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The Sparrow 300: An Advanced Agricultural Aircraft
Etan D. Karni* Purdue University, West Lafayette, Indiana, 47907
The Sparrow 300 was developed in response to the RFP issued by the AIAA Foundation for an advanced Agricultural Applications Aircraft in August 2003. The aircraft is a single engine, low-wing externally-braced monoplane with fixed tricycle landing gear. Power is provided by a 300 hp. turbo-diesel engine mated to a 3-blade constant-speed propeller. Empty weight is 1930 lbs., while design gross takeoff weight is 3650 lbs. with a 1200 lb. payload. The aircraft is 29 ft. long, 11 ft. tall, and has a wingspan of 37 ft.
An author-developed sizing code was used throughout the design process, and facilitated the rapid evaluation of thousands of designs before arriving at the final dimensions. Lessons learned from analysis of 299 recent accidents were incorporated in the design, resulting in the installation of innovative stall- and wirestrike- avoidance equipment, a seat rated to 40g impact loads, as well as a full-time cockpit overpressure system. The aircraft is highly maneuverable, and is capable of climb rates exceeding 1000 fpm under design gross weight and 10,000 ft. density altitude conditions. Estimated acquisition cost is $238,000, while direct operating costs are estimated at $62.50 per hour. The Sparrow 300 meets or exceeds all RFP requirements, and promises to be a safer, more economical mount for the next generation of agricultural pilots.
Nomenclature Ps = specific excess power Vs0 = stall speed, flaps fully deployed Vs1 = stall speed, flaps up Vv = vertical velocity Vx = best angle of climb speed Vy = best rate of climb speed
I. Introduction In August 2003, the AIAA foundation issued an RFP for an advanced Agricultural Applications Aircraft.1 This
new design was to fill the small hopper market segment currently dominated by aging aircraft designed in the 1960s and 1970s. The primary design goals were improving safety and performance while reducing costs. Key design parameters and attributes from Sections 2 and 3 of the RFP are summarized below in Table 1.
Other desired attributes: • Easy cockpit egress following a crash • Sealed cockpit, ram-air pressurized • Airframe constructed from corrosion-
resistant materials • Aft fuselage side panels removable for
cleaning • Slightly positive stability and high roll rate
with low stick forces • COTS components used where possible • Use of an in-production powerplant
* Undergraduate Student, Department of Aeronautics and Astronautics. Student Member AIAA.
Table 1. Selected RFP Design Parameters. Parameter Requirement Payload -300 gal. liquid or 1200 lbs. dry media
-Jettisonable in less than 5 sec. Airfield Compatibility
-3000 ft. x 50 ft. gravel, 50 ft. obstacle at each end
Spray Speed -100 kts. Ferry Range -300nm at 75% power, 6,500 ft. MSL,
standard day, 30 min. fuel reserve Service Ceiling -Greater than 15,000 ft. MSL, standard day Fuel -Unleaded gasoline (≤ 90 octane) or diesel
-Tanks not located in fuselage Cost -Purchase price less than $250,000
AIAA 4th Aviation Technology, Integration and Operations (ATIO) Forum20 - 22 September 2004, Chicago, Illinois
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A methodical approach to the design process was used. The first steps taken were to compile a database of existing agricultural aircraft and their key vehicle parameters, as well as a second database of the most common accident scenarios and outcomes. Conclusions stemming from analysis of those databases were then used to establish a vehicle configuration. Next, a comprehensive sizing and performance analysis code was written. This was executed to establish a design point, and to evaluate the characteristics of the design point aircraft. (Fig. 1) Finally, cost was estimated using data obtained from manufacturers of existing aircraft.
II. Pre-Design Efforts With the RFP requirements in mind, the first step was to research existing agricultural aircraft and establish
benchmarks, as well as to determine their shortcomings that would be addressed in the new design. A design database consisting of nine comparable agricultural aircraft was compiled. Most of the comparable aircraft were low-wing monoplanes with tailwheel landing gear. A notable exception was the highly successfully Grumman AgCat biplane. Piston engines operating on standard 100LL aviation fuel are used in all the existing designs, with five of the nine using Pratt and Whitney R-985 or R-1340 radial engines (last produced ca. 1960). The remaining designs used horizontally-opposed six or eight cylinder engines from Continental or Lycoming.
Examination of fundamental aircraft parameters also yielded much useful information. Wing aspect ratios were well-grouped in the 6.0 - 8.5 range. However, wing loadings, power loadings, and payload fractions varied considerably. Wing loadings ranged from 13.7 to 21.2 psf, power loadings from 0.074 to 0.120 lb./hp., and payload fractions from 0.196 to 0.517. The wing helix angle parameter was used to estimate the maximum sustained roll rate during the design point selection process. This technique yielded maximum roll rate estimates ranging from 32.5 to 42.7 deg./s for the monoplanes in the design database, and 46.1 deg./s for the AgCat biplane.
Another step taken to avoid the mistakes of the past was an investigation into 299 NTSB reports covering all accidents incurred under FAR Part 137 (Agricultural Operations) during calendar years 2000 - 2003 inclusive.2 The results were tabulated in spreadsheet form for various author-defined causes and effects, and where appropriate the data was normalized against the latest available (2001) FAA data for fleet composition and operating hours.3
Engine failure was overwhelmingly the dominant cause of accidents, responsible for 34% of the total. (Fig. 2) When normalized against hours flown, turbine engine powered aircraft had a slightly higher rate of engine failure, 0.44 per 10,000 hours, compared to piston engines at 0.29 per 10,000 hours. This contradicts the popular belief that turbine engines are more reliable. The second leading cause of accidents was loss of control, responsible for 21% of
Figure 1. The Sparrow 300.
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the accident total. Loss-of-control events were approximately equally distributed among the takeoff, landing, and spray phases. Many of the takeoff and landing events occurred while the aircraft was on the ground, leading to the conclusion that the unstable tailwheel configuration was a significant factor. The third leading cause of accidents was collision with powerlines or other suspended cables (13%). Cables are all but invisible to a pilot, so it is not surprising that so many wirestrikes occurred. Wirestrikes typically resulted in crashes, with the associated increased risk of pilot injury or death. All other causes individually constituted less than 8.5% of the accident total, and all save structural failure were at least partially attributable to pilot error. The author focused his design efforts on preventing the leading accident causes of engine failure, loss of control, and wirestrikes, as well as structural failures.
The results from the various accident causes considered are presented below in Fig. 3. Forced landings, defined for this paper as “a controlled descent to landing necessitated by aircraft malfunction,” were noted in over 50% of the accident reports. This is not surprising, given that engine failures (not due to fuel exhaustion or contamination) alone accounted for 34% of the total, and fuel exhaustion or contamination contributed another 6%. The remaining 11% is largely made up by collision incidents, where although some control was retained, the aircraft was sufficiently damaged to prevent sustained flight. Outright crashes, defined for this paper as “uncontrolled impact with objects or terrain,” were observed in 27% of cases. These were generally more severe than forced landings, due to the lack of control. Finally, other damage, defined for this report as “airframe damage incurred during circumstances other than a forced landing or crash,” made up the remaining 20%. Most incidents resulting in other damage involved loss of control while on the ground during takeoff or landing, or minor collisions that damaged a wingtip or landing gear.
Post-impact fires occurred in 12.7% of the accidents studied. In most cases, the fire did not start for several seconds post-impact, giving a conscious pilot some time to escape. However, fires were involved in 40% of the fatal accidents. From a psychological perspective, fire is many pilots’ worst nightmare, so these statistics represent a clear area for improvement. Finally, inversions and noseovers combined occurred in 26.4% of the accidents. Many of these events were directly associated with the tailwheel configuration that places the aircraft CG ahead of the main landing gear. The main landing gear then act as a fulcrum during heavy braking or landings on soft surfaces such as recently plowed fields. Although aircraft damage was often substantial, pilot injuries were generally not severe or fatal, indicating that existing pilot protection mechanisms are working adequately here.
Most accidents resulted in the pilot reporting no or minor injuries. (Fig. 4) This further suggests that existing designs are doing a good job of protecting the pilot under most circumstances. Analysis of the 20% of accidents that resulted in serious or fatal pilot injuries indicated that wirestrikes were the leading cause, followed by loss of control and collisions with miscellaneous objects. Not surprisingly, most of these events were categorized as crashes, and post-crash fires occurred in many cases. However, the initial crash impact was frequently not survivable, so in those events, the presence of a post-crash fire would have had no bearing on mortality. Also notable is the statistic that mid-air collisions were almost always fatal.
Engine Failure35%
Lost Control22%
Hit Utility Lines13%
Other31.4%
Figure 2. Accident Causes.
Other Damage
21%
Crash27%
Forced Landing52%
Figure 3. Accident Results.
Fatal12%Serious
8%
Minor18%
None62%
Figure 4. Injuries Sustained.
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III. Configuration, Propulsion, and Airfoil Selection
A. Configuration Selection To ensure coverage of the broadest possible range of configurations, a top-down configuration screen was
initially performed, based on the FAR vehicle categories and a variety of propulsion types. After considering the nonstandard options, it rapidly became apparent that none would be able to meet all of the RFP requirements, and that a traditional fixed wing aircraft powered by a piston or turboprop engine would be the best choice.
The propulsion issue was further refined by comparing the relative merits of conventional propellers against ducted fans. Although a ducted fan would potentially offer higher static thrust and protect bystanders from the rotating machinery, in practice tip losses and drag on the duct have been found to largely negate the benefits, so that option was discarded. Propeller placement was considered next. Pusher placement was rejected on the basis of FOD damage during rough-field operations, and the poor crashworthiness of an aft-mounted engine. It was felt that a twin-engine configuration would result in high maintenance bills and be a liability should a wing-mounted engine fail, so only single-engine configurations were considered. These factors resulted in the selection of a traditional single tractor engine configuration.
Fuselage layout was considered next. A traditional single fuselage was compared against both twin-boom and asymmetric designs. To the best of the author’s knowledge, no asymmetric design has ever entered production, so it was eliminated on the basis of terrible customer acceptance. A symmetric twin-boom layout seemed poorly suited to the single-engine configuration previously determined, and carried with it greater complexity and manufacturing costs. This made a conventional single fuselage the obvious choice. Crashworthiness dictated that the hopper (filled with potentially toxic materials) be placed forward of the cockpit. The engine was fixed at the nose to simplify installation. Thus, the layout of major components within the fuselage was rapidly established as engine, hopper, and cockpit, in order from nose to tail. With cockpit and hopper locations known, the wing layout could proceed.
Traditional aft-tail monoplane and biplane wing configurations were considered, as were canard and tandem wings. Since pilot visibility was paramount, the canard and tandem wings were quickly discarded. Although the biplane configuration would have significant disadvantages, including a narrower swath, high drag due to bracing, and the upper wing also obscuring pilot vision, the potential weight savings and high roll rate were tantalizing. Ultimately, the author concluded that an externally-braced monoplane with aerodynamically boosted ailerons would produce a superior swath width and good roll rate relative to a biplane while avoiding the fatigue issues associated with unbraced monoplane wings. Wing placement was considered next. Crashworthiness, pilot visibility, and structural clearance for the hopper all combined synergistically in the chosen low-wing position.
Empennage layout was examined at this point. Traditional horizontal and vertical stabilizers were evaluated along with mid-, T-, H-, and butterfly tails. The butterfly tail was soon eliminated based on the anticipated pitch/yaw coupling effects. For low speed rudder authority, it was desired to have the rudder in the propwash. Since the H-tail lacked this quality, it was dropped as well. The T-tail seemed likely to offer poor maintainability and increased weight, and the mid-tail did not appear to offer a significant advantage over mounting the stabilizer atop the aft fuselage. Once again, the traditional configuration won out, with the constraint that enough fin and rudder area remain unblanketed at high angles-of-attack for spin recovery purposes.
Landing gear options were quickly reduced either to tailwheel or tricycle layouts, with unicycle, bicycle, and quadricycle layouts being immediately discarded on the basis of poor ground handling characteristics. For comparative purposes, both tailwheel and tricycle options were carried forward to the sizing stage, although from a safety point of view the tailwheel option was unacceptable.
B. Propulsion Selection At this point the engine was selected. Based on prior designs in the design database, it appeared that the engine
would need to be in the 300-400 hp. class, so research focused on engines of this size and operating on non-traditional fuels as desired by the RFP.
Research into available piston engines failed to yield any capable of producing the required power while operating on low octane unleaded fuels. Investigation into diesel engines currently in the production or prototype stage revealed five companies with market-ready engines. Of the five, only Thielert and Zoche, both German firms, had 300 hp. units in the prototype stage. The stated weight of 271 lbs. and specific fuel consumption (SFC) of 0.365 lb./hp.-hr. for the Zoche model ZO 02A were far superior to the corresponding specifications for the Thielert unit, making it an obvious candidate.4 (Fig. 5)
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-0.5
0
0.5
1
1.5
2
0 0.05 0.1 0.15 0.2
Cd
Cl
NACA 35014.5NACA 4415
Turboprop engines were also considered. The turboprop market is highly constrained, since most engines of this type are intended for larger aircraft and helicopters. Among the available choices, only the Rolls-Royce (Allison) 250 is available in a variant producing a reasonable power for this design. Although it offered an outstanding power-to-weight ratio, its SFC was poor relative to the piston options. Similarly, although it has a longer time before overhaul (TBO) than the piston options, maintenance costs are somewhat higher, and acquisition cost is substantially greater. These make it a less desirable choice for the initial design, but appropriate for use in growth versions.
With the candidate engine identified, propeller selection began. To maximize efficiency throughout the operating range, a constant-speed propeller was chosen. A three-blade design was selected in order to maintain good ground clearance without excessive landing gear length, while simultaneously improving low-speed thrust. Using an empirical relationship from Raymer5 resulted in an approximate diameter of 7.0 ft. Aluminum propeller blades, while somewhat heavier than wood or composites, offer far greater damage tolerance and repairability, and so were selected as well.
C. Airfoil Selection The last step before sizing was the identification of an airfoil family for the wing. Wing airfoil demands for this
aircraft were traditional--a high Clmax and L/D, benign stall properties, and low moment. Additional criteria included a section tolerant of turbulent flow (due to the expected rapid accumulation of insects on the leading edge) and relatively loose surface tolerances to ease manufacturing and lower cost. Given the conceptual design nature of this project, a standard NACA section was preferred for ease of parametric evaluation. A key part of the preliminary design stage would be to refine the selected airfoil.
Explorations of various NACA airfoils with the JavaFoil program created by Hepperle6 at the approximate wing Reynolds number of 500,000 and with the early transition “bugs and dirt” model led to the NACA 350xx series of airfoils. These have a design lift coefficient of 0.5 and maximum camber at 0.25 x/c. The vehicle design point selection process (described below) ultimately arrived at an optimal thickness of 14.5%, and thus the NACA 35014.5 was selected.
Sectional properties for this airfoil, as well as for the NACA 4415 used on many aircraft in the design database are presented below. (Fig. 6 and 7) Although the Clmax of 1.67 is slightly lower than the 4415’s 1.80, this is largely attributable to its lower thickness. Drag coefficients are comparable throughout the normal operating region at approximately 0.02. However, the major advantage of the 35014.5 airfoil is its low Cm α=0 of -0.036 vs. -0.100 for the 4415. This should result in markedly reduced trim drag during level flight, which constitutes a sizeable part of the spray and ferry design missions.
Figure 6. Lift and moment coefficients vs. Alpha. Re=0.5M, early transition model.
Figure 7. Drag Polar with NACA 35014.5 section in inset. Re=0.5M, early transition model.
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
-10 -5 0 5 10 15 20 25
Alpha (deg.)
Cl
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Cm
NACA 35014.5NACA 4415
Figure 5. The ZO 02A Engine. (Zoche Image)
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IV. Design Code and Sizing Process To facilitate rapid evaluation of various configurations and parametric studies, the author developed a sizing
code in the C language, based primarily on the methods presented in Raymer.5 Raymer’s methods include empennage sizing by volume coefficients and parasite drag from a component-level buildup. As Raymer’s equations do not accurately capture the impact of taper on wing efficiency, an untapered wing (for manufacturability) with constant Oswald’s efficiency e=0.8 was assumed.
Fundamentally, the sizing process consists of estimating a neutral point, then shifting the engine location to establish a desired empty CG location based on static margin considerations. After this inner loop converges at an empty weight, the configuration is then iteratively “flown” through the design spray and ferry missions to establish fuel requirements and thus design takeoff gross weight. These steps are repeated in an outer loop until a converged takeoff weight is achieved. (Fig. 8)
During the design point selection phase, the sizing code was configured to perform full-factorial sweeps over ranges of wing areas, aspect ratios, thicknesses, and horizontal and vertical tail arms. The resulting data files were processed in Excel, and a manual progressive refinement method was then used to narrow the search space for the next batch.
The RFP suggested cost per acre sprayed as a figure of merit. The only direct operating cost parameter likely to depend strongly on aircraft configuration is fuel consumption, so fuel consumed per acre sprayed was selected as the primary figure of merit. The RFP also requested a high roll rate. Roll rate is dependent on geometry as well, so it was used as a secondary figure of merit. NACA Report No. 715 suggests a wing helix angle value of 0.07 rad. as being adequate for most aircraft, and 0.09 rad. for fighters, so an assumed value of 0.085 rad. was used to estimate roll rate at the spraying speed.7
These metrics were implemented by examining the output file in Excel. The data set was first sorted on the basis of fuel weight consumed per acre sprayed, then filtered by estimated roll rate. A cutoff of 40 deg./sec was used during the initial passes. For the final iteration, the roll rate cutoff was increased to 45 deg./sec, thus ensuring performance comparable to or better than existing aircraft. Figures 9 and 10 graphically depict these techniques.
Implicit in the optimization process described above was a trade study to determine the preferred horizontal and vertical stabilizer arms (distances between aircraft CG and surface aerodynamic center). To ensure enough of the rudder remained unblanketed by the stabilizer wake in a spin condition, the vertical stabilizer arm was constrained to be 0.5 ft. greater than the horizontal stabilizer arm. Ultimately, these methods arrived at the design point after four batch iterations. The design point aircraft has an untapered 182 ft.2, 14.5% thick wing of aspect ratio 7.45. The horizontal stabilizer arm is 12.4 ft. and the vertical stabilizer arm is 12.9 ft.
Parasite drag was computed via the buildup method described in Raymer.5 The large 15% margin is used to account for the exposed spray booms and supports, and for other miscellaneous items. Although the computed CD0 value of 0.0376 is high compared to other conventional aircraft, the value is low when compared to existing agricultural aircraft. The equivalent flat-plate area is 6.84 ft.2.
V. Weight and Balance Summary weight and balance information from the sizing code is presented below in Table 2. Airframe items
were computed using the statistical general aviation equations presented in Raymer.5 System items were computed in this manner as well. When unreasonable results were produced (e.g. 147 lbs. for furnishings), appropriate round number values were assumed. Pilot weight was taken as a 99th percentile, 250 lb. individual. A 10% margin on empty weight is assumed. The CG datum is the most forward edge of the cowl.
Initialization
Enter Outer Sizing Loop
Compute new CD0
End Outer Sizing Loop(Exit if TOGW Converged)
Post-Processingand Data Output
First Inner Loop(Empty W&B)
Second Inner Loop(Ferry Mission Fuel)
Third Inner Loop(Spray Mission Fuel)
Figure 8. Design Code Flowchart.
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The CG envelope for the aircraft is presented in Fig. 11. As intended, CG travel was minimally affected by
payload, even when operating with twice the design payload (i.e. hopper completely filled with aqueous media). The weight of the pilot is the dominant term, followed by fuel load. The envelopes shown define a static margin of 5 - 15% and the design takeoff gross weight of 3650 lbs. Static margin limits are notional, and are intended to ensure an adequate but not excessive level of longitudinal stability.
For a 180 lb. pilot, the static margin should be a comfortable 9.1% when fully loaded, increasing to 12.3% when empty. The unladen value of 17% for the 110 lb. pilot is unacceptably high. This dictates either adding ballast, or imposing a minimum pilot weight restriction. Should a survey of the agricultural pilot population reveal major incompatibilities with the present configuration, the sizing code is structured to readily permit a redesign.
VI. Structure and Materials A notional structural arrangement is presented below in Fig. 12. For ease of construction and eventual
maintenance in the field, a traditional metal-based design is proposed. The fuselage is an aluminum-skinned steel tube truss structure, with the steel tube elements powder- or epoxy-coated for corrosion resistance. Because the skin is non-structural, it may be designed for easy removal and cleaning in the aft section, as the RFP desires. Furthermore, although Alclad aluminum typically exhibits good corrosion resistance, if it is found to be unsatisfactory, fiberglass composite skins may be easily substituted without need for extensive structural analysis and testing. Fiberglass was not selected as the original material since it requires more cost and effort to manufacture (layup and cure) compared to aluminum sheet. Aluminum and steel are also ubiquitous--every mechanic is intimately familiar with the processes required to work with and repair them, making them preferable to other less common materials.
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The wing is a conventional aluminum semi-monocoque, dual-spar, strut-braced design. Because the wing is untapered, all ribs can be inexpensive, identical aluminum stampings. The wing leading edge is designed for easy removal and replacement, as leading edge damage is relatively common. Care was taken to ensure fatigue resistance, a notable cause of fatal accidents and costly airworthiness directives.
A built-up structure similar to the wing could be used for the empennage. An alternative fabrication technique would be a foam or honeycomb core with fiberglass skins, augmented by an aluminum spar or spars (shown for the vertical stabilizer in Fig. 12). This requires an alternative manufacturing process (vacuum bagging, probably in an autoclave) that is potentially less labor-intensive than traditional riveted aluminum. The relatively poor inspectability and difficulty in implementing quality control of repairs to composite structures in the field would dictate a “replace rather than repair” philosophy. Although outright replacement of empennage components may actually involve less downtime and be cheaper than repairing a metal structure after labor costs are factored in (depending on the degree of damage incurred), market research into customer acceptance is necessary since it strongly violates the status quo.
Lastly, the hopper is molded from any one of the modern highly-inert plastics, which should all but eliminate hopper corrosion concerns. The hopper is shaped such that the main wing spar passes uninterrupted beneath it. Wing strut loads tie into the fuselage structure above the hopper (not shown).
VII. Systems Highlights In the interest of brevity, only systems directly contributing to safety improvements are discussed here. The fuel
system is designed to keep the pilot well away from fuel that may be spilled in a crash. Accident analysis suggested that the integrity of an integral “wet” design would be compromised in even relatively minor accidents, so bladder tanks are used. Military-style foam tank packing was considered for further fuel containment, but this requires a degree of access to the inside of the tank only obtained via an integral design, so it could not be used.
The fuel tanks are located in the wing aft of the main spar, placing them well clear of the cockpit and in a location unlikely to be affected by leading edge damage. Feed lines are routed along the main wing spar, through the remote tank selector/shut-off valve, and forward to the engine. No lines pass through the cockpit, thus minimizing potential pilot exposure to a post-crash fuel fire.
As indicated earlier, inflight loss-of-control was found to be a leading cause of accidents. This was frequently due to pilots inadvertently stalling the aircraft while maneuvering. In lieu of the traditional discrete stall warning sensor, proportional pressure sensors sited at the critical location on each wing are proposed. These could be configured to generate a tone in the pilot’s headset varying in frequency and intensity when a stall is approached. Likewise, wirestrikes pose a serious and often fatal hazard. Existing wire avoidance technology is based on either millimeter-wave radar systems costing upwards of $100,000, or on omnidirectional EMF detection systems that would likely have an unacceptable false alarm rate. The author proposes a system using inexpensive digital cameras and real-time image processing to optically sense the wires and their support structures. Alternatively, a comprehensive obstruction database could be queried by an onboard GPS system, which would sound an alert when a potential conflict exists.
For pilot comfort, modern ergonomic cockpit layout techniques are used in the design, and air conditioning is a standard feature. Pilot fatigue and dehydration resulting from prolonged exposure to high temperatures is probably an unstated contributing factor in many accidents. This can easily be avoided by shading the cockpit and maintaining a pleasant temperature. The air conditioning is installed in lieu of the ram-air pressurization specified in the RFP. Even on cool mornings when air conditioning is not required, the minimal weight penalty and electrical demands of running a blower are far outweighed by the benefit of maintaining cockpit overpressure during hopper filling, when ram air is unavailable. Lastly, a COTS energy-absorbing seat is installed to meet the 40g vertical impact requirement stated in the RFP. The seat includes a five-point inertia reel harness, which provides excellent restraint for the pilot under crash loads while permitting free movement under normal circumstances.8
Figure 12. Notional Structural Layout.
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VIII. Stability and Control Static longitudinal stability is ensured by loading the aircraft within the static margin envelope presented in Fig.
11. This results in a static margin of 5 - 15%, which ranges from rather low (comparable to a P-51 and other WWII-era fighters) to moderate (comparable to a “sporty” general aviation type such as a Grumman Tiger).
Dynamic longitudinal stability was not examined in detail. The horizontal stabilizer was sized using a statistically-derived volume coefficient of 0.50, so dynamic parameters should be comparable to the aircraft from which the coefficient was derived, and thus satisfy the applicable FAR 23.181 requirements.
A trim plot is presented in Fig. 13 for a CG location resulting in a 10% static margin. This shows that for a vehicle at 0o angle of attack, trim is obtained via a tail Cl of approximately 0.28. The horizontal stabilizer incidence angle of -2o was arrived at by using the lift curve slope for the NACA 0012 to find the local angle of attack at which this Cl was attained.
The elevator was initially sized for adequate authority to stall the aircraft at the most-forward permissible CG. This required a horizontal stabilizer Cl of 1.0. A strip method was then used to determine the available maneuver margin. It was found that a 25% chord elevator extending over 90% of elevator span and deflected 25 degrees would provide a generous 63% maneuver allowance. Investigations with the X-PLANE simulator program (which attempts to model vehicle dynamics using strip theory) revealed satisfactory dynamic performance and control authority, within the limits of the simulator’s fidelity.
Aileron effectiveness was determined using the method presented in NACA Report 715. For the selected wing aspect ratio of 7.45, it was found that sealed ailerons located between 50% and 95% semi-span, covering 25% of chord, and deflected 30 degrees, would provide sufficient authority for the target 45 deg./s roll rate. The wing dihedral angle of 5 deg. is an estimate based on comparable designs, not a computed value, and thus should produce appropriate roll stability.
The vertical stabilizer was also sized using volume coefficients. Investigations with the X-PLANE simulator suggested that the statistically-derived value of 0.03 was too low, given the destabilizing effect of the long nose. A value of 0.04 was found to provide satisfactory damping for the X-PLANE model, and was used. The rudder was not explicitly sized. Crosswind requirements (perhaps 15 kts.) are the limiting case.
IX. Performance
A. Takeoff Takeoff was analyzed as a two-step process: acceleration to rotation speed (taken as Vx--best angle of climb
speed), and a climb at Vx to clear the 50 ft. obstacle at the runway departure end, both with flaps up. During the acceleration process, thrust was taken as the lesser of static thrust and thrust computed via the usual P/V relationship. Total acceleration was computed as thrust minus aerodynamic drag minus rolling drag. This was numerically integrated against time for velocity and distance traveled until rotation speed was achieved. For light aircraft, the rotation process is typically rapid, so the distance traveled and altitude gained during that phase were neglected. A theoretical best rate of climb speed (Vy) was computed, and checked against flaps-up stall speed (Vs1). The greater of the theoretical Vx and 1.2Vs1 was used. Vertical velocity was then computed from the specific excess power equation:
( ) WDTVPV sv −== (1)
This was numerically integrated against time until the target altitude was attained. As collisions with trees and other objects was a cause of many accidents, an additional 10 ft. was added to the obstacle height to allow for some clearance. Application of this technique resulted in a takeoff ground roll of 453 ft., with 763 ft. required to clear the 50 ft. obstacle by 10 ft. This is considerably less than the 3000 ft. runway length specified in the RFP, and will permit a safe rejected takeoff even when fully loaded.
-0.35-0.3
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0.350.4
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
Alpha (deg.)C
mcg
Cltail = 0.50Cltail = 0.25Cltail = 0.00
Figure 13. Trim Plot.
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B. Climb and Ceiling Climb performance was estimated by the specific excess power method described above. This is presented
graphically in Fig. 14 below. Specific power available increases with velocity when the static value is used, then remains constant when the P/V equation is active. Specific power required exhibits the characteristic parabolic profile, reaching a minimum near the stall. Subtracting specific required power from available power yields specific excess power. Examination of the graph shows the magenta line passing through the origin lying tangent to the excess power curve at a Vx of 63 kts., and excess power reaching a maximum at a Vy of 65 kts. Both of these are uncomfortably close to Vs1 at 59 kts (dashed black line); therefore a safe climb speed of 71 kts (1.2Vs1) is recommended.
When “hot and high” conditions are present, aircraft performance typically suffers. The open symbols and dashed lines in Fig. 14 depict specific power at a density altitude of 10,000 ft. (equivalent to a 95 oF day at 6,000 ft. MSL). Because the engine is turbonormalized, with a critical-altitude of 9,000 ft., this aircraft does not suffer a substantial penalty under these conditions. This is important, since the majority of missions are conducted during the hot summer months, and many agricultural regions of the United States are thousands of feet above sea level. Service ceiling was also examined using specific excess power. The service ceiling was found to be 32,800 ft. (standard day), clearly satisfying the RFP requirement of 15,000 ft.
C. Maneuver A V-n diagram is presented in Fig. 15. The
vertical dashed lines are located at the 1g flaps-up stall speed and maximum level flight speed at sea level, and indicate the limits of the normal flight envelope. Lines of constant turn radius are depicted in blue. For most speeds, the aircraft is stall-limited, meaning that the wing will stall before the pilot can overstress the airframe by positive loading--an important safety consideration. At higher speeds, the aircraft is limited by the +5g / -2g design loads. Turn radius is minimized to 330 ft. by flying at the corner velocity of 130 kts. A 2g steady turn (corresponding to a 60 deg. bank angle) at the design spray speed of 100 kts. will result in a turn rate of 18.9 deg./s and a radius of 511 ft.
D. Landing Landing analysis was also modeled as a two step process. An obstacle clearance margin of 10 ft. was again
introduced. Flap deflection resulting in a Clmax of 2.0 was also assumed. After clearing the 50 ft. obstacle at 60 ft. AGL, the aircraft descends to the runway along a steady 4 degree glidepath while simultaneously decelerating from an approach speed of 1.3Vs0 to Vs0 at touchdown. The landing flare is neglected, resulting in a carrier-style landing at 8.1 fps. Although this value is higher than normal, carrier landings occur at approximately 25 fps and transport-category aircraft are commonly designed for 9 fps, so it is not unreasonably high.
During the second step, the aircraft brakes to a stop on the remaining runway. This technique resulted in a ground roll of 928 ft., with a total of 2077 ft. required to clear the 50 ft. obstacle by 10 ft. This is sufficiently less than the 3000 ft. runway length specified in the RFP to permit a safe go-around in the event of a balked landing. Naturally, in actual service the pilot would be expected to flare before touchdown, runway length permitting, and thus avoid abusing himself and the airframe unnecessarily.
-1000
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0
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0 20 40 60 80 100 120 140 160
V (kts.)Sp
ecifi
c Po
wer
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Figure 14. Specific Power vs. Velocity. Open symbols indicate values at 10,000 ft. Density Altitude.
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Figure 15. V-n diagram with lines of constant turn radius.
American Institute of Aeronautics and Astronautics
11
X. Cost Analysis
A. Acquisition Costs The acquisition cost model was based on
price data obtained from three manufacturers (Gippsland Aeronautics, of Australia, Air Tractor, and Weatherly) for 2004 new production aircraft, Fly-Away-Factory. The Australian dollar has recently surged against the US dollar, so to compensate a historical (January 2000 - January 2004 average) exchange rate of $0.58AU to $1.00US was used.
After converting Gippsland price data to US Dollars, a linear least-squares fit of acquisition cost vs. weight was performed. Good agreement was noted for cost estimates based on both empty and certificated gross weight, with the gross weight model fitting the data somewhat better. (Fig. 16) Based on the certificated gross weight model, an acquisition cost of $238,000 was estimated for the Sparrow 300. This compares favorably to the GA200C at $232,000 (based on the historical exchange rate; approximately $300,000 using April 2004 exchange rates and both excluding shipping and importation fees), the Weatherly 620B at $245,000, and the somewhat larger AT-401B at $277,500.
B. Operating Costs Actual direct operating cost data was also obtained from Gippsland and Air Tractor. Gippsland data for the
GA200C and Cessna 188 was again converted to USD using the historical rate. Although Air Tractor’s smallest in-production aircraft, the AT-401B, is still somewhat larger than the Sparrow 300, as a piston-engined in-production agricultural aircraft it remains a valuable data point. Fuel costs of $2.67/gal. for avgas and $1.67/gal. for diesel were assumed, based on national averages for April 2004. Using conservative estimates for engine and propeller overhaul costs resulted in total direct operating costs of $62.44/hr. for the Sparrow 300. This is a $10.80/hr. cost advantage over the GA200C, and more than $28/hr. over the Cessna 188. Much of this advantage is due to the use of a cheaper fuel at lower rates than competing designs. It is no secret that fuel prices have been steadily increasing in recent years, and coupled with the eventual phase-out of leaded avgas, a significant lifetime advantage for the Sparrow 300 should be expected.
Indirect operating costs such as insurance and hangarage vary substantially by operator experience and region, and could not be reliably estimated. Qualitatively, one would expect that after the insurers gain confidence in the Sparrow 300 (a few years), the nosewheel configuration, excellent controllability, and modern crashworthy design characteristics should result in noticeably lower insurance premiums, much as airbags and anti-lock brakes have done for automobiles.
XI. Conclusion A new agricultural aircraft concept was developed to meet the goals of improved safety and economy of
operation set forth in the AIAA Foundation RFP. These improvements were greatly aided by the choice of a turbo-diesel engine with superior weight and fuel consumption characteristics. Areas for further investigation include continuing the aerodynamic and structural design to the preliminary level, and performing more detailed analyses of stability, control, and performance.
Acknowledgments The author wishes to thank the AIAA Foundation and those individuals who developed the RFP and
administered the competition for providing this opportunity. He would also like to acknowledge the guidance and assistance offered by his project advisor, Prof. William Crossley, by Prof. Crossley’s graduate students David Loffing and Jon Nehrbass, and by Julie Karni.
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