'10" 5'6" 3 Option Lavatory Containers Passengers Pitch Volume Per Person 1 yes " 55.0 ft^3 2 yes " 55.0 ft^3 3 no " 41.2 ft^3 4 no " 41.2 ft^3 5 yes " 54.8 ft^3 6 no " 36.5 ft^3 7 yes no " 54.4 ft^3 AAE 451 Group 1 page 64 of 79

66 14.5 Carpet Plots AR= Stall FAR 23 GTOW max 5000ft alt. on a hot day Climb rate 5 Sea Level, Takeoff Flight AAE 451 Group 1 page 65 of 79

67 TOGW AR= W/ S Stall FAR 23 GTOW max Sea level Takeoff Climb Rate 5 Sea Level, Takeoff Flight AAE 451 Group 1 page 66 of 79

68 TOGW (lbs) AR= W in g Lo ading (lbs./sq.ft) Stall FAR 23 GTOW max Sea Level Takeoff Climb rate 5 Sea Level, Takeoff Flight AAE 451 Group 1 page 67 of 79

69 TOGW (lbs) AR= Wing Loading (lbs./sq.ft) Stall FAR 23 GTOW max Sea Level Takeoff Climb rate 5 Sea Level, Takeoff Flight AAE 451 Group 1 page 68 of 79

70 14.6 Propeller Code % AAE451 - Spring 2006 % Tim Block % prop design close all clear all clc format short % --- design values --- V_cr=170*1852/3600; V_to=70*1852/3600; V_cl=110*1852/3600; D=110*2.54/100; n=1700/60; Sc=pi*(0.5)^2; z=4; P0=1250*0.7457; P_clcr=1000*0.7457; S_wet=24*40/ ^2; % imperial units V_cr_i=V_cr* ; V_to_i=V_to* ; V_cl_i=V_cl* ; D_i=D*100/(2.54*12); P0_i=P0/0.7457; P_clcr_i=P_clcr/0.7457; S_wet_i=S_wet* ^2; % key design parameters Pow_load=P0/(pi*D^2/4); % output: V_prop=D*n; % output: % suggested design values z_sugg=0.4*p0^0.35 % output: n_sugg=(433*p0^-0.4)*60 % output: Pow_load_sugg=4.7*P0^0.5 % output: D_sugg=3*(n*D)*P0^0.365*10^(-3) % output: % m / sec % m / sec % m / sec % m % rev per sec % m^2 % number of blades % kw % kw % m^2 % estimated wetted area in prop wash % ft / sec % ft / sec % ft / sec % ft % hp3 % hp % ft^2 % Power disc loading % Blade Tip speeds at static conditions % suggested amount of blades % suggested rpm % suggested power disk loading % suggested prop diameter (m) % 0 ft sea level take off and climb condition T_SL=288.15; % degree K rho_sl= ; % kg / m^3 p_sl=101327; % N / m^2 a_sl= ; % m / sec % imperial units T_SLi=518.67; % degree R rho_sli= ; % slugs / ft^3 p_sli= ; % lb / ft^2 a_sli= ; % ft / sec % ft cruise altitude T_100= ; rho_100= ; p_100= ; a_100= ; % imperial units T_100i= ; rho_100i= ; p_100i= ; a_100i= ; % degree K % kg / m^3 % N / m^2 % m / sec % degree R % slugs / ft^3 % lb / ft^2 % ft / sec % prop tip speeds V_tip=sqrt(V_cr^2+(pi*V_prop)^2); M_tip=V_tip/a_SL % output: % advance ratios J_to=V_to/(n*D); J_to_corr=J_to*( *Sc/D^2) J_cl=V_cl/(n*D); AAE 451 Group 1 page 69 of 79

71 J_cl_corr=J_cl*( *Sc/D^2) J_cr=V_cr/(n*D); J_cr_corr=J_cr*( *Sc/D^2) % max. achievable efficiency (@cruise): eta_max_low=0.82*j_cr_corr^0.4; eta_max_high=(0.82*j_cr_corr^0.16)/(10^(0.3*(log(j_cr_corr))^2.4)); % output: eta_limit=1.8*rho_100*z^0.15*(n*d)^3.7*j_cr_corr*p0^0.095*10^(-7) % output: % approx. cruise efficiency eta_cr_appr=0.59*p0^0.05 % output: % power cp_to=p0*1000/(rho_sl*n^3*d^5) cp_cl=p0*1000/(rho_sl*n^3*d^5) cp_cr=p0*1000/(rho_100*n^3*d^5) % read propeller efficiency from chart: eta_to=0.64; eta_to_corr=eta_to*( /d^2*.0035*s_wet) eta_cl=0.79; eta_cl_corr=eta_cl*( /d^2*.0035*s_wet) eta_cr=0.85; eta_cr_corr=eta_cr*( /d^2*(rho_100/rho_sl)*.0035*s_wet) % thrust ct_stat=0.0085*z^0.15*(p0/(pi*d^2/4))^0.65*( /d^2*.0035*s_wet) % output: T_st=cT_stat*rho_SL*n^2*D^4; T_st_lb=T_st/9.81* % output: lb T_to=eta_to_corr*P0_i*550/V_to_i ct_to=t_to/(rho_sli*n^2*d_i^4) T_cl=eta_cl_corr*P0_i*550/V_cl_i ct_cl=t_cl/(rho_sli*n^2*d_i^4) T_cr=eta_cr_corr*P0_i*550/V_cr_i ct_cr=t_cr/(rho_100i*n^2*d_i^4) T_cr_appr=eta_cr_appr*P0*1000/V_cr; % T_cr=eta_cr_appr*P0*1000/(J*n*D) T_cr_appr_lb=T_cr_appr/9.81* ; % output: % fuel consumption assumptions sfc_p_sugg_metr=2.88*( *p0*10^(-3))*(1-0*0.2*v_cr/a_100); sfc_p_sugg=sfc_p_sugg_metr/9.81* *0.7457; % output: sfc_t_sugg_metr=(v_cr/a_100)*(rho_100/rho_sl)^0.117*( *p0*10^(-3))*(1-0.2*v_cr/a_100)/eta_cr_appr; sfc_t_sugg=sfc_t_sugg_metr/9.81* *0.7457; % output: Performance Code %Miguel Alanis %AAE 451 Senior Design %Performance and Constraint Analysis %Spring 2006 clear clc %******************THRUST CURVE********************************** %Variable Definitions (ALL IN ENGLISH UNITS) Np=.825; %Taken from Assumption on pg 143 of Brandt TSFCsl=.1604; %Propeller Assumptions from Raymer pgs ESHP= 1670*550; %Effective Shaft Power (sea level) V=100:.1:400; %Velocity (ft/s) W=12432; %GTOW lbs rhosl=.00237; %density at sea level rho1= ; %density at 1000 ft rho2= ; %density at 5000 ft rho3= ; %density at ft AAE 451 Group 1 page 70 of 79

72 %******************TSFC CURVE********************************** ctsl=tsfcsl; Tsl=518.69; T=linspace(518.7,483.1,1791); ct=ctsl.*sqrt(t./tsl); h=linspace(0,10000,1791); figure(1) plot(h,ct) grid on xlabel('altitude (ft)') ylabel('thrust-specific Fuel Consumption') title('tsfc vs Altitude for Turboprop Engine') %******************POWER CURVES********************************** rho=rhosl.*exp(-(32.2./1716./t.*(h-h(1)))); V1=linspace(100,500,1791); S=397.2; q=.5.*rho.*v1.*v1; qmax=1.1.*.5.*rhosl.*v1(length(v1)).*v1(length(v1)); CL=W./q./S; k1= ; k2= ; CD0=0.0191; CD=CD0+k1.*CL.*CL+k2.*CL; Tr=CD.*q.*S; Pr=Tr.*V1.* ; figure(2) Pa=ones(size(Pr)); Pa=Pa*1248; plot(v1.* ,pr,v1.* ,pa,'--') grid on legend('power Required','Power Available') xlabel('true Air Speed (knots)') ylabel('power Required (hp)') title('required Power vs Speed for Turboprop Engine') figure(3) Ta=ESHP.*(rho(length(rho))/rhosl).*Np./V1; %Available Thrust plot(v1.* ,tr,v1.* ,ta,'--') grid on legend('thrust Required','Thrust Available') xlabel('true Air Speed (knots)') ylabel('thrust Required (lbs)') title('required Thrust vs Speed for Turboprop Engine') Msl=V./1116.4; M1=V./1112.6; M2=V./1097.1; M3=V./1077.4; %*********************** nmax vs velocity curve******************** figure(4) CLMAX=2.48; nmax=clmax.*rho(length(rho)).*s.*v1.*v1./2./w; plot(v1.* ,nmax) grid on xlabel('true Air Speed (knots)') ylabel('nmax') title('nmax vs air speed') %********************PERFORMANCE OUTPUTS****************************** display('vstall, in knots') Vstall=sqrt(2*W/rhosl/S/CLMAX)* Vstallfe=sqrt(2*W/rhosl/S/CLMAX)* AAE 451 Group 1 page 71 of 79

73 display('maximum Glide Range Velocity, in Knots') CLmgr=0.629; %CL at MAX L/D qmgr=w/clmgr/s; Vmgr=sqrt(2*qmgr/rho(length(rho)))* display('maximum Angle of Climb, in degrees') gamma=asin( max(ta-tr)/w)*180/pi display('maximum Rate of Climb, in ft/sec') RATE_ OF_CLIMB=max(Pa-Pr)*550/W display('endurance (hr) and Max Range (nautical miles)') Wfdot=450* ; %lbs/hr (N/s) c=wfdot/(1248* ) CLe=sqrt(3*CD0/(k1+k2)) CDe=CD0+k1.*CLe.*CLe E=(Np/c)*((CLe^(1.5))/CDe)*(sqrt(2*rho(length(rho))* * *S))*((( *8781) ^(-.5))-(( *W)^(-.5)))/3600 Range=(Np/c)*17*log(W/8781)* %******************OPERATING ENVELOPE***** ***************************** He=linspace(500,11000,7); V2=linspace(1,800,1791); %Energy heights (ft) for j=1:length(he), hfl(j,:)=he(j)-v2.*v2/2/32.2; figure(5) hold on plot(v2.* ,hfl(j,:),'--') end grid on xlabel('true Air Speed (knots)') ylabel('altitude and Energy heights') title('ps Diagram') %constant energy height curves V_STALL=sqrt(2*W./rho./CLMAX./S)* ; figure(5) hold on plot(v_stall,h) hmax=v2./v2.*10000; plot(v2.* ,hmax,'--') V_q=sqrt(2.*qmax./rho)* ; plot(v_q,h) V_p= *(2*550*1248./CD./S./rho).^(1/3); plot(v_p,h) 14.7 V-n Diagram Code % V-n Diagram % Becca Dale % AAE 451 clear all close all clc n_max_pos = 3.0; %max positive g-loading n_max_neg = -1.0; %nax negative g-loading n_positive = 0:(n_max_pos/200):n_max_pos; %range of positive structural g-loading n_negative = 0:(n_max_neg/200):n_max_neg; %range of negavtive structural g-loading rho10000 = ; %air density at 10,000 ft slugs/ft^2 rhosl = ; %air density at sea level slugs/ft^2 V_stall = 61; %kts velocity at stall (occrus when N_positive=1 V_cruise = 170; % cruise velocity V_dive = V_cruise*1.5; %dive velocity W_S = 31.3; %wing loading CLmax = 2.48; %CLmax AAE 451 Group 1 page 72 of 79

74 V_e = sqrt(rho10000/rhosl)*v_cruise; %equivalent velocity c_bar = 6.66; CLalpha =.0908; V_corner = 129.5; V_neg = 104.5; V1 = 0:(V_corner/200): V_corner; V2 = 0:(V_neg/200):V_neg; %9E-05x x n_plus =.0001.*V1.^ *V1; %-4E-05x x n_minus = *V2. ^ *V2; NPOS = [n_max_pos n_max_pos]; V_1 = [V_corner V_dive]; NNEG = [n_max_neg n_max_neg]; V_2 = [V_neg V_cruise]; V_3 = [V_dive V_dive]; N_3 = [n_max_pos 0]; V_4 = [V_cruise V_dive]; N_4 = [n_max_neg 0]; %Ude = [ ]; Ude = [ ]; upos = (2*W_S)/(rho10000*32.2*c_bar*CLalpha) %mass ratio positive uneg = (2*W_S)/(rho10000*32.2*c_bar*CLalpha) %mass ratio negative Kpos = (.88*upos)/(5.3+upos) Kneg = (.88*uneg)/(5.3+uneg) U1 = Kpos.*Ude U2 = Kneg.*Ude Vg = V_corner+12; % n1 = (1+(rho10000*U1(1)*(Vg*1.688)* CLalpha)/(2*W_S)) n1 = n_max_pos+(rho10000*ude(1)*(vg* 1.688)*CLalpha)/(2*W_S) n2 = n_max_pos+(rho10000*ude(2)*(v_cruise* 1.688)*CLalpha)/(2*W_S) n3 = n_max_pos+(rho10000*ude(3)*(v_dive*1.688)*clalpha)/(2*w_s) n4 = n_max_neg+(rho10000*ude(1)* (Vg*1.688)*CLalpha)/(2*W_S) n5 = n_max_neg+(rho10000*ude(2)*(v_cruise*1.688)*clalpha)/(2*w_s) n6 = 0+(rhoSL*Ude(3)*(V_dive*1.688)*CLalpha)/(2*W_S) ngplus = [1 n1 n2 n3]; ngminus = [1 n4 n5 n6]; Vgust = [0 Vg V_cruise V_dive]; gustp = [ ]; gustn = [ ]; plot(v1,n_plus,'r',v2,n_minus, 'r',v_1,npos,'r',v_2,nneg,'r',v_3,n_3,'r',v_4,n_4,'r',v_stall,1,'k* ') hold on %plot(0,1,'b-',vg,n1,'b-',v_cruise,n2,'b-',v_dive,n3,'b-',vg,n4,'b-',v_cruise,n5,'b- ',V_dive,n6,'b-') plot(vgust,gustp,'b:',vgust,gustn,'b:') %plot(vgust,ngminus,'b:',vgust,ngplus,'b:') title( 'V-n Diagram'); xlabel('velocity (kts)'); ylabel('load'); grid on % hold off AAE 451 Group 1 page 73 of 79

75 14.8 Competing Aircraft Data Acquisition Wing Aspect Gross Takeoff Cruise Aircraft Cost Span Ratio Weight Thrust Speed Range Cessna 208 caravan Cessna 206B Super Cargo Master TMB 700C Explorer 500T G 140TP Ranger G PA TP Meridian Beech King Air Beech King Air B Beech King Air C90GT Beech 1900D P.180 Avanti II Ae AP68TP-600 Viator PAC 750XL PC-12/ Yun-12 (Y-12) AAE 451 Group 1 page 74 of 79

76 14.9 Cessna Grand Caravan FLOPS Calibration.in file Caravan.in CARAVAN EXAMPLE for AAE 451, Spring 2006 Run a full analysis including costs - caution, costs probably not be accurate for single piston, use IFITE=2 $OPTION IOPT=1, IANAL=3, ICOST=1, IFITE=2, $END Enter fuselage dimensions assume all pax are first class, use one fuselage-mounted engines Tails are specified with volume coefficients and default parameters $WTIN ULF=3., WF=5.2, DF=4.3, XL=41.6, XLP=16.7, FPITCH=36., NFABR=2, TPITCH=36., NTABR=2, NEW=0, NEF=1,WENG=350, FULWMX=23.,NPF=0, NPT=10, NFLCR=2, NSTU=0, NGALC=0, CARGF = 0., CARGOF=0., FRLGN=75, FRLGM=175, WELEC=450, WAVONC=400, WFURN=700, FLAPR=.98, FSTRT = 1, DIH=3, FULWMX=13., WPPASS =160., $END Maintain constant wing loading, thrust/weight ratio, and modified tail volume coefficients - note: coefficients should be checked $CONFIN GW=8750, DESRNG=907., AR=9.555, WSR=31.3, TWR=.15168, TCA=.145, TR=.586, SWEEP=2, HTVC=0.975, VTVC=0.1, VCMN=0.2712, CH=25000., $END Moderate technology wing $AERIN CAM=.04, AITEK=1.0, FLTO=1365., FLLDG = 950., CLTOM=1.8, CLLDM=1.8, FCLDES=.629, FMDES=.277, $END Calculate cost information, starting development year 2006, fuel price Feb 2006 use 100 percent first class seating, production run 300 a/c $COSTIN DEVST=2006., DYEAR=2006, FUELPR=7. 50, NPOD=1, PLMQT=2014., Q=300., IWIND = 1, PCTFC = 100, SFC =.64, $END Generate engine deck in cycle analysis module and extrapolate to get consistent flight idle data $ENGDIN IDLE=1, IGENEN=1,FFFSUB=1.2, MAXCR=1, NGPRT=0, $ END Generate an internal combustion engine, use propeller input info $ ENGINE IENG=4, IPRINT=0, OPRDES=29.5, TETDES= ,ETAPRP=.8,FHV= ,SHPOWA=60.0, YEAR=2006, SFCMAX=.64, $END Size aircraft for specified range, fly minimum fuel-to-climb, optimum altitude for cruise Mach, and max L/D descent $MISSIN FCDSUB=1.065, IFLAG=2, IRW=1, TAXOTM=10., TAKOTM=0.4, TAXITM=10., TIMMAP=5., CLMMIN=.2, RCIN = 100., CRALT=10000, DEMMIN=.12, ITTFF=1, FWF=-1., RESRFU=0.05, THOLD=.05, $END START CLIMB CRUISE DESCENT END AAE 451 Group 1 page 75 of 79

77 14.10 Final Design FLOPS.in file FinalDesign.in SINGLE TUROBOPROP Aaron Mayne, Team 6 for AAE 451, Spring 2006 Run a full analysis including costs - caution, costs probably not be accurate for single piston, use IFITE=2 $OPTION IOPT=1, IANAL=3, ICOST=0, IFITE=2, $END Enter fuselage dimensions assume all pax are first class, use one fuselage-mounted engines Tails are specified with volume coefficients and default parameters $WTIN ULF=3, WF=5.5, DF=5.2, XL=52, XLP = 22.83, FPITCH=36., NFABR=2, TPITCH= 36., NTABR=2, NEW=0, NEF=1,WENG=530, EEXP=1 FULWMX=15.,NPF=0, NPT=10, NFLCR=2, NSTU=0, NGALC=0, CARGF = 0., CARGOF=0., WFURN=700, FLAPR=.98, FSTRT = 1,FCOMP=0, WPPASS =160., CGW=178.08, CGHT=415.62, CGVT=365.01, HHT=1,SHT=54.0, ARHT=5, TRHT=.6, SVT=49.7, ARVT=1.2, TRVT=.6, SWPVT=55., $END Maintain constant wing loading, thrust/weight ratio, and modified tail volume coefficients - note: coefficients should be checked $CONFIN GW=12500, DESRNG=1200., AR=9, WSR=31.3, TWR=.3, TCA=.12, TR=0.3, SWEEP=0, HTVC=0.69, VTVC=0.0665, VCMN=.29, CH=10000, $END Moderate technology $AERIN CAM=.04, wing AITEK=1.5,VAPPR=77.1, FLTO=2000., FLLDG = 2000., CLTOM=2.48, CLLDM=2.48,FCLDES=.629, FMDES=.277, $END Calculate cost information, starting development year 2006, fuel price Feb 2006 use 100 percent first class seating, production run 300 a/c $COSTIN DEVST=2006., DYEAR=2006, FUELPR=7.50, NPOD=1, PLMQT=2014., Q=300., IWIND = 1, PCTFC = 100, SFC =.546, $END Generate engine deck in cycle analysis module and extrapolate to get consistent flight idle data $ENGDIN IDLE=1, IGENEN=1,FFFSUB=1. 2, MAXCR=1, NGPRT=0, $ END Generate an internal combustion engine, use propeller input info $ENGINE IENG=4, IPRINT=0, OPRDES=29.5, TETDES=2660.0,ETAPRP=.8,FHV= ,SHPOWA=60.0, YEAR=2006, $END Size aircraft for specified range, fly minimum fuel-to-climb, optimum altitude for cruise Mach, and max L/D descent $MISSIN FCDSUB=1.065, IFLAG=2, IRW=1, TAXOTM=10., TAKOTM=0.4, TAXITM=10., TIMMAP=5., CLMMIN=.2, IOC=3, CRALT=10000 DEMMIN=.12 ITTFF=1, FWF=-1., RESRFU=0.05, THOLD=45, $END START CLIMB CRUISE DESCENT END AAE 451 Group 1 page 76 of 79

78 Rerun sized aircraft for shorter range with existing weights, wing, and engine $ RERUN mywts=1, wsr=0., twr=0., $END Use same mission excep t for design range above Turn off detailed segment output $MISSIN FCDSUB=1.35,IFLAG=0, IRW=2, TAXOTM=10., TAKOTM=0.4, TAXITM=10., TIMMAP=5., CLMMIN=.2, NCRUISE=1, IOC=3, DEMMIN=.12, ITTFF=1, FWF=-1., RESRFU=0.05, THOLD=45, CRALT=10000., NSOUT=2, NSADJ=2, MIRROR=8, $END START CLIMB CRUISE COMBAT COMBAT COMBAT COMBAT CLIMB CRUISE 1 DESCENT END Stability Code % Center of Gravity calculation and Static Margin % Becca Dale clear all close all clc We = 6113; %total empty weight of plane Wfuel = 3903; %weight of fuel Sw = 397.2; %ft^2 exposed planform area of wing bw = 59.79; %wing span c_ bar = 6.64; %mean chord for wing c_ ht = 3.34; %mean chord for h-tail %weights Wwing = 825; %weight of wing Whtail = 48; %weight of horizontal tail Wvtail = 56; %weight of vertical tail Wfuselage = 1244; % weight of fuselage Wland = 525/3; %weight of landing gear Wengine = 1.35*527; %weight of engine Wfueltanks =.7*130; %weight of fuel tanks Wfplumbing =.3*130; %weight of plumbing for fuel tanks to the engine Wsurface_ctrl = 102; %surface controls Winstraments = 107; %weight of intramentation Wavionics = 594; %weight of avionics W ac = 136; %weight of air conditioning unit Wunusable = 75; %weight of unusable fuel Woil = 17; %weight of engine oil Wcrew = 410; %Weight of Crew Wpayload = 2000; %weight of passengers/payload GTOW = We+Wfuel+Wcrew+Wpayload; %Take off Gross Weight % GTOW = 12432; t=wfuselage+3*wland+wwing+wengine+wvtail+whtail+wavionics+wfueltanks+... Wfplumbing+Wac+Winstraments+Wfuel+Wpayload+Wcrew+Wunusable+Woil+... Wsurface_ctrl; Welse = GTOW-t; w = 15.0; %Xac le = w-(c_bar*.25); %leading edge te = w+(c_bar*.75); %trailing edge AAE 451 Group 1 page 77 of 79

79 % ******************************************************************* %tail configuration %moment arms - distance from c/4 of wing to c/4 of tail Lvt = 36; %vertical tail moment arm from Htail c/4 to wing c/4 Lht = 38; %horizontal tail moment arm from Htail c/4 to wing c/4 Cht =.69; %horizontal tail volume coefficient Cvt =.0665; %veritcal tail volume coefficient Svt = (Cvt*bw*Sw)/Lvt %ft^2 exposed planform area of vertical tail Sht = (Cht*c_bar*Sw)/Lht %ft^2 exposed planform area of horizontal tail % ******************************************************************* L = w+lht+( c_ht*.75); %ft length of fuselage % components multiplied by their distance from the nose of the plane % then divided by the total weight of the plane to find CG in x-direction % datum that distance fractions are taken from is from nose of plane % +Wpayload*(17.4/L) Wcrew*(9.5/L)+ +Wfuel*((w+1)/L) num_takeoff = Wcrew*(9.5/L)+Wland*(6/L)+Wpayload*(17.4/L)+Wfuselage* Wwing*(w/L)+2*Wland*(23/L)+Wengine*(3/L)+Wvtail*((w+Lvt)/L)+Woil*(3/L)+... Whtail*((w+Lht)/L)+Welse*((17.0)/L)+Wavionics*(6/L)+... Wfplumbing*((w-8)/2)/L+Wac*(6/L)+Winstraments*(4/L)+Wunusable*(5/L)+... Wsurface_ctrl*(w+12)/L+Wfueltanks*((w+1)/L)+Wfuel*((w+1)/L); num_land = Wcrew*(9.5/L)+Wland*(6/L)+Wpayload*(17.4/L)+Wfuselage* Wwing*(w/L)+2*Wland*(23/L)+Wengine*(3/L)+Wvtail*((w+Lvt)/L)+Woil*(3/L)+... Whtail*((w+Lht)/L)+Welse*(( 17.4)/L)+Wavionics*(6/L)+... Wfplumbing*((w-8)/2)/L+Wac*(6/L)+Winstraments*(4/L)+Wunusable*(5/L)+... Wsurface_ctrl*(w+12)/L+Wfueltanks*((w+1)/L)+.1*Wfuel*((w+1)/L); m = GTOW; cg_takeoff = num_takeoff/m*l % ******************************************************************* xac = w; %aerodynamic center of plane xn = xac + Cht*c_ht %neutral point SM_takeoff = (xn - cg_takeoff)/c_bar %static margin at takeoff %SM_land = (xn - cg_land)/c_bar % ******************************************************************* %folling are calculations to be used for cg envelope diagram cg_1 = (num_takeoff); cg_2 = (num_takeoff-wpayload*(17.4/l)); cg_3 = (cg_2-wcrew*(9.5/l)); cg_4 = (cg_3-wfuel*((w+1)/l)); cg_5 = (num_takeoff-wfuel*((w+1)/l)); cg_6 = (cg_5-wpayload*(17.4/l)); cg_7 = (cg_6-wcrew*(9.5/l)); cgs = [cg_4 cg_3 cg_2 cg_1 cg_5 cg_6 cg_7]; SM2 = (xn - (cg_ 2/(GTOW-Wpayload)*L))/c_bar; %static margin w/fuel and crew SM3 = (xn - (cg_3/(gtow-wcrew-wpayload)*l))/c_bar; %static margin w/fuel SM4 = (xn - (cg_4/(gtow-wpayload-wcrew-wfuel)*l))/c_bar; %static margin empty SM5 = (xn - (cg_5/(gtow-wfuel)*l))/c_bar; %static margin w/payload and crew SM6 = (xn - (cg_6/(gtow-wfuel-wpayload)*l))/c_bar; %static margin w/crew SM7 = (xn - (cg_7/(gtow-wpayload-wcrew-wfuel)*l))/ c_bar; %static margin empty W_1 = We; W_2 = W_1+Wfuel; W_3 = W_2+Wcrew; W_4 = W_3+Wpayload; W_5 = We+Wcrew; W_6 = W_5+Wpayload; SMS=[SM4 SM3 SM2 SM_takeoff]; Ws=[W_1 W_2 W_3 W_4]; flight = [SM_takeoff SM5 SM6 SM7]; Wf = [W_4 W_6 W_5 W_1]; AAE 451 Group 1 page 78 of 79

80 % r = MAC4-.15; r =.05; fl = [r r r r]; %forward cg limit % k = MAC4+.3; k =.2; al = [k k k k]; %aft cg limit %figure(1) plot(sms,ws,'c-',sms,ws,'gs',fl,ws,'r--',al,ws,'r--'xlabel('c.g. location, %M.A.C. from datum'); ylabel('gross Weight'); title('center of Gravity Envelope Diagram Loading the Plane'); hold on %figure(2) plot(flight,wf,'b-',flight,wf,'b*',fl,ws,'r--',al,ws,'r--'); xlabel('c.g. location, %M.A.C. from datum'); ylabel('gross Weight'); title('center of Gravity Envelope Diagram Unloading the Plane'); %figure(3) % ******************************************************************* % Longitudinal Trim Mac = 0; %moment about aerodynamic center of wing xcg = cg_takeoff; %center of gravity of plane lt = Lht+(xac-xcg); %distance from aerodynamic center of h-tail to xcg R = [1 1;(xcg-xac) -lt]; K = [GTOW;Mac]; M=R^(-1); load_required=m*k; %answers: L & Lt NACA 4412 Airfoil Data AAE 451 Group 1 page 79 of 79