SIZING MATRIX AND CARPET PLOTS

Transcription

1 1. Introduction SIZING MATRIX AND CARPET PLOTS Serkan Özgen, Prof. Dr. Middle East Technical University, Dept. Aerospace Eng., Turkey Aircraft design is an intellectual process that combines engineering knowledge, creativity and art. For this reason, in major companies aircraft design work is undertaken by Integrated Product Teams (IPTs) consisting of engineers, technicians, industrial design experts, managers each with different backgrounds and even cultures. Therefore, aircraft design is not done by one person aimed at a single goal but rather is an activity with multiple objectives. A successful design is technically sound, feasible, affordable, safe, reliable and aesthetically pleasing. When one looks at the History of Aviation and the airplanes that have become benchmarks like the Douglas DC-3, Cessna 17, Supermarine Spitfire, McDonnell Douglas F-4 and others, one notices that these were not the fastest airplanes of their class, nor they were the ones carrying the heaviest payload, nor they were the cheapest or aesthetically the most pleasant. These airplanes were a good combination of technical soundness, feasibility, affordability, safety, reliability and aesthetics built around realistic requirements. Those were optimum airplanes designed at the right time at the right place. Therefore, the task of a designer is to create a flying machine that is technically sound, safe, reliable, feasible and affordable. These objectives is to be kept in mind from the very beginning, namely the conceptual design phase. However, the designer is immediately faced with contradicting requirements to meet these objectives. For example a very safe airplane will probably not be feasible or affordable. Likewise, an airplane with a high technological level will be very expensive. This brings us to the concepts of trade and optimization. A good design is an efficient compromise of performance, safety, reliability, cost and aesthetics. This manuscript aims at outlining the basics of optimization of the performance and the weight of a light sportive airplane. The simple methodology explained is most relevant for the conceptual design phase where sizing and performance calculations constitute the major task. A well-optimized airplane is less likely to encounter unsurmountable weight and cost increases and performance deficiencies as the design progresses into preliminary and detail design phases. The four main ingredients of the presented method are weight estimation, aerodynamics, installed thrust and performance. 1

2 . Requirements Each airplane is designed around a set of requirements. The key to the success of a design is a set of realistic and consistent requirements. The requirements involve purpose and operation of the aircraft, performance characteristics like speed, range, rate of climb, etc., and also mission characteristics like payload, low observability, etc. The requirements may be set by the customer, by safety and certification requirements or a combination of both. The sizing process in the conceptual design phase is usually driven by performance requirements. The requirements for the light sport aircraft for the VKI Short Course: UAVs & Small Aircraft Design are given in Table 1. In addition to these customer requirements, the designer may utilize additional requirements specified in the Certification Specifications. For this airplane, the EASA Certification Specifications that may be applicable are: CS-3: Certification Specifications for Normal, Utility, Aerobatic and Commuter Category Aeroplanes [1]; CS-VLA: Certification Specifications for Very Light Aeroplanes []; CS- LSA: Certification Specifications and Means of Compliance for Light Sport Aeroplanes [3]. Also FAR-3: Airworthiness Standards: Normal, Utility, Acrobatic, and Commuter Category Airplanes [4] is applicable. Relevant CS and FAR performance requirements are given in Table. In the current study, the light sport airplane will be designed and optimized according to the customer requirements but the final optimized design will be checked against CS and FAR requirements as well. It should be noted that CS-3 and FAR-3 are applicable to Normal, Utility, Aerobatic and Commuter Category airplanes. Normal, Utility and Aerobatic Category airplanes are those with a certified maximum take-off weight of 5670 kg (1500 lb) or less, and those having a seating configuration, excluding the pilot seats of nine or fewer. Commuter Category refers to propeller-driven twin engine aeroplanes that have a seating configuration, excluding the pilot seats of nineteen or fewer and a certified maximum take-off weight of 8618 kg (19000 lb) or less. Certification Specifications for Normal, Utility and Aerobatic category is further divided into two subcategories, namely airplanes heavier or lighter than 7 kg (6000lb). Certification requirements differ slightly between these three categories and only those specifications corresponding to Normal, Utility and Aerobatic Category airplanes for a certified maximum take-off gross weight of 7 kg or less with a single reciprocating engine are included in Table because the Light Sport Aircraft designed according to the requirements in Table 1 falls into this category due its weight, calculated below.

3 Table 1. Design requirements for the VKI Short Course: UAVs & Small Aircraft Design. Definition Light Sport Aircraft General Number of engines 1 Occupants (80 kg each) Performances Optimized for Cruise Speed range (km/h) 80 Altitude (m) 400 Range (km) 1000 Rate of climb (m/s) > 5 Take-off run (m) < 300 Stall speed (km/h) < 100 Useful weight Luggage/crew member (kg) 10 Miscellaneous Comfortable Green Safe Cheap Definition Applicability Maximum take-off weight Number of engines Type of engine Table. EASA and FAA design requirements and specifications for Normal, Utility, and Aerobatic Category airplanes (Wo 7 kg/6000 lb, single reciprocating engine category only). Number of crew Max. number of seats Performances Stall speed, VSO 1 Rotation speed, VR Climb speed (@15m/50ft height), VCL Climb rate or VCL Approach speed, VA Climb VA FAA FAR-3 7 kg one reciprocating 9 61 kt VS1 1.VS1 8.3 % 1.3VSO 3.3 % EASA CS-3 7 kg one reciprocating km/h VS1 1.VS1 8.3 % 1.3VSO 3.3 % EASA CS-VLA 750 kg one spark or compression ignition 0 83 km/h 1.3VS1 m/s 1.3VS1 1:30 1 VSO: stall speed in the landing configuration. VS1: stall speed obtained in a specified configuration. In this case, take-off configuration. EASA CS-LSA 600 kg one non-turbine or electric 0 83 km/h 3

4 3. The Baseline Design An airplane is designed, which will be referred to as the Baseline Design hereafter, using well-known methods outlined by Raymer [5], Roskam [6] and Anderson [7]. The Baseline Design is accomplished following the steps: i. Competitor study, ii. First weight estimation, iii. Airfoil and wing planform selection, iv. Power-to-weight ratio (P/W) and wing loading (W/S) selection, v. Refined sizing and a better weight estimation, vi. Geometry sizing and configuration, vii. Configuration sizing, viii. Aerodynamics, ix. Empty weight estimation using statistical component weight estimation method, x. Installed and uninstalled thrust, xi. Performance and flight mechanics. Sizing and trade studies is the twelfth step and is the subject of this study. The configuration of the Baseline Design is as follows: Low-wing monoplane with conventional tail configuration, Tricycle fixed landing gear, Single naturally aspirated reciprocating tractor engine with a three blade constant speed propeller, Number of crew: with side by side seating. Figure 1 shows the three view drawing of the Baseline Design prepared using OpenVSP [8], with its important design characteristics. Table 3 compares its performance characteristics with the requirements given in Table 1. Data in Figure 1 show that the designed airplane falls into the CS/FAR-3 Classification because of its weight but not the VLA or LSA Classification. Also, the positive limit load factor selected for the design puts this airplane in the Aerobatic Category. From Table 3, it can be seen that the airplane satisfies all the customer requirements by a comfortable margin. The questions that remain are: Is this the best airplane satisfying the requirements? Can a lighter, i.e. greener and less costly airplane to acquire and operate be designed that can still meet the requirements? 4

5 Characteristics Value Length (m) 7.54 Wing area (m ) 11. Wing span (m) 10.0 Aspect ratio 9.0 Maximum take-off gross weight (kg) Wing loading, W/S (kg/m ) 84.3 Wing airfoil NLF(1)-0115 [9] Engine Lycoming IO-360-L Propeller 3 blade/76 diam. Engine power (hp/kw) 160/119.3 Power-to-weight ratio (kw/kg) 0.16 g-limits +6, -3 Figure 1. Three view drawing of the Baseline Design with important characteristics. Table 3. Performance characteristics of the Baseline Design. Performance characteristic Baseline Design Requirement Satisfied? Range, R (km) 1050 > 1000 Rate of climb, R/C (m/s) 7.8 > 5 Take-off run, sg,to (m) 68 < 300 Stall speed, VSO (km/h) 94.3 < Sizing and Trade Sizing and trade studies constitute an important part of conceptual design. After this step is completed, the designer knows that the calculated design parameters represent a good combination of performance and weight. Since the weight of the airplane has a direct influence on cost, in a way, the cost is also optimized. For sizing and trade studies, two methods are outlined in the present study, namely the sizing matrix plot and carpet plot analyses. These methods are basically identical, they essentially represent the same data in different formats. 5

6 4.1. Sizing Matrix Plot The sizing matrix plot quickly allows the designer to find an optimised combination of selected design parameters. The outline of the method is as follows: i. The parameters to be varied or optimized are selected. These are chosen among wing loading (W/S), thrust-to-weight (T/W) or power-to-weight (P/W) ratio, taper ratio (), aspect ratio (A), etc. However, as the number of parameters increase, the number of combinations increase by at least 3 n, n being the number of parameters chosen, and the process becomes more cumbersome. The smallest number of parameters to be chosen is, which means that the minimum number of combinations to be worked with is 9. Usually, wing loading (W/S) and thrust-to-weight (T/W) or power-to-weight (P/W) ratios are chosen for the sizing and trade studies since these have the greatest effect on performance and weight. Actually, in this study, S (trapezoidal wing planform area) and P (power) are chosen as the trade parameters because the weight estimation method utilized requires these parameters as inputs. ii. The Baseline Design is perturbed by ±0% for W/S and ±0% for T/W or P/W. One can increase the number of perturbed designs both for W/S and P/W but this will result in 5 n or 7 n designs to work with. In this study, the trapezoidal wing reference area is perturbed by ±0% and power is varied such that more powerful and less powerful engines belong to the same engine family as the Baseline Design, which may not always correspond to ±0% variation. While choosing candidate engines, choosing engines that have similar sizes to the Baseline Design simplifies the analysis significantly because the nacelle and the fuselage size will be unaffected from the engine choice. The trapezoidal wing planform areas and the engines that are studied are as follows (those of the Baseline Design are underlined): Wing planform areas: 9.0 m, 11. m, 13.4 m. Engines: Lycoming O-35-F (15 hp), Lycoming IO-360-L (160 hp), Lycoming IO-360-F (180 hp). While perturbing the wing planform area, the horizontal and vertical tail sizes (SHT and SVT) are varied proportionately in order to keep the tail volume ratios (VHT and VVT) the same as the Baseline Design. This also relieves the designer from the burden of varying the fuselage length in order keep the tail volume ratio constant. 6

7 Fuselage size is kept constant for all perturbed designs since the cockpit size and tail moment will remain constant, independent of the wing size and the powerplant. Fuel volume is initially kept constant for the sake of simplifying the analysis. If the available fuel is enough to satisfy the mission requirements (especially the range), the designer may keep the original fuel volume. If the range requirement is not satisfied, one needs to increase the fuel volume, which will have an effect on the total weight. iii. The preliminary sizing matrix is constructed. Table 4 shows the preliminary sizing matrix constructed for the current design. Table 4. Preliminary sizing matrix. S=13.4 m S=11. m S=9.0 m P=180 hp Config.1 Config. Config. 3 P=160 hp Config. 4 Config. 5 Config. 6 P=15 hp Config. 7 Config. 8 Config. 9 iv. The performance requirements that will be used for optimization are selected. For a sound analysis, at least three requirements shall be selected. The chosen requirements shall be balanced between the ones where wing loading (W/S) has a dominant effect like the stall speed (VSO) and the landing distance (sg,l), and those where power-toweight ratio (P/W) has a dominant effect like the rate of climb (R/C), maximum speed (Vmax), and take-off distance (sg,to). In this study, the performance requirements chosen are the range (R), rate of climb (R/C), take-off run (sg,to), and the stall speed (VSO), which are the customer requirements. v. The empty (Wempty) and take-off gross weights (Wo) of each configuration is calculated. The empty weights are calculated using the Statistical Weights Method explained in [5]. This method consists of 14 empirical relations for estimating the weights of the wing, horizontal tail, vertical tail, fuselage, main landing gear, nose landing gear, installed engine, fuel system, flight controls, hydraulics, electrical system, avionics, air conditioning/anti-icing system and furnishings as a function of design gross weight, ultimate load factor, sizes and the geometric shapes of the major components, cruise speed of the airplane, dry engine weight, etc. It is highly recommended to use this method for sizing and trade, although it is a bit more cumbersome than other less comprehensive weight estimation methods since it results in a more detailed and accurate weight breakdown. 7

8 vi. The Aerodynamics module is updated for each configuration. The Aerodynamics module is a spreadsheet involving calculations of the maximum lift coefficient (CLmax), parasite drag coefficient (CDO), induced drag factor (K), and the drag polar as a function of speed and altitude. In these calculations, the effect of high lift devices and the landing gear are taken into account. vii. The uninstalled thrust or power data obtained from the engine manufacturer or by using a scaling approach is analysed in order to obtain the installed thrust values. Here, the losses due to altitude, power extraction, blockage, compressibility, scrubbing drag, cooling and miscellaneous drag are calculated and the installed thrust is calculated as a function of speed and altitude. Here, the methods outlined in [5] are used. viii. Performance calculations are performed for the requirements selected in step iv. Stall speed (VSO): Here, the lift equation is employed with the wing planform size (S) selected for the configuration in step i, and the maximum lift coefficient (CLmax) calculated in step vi. Here, the airplane is in landing configuration, where the flaps are fully extended. 1 W L VC L max S. (1) Rate of climb (R/C=dh/dt): For the calculation of the rate of climb, the specific excess power equation is used, which can also be used in order to calculate other performance characteristics like the maximum speed, acceleration, service ceiling and the maximum sustained load factor that can be achieved at a given altitude and speed [5]. P s T qcdo K W dh V dv V n W W /S q S. () dt g dt For rate of climb calculations, the load factor n=1 and take-off conditions are used. For take-off, flaps are partially extended and their effects on the parasite drag coefficient and induced drag are accounted for. Take-off run (sg,to): Take-off distance is calculated using the expression given in equation (3) [5]: 1 KT K AVTO s g,to ln, (3) gk A KT 8

9 K T T / W, (4) K A C L C DO KC L. (5) (W /S) In the above equations, μ=0.03 is the coefficient of rolling friction between the runway and tyres. The parasite drag coefficient, CDO includes the additional drag of the partially extended flaps and the induced drag factor, K is corrected for the ground effect. During take-off, the airplane is fairly horizontal so CL 0.1 is assumed. Range (R): Range is calculated from the Bréguet Range Equation [7]: p L W R ln i. (6) Cpower D Wf In this equation, ηp is the propeller efficiency, calculated as a function of the advance ratio, J=V /nd, n: propeller revolutions per second and D: propeller diameter. The propeller efficiency is corrected for blockage, compressibility and scrubbing drag effects. The specific fuel consumption is denoted by Cpower and is dependent on the engine chosen. For the candidate engines in this study, the specific fuel consumptions are obtained for the cruise condition from manufacturer s data and have slightly different values for the three different engines: Lycoming O-35-F, Cpower= lb/h/hp=0.773*10-6 N/W/s, Lycoming IO-360-L, Cpower= lb/h/hp=0.750*10-6 N/W/s, Lycoming IO-360-F, Cpower= lb/h/hp=0.741x10-6 N/W/s. L/D is dependent on the weight and the speed of the airplane. In order to maximize range, a propeller-driven airplane must fly at L/D)max. For the Baseline Design and the remaining configurations this occurs at a speed around 7 m/s (59 km/h) at the cruise altitude of 400m. However, it is seen in the calculations that, cruise flight at a speed of 80 km/h does not significantly alter the range performance of the airplane. When the performance calculations are performed, the final sizing matrix can be constructed as can be seen in Table 5. The requirements that are not satisfied are shown underlined. From Table 5, we immediately see that the range requirement is satisfied by all 9 configurations. This means that there is no need to vary the fuel weight between configurations but the range data cannot be used for sizing trade. 9

10 We also see that there is 100 kg difference between the heaviest (configuration 1) and the lightest configurations (configuration 9). Configurations 3 and 6 do not satisfy the stall speed requirement, while the take-off distance requirement is violated by configurations 7, 8 and 9. Configuration 7, which has the large wing but the small engine violates the rate of climb requirement also. Configurations 1,, 4 and 5 satisfy all the requirements. Table 5. Final sizing matrix. S=13.4 m S=11. m S=9.0 m 1 3 P=180 hp Wo=994. kg VSO=88.5 km/h R/C=7.9 m/s sg,to=8 m R=1006 km Wo=965.4 kg VSO=95.5 km/h R/C=8.3 m/s sg,to=59 m R=1034 km Wo=937. kg VSO=10 km/h R/C=9.3 m/s sg,to=69 m R=1080 km P=160 hp Wo=973. kg VSO=87.6 km/h R/C=7.4 m/s sg,to=35 m R=108 km Wo=944.7 kg VSO=94.3 km/h R/C=7.8 m/s sg,to=68 m R=1050 km Wo=916.7 kg VSO=101 km/h R/C=8. m/s sg,to=9 m R=1088 km P=15 hp Wo=950.8 kg VSO=86.6 km/h R/C=4.9 m/s sg,to=319 m R=1041 km Wo=9.6 kg VSO=93.4 km/h R/C=5. m/s sg,to=365 m R=1061 km Wo=894.9 kg VSO=99.8 km/h R/C=5.6 m/s sg,to=398 m R=1100 km ix. The next step is to crossplot the data in Table 5 as illustrated in Figure. First, for each power value, the take-off gross weights are plotted as shown in the first column of Figure. In the plots, hollow circles denote data from Table 5. From the take-off gross weight graphs of Figure, wing areas corresponding to regularly-spaced gross weights are determined, shown with full circles in the plots. Then the data is transferred to a wing area (S)-engine power (P) graph as shown in Figure 3. This graph is already useful as it is because it yields the take-off gross weight for any combination of wing planform area (S) and engine power (P). 10

11 Take-off weight, Wo Stall speed, VSO Rate of climb, R/C Take-off distance, sg,to P=180 hp P=180 hp S=13.4 m S=13.4 m P=160 hp P=160 hp S=11. m S=11. m P=15 hp P=15 hp S=9 m S=9 m Figure. Sizing matrix crossplots. 11

12 Figure 3. Preliminary sizing matrix plot. Then, stall speeds, climb rate and the take-off runs are crossplotted in the most convenient manner as shown in the second, third and fourth columns of Figure. In Figure, the hollow circles represent the actual data from Table 5, while full circles correspond to the wing area (S)-power (P) combinations that exactly meet a given requirement. The combinations that exactly meet the requirements are transferred to the sizing matrix plot of Figure 3 and joined by smooth curves, resulting in Figure 4. Again, the hollow circles represent the actual data from Table 5. These curves constitute the constraint lines and the small arrows indicate the direction of the feasible region. The Baseline Design is also included in the figure, shown with a large circle having a dashed outline. The Optimum Design is the one satisfying all the requirements, having the lowest take-off gross weight. The Optimum Design will therefore will be at the intersection of two constraint curves. Hence, the Optimum Design lies at the intersection of the stall and take-off distance constraint curves, shown with a big black circle at the lower left of the Baseline Design. 4.. Carpet Plot As mentioned previously, the carpet plot is an alternative format for presenting the data in Figure. The take-off gross weight plots in the first column of Figure are superimposed as illustrated in Figure 5. When the data points corresponding to the same wing areas are connected with straight lines, the resulting shape looks vaguely like a carpet! In the same 1

13 figure, the data points in Figure that exactly meet the stall speed, take-off run and rate of climb requirements are plotted and joined by smooth curves, constituting the constraint lines. The optimum design is the lowest point in the carpet plot, i.e. the lightest airplane that meets all the requirements, which is shown with a full circle in Figure 5, at the intersection of two constraint lines. The Baseline Design is also shown in the figure with a large dashed circle. Figure 4. Final sizing matrix plot. Figure 5. Carpet plot. 13

14 4.3. Optimum Design As mentioned above, the Optimum Design is the one satisfying all the requirements, with the lowest take-off gross weight. Therefore, judging from Figure 4 and 5, the Optimum Design corresponds to S=9.6 m and P=154.5 hp and Wo=915 kg, about 9.7 kg lighter than the baseline design. However, the engine found that delivers 155 hp is heavier and to be on the safe side (exceeding the requirements with a comfortable margin) the Optimum Design is chosen as S=9.7 m, P=160 hp and Wo=96.4 kg shown in Figures 4 and 5 with a dotted circle. The Optimum Design is illustrated in Figure 6, together with important characteristics. The group weight statement of the Optimum Design is presented in Table 6. Characteristics Value Length (m) 7.54 Wing area (m ) 9.7 Wing span (m) 9.34 Aspect ratio 9.0 Maximum take-off gross weight (kg) 96.4 Wing loading, W/S (kg/m ) 95.5 Wing airfoil NLF(1)-0115 [9] Engine Lycoming IO-360-L Propeller 3 blade/76 diam. Engine power (hp/kw) 160/119.3 Power-to-weight ratio (kw/kg) 0.19 g-limits +6, -3 Figure 6. Three view drawing of the Optimum Design with important characteristics. In the cruise conditions, the drag polar of the airplane is estimated as: C D L C. (7) The performance data are presented in Tables 7 and 8. In Table 7, the performance characteristics are compared with the customer requirements, while in Table 8 comparison with respect to CS/FAR requirements is presented. Table 9 depicts the manoeuvrability characteristics of the Optimum Design. 14

15 Table 6. Group statement format of the Optimum Design. Group Weight (kg) Structures Wing Horizontal tail 7.4 Vertical tail 4.7 Fuselage Main landing gear 57.5 Nose landing gear 18.7 Propulsion Engine Fuel system/tanks 17.4 Equipment Flight controls 19.4 Hydraulics.0 Avionics 30.0 Electrical 61.0 Air conditioning & anti-ice 18.7 Furnishings 4.3 Total empty weight Useful load Crew 160 Fuel 96.5 Payload 0 Take-off gross weight 96.4 Table 7. Performance characteristics of the Optimum Design compared with customer requirements. Performance characteristic Optimum Design Requirement Satisfied? Range, R (km) 1069 > 1000 Rate of climb, R/C (m/s) 6.6 > 5 Take-off run, sg (m) 78.5 < 300 Stall speed, VSO (km/h) 98.0 < 100 Table 8. Performance characteristics of the Optimum Design compared with CS/FAR requirements. Performance characteristic Optimum Design Requirement Satisfied? Stall speed, VSO (km/h) 98.0 < 113 (CS/FAR) Climb VCL, γ 13 % > 8.3% (CS/FAR) Climb VA, γ 9.% > 3.3% (CS/FAR) 15

16 Table 9. Manoeuvrability characteristics of the Optimum Design. Parameter Value Instantaneous turn rate 43.6 Vcorner = 71 km/h, n=6 Instantaneous turn radius 98 Vcorner = 71 km/h, n=6 Sustained turn rate 5 V=45 km/h, n=3. Sustained turn radius V = 45 km/h, n=3. In Table 9, the most forward and backward positions of the centre of gravity with respect to the mean aerodynamic chord are given together with the corresponding static margin values. The neutral point is calculated using the method outlined by Etkin and Reid [10]. As can be seen, the airplane is stiff in longitudinal flight, which can be easily remedied with relocating certain systems in the airplane during preliminary and detail design phases or moving the wing a few inches forward. Table 10. CG positions and longitudinal stability of the Optimum Design. CG position Chordwise CG position Static margin Most forward % Most backward % Finally, in Table 11, the characteristics of the Optimum Design are compared with those of competitor aircraft. Seven competitors are chosen, which are: Grob 115E, Grob 10A, Slingsby T-67, Aermacchi Sf.60D, Cirrus SR.0, Cirrus SR., and Diamond DA.0. As can be seen, the Optimum Design compares well with the competitors. Although it has the smallest engine except the Diamond DA.0 (which is a VLA Class airplane), it promises superior performance than the competitors for most of the performance characteristics. It is also the lightest airplane except for Diamond DA.0. The superior performance is possible due to laminar flow airfoil, use of smooth moulded composites for the entire airplane that offers a potential for significant amount of laminar flow (~5% over the fuselage, ~50% over the wing and tails) and finally optimized weight and performance as explained above. Had a lighter aeroengine existed delivering 155 hp, it would have been possible to reduce the weight of the airplane further. The unit civil purchase price of this airplane is estimated to be $ ( ) in 014 prices estimated using the DAPCA IV Cost Model assuming that 50 airplanes will be manufactured in 5 years after commencement of production [5]. 16

17 Characteristic Optimum Design Grob G115E Grob G10A Slingsby T-67 Aermacchi Sf.60D Performance Maximum speed (km/h) Range (km) Rate of climb (m/s) Take-off run (m) Stall speed (km/h) Cirrus SR.0 Cirrus SR. Diamond DA.0 Geometric Length (m) Wing area (m ) Wing span (m) Aspect ratio Weights Maximum take-off weight (kg) Wing loading (kg/m ) Empty weight (kg) Empty weight fraction Power Engine power (kw) Power to weight ratio Table 11. Comparison of the Optimum Design with competitor aircraft (data for competitor aircraft obtained from Internet sources). 17

18 5. Conclusions Sizing trade and optimization of a light sport aircraft is outlined. The trade study is performed for obtaining the optimum wing area-engine power combination. Two methods are described, namely the sizing matrix plot and carpet plot approaches, both methods having visual emphasis, which is their main strength. These methods are applicable using widely used general purpose computational and graphical tools, without the need for costly, dedicated software. These aspects render the methods suitable for student projects, academic purposes and also for design of real airplanes in the conceptual design phase. The methods can be developed further to include a higher number of parameters but then their simplicity and visual aspects will quickly fade away and programming the methods as a software will become necessary. The methods are applicable to conventional configurations and should be used with care when the designed airplane configuration is unconventional like UAVs, tailless aircraft or aircraft powered by unconventional powerplants like electrical. While dwelling in the fascinating world of aircraft design, technical knowledge, experience, and creativity are all vital. On the other hand, it is also beyond doubt that the airplane is aesthetically the most pleasant invention of mankind. We, aircraft designers are privileged to be following the footsteps of great designers like Marcel Dassault, quote: For an aircraft to fly well, it must be beautiful 18

19 References 1. European Aviation Safety Agency, Certification Specifications for Normal, Utility, Aerobatic, and Commuter Category Aeroplanes, CS-3, Amendment 3, 01.. European Aviation Safety Agency, Certification Specifications for Very Light Aeroplanes, CS-VLA, Amendment 1, European Aviation Safety Agency, Certification Specifications and Acceptable Means of Compliance for Light Sport Aeroplanes, CS-LSA, Amendment 1, Federal Aviation Administration, Airworthiness Standards: Normal, Utility, Acrobatic and Commuter Category Airplanes, Amendment 55, Raymer, D. P., Aircraft Design: A Conceptual Approach, 5 th Ed., AIAA Education Series, Roskam, J., Airplane Design, DARCorporation, Anderson, J. D., Aircraft performance and Design, Mc Graw-Hill, OpenVSP Core Team, OpenVSP.3.0, Selig, M. S., Maughmer, M. D. and Somers, D. M., Natural-laminar-flow airfoil for general aviation applications, J. Aircraft 3(4), Etkin, B. and Reid, L. D., Dynamics of Flight: Stability and Control, John Wiley & Sons, Inc.,