Preliminary Design Review - Purdue University
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Preliminary Design Review
|Stephen Beirne |Charlie Rush |
|Miles Hatem |Zheng Wang |
|Chris Kester |Brandon Wedde |
|Jim Radtke |Greg Wilson |
[pic]
Executive Summary
The Barn Owl is Team V’s solution to the need for an alternative fuel aircraft within the single engine general aviation market. This need will arise as peak-oil approaches and petroleum-based fuels become scarce and expensive. The Barn Owl has also been designed with the near-term need for a replacement for 100 octane low-lead aviation gasoline in mind. 100 low-lead is expected to be phased out in the next 10 years. The value of this near-term market has been estimated at over $1 billion annually once 100 low-lead disappears.
Previous work by Team V has focused on defining requirements for the Barn Owl and developing the aircraft concept. In this Preliminary Design Review, the feasibility of the Barn Owl is demonstrated by detailed analysis of the concept and its features.
A weight fraction-based sizing code was used to produce constrained carpet plots. A light-weight design was selected from the feasible space, and used for further detailed design. This sizing approach was continually updated as the detailed analyses were refined.
Detailed aerodynamic analysis consisted of several coordinated efforts. The airfoil cross-section was designed using a genetic algorithm. The wing planform was optimized to have an elliptical lift distribution at the cruise condition. A three-dimensional CMARC analysis provided detailed aerodynamic performance predictions.
The team developed a structural layout and selected materials based on cost considerations. Detailed structural analysis was carried out, optimizing the wing structure and confirming the viability of the fuselage structural layout.
Component weights were determined and used in calculating the static longitudinal stability of the Barn Owl. The team succeeded in demonstrating reasonable stability. Stall-spin stability was also considered and assured.
For propulsion, an existing diesel engine and existing propeller were selected. The use of this off-the-shelf technology will reduce the cost of development and ease manufacturing.
The Barn Owl is projected to cost $278,700. This price and the Barn Owl’s solid performance will make it a competitive aircraft in the general aviation market.
Table of Contents
Introduction 2
Design Requirements 2
Proposed Concept 2
Design Mission 2
Sizing 2
2D Aerodynamics 2
3D Aerodynamics 2
Performance 2
Structures 2
Weight and Balance & Stability 2
Propulsion 2
Cost 2
Final Design Comparisons 2
References 2
Appendix A – Additional Barn Owl Pictures 2
Appendix B – Sizing/Carpet Plot Code 2
Appendix C – Drag Polar Data 2
Appendix D – Wing Structure Optimization Code 2
Appendix E – Wing Optimization Code Outputs 2
Appendix F – Empty Weight Calculation Code 2
Appendix G – Aluminum Equivalent Inputs for Appendix C 2
Appendix H– Fiberglass Property Calculation Code 2
Appendix I – V-n Diagram Code 2
Appendix J – Flight Envelope Code 2
Introduction
This team’s system requirements review [14] described a plan to target the general aviation market with a single-engine, four-seat aircraft – the Barn Owl. It was the goal of Team V to design a product running on an alternative fuel that will be marketable to hobbyists, fixed base operators, and training fleets in the phase-out of 100 octane low-lead (100LL) aviation gasoline and the transitional times of “peak-oil.” The system requirements review also included an estimate of the potential market. It was determined that sales of 500 aircraft per year, or more, could be expected in the wake of the 100LL phase-out.
A system definition review was conducted to develop the concept of the aircraft [13]. Bio-diesel was selected as the alternative fuel for the Barn Owl. The configuration was set as a low-wing, conventional tail aircraft with a piston engine powering a tractor propeller.
The following report describes the method used to determine the preliminary design.
Design Requirements
The current design requirements shown below in Table 1 are still the same as presented in this team’s System Definition Review [13]. Through the work presented in this report, it will be shown that at the current level of detail an alternate-fueled aircraft can meet all the given requirements.
Table 1 - Design Requirements
|Design Requirements Summary |
|≤1500 ft takeoff distance to clear a 50 ft obstacle |
|≥600 lb payload with max fuel |
|≥125 kts max cruise speed, Target = 150 kts |
|≥500 nm range, Target = 600 nm |
|≥48x44 cabin height x width |
|Target GTOW of 2800 lbs |
|Target base price of $300,000 |
Proposed Concept
Team V’s proposed concept is shown in Figure 1. The Barn Owl is a low wing, conventional tail, single engine, tractor prop, 4 seat general aviation aircraft.
[pic]
Figure 1 - Concept 3 View
Design Mission
Based upon this team’s QFD analysis, as presented in the system requirements review, it was determined that to be competitive in the chosen market the aircraft would need to have a range of 600 nautical miles and cruise near 8000 ft. From this the design mission was formulated.
Figure 2 – Design Mission
[pic]
Table 2 – Design Mission Legend
|A |Taxi 14 minutes |F |Climb to divert altitude (2000 ft MSL) |
|B |Take-off roll at sea level |G |45-min loiter / divert |
|C |Climb to cruise (8000 ft MSL) |H |Descend to sea level |
|D |Cruise at 150 KTAS |I |Landing Roll |
|E |Descend to sea level |J |Taxi to hanger |
The mission begins with an estimated 14 minute taxi to the runway. Next, the plane will begin its takeoff roll at a runway located at sea level. The mission has been designed from sea level since it is a good benchmark from which to measure altitude. After takeoff the plane will climb at 700 fpm to its cruising altitude of 8000 ft MSL and cruise at that height at a speed of 150 KTAS. After cruising the specified 600 nmi, the aircraft will descend back down to sea level. Just before touching down, it will then climb to a divert/loiter altitude of 2000 ft MSL. It will then either spend 45 minutes loitering in pattern or diverting to an alternative airport as per FAR fuel requirements for IFR flight. Finally it will descend again to sea level, land, and taxi back to the hanger.
Sizing
Sizing and Carpet Plot Code
Sizing of the Barn Owl was done through the use of carpet plots based on a weight fraction approach and its implementation in a Matlab script. The script was used to automatically generate the carpet plots with constraint lines, so that the lightest weight feasible design point could be determined. Since an existing engine was selected for the Barn Owl, as described below, fixed-engine sizing was used. Thus, carpet plots sizing the aircraft with different aspect ratios over a range of wing loadings were used to set the design.
The script uses an iteration scheme which assumes an initial guess for gross takeoff weight (GTOW), then calculates GTOW based upon that guess. It then iterates the guessed weight until the two weights are within 0.01% of each other (approximately 0.27 lbs). Within the code, GTOW was calculated using the following equation:
[pic] Equation 1
The empty weight fraction [pic] was calculated by first calculating all of the component weights based upon chapter 15 of Raymer [10]; the details of which are discussed later in this report. The weights of the individual components were then summed to give the total empty weight which is then divided by the GTOW guess. This yields the empty weight fraction.
The fuel fraction [pic] was calculated using the equation:
[pic] Equation 2
In Equation 2,[pic] are weight fractions for the team’s design mission. Specifically, [pic] represents the fuel used during the taxi segment and is calculated using Raymer’s equation 19.7:
[pic] Equation 3
where C is specific fuel consumption (SFC), d is duration in hours, and T/W is the idle (20%) thrust-to-weight ratio. Duration for this segment is assumed to be 14 minutes as specified in chapter 19 of Raymer [10]. Since the engine of the aircraft was known to be 200 horsepower,the thrust-to-weight ratio was calculated using the equation:
[pic] Equation 4
where ηp is the propeller efficiency, which is assumed to be 0.86 based upon the propeller analysis discussed later. The SFC was calculated from the brake horsepower SFC (BSFC) which was calculated for the aircraft’s engine to be 0.439. Engine selection and SFC calculation is discussed later in this report. The equation used to calculate SFC from BSFC is:
[pic] Equation 5
where V is speed and ηp is the propeller efficiency.
[pic] corresponds to the fuel used during takeoff and is also calculated using Equation 3 with 100% thrust. Duration for the takeoff segment is assumed to be one minute as specified in Raymer’s chapter 19 [10].
[pic] represents the fuel weight used in climbing to the cruise altitude of 8000 ft. It is calculated using Raymer’s equation 19.8:
[pic] Equation 6
where C is SFC (same as previously discussed), Δhe is the change in height energy, V is the average climb speed and D/T is the average drag divided by the average thrust during climb. It should be noted, however, that D/T is not actually calculated within the code, and is instead replaced by:
[pic] Equation 7
In Equation 7, L/D is calculated implicitly by calculating CL/CD. CL is calculated using the equation:
[pic] Equation 8
where W/S is wing loading (an input parameter) and ρ is air density at sea level. CD is calculated using the curve fit for the plane’s drag polar:
[pic] Equation 9
Δhe is calculated using Raymer’s equation 19.9:
[pic] Equation 10
where h is altitude, g is the gravity constant, and V is speed. Note that Vtakeoff is calculated as 1.1 times stall speed. This is conservative since it does not consider the acceleration that will occur as the plane climbs to the 50 foot altitude accounted for in the takeoff fuel weight fraction equation. The average climb speed is calculated using the Raymer’s equation 17.13:
[pic] Equation 11
where W/S is wing loading (an input parameter), ρ is air density at sea level, CD0 is the zero lift drag coefficient, and K is the aerodynamic constant. CD0 was calculated to be 0.023 in the aerodynamic analysis. K was calculated using the equation:
[pic] Equation 12
Where AR is the aspect ratio and e is the Oswald Efficiency Factor. The Aspect ratio is an input parameter which was chosen through the use of carpet plots (discussed later) and the Oswald Efficiency Factor was determined as a function of aspect ratio via a curve fit of CMARC analysis data for the plane which yielded the equation:
[pic] Equation 13
[pic] represents the fuel weight used during the cruise segment and is calculated using the Breguet range equation (also Raymer 19.10):
[pic] Equation 14
where R is range (less the distance traveled during climb), C is SFC (same as before), V is cruise speed, and L/D is the lift to drag ratio at cruise conditions. Distance traveled during the range segment is calculated by subtracting the average climb velocity multiplied by the time it will take to reach 8000 ft at a climb rate of 700 fpm from the design mission’s range of 600 nmi. Cruise speed is set at the design cruise speed of 150 kts. Cruise L/D was calculated in the same manner as it was for climb, except that the density and speed used were the cruise condition values, and not those of climb.
[pic] represents the fuel used during descent and is assumed to be 0.9989. This was approximated by estimating the fuel usage per minute and multiplying it by an estimated time to descend.
[pic] represents a missed approach and climb to a 2000 ft divert altitude. It is calculated in the same manner as the fuel used to climb to cruise altitude[pic].
[pic] represents a divert distance, however, the team opted to use a 45 minute loiter/divert segment, thus this fuel fraction is 1.
[pic] represents the fuel used during the 45 minute loiter/divert segment and is calculated using the loiter equation (also Raymer 19.11):
[pic] Equation 15
where E is endurance time (in hours), C is SFC (same as before), and L/D is the lift to drag ratio at cruise conditions. The endurance time is specified as 45 minutes to accommodate IFR regulations and the L/D used in the loiter/divert segment is the same as that for cruise.
[pic] is another descent segment and is assumed to be equal to[pic]which should be conservative considering the aircraft is descending from a lower altitude.
Finally [pic] represents the fuel used during landing and is assumed to be 0.995. This is based upon Raymer’s equation 6.23 which simply states it should be between 0.992 and 0.997 [10].
The Wcrew and Wpayload were taken from the design requirement of having a 600 lb payload including crew.
Once all of these sizing equations were compiled together, it was possible to place them inside of two for loops. The first of these loops varied aspect ratio through a specified range; the other varied the wing loading. This made it possible to plot a curve of GTOW vs. wing loading for each aspect ratio. Using this for loop approach allowed the team to rapidly generate numerous data points which (with a small enough wing loading increment) could be linearly connected to adjacent points to form a smooth curve.
In order to find the optimal aircraft design (i.e. the one with the minimum GTOW), Team V calculated and plotted various constraints along the aspect ratio curves. The constraints used were stall speed, cruise speed, climb rate, takeoff distance, and turn load factor (n) value.
For each aspect ratio and wing loading combination, cruise speed, climb rate, takeoff distance, and the turn load factor (n) value were calculated as discussed below and placed into an individual matrix for each constraint. Then for each row in the matrix (which corresponded to a constant aspect ratio) the value above and below the desired value was found. Next, a linear interpolation was used to find exact GTOW that corresponded to the desired value for that aspect ratio. Finally, all that had to be done to create the constraint lines was plot a curve through these data points.
The cruise speed was calculated by using Matlab’s fsolve function to solve the following equation for V:
[pic] Equation 16
In Equation 16, ηp is the propeller efficiency, bhp is the horsepower of the engine (200), V is the cruise speed, ρ is the air density at cruise altitude, S is the area of the wing, CD0 is the zero lift drag coefficient, K is the aerodynamic constant, W is the aircraft GTOW, and CL_min_drag is the coefficient of lift which corresponds to the minimum drag coefficient. ηp, V, K, and CD0 were previously discussed. CL_min_drag is based upon the drag polar generated by the aerodynamic analysis and S is calculated by dividing the GTOW by the wing loading. It can be noted that the factor of 0.75 in Equation 16 signifies that this velocity will be the cruise speed at 75% power.
Climb rate is calculated using the Raymer’s equation 17.44:
[pic] Equation 17
Where ηp_climb is the propeller efficiency during climb, bhp is the horsepower of the engine (200), V is the cruise speed, W is the GTOW, and D is the drag force of the aircraft during climb. ηp_climb is assumed to be 0.76 based upon the propeller analysis (discussed later) and other than D all other parameters have been previously discussed. D is calculated using the equation:
[pic] Equation 18
Where ρ is the density at sea level, V is the average speed during climb, S is the wing area, and CD0 is the zero lift drag coefficient. All of these values have been previously discussed.
Takeoff distance was calculated using Raymer’s equation 17.112 [10]:
[pic] Equation 19
In Equation 19 W/S, ρ, ρsl (same as ρ), CL_climb, g, and W are as previously discussed. hobstacle is the height of an obstacle to be cleared during takeoff (50 ft). G is calculated using the equation:
[pic] Equation 20
where T/W is the thrust to weight ratio, D is the drag force during climb, and W is the GTOW. All of these values have been previously discussed. U was calculated using the equation:
[pic] Equation 21
where CL_max is assumed to be 1.6 based upon the aerodynamic analysis. Tav was calculated using equation 17.144 of Raymer [10]:
[pic] Equation 22
In Equation 22 bhp, ρ, and ρsl have been previously discussed. Ne is the number of engines in the aircraft (one) and Dp is the propeller diameter of 6.166 ft (74 in.) as determined by the propeller analysis.
Turn load factor was calculated using an altered version of Raymer’s equation 17.54 to account for a non-symmetric airfoil:
[pic] Equation 23
Where ρ is the density at cruise altitude, V is the cruise speed, W/S is the wing loading, CD0 is the zero lift drag coefficient , CL is the coefficient of lift during cruise, and CL_mindrag is the minimum drag coefficient of lift. All of these values have been previously discussed.
The final constraint - stall - was calculated in a different manner. Since stall speed is only a function of air density, CL_max, and wing loading, the wing loading at which the plane stalled at 57 kts at sea level could be calculated directly from the equation:
[pic] Equation 24
57 kts was chosen as Team V’s designed stall speed in order to leave room for error and still meet the FAR requirement of a 61 knot stall speed. Once the wing loading for stall was calculated, it was plotted as a vertical line on the carpet plot.
For completeness, landing distance, best range cruise speed, and best range cruise distance are also calculated in the sizing code. Best range cruise distance is calculated because the 600 nmi range is not the best range distance, but the range for a cruise at 150 kts.
Landing distance was calculated using a summation of approach distance, flare distance, ground roll distance and a two second frictionless roll at stall speed to account for the time before the pilot applies the brakes. Approach distance was calculated using Raymer’s equation 17.111:
[pic] Equation 25
hobstacle and γclimb have been previously discussed. hTR was calculated using Raymer’s equation 17.109:
[pic] Equation 26
where R is calculated using Raymer’s equation 17.106:
[pic] Equation 27
where Vstall is a design parameter equal to 57 kts and is explained in further detail later. Flare distance was calculated using Raymer’s equation 17.108:
[pic] Equation 28
where T/W is the thrust to weight at idle speed (20%) and L/D is the lift to drag ratio with full flaps which is assumed to be 5 based upon the aerodynamic analysis/engineering judgment. Ground Roll distance is calculated by using Raymer’s equation 17.101:
[pic] Equation 29
where g is the gravity constant, Vi is the initial speed (assumed to be stall speed at touchdown). KA and KT are calculated using the following 2 equations:
[pic] Equation 30
[pic] Equation 31
All of the above values have been previously discussed except for μ which was estimated to be 0.4 based upon Raymer’s Table 17.1 [10].
Best range cruise speed was calculated using Raymer’s equation 17.13 which is seen above in Equation 11. Best range cruise distance was calculated using equation 17.28 of Raymer:
[pic] Equation 32
Where ηp is the propeller efficiency, Cbhp is the BSFC, L/D is the minimum drag lift-to-drag ratio and Wi/Wf is the weight ratio of the segment. The minimum drag lift-to-drag ratio is calculated in the same manner as the climb and cruise lift-to-drag ratios. The Wi/Wf is the inverse of [pic], the fuel ratio used during cruise.
The final result for the compilation of all these equations is shown in Figure 3. For the complete Matlab script, see Appendix A.
[pic]
Figure 3 - Carpet Plot
It can be seen in Figure 3 that the lowest GTOW is approximately 2610 lbs which corresponds to a wing loading of 17.77 lbs/sq ft and an aspect ratio of approximately 8.1. For the final design, Team V chose to use a wing loading of 17.7 and an aspect ratio of 8.2 to allow room for error. Also note that in Figure 3 the climb constraint plotted is for a climb rate of 1350 fpm, not the 700 fpm climb rate used for the design mission. This was done so that the climb constraint would appear on the carpet plot, as 700 fpm was too far to the left.
Plugging this wing loading and aspect ratio back into the sizing/carpet plot code gave the final sizing numbers. These can be seen in Table 3. It should be noted that our 75% power cruise speed is not our designed cruise speed, thus the power required to fly at 150 kts during cruise was calculated to be approximately 61% using Equation 16 above.
Table 3 – Sizing Code Notable Inputs/Outputs
[pic]
Miscellaneous Sizing Considerations
Takeoff Rotation Angle
From the three-dimensional CMARC analysis, described below, it was determined that an angle of 15° was needed for takeoff. Thus, the fuselage and landing gear were arranged so this rotation angle was possible (see Figure 4).
[pic]
Figure 4 - Takeoff rotation
Engine Mounting Room
Using an engine CAD model obtained from the engine manufacturer website, the engine was integrated into the plane CAD model to determine if its position as required by the center of gravity and stability requirements would interfere with the fuselage. It was found that the nose of the aircraft has adequate room for the engine and all related components.
[pic]
Figure 5 - Mounted engine
Fuel Volume
Concerns were raised that there might not be enough room inside the wing for 54 gal of fuel. Calculations from the Catia model showed that the wing had enough room for 240 gal.
2D Aerodynamics
In order to improve the performance of the aircraft, it was suggested that a new laminar flow airfoil be designed specifically for the Barn Owl. The goal of the design is to use optimization methods to create an airfoil that has lower drag during cruise than the NACA four-digit series airfoils used on some GA aircraft, while simultaneously maintaining good performance at high angles of attack and under fully turbulent conditions.
Methodology
The optimization procedure is shown in Figure 7 as a flow chart. First, the Matlab optimizer generates a vector of design variables with information regarding the x-y location of control (or “handle”) points the airfoil’s surface needs to pass through, as well as the tangency and curvature at the trailing and leading edges for both halves of the airfoil. The number of control points can be changed within the call script that runs the optimizer. The design vector is fed into the objective function, which fits a spline curve through these “handle” points and the tangencies provided at LE and TE (see Figure 6). The spline curve is converted into data points and saved as the airfoil coordinate input file for XFoil.
[pic]
Figure 6 - Illustration of airfoil geometry definition
XFoil is called through a DOS batch file, and instructed to load the airfoil coordinate input file and perform the analysis through a VB script. The analysis involves a lift and drag evaluation at lift coefficients of 0.15, 0.6 and 0.8. The drag polar and the pressure coefficient data are saved as files to be loaded back into the Matlab.
The objective function parses the XFoil output files, extracting the drag, lift and pressure information. The final objective function value is a weighted sum of drag at lift coefficients of 0.15, 0.6 and 0.8, and the maximum pressure coefficient at 3° angle of attack. It was decided that drag coefficients at Cl of 0.15 and 0.6 are equally important, since the airfoil would be subjected to this range of Cl values during normal operation. Cl of 0.8 is weighted lower since it is not as important. A very large (negative) pressure coefficient can often lead to high skin friction due to high flow speed on the airfoil. It can also lead to a high adverse pressure gradient and is therefore a likely feature of a bad airfoil and is also included as the objective function result. Cp is obviously less indicative of drag than the drag coefficient and therefore it receives less weight. The function result is returned back to the optimizer for evaluation, completing the iteration. Each iteration takes about 2 seconds.
[pic]
Figure 7 - Optimization flow chart
The need for a global optimization routine that does not use gradient information, is robust enough for a not-so-well behaving system, and had explicit constraints for design variables prompted the use of a Genetic Algorithm optimizer (GAO). The Matlab GAO code developed by Professor William Crossley of Purdue University was utilized. It was found that GAO was very easy to set up for this problem. 13 bits were used to encode each control point (6 for x, 7 for y), and 4 bits used for both LE and TE tangencies.
Not using any gradient information also avoided problems involved with XFoil not converging. If XFoil does not converge, it is usually because of the airfoil has large areas of separation. With this implementation of GAO, the objective function simply assumes a very large drag for the airfoil if this occurs.
Significant Results
The final Airfoil used three control points on the upper surface and two for the bottom. The airfoil, dubbed FVGA 5121 (see Figure 8) is 12.1% thick, and is designed to be laminar up to 50% cord.
[pic]
Figure 8 - FVGA 5121 airfoil
[pic]
Figure 9 - Polar comparison
The polar of the airfoil compared to NACA four digit airfoil of the same thickness is shown in Figure 9. The newly designed airfoil has a wide laminar bucket ranging from 0.15 to 0.6, and its CD is 30% lower than that of the NACA2412 for the cruise CL of 0.23. To make sure that the airfoil will still work under turbulent conditions, such as from rain or dirt contamination, a fully turbulent flow polar (“Tripped”) was generated for the airfoil and was compared to the 2412 at the same conditions. It was shown that under turbulent flow, the airfoil still had better performance than the 2412 over a large range of CL’s .
It was also determined that a CLmax of 1.4 was possible for the airfoil. However, since XFoil usually over estimates this value, it was down graded to 1.2. With the addition of a simple single-element flap, a CLmax of 1.6 needed to take off in 1500ft can be justified.
Wing Plan-form Design
The most efficient wing plan-form produces an elliptical lift distribution. The best way to accomplish this is to have an elliptic wing, such that the lift coefficient along the span stays the same, and the wing will have the highest efficiency at any Cl. However, due to the high cost of designing and building such a wing, a combination of twist and taper is often used on straight wings to achieve close to elliptic distribution at a designed lift.
For the airplane which has an AR of 8.2 and span of 34.8, the optimal taper ratio is about 0.4-0.5. However, a wing with a high taper ratio is usually more heavily loaded at the tip and thus is prone to tip stall. Hence a safer taper of 0.7 was chosen to make the stall start at the root, allowing the pilot to have roll control when stall begins.
A Matlab vortex lattice code developed by Professor Marc Williams of Purdue University was used to optimize the twist distribution. The code divides the wing into a series of rectangular patches and solves the pressure on each patch and the effect of the remaining patches on it.
An optimization routine was used to optimize the coefficients of a third order polynomial, which describes the twist. The designed lift coefficient of wing was chosen to be 0.3. Figure 10 shows the lift distribution of the twisted wing compared to the elliptical distribution, and Figure 11 shows the actual twist distribution of the wing. A total of 1.51 degrees of twist was needed to achieve the desired elliptical lift.
[pic]
Figure 10 - Lift distribution comparison
[pic]
Figure 11 - Wing twist
3D Aerodynamics
Method and Implementation
Building upon the success of a 2D airfoil and planform optimization, further analysis was completed using the 3D panel method, CMARC. It was deemed necessary to have an accurate 3D aerodynamic analysis to support and refine the assumptions in the sizing model.
The ga4half_fvga5121_rev3.m script, with the functionality to support the Team V design was an evolution of three other general aviation geometry scripts with slightly different goals. The development of this tool is outlined in Table 4 below. The scripts entitled ga[1-5].m were purely developmental, and the scripts titled ga4_[airfoil].m were used for analysis. The script ga5.m incorporates the functionality of the developmental ga4.m script with the addition of winglets. This concept was not used in the final analysis. The ga4.m concept without winglets was carried forward into the analysis stage in which various fuselage shapes, wing planforms, and airfoils were investigated.
Table 4 - Developement of 3D Aerodynamic Analysis
[pic]
CMARC provided accurate predictions of induced drag using a Trefftz plane integration. Additionally, a more technical parasite drag prediction was accomplished using a skin friction integration. CMARC assumes a perfectly smooth body with no leakage, and applies a series of 2D streamlines to cover the body. From the streamlines, boundary layer parameters such as thickness, velocity profile, transition and separation can be estimated from 2D experimental models. The adaptation from 2D experimental theory to a 3D numerical method is valid for bodies with little separation and cross-flow. To account for this, the aerodynamics of the static landing gear were added separately, and based upon empirical data.
To efficiently use the computing ability of CMARC to investigate various aerodynamic configurations, inputs files had to by dynamically generated according to the parameters in Table 2 below. This was done using the ga4half_fvga5121_rev3.m script shown in the Appendix. Using the final version of this script provided a useful tool to size the fuselage and wing
Table 5 - Input parameters for aerodynamic model
[pic]
The ga4half_fvga5121_rev3.m script also had a series of supporting functions that performed paneling routines, geometry intersections and airfoil translations from the 2D analysis. The relationship between the programs within the 3D analysis to ga4half_fvga5121_rev3.m, along with the overall relationship to the 2D aerodynamic analysis and the sizing routine is shown in Figure 1.
[pic]
Figure 12 - 3D Aerodynamics flow chart
Determination of Span Efficiency Factor
The first investigation was to determine the proportion to which drag is related to the square of lift, the Oswald span efficiency factor, e. Initial analysis showed that aspect ratio affected induced drag more complexly than the initial theoretical model used to size the aircraft. The determination of the span efficiency factor was of paramount importance to the sizing of the Barn Owl. The implementation of the Oswald span efficiency factor in the sizing program was purely as a constant in the definition of the 3D drag polar given by Equation 1.
[pic] Equation 33
Using CMARC, span efficiency was determined by calculating the lift and drag coefficients at a range of aspect ratios and fitting the data to the form used by the sizing program. This provided a much more realistic relationship between span efficiency and aspect ratio as can be seen by in Table 6 and Figure 13.
|INPUTS | |
|0.595 |0.695 |
|0.647 |0.676 |
|0.781 |0.644 |
|0.815 |0.645 |
|0.845 |0.656 |
|0.868 |0.677 |
|Mean |0.665 |
Table 7 - Span efficiency analysis
The determination of CD0 was done using a combination of data from CMARC for non-separated fuselage drag, and empirical data for landing gear drag. The distinction is shown by the drag polar in Figure 3. The value of CD0 was determined to be 0.023 from this analysis. While this is lower than the CD0 of 0.027 for a Cessna 172, this is reasonable because of the laminar FVGA5121 airfoil, and lack of wing bracing struts.
[pic]
Figure 14 - Drag Polar
L/DMAX was measured to be 11.7 using the data obtained from CMARC. This occurs at a CL of 0.53 as shown in Figure 4. Figure 5 shows the recorded lift curve versus fuselage angle of attack, depicting how the fuselage is close to level at cruise, where CL is low. The supporting data is shown in Table 5 below.
[pic]
Figure 15 - L/D vs CL
[pic]
Figure 16 - Lift Curve
Performance
A flight envelope plot was created to give a picture of what altitude and speeds the Team V Barn Owl aircraft is capable of flying. Using standard atmosphere equations, the temperature, pressure, and density of the air were calculated up to a ceiling of 12,000 feet. Because of this change in atmospheric conditions at increasing altitude, the speed of the Team V aircraft will vary. The speed of the aircraft was calculated when the excess power (Ps ) available is zero. The excess power can be calculated from Equation 34 below:
[pic] Equation 34
where V=Velocity, T=Thrust, D=Drag, and W=Weight of Aircraft
Assuming Ps =0, manipulation of equation 34 results in an expression that finds aircraft velocity as a function of air density. Equation 35 below shows this expression of aircraft velocity:
[pic] Equation 35
where P=Engine Power, ηp =Propeller Efficiency, ρ =Air Density,Cd = Drag Coefficient,
and S=Wing Planform Area
To calculate stall speed with increasing altitude, equation 36 was used:
[pic] Equation 36
where W/S = Wing Loading, ρ =Air Density, and CLMax = Max Lift Coefficient
Several variables were used with the above equations. Table 8 lists the variables and their corresponding values:
Table 8 - Variables and Corresponding Values
|P |150 Hp @ Cruise, 200 Hp @ Max Cruise |
|ηp |0.86 |
|Cd |0.026 |
|S |148 ft2 |
|W/S |17.7 lbf/ft2 |
|CLMax |1.6 |
Using the above equations and variables, the altitude was varied up to 12,000 feet and the stall speed, cruise speed and max cruise speed in knots were plotted against altitude in feet. The cruise altitude of the Team V aircraft is set at 8,000 feet, although the maximum ceiling is set at 12,000 due to Federal Aviation Regulation (FAR) Sec. 135.89. This FAR states that any aircraft can not fly above 12,000 feet without supplemental oxygen or a pressurized cabin. Figure 17 below shows the flight envelope and varying velocities of the Team V Flying Bran Owl aircraft.
[pic]
Figure 17 - Flight Envelope Plot
As can be seen from the figure, the blue stall speed line is the left boundary of the flight envelope, while the red max cruise speed line is the right boundary. The teal 12000 ft. FAR altitude ceiling is the top boundary of the envelope. The Team V aircraft can attain any speed and altitude within the shaded flight envelope area. The stall speed starts at about 57.1 knots at sea level and increases to about 68.7 knots at the FAR ceiling. The cruise speed increases from 141.3 to 159.7 knots, while the max cruise speed varies from 155.5 to 175.8 knots at 12,000 ft. altitude.
V-n Diagram
Defining the load limits of an aircraft is an essential step to producing a safe and durable product. For lightweight general aviation aircraft, Federal Aviation Regulation 23.337 states that the max design loading of an aircraft must be 3.8 Gs (Multiples of acceleration due to gravity) or more and the minimum negative loading must be -1 G or less. A V-n diagram shows how loading on the aircraft varies with velocity. Equation 37 below relates n (loading) as a function of aircraft equivalent velocity (Ve ):
[pic] Equation 37
where ρ=air density, [pic], CLMax=Max Lift Coefficient, W/S=Wing Loading
A main constraint of the V-n diagram is that the stall speed be attained at exactly 1 G of loading. Another constraint is that the dive speed of the aircraft is approximately 150% of the cruise speed. Along with these constraints, Federal Aviation Regulations also state that an aircraft must withstand a gust of 50 ft/s at cruise velocity and 25 ft/s at dive speed. Figure 18 below shows a V-n diagram for the Flying V Barn Owl with design and gust loading constraints.
[pic]
Figure 18 - Flying V Barn Owl V-n Diagram
Looking at Figure 18, VCRUISE is 99.75 knots equivalent at 8000 ft. altitude, while VDIVE
is around 149.6 knots equivalent. The maximum allowable dynamic loading of 3.8 Gs occurs at the 149.6 knot dive speed. In the figure, the blue curves and lines refer to the design loading and the red to the gust loading. As can be seen from the figure, the design loading of 3.8 Gs is enough to withstand the positive g gusts, while the design should be modified to meet the negative g gust loadings.
Structures
Material Selection
The Barn Owl will be constructed as a hybrid of aluminum and fiberglass/epoxy composite. The thicker internal components, such as the spar and fuselage frame, will be constructed of aluminum, and a fiberglass skin will be bonded to the outside. This section describes how this material combination was selected.
Using Pugh’s method of concept selection, described in previous work [13], the Team had arrived at two possible material concepts for the structure of the Barn Owl: a traditional all-aluminum structure or a hybrid concept with an aluminum frame bonded to composite skin. It was noted in Team V’s SDR report [13] that no clear historical trends in performance, weight, or cost between aluminum and composite aircraft were available for aircraft in the GA market. The SDR concluded that it was up to considerations specific to the Barn Owl to drive material selection.
Several factors influenced the choice of material for the Barn Owl. The most significant was cost. In terms of material cost, for which general numbers are given in Table 9, aluminum and unidirectional S2 fiberglass are competitive, whereas high quality graphite/epoxy composites are very expensive. For most applications in general aviation aircraft, the high performance of carbon fiber is not worth the high material cost. Thus, for composite general aviation aircraft, fiberglass is the reinforcing material of choice. From this point forward, the discussion will only consider aluminum and fiberglass skin materials.
Table 9: Material cost estimates
|Material |Typical Price [$/lb] |
|Aerospace Aluminum |4-8 |
|S2 Fiberglass Prepreg |6-10 |
|Graphite Fiber Prepreg |20-30 |
The slight difference in material cost between fiberglass and aluminum is offset by the generally higher buy-to-fly ratios of aluminum structure.
Manufacturing cost is the area in which the greatest difference was found between the two materials. In order to differentiate between the manufacturing costs of aluminum and fiberglass skins, the knowledge of the team was applied to estimate the steps and costs involved in the process of manufacturing the skin of a wing. Details associated with manufacture of the spar and ribs are not considered, because these will be similar for either skin material.
To manufacture the wing skin using fiberglass, the skin would be divided into four subassemblies. The top and bottom of each side of the wing would be laid-up and cured separately, and then bonded to the frame. Tooling required includes a freezer in which to store the prepreg, molds for each of the subassemblies, a ply-cutting machine to prepare the prepreg, additional molds for other components such as flight control surfaces, jigs to facilitate secondary bonding to the frame, and an autoclave in which to cure each subassembly. The most expensive item is the autoclave, which typically costs several million dollars for the size required. The autoclave supplies heat to cure the resin and pressure to ensure that the proper fiber-to-resin ratio and inter-ply bond strength are achieved. Since the Barn Owl does not have a need for extreme structural performance, it may be possible to achieve the desired performance using a prepreg that can be laminated in an unpressurized oven, employing vacuum bagging for pressure. The unpressurized oven would cost on the order of hundreds of thousands of dollars, rather than millions. However, to demonstrate that it would be acceptable would require detailed analysis beyond the scope of this project. Thus, the cost of an autoclave was used as a worst case assumption.
Labor tasks involved in the manufacture of the fiberglass wing skin include cutting the prepreg, cleaning and coating the molds, laying up the fiberglass, curing the laminate in an autoclave or oven, removing the laminate from the mold, and bonding it to the aluminum spar and ribs. The man-hour estimates for each of these tasks are based on the experiences of the team in working with composite materials.
Raymer [10] gives an estimate of $73 per manufacturing man-hour in 1999 dollars. Adjusted to 2006 dollars, the value of $83 per man-hour was used in the cost estimate.
Much less tooling is required for the manufacture of metallic skin. In the estimate, Team V has accounted for the cost of sheet bending presses and brakes; drills, rivet guns, and other power tools; and a jig on which to construct the wing.
The labor involved in this estimate included cutting, forming, and drilling the aluminum sheet and riveting the skin panels to the spar, ribs, and stringers. The number of rivet holes per wing was estimated to be on the order of 2000, with 90 seconds required to set up and complete each drilling and riveting operation.
A summary of the wing skin manufacturing costs estimate is given in Table 10. Note that this only considers factors directly associated with the manufacture of the wing skin, and does not account for material cost, since these values will be similar. The results of the table are given as cost for plane for a given number of aircraft produced. This amortizes the cost of tooling evenly over each aircraft. Since the fiberglass-skinned wing requires a much greater tooling investment than an aluminum-skinned wing, the cost for small production numbers of aircraft is greater with fiberglass skin. However, for production of 750 aircraft or more, the fiberglass skin becomes the cheaper option. Since the basis of the cost analysis discussed later in this report is the production of 2000 aircraft, fiberglass is the preferred wing skin material from a manufacturing cost perspective. It is expected that a similar cost difference would be seen for fuselage skin.
It should be noted that this estimate is highly dependent on the degree of automation assumed in the production process. For the fiberglass skin, it would be possible to employ automated layup machines, and for the aluminum skin, computer controlled drilling and riveting machines could be used. The assumptions used are based on the team’s knowledge of typical current practice in general aviation.
A further assumption implicit in these estimates is that the production of the Barn Owl starts from scratch. If an existing company were to produce the aircraft, its material experience would affect the costs associated with each material. A company which has done all its prior work in metallics would have available tooling and experienced machinists on hand, thus creating economic incentive to use aluminum. Such a company may even have difficulty acquiring enough employees with composites expertise, if it were to go that route. Similarly, a company with many experienced composite technicians on staff would have added preference for fiberglass.
Table 10: Summary of wing skin production cost estimate (Used as comparison between skin materials only)
|Fiberglass skin |Aluminum Skin |
|Tooling |
|Molds (4) |$360,000 |Sheet Bending Presses |$500,000 |
|Autoclave |$4,000,000 |Drills, rivet guns, etc |$100,000 |
|Tooling for Control Surfaces |$100,000 |Jig |$100,000 |
|Freezer |$120,000 | | |
|Additional Jigs, etc |$100,000 | | |
|Ply-cutter |$150,000 | | |
|Total Tooling |$4,830,000 |Total Tooling |$700,000 |
|Man-Hours |
|Mold and Prepreg Prep |16 |Sheet Cutting |10 |
|Layup |25 |Forming |30 |
|Autoclave |12 |Drilling |50 |
|Secondary Bonding |15 |Riveting |50 |
| | | | |
|Total Hours |68 |Total Hours |140 |
|Cost per Man-Hour |$83 |Cost per Man-Hour |$83 |
|Recurring cost |$5,644 |Recurring Cost |$11,620 |
|Results |
|Number of Aircraft |Cost Per Plane |Number of Aircraft |Cost Per Plane |
|100 |$53,944 |100 |$18,620 |
|200 |$29,794 |200 |$15,120 |
|250 |$24,964 |250 |$14,420 |
|500 |$15,304 |500 |$13,020 |
|750 |$12,084 |750 |$12,553 |
|1000 |$10,474 |1000 |$12,320 |
|1250 |$9,508 |1250 |$12,180 |
|1500 |$8,864 |1500 |$12,087 |
|2000 |$8,059 |2000 |$11,970 |
|2500 |$7,576 |2500 |$11,900 |
|3000 |$7,254 |3000 |$11,853 |
One additional cost factor considered is the affect of skin material choice on maintenance cost. While fiberglass is more susceptible to impact damage and can be more difficult to inspect than aluminum, it has the advantage of reduced concern for corrosion and fatigue. Because of the relative novelty of composite structures in general aviation aircraft, limited data is available regarding actual maintenance cost differences between aluminum and composite skins. However, the current high sales of composite aircraft such as the Cirrus SR-20 and SR-22 models and the Diamond DA-40 do ensure that the mechanics responsible for the maintenance of the GA fleet will be sufficiently experienced to be competent to perform such maintenance on the fiberglass skin of the Barn Owl once it enters the fleet. Thus the maintenance cost difference is expected to be negligible.
The other considerations guiding material choice were those of aerodynamic performance and marketing. As will be discussed in the aerodynamics section of this report, the Barn Owl incorporates several aerodynamic features that are considered advanced for a GA aircraft. Such features include a bathtub wing-fuselage interface, a laminar airfoil, and span-wise wing twist. Structural considerations associated with these features, such as compound curvature and smooth surfaces, are more easily produced with composite skin than aluminum. The selection of fiberglass skin allowed the Team V aerodynamics group full reign to employ such advanced features.
From a marketing perspective, composites are quite popular in today’s general aviation market. Of the 2465 piston aircraft sold in 2005, 1043, or 42.3% were of composite construction [6]. Buyers like the modern technology and the sleek look of composite aircraft. By using fiberglass skin, the Barn Owl will take full advantage of this fact. It will further differentiate itself by being the first four-seat GA aircraft with hybrid structure. Currently, only the Symphony 160 and Liberty XL2, both of which are low performance two-seat aircraft, have metal frames and composite skin.
One caveat for the use of composite skin with an aluminum frame is that bonding is the preferred joining method between the two components. The increased use of composites in general aviation necessitates structural bonding between composites, so the expertise with bonding is growing. However, bonds between aluminum and composite are less common. There is currently no cause to doubt that the necessary bond strength could be achieved in the Barn Owl, but continued, detailed design of this aircraft would require investigation of this feature. Failure of bonding to meet the needs of the Barn Owl would not be insurmountable. Other means of joining the skin to the frame exist, such as bolting or riveting. Also, aluminum skin would still be a feasible substitute, but with added costs.
Structural Layout
The layout of the internal components of the structure is shown in Figure 19. This layout is intended to represent the significant features of the Barn Owl’s structure. Not included are the tail structure, skin, and engine mount.
The skin is not shown for simplicity, allowing the internal members to be seen.
The engine mount was not included in this stage of structural design because the manufacturer of the existing engine selected for the Barn Owl accounts for mount weight in the total installed weight provided. Further, the manufacturer has designed mounts for several other aircraft, and the conventional layout of the Barn Owl firewall-forward suggests that no difficulty would be encountered in mounting the engine.
Likewise, there are no radical features of the Barn Owl’s tail. Thus, for this stage of the project, a detailed design of the tail structure was not conducted. The tail structure would have aluminum spars, ribs, and attachment fittings. The structure would be joined to the structure at the connection of the empennage longerons. The skin of the stabilizers and control surfaces of the tail would be fiberglass, as on the rest of the aircraft. Foam core could potentially be utilized for increased stiffness.
[pic]
Figure 19: Internal structural layout
Several noteworthy features of the structural layout can be seen in the figure. The wing spar is to be an I-beam cross-section. This will allow simple production, with the spar purchased as an I-beam extrusion and milled down to the desired dimensions as determined by the wing structure optimization, discussed below. The milling will also easily enable cutouts in the spar web to be surrounded by regions of increased thickness to reduce stress concentrations. Compared with this method of manufacture, the traditional spar design, with separate web and caps riveted together, would have a better buy-to-fly ratio, but would have increased manufacturing time and cost due to the need to drill and fasten rivets along the length. The large number of holes would also introduce stress concentrations, requiring the components of the spar to be thicker than calculated in the optimization.
The spar is to carry through the fuselage as shown. Care was taken in positioning the components of the cabin and the wing such that the spar would not interfere with the cabin layout. Figure 20 verifies this, showing the spar at the front of the rear seats with plenty of room for the passengers’ legs. This portion of the spar could be constructed in two ways. The entire spar could be extruded as one piece, and then bent in the middle with a forming process to achieve the desired dihedral. Alternatively, the spar could be constructed of two separate extrusions, joined at the center at the necessary angle with a friction stir weld or a butt joint with doublers on the web and each cap.
[pic]
Figure 20: Cabin location of spar carrythrough
The use of a main spar with no auxiliary spars is made possible by the small size and weight of the Barn Owl. The combination of skin and spar creates a two-cell thin wall section capable of withstanding torsional loading. Furthermore, the use of fiberglass in the Barn Owl is beneficial because the ply orientations of the laminate can be adjusted to yield beneficial shear properties. The choice of wing laminate lay-up and analytical confirmation that the wing can sustain the torsion loads are discussed in the wing optimization section. Another significant feature of a typical dual spar design is that the rear spar can be used to attach the control surfaces. In the Barn Owl, the ribs can serve this purpose.
Placement of the spar was determined by the selected airfoil. The FVGA 5121 airfoil designed for the Barn Owl has maximum thickness at 35% chord. So that the spar could have the greatest possible height, resulting in the most efficient configuration for bending, the spar was placed at 35% chord. The center of pressure of the airfoil is approximately located at 25% chord. The distance between the center of pressure and the centroid of the airfoil, with the spar moved back, was accounted for in the torsional analysis.
A total of ten ribs, spaced 30.6 inches apart, will be joined to the spar. This large spacing was chosen because the skin will be stiffened against buckling through the use of stringers. Since the skin is a fiberglass laminate, the stringers can be laid up integrally over foam core, as depicted in Figure 21. The number of stringers and ribs to be used was determined by varying the inputs to the wing optimization code, discussed below. Though the ribs are sparsely spaced compared with existing aircraft, they will provide ample attachment points for the control surfaces. For example, a five foot wide flap can be attached to three ribs, providing some redundancy.
[pic]
Figure 21: Schematic of simple integral stringers
The fuel is to be stored in the wing. The use of fiberglass skin prevents the use of a wet-wing configuration, and fuel bladders or tanks must be used. Due to the central location of the spar in the wing, the fuel tanks will be placed both fore and aft of the spar. Cutouts in the spar web would be used to join the two tanks, so that they can be filled as one. This will make operation identical to that of an identical GA aircraft with one tank in each wing. Milling a pad-up around the cutouts would preserve spar strength.
The layout of the fuselage structure was designed for ease of manufacture. A small number of large components are used. Each member is an extruded aluminum C-channel, which would be purchased with extra thickness and milled to a designed thickness and to follow the contour of the fuselage skin. For some of the members with greater curvature, such as those around the cabin, forming operations would be required. Detailed analysis beyond the scope of this report would be required to design the joints between the members. It is possible that advanced methods, such as joining with high strength titanium fasteners or friction stir welding, could be used.
The C-channels will be oriented such that the flat face is on the outside of the fuselage. This will facilitate bonding of the skin to the fuselage frame.
The advantages of this “big-bones” fuselage structure over conventional structure include reduced part count and fewer manufacturing steps. This configuration does not require the many drilling and riveting operations required to assemble a conventional GA fuselage. Both of these features will result in a reduced manufacturing cost.
Note that the vertical members of the frame around the cabin were placed so as to align with the window frames, as seen in the three-view. Thus the frame will not obstruct the view from the cabin, and there is ample space for doors encompassing the first windows aft of the windshield. Windows would likely be constructed of Lexan.
The main landing gear struts are positioned to connect to the wing spar. The nose wheel strut will be linked to the fuselage frame members at the bottom of the firewall within the cowling.
Wing Structural Optimization
Detailed design of the wing structure was carried out with the goal of minimizing weight while guaranteeing structural integrity and performance. Thus, the design was posed as a constrained optimization problem. To simplify the analysis, several assumptions were made regarding the layout.
For bending analysis, the cross-section of the wing was assumed to be as shown in Figure 22(a). An elliptical skin shape was used to simplify bending moment calculations. The major axis of the ellipse was set equal to the wing chord at each spanwise position, and the minor axis to the maximum airfoil thickness. The chordwise location of the spar does not affect the bending characteristics, since only bending about the major axis was considered.
[pic]
Figure 22: Comparison of simplifying assumptions to actual layout
Figure 22(b) shows a schematic of the approximation used in the torsion analysis. The effect of the stringers was neglected. The front enclosed area was approximated as half of an ellipse with the major axis half-length equal to 35% of the chord and the minor axis length equal to the maximum thickness. The rear enclosed area was approximated as 1.5 times the area of a triangle connecting the top and bottom of the spar with the trailing edge. The path lengths of the skin surrounding each area were determined from the actual airfoil shape as a function of chord.
A Matlab script was written to carry out the optimization. It is reproduced in the Appendix. It optimizes the wing by minimizing the weight of the cross-section at increments along the span, subject to constraints affected by both bending and torsion.
Initially the script calibrates a function for the elliptical load distribution such that the sum of the load matches the design gross takeoff weight of the Barn Owl. It then begins incrementing along the span, starting at the tip. At each increment, the shear force, bending moment, and twisting moment are calculated. The shear force and bending moment were calculated with simple beam theory. The twisting moment was the sum of the aerodynamic moment at the cruise condition, which was downward pitching, and the moment due the difference between the center of lift and wing centroid, which was upward pitching. The aerodynamic moment was found by calculating the section lift coefficient at each spanwise increment, then calculating the moment coefficient based on a curve fit of cm vs. cl from XFOIL data.
The script then invoked the Matlab function fmincon, an optimizer using sequential quadratic programming, to adjust the five design variables to minimize weight while meeting all of the eleven constraints.
The design variables included the skin thickness, stringer area, spar cap thickness, spar cap width, and spar web thickness. The three thickness variables were bounded with lower bounds representing minimum gauge thickness. For the spar web and caps, a minimum gage of 0.05” was used. For the skin, the minimum gage was 0.03”. These values were based on experience and examination of general aviation aircraft wings.
The eleven constraints include allowable stresses, buckling of both skin and spar web, and twist limits. They were all conditioned in the form given in Equation 38:
[pic] Equation 38
The bending stresses were calculated using simple beam theory [3]. The moment of inertia about the chord was calculated with standard equations for the geometries. The stresses in the spar caps and in the top and bottom of the skin were calculated in this way. The moment was multiplied by the load factor under consideration: 3.8 for the limit load and 5.7 for the ultimate load.
These stresses were compared to yield stresses under limit load and ultimate stresses for ultimate load in the spar and skin materials. This accounts for four constraints.
The buckling allowable stresses were computed using sheet buckling equations [11, 7]. These allowables were functions of the thickness design variable, stringer spacing, and rib spacing. For the spar web, shear buckling load was calculated, and for the upper skin, compressive load was calculated. The shear stress in the spar web and bending stress in the upper skin were calculated for ultimate load, and these numbers were compared to the respective allowables.
Since the wing is being designed with only one integral spar, damage tolerance is an important consideration. In a two-spar wing, damage tolerance can be assured by showing that the limit load can be carried by the remaining spar if one is severed. With a riveted spar, rather than integral, a fail-safe design can be demonstrated with one spar component - such as a cap - severed, and the remaining components intact.
To ensure damage tolerance in the Barn Owl’s wing, two failure conditions were considered. One is complete failure of the spar, leaving the skin intact, the other is complete skin failure with an intact spar. The bending moment of inertia was recalculated for each of these cases, and the bending stresses were recalculated at limit load. These were compared to the material ultimate stress allowables, creating two more constraints. Additionally, the skin stress under limit load in the severed spar case was compared to the skin buckling allowable, and the spar web shear stress at limit load in the damaged skin case was compared to the shear buckling allowable.
The final constraint came from the desire to limit the twist of the wing. The twist per unit span was calculated at each increment using shear flow methods for two-cell thin wall section torsional analysis described by Sun [11]. The allowable twist was set as the average twist that would result in a forward tip twist of 1.5 degrees. This value was determined as the optimal twist for the cruise condition, as discussed in the aerodynamics section.
This method of constraining for twist is a simplification, only meant to show the feasibility of taking the torsion loads with the proposed wing layout for the Barn Owl. It also allows the added weight of the required skin thickness to take the torsion loading to be calculated. If this aircraft were carried forward in design, detailed aeroelastic analysis at a variety of flight conditions would be required. Even if the single-spar concept proved insufficient to handle the torsion in the wing, the problem could be easily overcome by adding a small rear spar to stiffen the wing in torsion. The added weight would be fairly small.
The script then sums the weight for each optimized cross-section and adds the weight of the ribs to calculate the total weight of the wing. The rib weight was estimated by computing the weight of a typical rib configuration for the average chord of the wing. This was found to be six pounds.
Allowable stresses and material properties for the aluminum spar were based on those for extruded 7055-T6511. This alloy and temper was selected for its high strength and ability to be extruded. Though not significant due to the fail-safe design, it has moderate toughness as well. S-glass properties given by Raymer [10] were used to determine laminate properties and allowables. A [0/(±45)2]S fiberglass ply layup was used. Elastic properties of the laminate were calculated with a Matlab script, reproduced in the Appendix, adapted from one created for the course AAE 555. This script uses methods described by Sun [11, 12] which are beyond the scope of this report. Another such script was used to estimate the stresses at which the first matrix and fiber failures occur. These stresses were used as the yield and ultimate stresses respectively. The material properties used in the wing optimization are summarized in Table 11.
Table 11: Material properties used in wing structural analysis and optimization
|Material |Al 7055-T6511 |S2-Glass/Epoxy [0/(±45)2]S |
|Density [lb/in3] |0.103 |0.072 |
|Longitudinal Elastic Modulus [Msi] | | |
| |10.4 |3.32 |
|Shear Modulus [Msi] |4 |1.94 |
|Poisson’s Ratio |0.3 |.598 |
|Yield Stress [ksi] |60 |35 |
|Ultimate Stress [ksi] |70 |50 |
|Typical Ply Thickness [in] |- |0.004-0.006 |
The [0/(±45)2]S lay-up was selected due to its balance of longitudinal strength and shear modulus. The large number of ±45 degree plies provides the high shear modulus, resulting in improved capability of the skin to bear torsional loads. Several other layups were considered, all including some zero and some 45 degree plies. The properties of each were calculated and used in an optimization run. The selected laminate configuration was found to result in the lowest optimized weight.
To validate this approach to the design of the wing, an optimization run with all aluminum components was conducted. The weight calculated for an all-aluminum wing was 274 lbs. For comparison, the wing weight was calculated using a statistical group weights method from Raymer [10, eq. (15.46)] - described in more detail below - giving a predicted weight of 304 lbs. The difference of 30 lbs between the optimized and statistical predictions may account for such features as access panels, control surface fixtures, landing gear attachment to the spar, paint, and extra material for joining to the fuselage, all of which are not included in the simplified optimization models. Thus, the optimization approach gives a reasonable prediction for preliminary sizing of the primary structure of the wing.
The result of this sizing using fiberglass skin with aluminum spar and ribs is a total wing weight of 278 lbs. With this result so close to that for an all-aluminum wing, and assuming a similar weight for miscellaneous fixtures, the wing weight calculated with the statistical method will be used in the weight statement as the expected weight of the wing.
Additional output from the wing sizing script includes span-wise plots of all five design variables. The data in these plots - reproduced in the Appendix - would serve as an initial point from which to begin further analysis. The plots could also be used for preliminary work in designing the manufacturing processes to produce the components of the wing.
Future work in designing the wing structure would include many improvements to the analysis. The current code assumes that the fiberglass stringers have the same elastic properties as the skin. In detailed design of the Barn Owl wing, all stringer plies would likely be oriented in the span-wise direction, thereby improving the efficacy of the stringers in bending.
A constant skin thickness at a given cross-section was used for simplicity. Detailed work would likely find that it is more efficient to vary the thickness, and perhaps even the lay-up orientation, around the contour of the wing.
The effect of the stringers on the buckling of the upper wing skin is currently handled by reducing the unsupported width of the skin in the buckling allowable calculation. Detailed analysis would be required to model the increased stiffness due to the stringers, which is more appropriate.
The twist constraint is based on the designed geometric wing twist of 1.5 degrees, optimized for the cruise condition. This being the case, it may be possible for the wing to be manufactured with no twist, adding some simplicity to the manufacture of the wing. With the Barn Owl cruising at 150 kts at 8000 ft, the wing would deform to achieve the desired twist angle at the tip. The twist distribution calculated in this structural sizing is shown in Figure 23. Due to the way the constraint was applied, as an upper limit on twist per unit span, this distribution is fairly linear, whereas the aerodynamically optimized distribution is roughly parabolic. The constraint could be refined as a limit on twist per unit span that is a function of span-wise location, allowing the parabolic distribution to be matched.
Due to the dependence of the structural deformation on the applied aerodynamic load, and the dependence of the aerodynamic performance on the shape of the structure, detailed aeroelastic analysis would be required in the further development of the Barn Owl. It must be used to show that the desired twist and performance are attainable at the design condition. Since significant twisting is expected, aeroelastic analysis must also be employed to ensure that flutter does not occur and that off-design-point performance is not negatively impacted too severely.
[pic]
Figure 23: Calculated twist distribution due to loading at 150kts and 8000 ft. Twist angle is given relative to the angle of attack at the root.
Other details that should be addressed in future wing structural design include addition of the forces induced by control surface deflection, accounting for the effect of the weight of the fuel and wing itself in reducing the net upward force on the wing, and the forces transmitted to the spar by the landing gear at landing.
Fuselage Structural Analysis
To demonstrate that the structural concept of the fuselage was feasible and could bear the design loads, a beam-element model was constructed with I-DEAS finite element software. The fuselage frame elements were modeled with a uniform C-channel cross-section, the dimensions of which were based on expectations for the sizes of the thicker components. The spar carrythrough member was an I-beam which was sized based on the output of the wing optimization. Skin was modeled using plate elements connecting the frames. The model was run with and without the skin for comparison. A thin aluminum firewall was also included.
The loading was applied by constraining the model at the wing roots and at the tip of the tail. Downward point loads were applied at or near the locations of major components, such as the engine and passengers. Load magnitudes were weights multiplied by a load factor of 3. The densities of the fuselage frame and skin were also included, and a gravity load of 3 was applied. In all, the applied loading accounted for a 3G load factor, near the design limit load of 3.8G.
The results of the with-skin model are shown in Figure 24, with the skin removed for clarity. As expected, the peak stress was found to be at the joint between the spar and the fuselage frame. With the initial frame cross-section, the maximum stress is 5 ksi short of the 7055-T6511 yield stress. To handle the full 3.8G limit load, some thickening in this region would be required. Additional bracing in this section could also alleviate the high stress. The stresses in the rest of the model are much lower. Thus, most of the fuselage is over-designed with the assumed cross-section, and a detailed structural design of the fuselage would result in a reduction in the dimensions of most of the members.
[pic]
Figure 24: Results of I-DEAS fuselage model. Skin removed for clarity.
Comparison between the models run with and without skin revealed that the skin greatly increases the stiffness of the empennage region but contributes little in the cabin structure. The empennage required additional stiffness due to the extreme unsupported length of the longerons in the skinless model. Sufficient additional stiffness could also be achieved by adding a small number of circumferential frames to the empennage.
The weight of this I-DEAS model, including the spar carrythrough, fuselage frame elements, firewall, and skin, was calculated to be within three pounds of the 240 lb weight calculated using the statistical group weights method, described below. Since the current model is over-designed, future detailed fuselage design optimization would allow sufficient weight reduction in the structure to account for additional weight in the fuselage while maintaining the predicted total weight of 240 lbs. Such additional weight would include doors, window frames, cabin floor, seat fixtures, and access panels. Thus, this fuselage structural concept is feasible for use in the Barn Owl.
Weight and Balance & Stability
Weights
Component weights were calculated using a statistical group weights method. Raymer [10] provides equations compiled from several sources which estimate the weights of each component for a general aviation aircraft. These equations are based on statistical fits to historical data, using aircraft data, such as wing area, design gross weight, taper ratio, landing gear length, and fuselage length, as input variables.
Structural components calculated by the statistical method include wing, fuselage, vertical and horizontal tails, and landing gear. Systems weights included were avionics, fuel system, electrical system, and hydraulic systems weights. Additionally, the equations include a furnishings weight, which accounts for seats and other cabin details.
The fuselage and wing structural analyses showed the feasibility of the structural layout for the Barn Owl. Due to the similarity of the weights derived in the analyses to the statistically calculated weights, the statistical weights are included in the weight statement, presented in Table 12.
Since an existing propeller-spinner assembly and engine were selected, the installed weights given by the manufacturer were used.
Table 12: Barn Owl Weight Statement
[pic]
The final empty weight fraction of the Barn Owl is 62%. This is similar to other GA aircraft. The aircraft in Team V’s database have empty weight fractions ranging from 61.5% to 69.4%. Aircraft with similar empty weight fractions include the EADS-Socata Trinidad and Tampico GT, Cessna 206, and Grumman AF-5B Tiger, with empty weight fractions of 61.9%, 61.6%, 62.1% and 62.5%, respectively.
C.G. and Static Longitudinal Stability
The weight statement in Table 12 includes the longitudinal distance of each component from the spinner tip. For most components, these distances were measured directly from the CATIA model of the Barn Owl. For those not included in the model, such as flight controls, hydraulics, and electrical system, the location was estimated based on their relation to measured components. For example, the avionics weight was put slightly forward of the instrument panel location.
The weight of the wing was located at 35% of the chord, the location of the spar. The fuselage center of gravity (c.g.) was estimated using the I-DEAS model.
Static margin was used as a measure of longitudinal static stability. The static margin was calculated with Equation (2), where xn is the location of the neutral point, [pic] is the location of the c.g., [pic] is the wing mean chord., lht is the distance from the c.g. to the horizontal tail quarter chord, Sht and Swing are the planform areas of the horizontal tail and wing, respectively, [pic] is the relation between the lift curve slopes of the tail and fuselage, assumed to be equal to one for this stage of design, and xac is the location of the wing quarter chord.
[pic] Equation 39
For the Barn Owl, a static margin in the range of 10% to 25% was desired. This range was set to provide sufficient stability for service as a trainer aircraft without sacrificing maneuverability. The static margins of existing aircraft were also considered [10].
The static margin for the Barn Owl fully loaded with passengers and fuel is 12.1%. The static margin with no fuel and one pilot is 21.67%. In order to ensure that the static margins were in the desired range, the planform area of the horizontal tail was adjusted. A final size of 17.9 ft2 was used.
Figure 25 shows the travel of the c.g. in reference to the static margin limits for various flight conditions. Point B in the figure is at a static margin of 9.4%. However, this point represents the aircraft loaded with a full fuel tank and two passengers in the rear seats. This configuration is possible when the aircraft is being loaded on the ground, but it is not possible to fly without a pilot.
More detailed static longitudinal analysis would be needed to refine the static margin limits, basing them on actual performance characteristics. More refined calculations of static stability, including a neutral point derived from aerodynamic modeling, would also be needed for future analysis.
[pic]
Figure 25: Center of Gravity position in various flight conditions.
Lateral Stability
To help size the tail of the aircraft, Team V decided to use stall/spin recovery parameters to determine the size of the vertical tail. The team thought that since the spin recovery is based on the amount of rudder area that is available during a stall that it would allow the team to accurately estimate the amount of rudder and vertical tail area needed. Added emphasis was placed on the stall-spin stability of the Barn Owl due to the similarity of its appearance to the Cirrus SR22, which is known to be deficient in this aspect.
In order to figure out the amount of tail area needed to avoid a bad spin, equations and a graph were used from Raymer’s text book [10]. The equations were used to calculate the minimum allowable tail-damping power factor (TDPF) using the tail damping ratio (TDR) and the unshielded rudder volume coefficient (URVC). The equations for these parameters can be seen below.
[pic] Equation 40
[pic] Equation 41
[pic] Equation 42
The S values in the equations above corresponded to the areas of the tail and rudder that can still control the airplane during a spin. The wing area is also included in the equations since the wings can still help recover from a spin. The L values are the lengths from the center of gravity of the aircraft to the center of the different tail areas. A picture of what the different S and L values correspond to can be seen below in figure 1. The dotted lines drawn at 60o from the leading edge of the horizontal stabilizer and 30o from the trailing edge represent the area affected when an aircraft is in a spin.
[pic]
Figure 26 - Geometry for spin recovery estimation (From Raymer [10])
To know what area values were needed to control a spin the team needed a TDPF value for are cruising altitude of 8,000 ft. To find this value another figure in Raymer’s text was used. The graph in Raymer plots TDPF versus the spin recovery criterion which is given by the equation, [pic][pic]. From Team V’s structural analysis it was determined that the plane is body heavy, meaning it has a negative spin recovery criterion. The graph also plots multiple lines for different relative density parameters, μ. μ is given by the equation,[pic], which for the aircraft at a cruising altitude of 8,000 ft was approximately a value of 7. Using these two pieces of information, the spin recovery criterion and the density parameter, it was possible to find a TDPF for the aircraft from the graph in Raymer. It can easily be seen from the graph that for a body heavy aircraft with a μ value of 7, the TDPF value for the aircraft would be 2E-4. The graph that was used can be seen below in Figure 27.
[pic]
Figure 27 - Spin Recovery Criteria (From Raymer [10])
Now that a TDPF value was found, the areas and lengths could be adjusted as necessary to make sure the plane could recover from a spin if the plane stalled. The SF and SR2 areas had little room to change since the horizontal stabilizer had been fixed at the bottom of the tail for aerodynamic reasons. The only area that could be significantly adjusted was the top of the rudder and vertical tail, SR1. In the end the adjustments made to ensure the plane would pull out of a spin were slight. The vertical tail area was only increased by a 1 ft2 from what the aerodynamics had previously sized it to. The resulting area of the vertical tail ended with a size of 10 ft2.
Propulsion
Engine
For the engine design Team V had three major constraints. The first was that the engine that was chosen or designed had to be capable of running on the selected alternative fuel, bio-diesel. The second constraint was that the engine had to be below 200 horsepower in order to target the trainer market. The third constraint was that the engine had to fit in the nose of the aircraft.
From these constraints the decision had to be made to design an engine or to use an engine manufactured by another company. After some discussion, the designing of an engine was decided to be impractical, because such development and design would hinder the early market introduction target for the Barn Owl. Therefore, Team V decided to find an existing engine that would meet the above constraints.
After doing some research the perfect engine was found. This engine was diesel aircraft engine made by the company DeltaHawk. The fact that the engine was already a diesel engine ensured that only minor modifications would be needed for the engine to run on bio-diesel. A picture of the chosen engine can be seen below in Figure 28.
[pic]
Figure 28 - DeltaHawk DH200V4 engine (From )
The DeltaHawk DH200V4 met all of the design specifications. It has a maximum horsepower of 200 hp, dimensions of 30x23x32 inches, which fits perfectly into the nose along with room for a radiator, and a total installed weight of 390 lbs including engine mounts. The per-unit cost is around $32,450 which is not terribly expensive. This is also far less expensive than an engine designed from scratch by Team V, thanks to the reduction in development and certification costs. The DeltaHawk engine is currently certified for use with Jet A fuel and is awaiting certification for use with diesel fuels. It is expected to receive its certification for diesel near future.
The fuel of choice to power this design is Bio-Diesel. Team V decided to use Bio-Diesel to fuel the aircraft for several reasons. First, its brake specific fuel consumption (BSFC) is only slightly worse than regular diesel fuel: 0.425 average for Bio-Diesel versus 0.375 for Diesel #2. Second, using Bio-Diesel requires only minor modifications to the engine it will fuel. At times this fuel can soften rubber hoses, but this is easily fixed by replacing those hoses and it only a problem in older engines. The fuel can initially clog fuel filters because it has a solvent action that will dissolve deposits in an older vehicle’s fuel tanks. This is easily remedied by replacing the filters, however the engine will be a new installation modified to run on Bio-Diesel so this airplane will not face any of these problems. Third, the supply of Bio-Diesel is readily available and the amount refined is growing rapidly each year, between 2004 and 2005 the quantity of Bio-Diesel refined grew by a factor three. Fourth, Bio-Diesel does not have any special handling requirements like Hydrogen or Ethanol. This makes it easy to transport and much of the already existent infrastructure can be used to distribute it in the future. Lastly, unfortunately Bio-Diesel does experience cold flow problems like regular diesel. This can be solved by the use of additives to lower the gel point to a desired level. Certain additives like Artic Flow+ can lower the cloud point of Bio-Diesel 25 degrees Fahrenheit, which covers the operating range of this aircraft.
This design uses the DeltaHawk V-4 aviation diesel engine. With this choice, a new BSFC had to be calculated specifically for the DeltaHawk engine. According to DeltaHawk’s website, the engine that will be incorporated into this design has a BSFC of 0.38 lbs/hp*hour running on Jet A. The following calculation shows how the new BSFC was calculated for this particular engine.
Determining the power requirement for this engine:
[pic] Equation 43
[pic]
BSFC Calculation for 100% Bio-Diesel:
[pic] Equation 44
[pic]
This resulting BSFC of 0.439 lbs/hp*hr may seem a little high, however it is correct. All of DeltaHawk’s tests were run using Jet A instead of Diesel. This affects the BSFC they report on their website. Jet A is less dense than diesel which will lower the BSFC some, but Jet A has less energy per volume then diesel. This lower energy density translates to a higher BSFC for that engine, and combining these circumstances with the properties of pure Bio-Diesel lead to the higher computed BSFC.
Another contributing factor to what seems to be an abnormally high BSFC could be the fact that the BSFC for the DeltaHawk engine is higher than the average BSFC of 0.375 lbs/hp*hour from Team V’s engine library. This value was used in the initial sizing of the aircraft until the team decided which specific engine was going to be installed on this aircraft. The higher BSFC of the engine choice will be offset by several factors. First, since an existing engine has been chosen to power the aircraft, this team avoided the extra cost associated with developing and certifying a brand new power plant. Second, using off the shelf technology will help the design to be certified faster since it has a proven source of power. Third, manufacturing the aircraft will be much easier and cheaper because the engine comes pre-assembled from DeltaHawk with all of the major accessories installed. This means that the technicians who assemble the aircraft just need to mount the engine on the firewall and complete the installation.
Determination of Propeller
Once an engine was selected and forward velocity was known, the time was right to select a propeller. Initially, it was the intention of this team to design a propeller specifically for application with the Barn Owl. This however proved infeasible with both allocation of resources and complexity.
Initial research was done to find some general sizing characteristics. Raymer presented a few equations in Chapter 10 of his text that relate propeller diameter to engine horsepower, based upon his plane library [10]. These equations are presented below.
[pic] Equation 45
When compared to similar general aviation aircraft, with an average engine RPM of 2700, the 2 blade diameter is too large and the helical tip speed becomes larger than 0.85M, causing a red flag. Helical tip speed is determined as follows (where D is diameter in ft, n is RPS, and V is forward velocity in ft/s) and is the constraining factor in terms of propeller speed because the tip moves faster than any other part of the propeller, and adding in the forward velocity vector makes helical tip speed faster than tip speed. It is important to have helical tip speed less than .85M (measured at sea level) to avoid the possibility of a shock forming on the propeller and losing valuable thrust.
[pic] Equation 46
The relations stated by Raymer were compared to aircraft in Team V’s library, when propeller types and diameters could be found (18 aircraft). This comparison is presented in Figure 29.
[pic]
Figure 29 - Blade Diameter v. Hp
It is clear that the equations presented in the text over-predict the diameters for two bladed propellers and under-predict the diameters for three bladed propellers for the Hp range of 150-300. It is clear however, that the three bladed propellers are all on high performance planes with greater than 220 Hp. Despite the greater power, these aircraft are not necessarily much faster, as is shown below.
Taking another route, this team decided to compare blade diameter to RPM, since they seemed to have more of a connection to each other than with horsepower. The results appear in Figure 30.
[pic]
Figure 30 - Blade Diameter v. RPM
[pic]
Figure 31 – Blade Diameter v. Speed
If the decision were based upon RPM alone, Team V could have its choice of either a two or three bladed propeller, but looking at horsepower, it seemed that the likelihood of having a three bladed propeller was small, in that it would be unconventional for a plane with similar power to the Barn Owl and therefore most likely a luxury. Further comparison of diameter against cruise speed was done, as shown above in Figure 31.
In looking at all three charts each with importance in determining a propeller, there is one aircraft that matches up with the Barn Owl exactly on two of the parameters and is relatively close on the third. The Piper Arrow has 200 hp, an engine that runs at 2700 rpm and a max speed of 145 kts. In looking up the Arrow’s Type Certificate Data Sheet (TCDS), it was determined that the arrow’s speed of 145kts was limited by the structure of its wings and not by the propeller [16].
The propeller used on the Piper arrow is a 74 inch version of a two blade, constant speed propeller manufactured by Hartzell Propeller Company - the “Hartzell HC-C2YK-1 ( )/7666A-2.” The TCDS for the propeller was looked up, and it was indicated that the max constant RPM is 2700 and the max constant Hp is 250 [16]. The Team V aircraft are therefore within the limits of performance for this propeller. The propeller and the spinner weigh 51 lbs, which keeps the Barn Owl well within static stability limits and the cost of the propeller and kit are about $8,000 (2006 $US) and are thus not cost prohibitive. These values are summarized in Table 13.
Table 13 - Propeller Specifications
|Parameter |Value |
|Blades |2 |
|Diameter |74 in. |
|Max RPM |2700 RPM |
|Max Hp |250 hp |
|Weight (Spinner incl.) |51lbs |
|Cost |~$8,000 (2006 $US) |
Cost
Acquisition Cost Estimation
A very important aspect of this project is being able to predict acquisition cost, and maintain the quality of this prediction. One of the best ways to predict cost at the level of this project is by means of cost estimating relationships (CER). There were three acquisition CERs employed in determining the current predicted cost of $279k.
The first model utilized is one based upon the general aviation library created by the team for this project. The library contains a variety of single-engine piston-prop-powered aircraft from the Liberty XL2 to the Piper Saratoga 2TC. It is understood that this is quite a range of aircraft, with acquisition costs ranging from $140k to $570k (2006 $), however it was reasoned that such a variety of aircraft could reinforce the models created, barring any unforeseen trends that did not make intuitive sense.
A few relationships discovered with this CER are presented in Figure 32 and Figure 33 below. The associations represented are GTOW and max speed vs. acquisition cost. In each case, the purchase price is presented as is, along with an exponential trend line.
[pic]
Figure 32 - Acquisition Cost v. GTOW
[pic]
Figure 33 - Acquisition Cost v. Max Speed
The findings from the GA library seem to make intuitive sense: as takeoff weight and max speed increase, acquisition cost follows suit. It is also clear just by inspection of the charts that GTOW follows a closer packed trend than max speed and will be the variable of focus from now on..
As mentioned before, two other models were used. One used was a version of the RAND DAPCA model, as presented in chapter eighteen of Raymer [10]. The model traditionally takes the input presented below in Table 14. Constant values were assumed for some input parameters. These include the values associated with production (total quantity, five year goal, number of test aircraft) as well as avionics cost. Avionics cost was added into the DAPCA model as suggested in the text. The cost – and therefore the mass – of the avionics was set at 7.5% of the team’s goal of $300,000 at ~$4500/lb [10]. It should be noted that while total quantity was fixed at 5000, the DAPCA model does not take this into account. It takes into account the lesser of production quantity and five year production.
The DAPCA model as presented was developed for aircraft with turbine engines. Since the Barn Owl is not a turbine aircraft but rather a piston aircraft, the CER was modified such that the engine production cost was not factored in. This is a reasonable modification because the DAPCA output needed to be scaled to better match the cost of planes in the team’s library. If engine production cost had been figured into the model, the multiplication factor would have just been larger.
Table 14 - DAPCA CER Input
|Class |Parameter |Value |
|Weight |GTOW |-- |
| |Empty weight |-- |
|Speed |Max velocity |-- |
|Production |Total Quantity |5000 |
| |5 year Goal |2500 |
| |Number of flight test aircraft |1 |
|Turbine Engine |Number of engines |-- |
| |Max thrust |-- |
| |Max mach |-- |
| |Turbine inlet temp |-- |
|Avionics |Avionics mass |5 lb |
Each aircraft of the team’s database was run through the DAPCA model with an investment factor of 1.1 (10% profit per unit). A few examples of output are presented in Table 15 below.
Table 15 – Sample DAPCA Output
|Aircraft |Published Acq. Cost |DAPCA Prediction |
|Cessna 172S |$ 241,000.00 |$ 452,252.69 |
|Cessna 182s |$ 326,150.00 |$ 563,444.45 |
|Cirrius SR 22 |$ 448,685.00 |$ 717,619.85 |
It is readily apparent that the model was a poor predictor as is, overestimating by as much as 70%. To alleviate this problem, a fudge factor was introduced (as mentioned earlier). The actual price of the aircraft was on average 59% of the DAPCA output, therefore it was clear that if the output were multiplied by the above percentage, that it might better represent the Barn Owl’s class of aircraft. Once done, the average agreement between prices was an even 100%. This does mean that some aircraft were over predicted and some were under predicted when compared to published acquisition cost; however, the biggest discrepancies occurred at GTOW of 3400lb or greater and 2500 lbs or less where price error was greater than 10%. The resulting CER is displayed below in Figure 34 where it can be seen that the DAPCA model as modified above is a reasonable estimator of cost within the Barn Owl’s target GTOW range of ~2500 - 3000 lbs and over predicts the acquisition cost for all aircraft in this range.
[pic]
Figure 34 - Purchase Price CER v. DAPCA CERs
The multiplication factor is also responsible for bringing the model up to 2006 $US. The factor was implemented to minimize the difference between DAPCA and the 2006 $US listed prices, therefore it automatically updates to 2006. Similarly, if the model was used to predict 2000 costs, the multiplication factor would update the model and would be different than the factor presently used.
In addition to the DAPCA model, a third model using estimates of airframe unit weight cost was employed. This CER appears again in chapter 18 of Raymer [10] and was optimized for the present application. According to the text, the 1999 $ cost-per-pound of airframe unit weight (AMPR weight) was between $200 and $400. This AMPR weight is approximately 60 – 70% of the aircraft empty weight and for this application was set at 65%. The empty weight fraction of each aircraft was also assumed to be 65% which is a slightly conservative consumption (as higher We = higher AMPR = higher CER Cost).
The only aspect of the CER remaining was to pick the value between $200 and $400 that would best fit the GA library. Three approaches to the optimization were taken: maximize the average percent agreement [Average(actual/CER) =100%]; set the sum of the difference to zero [Sum(actual-CER) = 0]; and minimize the maximum difference [Max(actual-CER)]. Microsoft Excel’s Solver with default settings was utilized to complete these fits. The values determined are presented in Table 16 below.
Table 16 – AMPR CER data fitting results
|Method |$/AMPR ($/lb) |
|Average % Difference = 100% |$ 257.25 |
|Σ (Price Differences) = 0 |$ 277.05 |
|Minimize (Max. Price Difference) |$ 260.37 |
After completing the fits, it was determined that setting the sum of the price differences to zero yielded the best agreement with the actual purchase prices and the DAPCA CER. As in the DAPCA model, the prediction is not perfect. The AMPR model over-predicts all aircraft up until about 3200 lbs. Within the range of 2500-3000 however, the prediction is within 12% of published purchase prices.
All three final cost estimating relationships for acquisition cost are presented in Figure 35 and the equations for the exponential trend lines are presented in Table 17.
[pic]
Figure 35 - Finalized CERs
Table 17 – Trendline and [pic] values for utilized CERs
|CER |Exponential Trendline |[pic] |
|Purchase Price |[pic] |0.86 |
|DAPCA |[pic] |0.86 |
|AMPR |[pic] |0.95 |
It is apparent that the AMPR CER has the best [pic] value, but this is most likely because it is the simplest relationship used, breaking the complex association between aircraft and purchase price down to two parameters – AMPR and $/AMPR. The other CERs are still very good. It is interesting to see that all three models intersect at approximately (3250 lb, $375,000).
Once all of the CERs were ironed out, a weighted average was applied. The average favors the CERS with the higher acquisition cost estimate. In team V’s range of weight, both the DAPCA and the AMPR models are higher than published prices and a factor of 2 was applied to both as shown below in Equation 47.
[pic] Equation 47
With the team’s final GTOW of 2620 lbs, the final acquisition cost, presented in Table 18, comes to be $278,732.00 which is successfully less than Team V’s goal of $300,000. It is important to note that this value is found from the models themselves and not the regression lines presented in figures above. The value obtained from the regression lines in the figures above with the same weighting is $286,930.22, but this is not the proper value.
Table 18 - Acquisition Cost
|$ AMPR |$ DAPCA |$ Library |$ Weighted Average |
|$ 292,170.00 |$ 276,639.00 |$ 256,044.00 |$ 278,732.00 |
To determine a breakeven point, the estimate by DAPCA of Team V’s research, test, development and evaluation (RTD&E) costs is divided by a typical return value per plane (set at ~20% of plane acquisition cost with 80% going toward production [10]). RTD&E costs are estimated by the DAPCA model at ~$139mil to $160mil. This would set the breakeven point at around 2500 aircraft, or five years into production.
Direct Operating Cost Estimation
Another important factor in a feasible design is attaining a reasonable direct operating cost. To create a model for direct operating cost (DOC), both variable and fixed factors were taken into account. Values for most planes in Team V’s plane library were taken from Plane Quest, an independently owned and operated website with pilot reported DOC values [9]. On Plane Quest, variable and fixed DOCs include the parameters listed in Table 19 below.
Table 19 - DOC Parameters
|Variable DOC |Fixed DOC |
|Fuel (GPH) |Average Speed (MPH) |
|Fuel Costs/Gallon |Cost/SM |
|Fuel Costs/Hour |Annual Insurance |
|Oil Costs per Hour |Annual Hangar/Tiedown |
|Maintenance Cost/Hour |Training |
|Hourly Engine Reserve |Total Fixed Costs |
|Prop T/R Reserve |Hours/Year |
Figure 36 results from the data obtained for planes in Team V’s library, as listed on Plane Quest as a function of GTOW.
[pic]
Figure 36 - Direct Operating Costs v. GTOW Plane Quest
It is indicated that the above figure has Plane Quest listed fuel price. The fuel prices listed are slightly outdated, at an average of only $2.30 per gallon for 100LL. It is understood that fuel prices can differ by as much as a few dollars depending upon location across the US, but the team decided to indicate a standard value of $4.27 per gallon – the price of 100LL at LAF, the airport on Purdue’s campus [2]. This new value greatly affects variable DOC as before the exchange, fuel costs accounted for an average of 37% of the variable DOC, and afterward they accounted for an average of 52%. Fixed operating costs stay fixed as should be expected by the nomenclature and total operating costs raised appropriately. Figure 37 displays the resulting prices and the associated trend line equations are presented in Table 20.
[pic]
Figure 37 - DOC v. GTOW with 100LL at $4.29/gal
Table 20 – DOC curves
|Type of DOC |Curve Fit Equation (2006 $US) |
|Fixed |[pic] |
|Variable |[pic] |
|Total |[pic] |
The Barn Owl does not use 100LL fuel, but rather B100 (100% pure bio diesel). The cost of B100 is $2.95/gallon as of 25 April 2006 according to Feece Oil of Illinois [5]. To compute the fuel consumption of the Barn Owl, and thus the cost of fuel per flight hour, the following equation was utilized.
[pic] Equation 48
Using cfuel of $2.95, tank capacity of 54 gallons and time of flight of about 4.5 hours, the barn owl has a fuel cost of $35.40/hour.
Making use of the relationships created by the regression lines in Table 20 above and this team’s weight of 2620 lbs, preliminary numbers for the Barn Owl were determined – values that would be accurate if the Barn Owl used 100LL, assuming the same fuel consumption. They are presented below in Table 21 along with modified values that take into account the use of B100 at $2.95/gal.
Table 21 - Barn Owl DOC
|Barn Owl DOC |Hypothetical 100LL |B100 |
|Fixed |$ 23.00 |$ 23.00 |
|Variable |$ 65.00 |$ 49.00 |
|Total |$ 89.00 |$ 72.00 |
This value for DOC is very competitive, and with B100 is much less than any other plane directly surrounding the Barn Owl’s weight. One can see how the Barn Owl compares to a few benchmark aircraft in Table 22 below.
Table 22 - Benchmark Comparison (2006 $US/hr)
|Plane Type |GTOW (lbs) |DOC/hr Variable |DOC/hr Fixed |DOC/hr Total |
|Diamond DA 40 |2535 |$ 55.00 |$ 15.00 |$ 70.00 |
|Flying V Barn Owl |2620 |$ 49.00 |$ 23.00 |$72.00 |
|Cessna 172S |2558 |$ 64.00 |$ 26.00 |$ 90.00 |
|Cessna 182s |3110 |$ 87.00 |$ 44.00 |$ 131.00 |
|Cirrus SR 22 |3400 |$ 98.00 |$ 40.00 |$ 139.00 |
Life Cycle Cost Estimation
Another model that was to be used solely for life cycle cost estimation and developed independently of the above DOC CER proved to be quite an accurate predictor of DOC. The model was modified from chapter 18 in Raymer [10] to be a more accurate measure of life cycle cost. Using predictions for cost of fuel, maintenance, and insurance it predicts that for 500 flight hours (FH) per year the Barn Owl will cost $79 per hour. This value matches closely with the DOC CER presented above with an agreement of 91%.
As mentioned above, this model was originally intended to predict life cycle cost for owners and operators. The input values are set as follows in Table 23 where MMH/FH is equal to maintenance man hours/flight hour.
Table 23 - Life Cycle Input
|Input Parameters |Values |Typical values [10] |
|Purchase Price |$ 278,732.00 |2006 $US | |
|Flight Hours |500.00 |hr |~ 500 -1000 |
|MMH/FH |0.50 |-- |~ .25 - 1.0 |
|$ Maintenance/ hr. |$ 80.00 |2006 $US |Labor + parts |
|Fuel Consumption |12.00 |gal/FH |gal/FH |
|Fuel |6000.00 |gal/yr | |
|Cost of Fuel |$ 2.95 |(2006 $US)/gal | |
The output of the life cycle cost model for the Barn Owl is based upon some typical values as presented by Raymer with modifications to his model where more accurate data was available [10]. He states that the airframe will depreciate by 1/12 its purchase price every year for 12 years and that the engine depreciates ¼ every year for three years. This depreciation seems excessive, as some 20 year old (or older) planes in the same class have been known to sell for around $100,000 or more. If this were the case then life cycle cost would end up a much smaller value over the short term.
Table 24 – Barn Owl Life Cycle Output
|Factors |Cost (2006 $US) |Notes |Ref. |
|Purchase Price | $ 278,732.00 | | |
|RTD&E/unit | $ 50,171.76 |~20% purch./1.1 |[10] |
|Production/unit | $ 203,474.36 |~80% purch./1.1 |[10] |
|+O&M (total over yrs.) | $ 628,633.06 | | |
|Fuel | $ 177,000.00 |Fuel/yr *$Fuel *Age | |
|Maintenance | $ 200,000.00 |FH*MMH/FH*$M/Hr*Age | |
|Insurance | $ 19,356.39 |~Age*Purch/144 |[10] |
|Depreciation{f(age)} | $ 232,276.67 |Age*Purch/12, age =)
BFL_target=1500; % balanced field length [ft]
Range=600; % [nmi]
AA_Range=0; % alternate airport range [nmi]
Speed=150; % Cruise speed [kts]
Endur=.75; % loiter endurance [hrs]
W_crew=150; % crew weight [lbs]
W_payload=450; % payload weight [lbs]
Alt=8000; % cruise altitude [ft]
divert_alt=2000; % divert/loiter altitude [ft]
Prop_Eff=.86; % prop efficiency in cruise
bhpSFC=.439; % brake horsepower Specific Fuel Consumption
SFC=bhpSFC.*Speed.*1.687./(550.*Prop_Eff); % SFC Calculation
Stall_speed=57; % stall speed [kts]
WingSweep = 0; % Wing Sweep
taper = .5; % Taper Ratio of wing
t_c = .12; % Thickness to chord of wing
Limit = 3.8; % Limit Load Factor
Nz = 1.5*Limit; % Ultimate Load Factor
Sweepht = 0; % Horiz Tail Sweep
taperht = .5; % Horiz Tail taper ratio
Ht_Hv = 0; % 0 for conventional tail, 1 for T-tail
Sweepvt = 0; % Vertical Tail Sweep
tapervt = .5; % Vertical Tail Taper ratio
Sf = 258.3; % Fuselage wetted area [ft^2] (From Zheng's model)
Lt = 18; % Tail length (wing MAC to tail MAC) [ft]
L = 26; % Fuselage Structural Length [ft]
D = 4; % Fuselage Structural Depth [ft]
Nl = 1.5; % Ultimate Landing load factor
NumMainGear = 2; % Number of Main landing gear
Lm = 37; % Extended Length of Main Gear [inches]
Ln = 29; % Extended Length of Nose Gear [inches]
Wen = 350; % Weight of Engine [lbs]
Nen = 1; % Number of Engines
Nt = 2; % Number of Fuel Tanks
Wuav = 30; % Uninstalled Avionics Weight [lbs]
idle_thrust=.2; % idle speed thrust percentage
idle_SFC=SFC; % idle speed SFC percentage
takeoff_thrust=1; % takeoff trust percentage
takeoff_SFC=SFC; % takeoff SFC percentage
climb_rate=700; % climb rate [feet/minute]
CD0=.023; % Parasite drag
CL_mindrag=.075; % Minimum drag CL
LD_full_flaps=5; % lift-to-drag ratio with full flaps
q_cruise=.5*.001869*(Speed*1.6878)^2; % Cruise Dynamic Pressure (8000ft 150kts)
climb_time=Alt./climb_rate./60; % time to climb [hr]
rho_to=0.0024; % air density at takeoff [slug/ft^3]
rho_sl=0.0024; % air density at takeoff [slug/ft^3]
rho_climb=0.0024; % air density at climb [slug/ft^3]
rho_cruise=.001869; % air density at cruise [slug/ft^3]
% For loop indicies
j=1;
% For loops
for AR=12:-1:6; % aspect ratio
i=1;
e=0.0286*AR+0.4359; % Oswald's efficiency factor
for WS=23:-.2:14; % wing loading
% While loop inputs
W0_guess=2750; % initial GTOW guess [lbs]
W0=W0_guess-W0_guess*.05; % initialize W0 for loop
Wf_guess=300; % Initial fuel weight guess [lbs]
w4w3=.9; % initial guess for cruise fuel fraction
LD_climb=10.2; % initial guess for lift-to-drag ratio at climb
tol=.0001; % convergence tolerance
iteradd=.05; % amount added/subtracted from weight guess each iteration until ...
% W0_guess and W0 are within "tol" of each other
while(abs((W0_guess-mean(W0))/mean(W0)) > tol)
% loop dependant inputs
Swing=W0_guess./WS; % Wing Area [ft^2]
CL_cruise= W0/(.5*rho_cruise*(Speed*1.6878)^2*Swing); % lift coefficient at cruise
CD_cruise=0.0756*CL_cruise^2-0.0008*CL_cruise+0.0233; % drag coefficient at cruise
LD_cruise=CL_cruise/CD_cruise; % lift-to-drag ratio at cruise
k_factor=1./(pi.*AR.*e); % aerodynamic constant "K"
CL_minthrust=sqrt((CD0+k_factor*CL_mindrag)/k_factor); % CL at minimum thrust
CD_minthrust=0.0756*CL_minthrust^2-0.0008*CL_minthrust+0.0233; % drag coefficient at min thrust (Raymer 17.14)
LD_minthrust=CL_minthrust/CD_minthrust; % lift-to-drag ratio at min thrust
PW=200./W0_guess; % power-to-weight ratio
TW=PW./(Speed.*1.6878).*550.*Prop_Eff; % thrust-to-weight ratio
Wfw = Wf_guess; % Weight of Fuel in Wing [lbs]
Wdg = W0_guess; % Flight Design Gross Weight [lbs]
Wl = Wdg; % Design Landing Weight
Vt = Wfw/7.344; % Total Fuel Volume [gal]
Vi = Vt; % Internal Tanks Volume [gal]
Sht = Swing*.12117; % Horiz Tail Area [ft^2]
Svt = Swing*.071; % Vertical Tail Area [ft^2]
Bw = sqrt(AR*Swing); % Wing Span
% Weight calcs
% Design Mission Weight Ratios
w1w0=1-idle_SFC.*(14./60).*(idle_thrust); % Taxi to runway (Raymer 19.7)
w2w1=1-takeoff_SFC.*(1./60).*(takeoff_thrust); % Takeoff (Raymer 19.7)
w3w2=exp(-SFC./3600.*((Alt+1./(2*32.2).*(Speed.*1.687).^2)-(50+1./(2*32.2).*(Stall_speed.*1.1.*1.687).^2))...
./((Speed-Stall_speed*1.1)./2.*1.687.*(1-(1./(LD_climb.*TW))))); % Climb (Raymer 19.8)
w4w3=exp(-(Range-climb_time.*Speed).*SFC./(Speed.*LD_cruise)); % Cruise Climb (range equation) (Raymer 19.10)
w5w4=.9989; % Descend
w6w5=exp(-SFC./3600.*((divert_alt+1./(2*32.2).*(Speed.*1.687).^2)-(50+1./(2*32.2).*(Stall_speed.*1.1.*1.687).^2))...
./((Speed-Stall_speed*1.1)./2.*1.687.*(1-(1./(LD_climb.*TW))))); % Missed Approach (climb again) (Raymer 19.8)
w7w6=exp(-(AA_Range.*SFC)./(Speed.*LD_cruise)); % Cruise to alternate airport **NOT USED** (range equation)
w8w7=exp(-(Endur.*SFC)./LD_cruise); % 45 minute loiter (endurance equation) (Raymer 19.11)
w9w8=w5w4; % Descend again
w10w9=.995; % Landing (Raymer 6.23)
% Empty Weight
Wwing = 0.036.*Swing.^0.758.*Wfw.^0.0035.*(AR./cos(WingSweep).^2).^0.6.*...
q_cruise.^.006.*taper.^.04.*(100.*t_c./cos(WingSweep)).^-.3.*(Nz*Wdg).^.49; % Wing Raymer (15.46)
Whtail = 0.016.*(Nz.*Wdg).^.414.*q_cruise.*.168.*Sht.^.896*...
(100.*t_c./cos(WingSweep)).^-.12.*(AR./cos(Sweepht).^2).^.043.*taperht.^-.02; % Horizontal Tail Raymer (15.47)
Wvtail = 0.073.*(1+.2.*Ht_Hv).*(Nz.*Wdg).^.376.*q_cruise.^.122.*Svt.^.873.*...
(100.*t_c./cos(Sweepvt)).^-.49.*(AR./cos(Sweepvt).^2).^.357.*tapervt.^.039; % Vertical Tail Raymer (15.48)
Wfuselage = .052.*Sf.^1.086.*(Nz.*Wdg).^.177.*Lt.^-.051.*(L./D).^-.072.*q_cruise.^.241; % Fuselage Raymer (15.49)
Wmaingear = .095.*(NumMainGear.*Nl.*Wl).^.768.*(Lm./12).^.409; % Main Landing gear (15.50)
Wnosegear = .125.*(Nl.*Wl).^.566.*(Ln./12).^.845; % Nose Gear Weight (15.51)
Winstalled_engine = 390+51; % Weight of Installed Engine (15.52)
Wfuel_system = 2.49.*Vt.^.726.*(1./(1+Vi./Vt)).^.363.*Nt.^.242.*Nen.^.157; % Fuel System (15.53)
Wflight_controls = .053.*L.^1.536.*Bw.^.371.*(Nz.*Wdg.*10.^-4).^.80; % Flight Controls (15.54)
Whydraulics = .001.*Wdg; % Hydraulics (15.55)
Wavionics = 2.117.*Wuav.^.933; % Avionics (15.57)
Welectrical = 12.57.*(Wfuel_system+Wavionics).^.51; % Electrical system (15.56)
% A/C and Anti-Ice not included (15.58)
Wfurnishings = .0582.*Wdg -65; % Furnishings
% Empty Weight total
We=Wwing+Whtail+Wvtail+Wfuselage+Wmaingear+Wnosegear+Winstalled_engine+Wfuel_system+...
Wflight_controls+Whydraulics+Wavionics+Welectrical+Wfurnishings;
% Weight Fractions
WeW0=We./W0_guess;
WfW0=1.01.*(1-w1w0.*w2w1.*w3w2.*w4w3.*w5w4.*w6w5.*w7w6.*w8w7.*w9w8.*w10w9);
% Iteration of W0
if W0_guess < W0
W0_guess=W0_guess+iteradd;
elseif W0_guess > W0
W0_guess=W0_guess-iteradd;
else
fprintf('ERROR, suggest changing "iteradd" or "tol"\n')
end
W0=(W_crew+W_payload)./(1-WfW0-WeW0); % Empty Weight Calculation
Wf_guess=W0_guess.*WfW0; % Fuel Weight
AMPRPrice=W0.*WeW0.*.65.*.27705; % Price estimate
% Diverging W0 and W0_guess correctoin (allows code to continue through a non-converging senario)
if W0=BFL_target & BFL_outside(ii,jj+1)=Turn_n_target & Turn_n_outside(ii,jj+1)=climb_target & Climb_outside(ii,jj+1)=cruise_target & V_cruise_outside(ii,jj+1) ................
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