AE 440: Conceptual Design Report for the Agricultural Unmanned Aircraft System 

 

X‐Duster: XD‐44X      

Aerodynamics and Team Leader: Timothy Lingner Configuration: Matthew Fuesz Cost and Components: Wesley Hammes Performance: Timothy Farber Propulsion: Kyle Poycker Stability and Control: Christopher Kelley Structures: Michael Duffy 

        

11/16/2007 

Table of Contents Section                                                                                              Page  Nomenclature...............................................................................................................................2 

Executive Summary.....................................................................................................................3 

1. Initial Design Down‐selection……………………………………………………………..4 

2. Configuration………………………………………………………………………………...6 

3. Structures…………………………………………………………………………………….18 

4. Initial Sizing and Constraint Analysis…………………………………………………..27 

5. Performance…………………………………………………………………………………34 

6. Aerodynamics……………………………………………………………………………….39 

7. Propulsion…………………………………………………………………………………...47 

8. Stability and Control……………………………………………………………………….54 

9. Cost………………………………………………………………………...............................62 

10. Ground Operations………………………………………………………………………..66 

Conclusion 

References 

Appendix  

  A.1 Structures V‐n & Trim Diagram MATLAB Code 

  A.2 Stability and Control: Equations Used 

  A.3 Thrust vs. Velocity Curve and Propeller 

  A.4 Aerodynamic Equations 

 

     

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Nomenclature 100LL -100 Low Lead α – angle of attack αCLmax – angle of attack at the maximum lift coefficient Aeffective – effective aspect ratio AR – Aspect Ratio BWB – blended wing body Cbhp – propeller specific fuel consumption CD – Drag coefficient CDi – Induced drag doefficient CDmin – minimum drag coefficient CD0 – Zero-lift drag coefficient CER – Cost Estimation Relation Cf – chord length of flap

htc - Horizontal tail volume ratio CL – Lift coefficient CLα – Wing lift-curve slope CLαh – Horizontal Tail Lift Curve Slope CL,max – Maximum lift coefficient CM – Moment Coefficent

0MC - Zero lift Moment Coefficient

wMCα

- Moment slope as function of angle of

attack of wing vtc - Vertical tail volume ratio

δflap – flap deflection angle hαα

∂∂

-Horizontal Tail Downwash Derivative

DAPCA IV –Development and Procurement Costs of Aircraft IV

oε - Downwash angle on elevator E – Young’s modulus e – Oswald’s efficiency factor F – fuselage lift factor FF – component form factor G – Shear modulus gal – gallon gph – gallons per hour η – airfoil efficiency factor ηh – horizontal tail efficiency

hr – hour K – drag-due-to-lift factor Λmax t – sweep of the wing at the chord location l – characteristic length lbf – pound force lt – distance between aerodynamic chords lv – distance between aerodynamic chords (L/D) – Lift to Drag ratio μ – viscosity of air M – Mach number min – minute n – load factor P/W – power to weight ratio ρ – density of air R – Reynolds number RFP – Request For Proposal rpm – revolutions per minute S – Planform Wing Area Se – Reference area of each elevator SFC – Specific Fuel Consumption Sh – Reference area of horizontal stabilizer

.S M .- Static Margin Sr – Reference area of rudder Sref – Reference area Sv – Reference area of vertical tail TOGW – Takeoff Gross Weight TSFC – thrust specific fuel consumption (T/W) – Thrust to Weight ratio V – velocity We – Empty weight Wf – Fuel weight W0 – Takeoff Gross Weight (W/S) – Wing loading

achx - Neutral point distance from front wing

LE as % of chord cgx - Center of gravity wrt LE as % of chord

npx - Neutral point of entire aircraft as % of chord

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Executive Summary

Three configurations were proposed to meet the Request for Proposal (RFP) for an

economical unmanned agricultural aircraft to perform crop dusting missions. The first option

was a blended wing body configuration meant to be more efficient by lowering drag and

increasing lift. A second option was a biplane configuration to minimize aircraft dimensions.

The remaining option was a low wing conventional configuration to keep the system simple and

cost effective. All the configurations used a tractor propulsion system and tail dragger landing

gear configuration. The blended wing body configuration used a single vertical tail while the

biplane and conventional configurations use a conventional tail set-up.

The Agricultural Unmanned Aircraft System (AUAS) needed to be “rugged, low cost,

and easy to fly.” In order to meet the ruggedness requirement, the three configurations were

designed with strong and durable landing gear. In order to meet the low cost requirement as well

as a requirement for “off the shelf” components, an existing engine and avionics components

were used. To meet the easy to fly requirement an autonomously operated aircraft was proposed,

which includes provisions for advanced software. Another given requirement was that the

aircraft needed to be completely transported by a pick up truck, and to allow for this the

conventional configuration was proposed to have folding wings; the biplane configuration and

blended wing body configuration were designed to be small enough to not need folding wings.

The studies contained herein on the three candidate configurations show that the RFP

requirements are best satisfied by the conventional monoplane variant. Therefore, this is the

configuration on which to proceed with future design work.

 

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1. Initial Design Down‐Selection (MD) 

1.1 Candidate Configurations

The three evaluated design variants were selected from a pool of candidate

configurations, which were trimmed down via simple conceptual considerations as to the design

requirements of the craft as it was too early for any detailed analysis. Table 1.1 lists the different

aircraft components that were considered to be combined together in varying combinations.

Table 1.1 Aircraft Component Variants Component Variants

Wing Upper monoplane, Lower monoplane, Biplane, Tandem, Flying wing Fuselage Conventional, Blended wing, Twin boom Empennage Conventional, T-tail, V-tail, Canard, Ring tail Landing Gear Tail dragger, Tricycle, Retractable Propulsion Pusher, Tractor, Multiple Engine

1.2 Wing Variant Down-Selection The main motivator in selection of a wing configuration was making sure that the sprayer

system performed optimally. This allowed for the selection of a lower wing monoplane over an

upper wing version as the spray pattern would be obstructed less. The same can be said of a

flying and tandem wing to some extent, but the main factor in not pursuing those configurations

was the unneeded complexity and cost that would be associated with each, being more

complicated than a simple mono or biplane wing configuration.

1.3 Fuselage Variant Down-Selection

The twin boom was not selected as a candidate fuselage because, given the payload that

the plane would be required to carry could fit in a single cylindrical fuselage easily, there would

be no benefit to a twin boom configuration. Further, the added structural weight would be a

hindrance. This made for the simple choice of choosing a conventional cylindrical fuselage,

although a blended wing configuration was also considered to offer greater efficiency.

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1.4 Empennage Down-Selection

For the empennage, the selection was made mainly on the basis of simplicity. Having a

V-tail, T-tail or other control surface configuration more complicated that a conventional tail

conferred no benefits necessary to meet the RFP performance requirements. All would simply

increase the complexity and cost of the system, which the RFP is intended to keep down.

Therefore, sticking with a conventional tail across variants was the logical choice.

1.5 Landing Gear Down-Selection

For a crop duster, the only landing gear configurations that are generally used are either

tail dragging or tricycle setups as they are simple and robust. A retractable version of either was

ruled out as again adding only complexity and not any needed boost to flight performance. The

tail dragger was chosen for each because it would be cheaper and easier to control on the ground

than the tricycle, where some sort of steering or articulation of the gear would be required.

1.6 Propulsion System Down-Selection

Engine choice was motivated both by cost and the nature of the mission. A pusher engine

would suck in the spray from the wing mounted sprayers, making that a poor choice. Further, the

payload was not nearly large enough to require the thrust of multiple engines. Thus a single

engine in tractor configuration would be the choice across variants.

1.7 Three Variant Selection

After eliminating the obviously less efficient component choices, a few configuration

combinations remained. From these, the three variants were chosen to be a monoplane, biplane

and blended wing with conventional tails, a single tractor engine and tail dragger landing gear.

 

 

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2. Configuration (MF) 

2.1 Core systems configuration

Having established the three core design types, initial design on the internal and external

configuration of the aircraft could begin. Preliminary design focused around determining rough

size, shape, and placement of the core systems necessary for basic aircraft functionality.

2.1.1 Propulsion

Rough estimates were used to approximate the volume required for both fuel tanks and

overall engine size, both based on historical data. The fuel tanks were represented by slender

rectangular sections, while the engine was assumed to occupy a roughly cubic volume.

2.1.2 Payload

As designated by the RFP, the aircraft would be required to utilize a self-contained

pumping apparatus for liquid payload dispersion. The volume of payload – both liquid and solid

– was also specified by the RFP, making preliminary modeling relatively simple. In order to

achieve a more streamlined fuselage shape, the payload volume was constrained to a slender

cylindrical or rectangular section. This proved to be greatly advantageous over the spherical

shape of the pumping apparatus, which caused numerous design problems due to both its size

and shape. Additionally, the solid and liquid payload volumes were superposed, with the

intention of using a fixed hopper for the solid payload and a removable tank for liquids, the latter

of which could be placed inside the former. This greatly reduced the anticipated fuselage size,

which is preferable for low weight, a primary concern on this project.

2.1.3 Avionics

A final volume block was allocated to the necessary avionics. This volume was treated

rather amorphously, conforming to whatever space was available in the desired fuselage

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configuration. This would later be refined after actual avionics would begin to be selected. For

the meantime, it provided a reasonable estimate for general sizing concerns.

2.2 External configuration

The volumes and shapes determined from the initial systems analysis were then placed in

several configurations. All configurations were built around anticipated static stability, placing

the varying payload sections near the expected center-of-gravity of the overall aircraft. Several

variations involving the placement of the pumping apparatus and the avionics bay were

produced. However, after creating preliminary external structures to house the estimated

volumes, it was quickly decided that the pump, with its spherical configuration – would have to

be placed near the front of the fuselage. Placing the spherical apparatus rearward resulted in

either consistently thick fuselage sections or a bulge in the fuselage near the pump. Both

conditions are detrimental to aerodynamic efficiency, and so any configuration locating the

pumping apparatus in the aft fuselage were dismissed from the design.

External structure was then developed around these initial volume arrangements, based

on the three selected configurations: monoplane, biplane, and a blended wing body. Several 3D

concept sketches were developed for each of these general configurations, with those with the

most desirable characteristics being chosen for continued development. Commonality became a

key concern for the biplane, as a complete redesign versus the monoplane would be cause for

extensive amounts of additional analysis, which would not further the goal of determining

whether a biplane or monoplane configuration was better suited to the design conditions. The

finalized external designs are illustrated through use of dimensioned three-view drawings in

Figures 2.1-2.3.

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Figure 2.1 Monoplane configuration layout.

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Figure 2.2 Biplane configuration layout.

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Figure 2.3 Blended wing body configuration layout.

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2.3 Structural configuration

Using data gathered by the Structures group, the basic underlying structure for each

resultant external airframe shape was estimated. The structure was determined largely by the

characteristic shape of the airframe as previously determined, and did not contribute significantly

to the external designs. The structural data did, however, become vitally important in the later

weight build-up and balancing operations. Please refer to Structures for more information.

2.4 Additional systems configuration

2.4.1 Avionics

After the preliminary airframe designs were completed, avionics began to be selected.

This allowed for both a more accurate bounding volume for the avionics bay and an estimated

weight value, which was used in roughly determining initial configuration positions.

2.4.2 Propulsion

With an engine selected, the estimated propulsion bounding cube was replaced with an

accurate model of the actual engine to be used by the aircraft, which allowed for significant

airframe improvement in and around the engine area of the fuselage. Nacelles with air inlets

were added to the sides of the cowling for the more conventional configurations, sheltering the

engine cylinder heads from the elements while still allowing sufficient airflow to provide both

power (through combustion) and cooling effects. Fuel consumption requirements were also

calculated at this point, allowing the fuel tanks to be appropriately sized. The fuel tanks also

began to conform to the wing geometry, instead of merely representing a necessary design

constraint.

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2.4.3 Payload delivery system

An initial liquid payload delivery system was also designed, consisting of a length of

piping outfitted with specialized nozzles at regular intervals. This structure was suspended

beneath the wing, offset from the trailing edge. A number of brackets were utilized on each wing

to support this added load, being spaced at intervals along the overall span.

2.5 Weight and balance

2.5.1 Structural weight

The primary concern during the weight build-up procedure was the overall weight of the

airframe – i.e., the empty structural weight of the aircraft. In order to best estimate this weight,

significant cooperation was made between the Configuration and Structures groups. Skin

thickness over all external surfaces was assumed to be a uniform 1/16 of an inch and made

entirely of 2024 Aluminum. Wing ribs were placed uniformly throughout the structure, and were

assumed to have an average cross-sectional area equivalent to 50% of the cross-sectional area at

the mean chord of the wing. Additionally, the ribs were assumed to be 1/16 of an inch thick and

made of 2024 Aluminum. The fuselage was assumed to be supported primarily by a set of ring

frames along the length, which were also assumed to be made out of 1/16 inch 2024 Aluminum.

The cross-sectional area of the ring frames was assumed to be 50% of the cross-sectional area of

the fuselage at 2/3 of the length. Similar schemes were used for the small number of supporting

ribs in the horizontal stabilizer and vertical tail structure. Additionally, I-beam cross-sections

were used to estimate linear density for aluminum spars and stringers used through the wings and

fuselage to add additional structural support and stiffness.

Many of these estimates were purposely made higher than the anticipated actual values.

This provides for any additional weight due to intermediary support structures, cables, linkages,

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and any other unanticipated weight increases. Overall, such analysis yielded reasonable values

with a much greater basis in physical reality than many general formulae presented in academia

based on historic trends, which may or may not be applicable due to differences in materials and

construction techniques.

2.5.2 Component weight

Component weights were easily obtained from either stated values (e.g., the payloads) or

from manufacturers’ published data (e.g.., the engine). Necessary structural members for

components, including the engine firewall and the spray system support struts, were calculated in

a manner similar to that outlined above for the overall airframe. Fuel mass was calculated using

standard density for 100LL multiplied by the total fuel tank capacity. These values combined

yielded overall payload, component, and fuel weights.

2.5.3 Center of gravity calculation

In order to facilitate calculation of the center of gravity in all three dimensions, the

standard Z-up coordinate system used in solid modeling was utilized, with all points referenced

to the modeling datum. Using a series of software scripts, centroids for each major airframe and

subsystem component were able to be calculated and plotted in modeling coordinates. Combined

with the mass data from the weight build-up, these individual centroids were appropriately

weighted, and the overall C.G. of the aircraft was able to be easily determined. It should be noted

that the centroid calculations were based on homogenous materials with uniform, constant

density throughout their volume. Any variations in density (e.g., due to different sections of

material within a single structure or component) were assumed to be negligible; if this were not

the case, the analysis would provide only approximate (and not exact) C.G. locations.

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2.5.4 Static margin calculation

Using the neutral point location determined by the Stability & Control group, the static

margin was able to be calculated. By translating the neutral point to the modeling coordinate

system, the static margin for each configuration was easily obtained. These values were then

passed back to Stability & Control for further analysis.

2.5.5 Balancing

In order to maintain positive static stability by at all times, it was dictated by the Stability

& Control group that the C.G. must remain forward of the previously-calculated neutral point

during the full range of flight conditions. In order to achieve this, numerous sub-systems were

adjusted to balance out the overall aircraft C.G.; in fact, the fuselage was actually increased in

length over its original (pre-balancing) configuration by nearly an inch in order to provide for

sufficient component shifting to achieve the desired stability conditions. This increase allowed

the engine to be seated further forward, pulling the C.G. significantly forward due to the large

mass of the engine and propeller assembly. Additionally, this freed up an extra inch of

longitudinal movement between the remaining subsystems housed within the fuselage. The

finalized, balanced internal layouts for each of the three primary configurations can be seen

through the use of cut-away drawings in Figure 2.4. The C.G. locations noted are those for the

empty weight set-up.

2.6 Final configuration

After numerous iterations due to airframe, airfoil, wing geometry, and other changes, the

designs were externally finished. Further work was required in order to balance the internal

configuration in order to maintain the necessary static stability. At each iteration point, the

resultant geometry, weight, and C.G. data was passed off onto all other design groups for further

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analysis and development. This continued in a mutual fashion until the configurations were

finally finalized.

Figure 6.4 Cut-away drawings detailing internal configuration for primary designs.

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2.7 Landing gear trade study

Typically, advanced-lift aircraft such as flying wings and blended wing bodies utilize

some form of tricycle landing gear, as opposed to the taildragger (or “conventional”)

arrangement used here. Tricycle gear were considered for the BWB design, but were found to

provide insufficient ground clearance due to the presence of the relatively low-handing spray

booms on either wing. Utilizing a taildragger configuration allows for an allowable ground

clearance with reasonably-sized gear. In contrast, a tricycle configuration would require much

longer gear struts in order to provide sufficient ground clearance when pitching up during

takeoff. In addition, tricycle configuration gear are typically not particularly robust in

comparison to most tail dragger arrangements. This is of great importance due to the RFP

requirement for this aircraft to operate on dirt, gravel, or other improvised airstrips. Such

conditions produce much more stress on the landing gear in overall use, and are more suited to

large main oleo or spring-steel struts with a spring-steel tailwheel than to the possibly more

complex tricycle configurations, with more delicate steerable nosewheels.

2.8 Detailed analysis of payload delivery system

2.8.1 Onboard Storage

As the primary function of the aircraft is aerial application of solid particles and fluid

pesticides, components that provided ways to deliver both types of product to the crops were

needed. For the storage tank, a solid particle hopper with a funnel shape was designed. At the

base of the tank was an auger to pull product down into the dispersion outlet.

The fluid storage tank was designed to “plug into” the solid particle hopper. A hose that

can be stored beneath the solid particle hopper connects to the fluid storage tank. The hose is

then connected to a pump which pumps the fluid into the spray booms and out the spray nozzles.

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2.8.2 Application Techniques

After being pulled down from the solid particle hopper by the auger, the solid particles

are released into the atmosphere through the dispersion outlet. The solid particle drop

mechanism is purely a gravity fed system; the solid particles simply fall out of the aircraft. A

fairing around the dispersion outlet helps to decrease the aerodynamic drag and also helps to

produce an even spread behind the aircraft.

The liquid product is applied through a series of nozzles on the boom below and behind

the trailing edge of the trailing edge of the wing. From the fluid storage tank a pump pulls the

fluid into the booms and then the fluid is sprayed on to the crop by way of the nozzles. The

nozzles are an “off the shelf” product designed specifically for aerial application.

2.9 Future work

2.9.1 General configuration

The largest area to be addressed is that of more intricate modeling of the internal and

external structure of the overall aircraft. With future work from the Structures group, the internal

configuration of structural members can be established and actually calculated, as opposed to the

estimation used for this analysis. This will also contribute to perfecting the internal arrangement

of other subsystems, as they will be able to be precisely arranged according to the positioning of

nearby structural members. All of this will be used to better balance the aircraft to not only

achieve stability, but to achieve the smallest range possible of C.G. (and hence static margin)

shift over the entire flight profile. The solid payload hopper will also be designed in detail to

allow the liquid payload tank to mount securely using some sort of quick-release fastener system.

Similarly, the access hatches for the payload and avionics will also be modeled for best user use

with minimal detrimental effects on aerodynamics and structural concerns.

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2.9.2 Payload delivery system

Once an airplane configuration is selected the process of optimizing the spray system to

suit the particular configuration can begin. The angle at which the nozzles are aligned with

respect to the wing needs to be optimized for maximum coverage. The angle at which a

particular nozzle is aimed with respect to the longitudinal axis needs to be optimized for

maximum coverage as well. To reduce aerodynamic drag produced by the spray system, a

streamlined spray mechanism needs to be designed. Once the streamlined spray mechanism is

designed a trade study on production cost effectiveness vs. drag reduction will need to be done.

The method for dispersing solid particles needs to be investigated as worries about

coverage are inherent in the use of a single dispersion outlet. Possible solutions to the solid

particle dispersion problem include creating more dispersion outlets along the wingspan of the

aircraft and dropping the solid particles over that greater length, which would in turn produce

more coverage for the solid particle dispersion. Another, simpler solution would be to engineer a

divergent duct designed for optimum coverage with a certain size of particulate matter.

 

3. Structures and Loads (MD) 

3.1 RFP Requirements 

The RFP performance demands as related to the structural design area are relatively

straightforward. First, the aircraft is supposed to be of a fixed wing design. Additionally, the

craft’s payload will consist of 235 or 300 pounds of liquid or solid material to spray over the

field, operating just above ground level or at 1000 feet without a payload. Given these

parameters, these payload requirements will not put tremendous strains on any common aircraft

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structure. Instead the challenge will be to eventually optimize the design in such a way as to be

as efficient, simple and cost effective as possible.

3.2 Structural Considerations

The main structural consideration for any aircraft is both designing the individual parts to

withstand the loadings it is expected to undergo and maintaining the load paths throughout the

entire aircraft to transfer the load throughout to achieve an efficient design. This necessitates that

the structures in and connecting the fuselage, wings and control surfaces of the aircraft be

properly configured. However, because of the standard tail configuration used in the designs the

control surfaces are not intended to generate any significant percentage of lift for the aircraft.

Because of this the main concerns for the design, at least at present, are in making sure that the

wing is able to support the lift force of the aircraft, transfer it through the fuselage and make sure

the fuselage is able to properly support all of the internal payloads.

3.2.1 Fuselage Structures

In each variant, in order to accommodate the payload, sensors, pumping systems and

engine it was decided that a ring frame structure would be best for the fuselage. The other main

choice of a wing-box carry through configuration would have either forced the fuselage to

become larger to accommodate the internal payload or require other payload modifications that

would have adversely affected the center of gravity of the aircraft. In order to transfer load along

the fuselage between the ring frames, again to best fit around the internal payloads, stringers

along the length of the fuselage will be used. The stringers at the bottom of the fuselage will

simply be thicker in order to directly carry the weight of the internal payloads, whereas the

stringers at the top can be relatively thin as they have little load to carry. The vast majority of

these structures will be made out of aluminum, as it is light, relatively strong and cheap. Certain

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structural elements that require greater reinforcement will be supplemented with steel structure to

add stiffness.

3.2.2 Wing Structures

The wing of each variant has to be designed in such a way that it can withstand the forces

due to lift and drag on the wing as well as the twisting moment generated by the varying lift

distribution along the wing cross section. This requires that the wing both have main spars going

down its length and that the skin on the wing be thick enough to carry most of the moment on the

wing, which is normal in a thin walled structure such as an airplane wing. Ribs will be needed

near the wing root where the fuel tanks are located in order to transfer the weight of the tanks to

the wing spars effectively, however as the wing is meant to have three spars there is little need

for ribs past the fuel tank locations. This is because the only additional attachments to the wing

past the fuel tank areas will be the sprayers, which will add negligible loading. A diagram of the

wing and fuselage carry through structure is shown below in Figure 3.1

Figure 3.1 Basic wing/fuselage structural configuration – isometric view.

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Additionally, the monoplane variant’s wingspan is too long to fit the transport

requirements of the RFP. This necessitates that the portion of the wing past the fuel tanks be

folding. However, designing the folding wings is too complex for this stage of development.

Also, while it is difficult at this time to calculate precise wing loading values one can get a rough

estimate of the forces and moments at the wing roots by assuming that the wing generates the

whole lift of the aircraft and that lift is distributed uniformly along the wing. By then treating the

wing as an Euler-Bernoulli beam one can then calculate rough reaction values at the wing root

that are likely to occur in steady and level flight, which are shown below in Table 3.1.

Table 3.1 Wing Root Forces and Moments at Maximum Payload Variant Root Force (lbf) Root Moment (lbf-ft)

Monoplane 680.2 7047 Biplane (upper) 680.2 0 Biplane (lower) 340.1 1700.5

BWB n/a n/a

3.2.3 Landing Gear

Landing gear is of course necessary to have on any aircraft. Given the relatively low

overall weight of the aircraft and the need for the ability to land in rough fields, keeping the

configuration as simple as possible was ideal. All the variants were designed as tail draggers

because it is a configuration that is simple and cheap to build and also easy to control on the

ground, which is why it is found on many manned crop dusters. Therefore the only question

remaining was what type of landing strut the two forward wheels had. The main choices for this

include solid spring, levered bungee or oleo shock-strut designs. All of these are comparatively

simple and robust enough to withstand a rough landing, but given that the aircraft is unmanned

the shock absorbing requirements for each are somewhat more relaxed than for a manned aircraft

so long as the sensors and other payloads remain intact. In order to best withstand the shock

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loads of landing the gear is going to be made out of steel regardless of the configuration.

Currently the preferred design is that of the oleo shock-strut, because the solid spring design

tends to be heavier while the levered bungee generates more drag than the others. However,

these configurations will be compared in depth to find the optimal choice later once weights and

configurations are fixed; the general location can be seen on the previous variant images.

3.3 V-n Diagrams

Having an idea of the maximum loading that an aircraft is expected to undergo during

flight at various velocities is essential to properly designing the structure of the aircraft. This can

be done through the creation of V-n diagrams, the calculations for which are given in the code in

Appendix Y, which give a visual representation of the maximum g-loading that the aircraft is

expected to experience and survive during flight. Pictured below are the V-n diagrams for each

of the different variants at the maximum weight of full fuel and solid payload.

Figure 3.2 Monoplane variant V-n diagram (max weight).

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Figure 3.3 Biplane variant V-n diagram (max weight).

Figure 3.4 Blended wing body variant V-n diagram (max weight).

From these one can see that there is only a short range of velocities in which the

maximum loading will occur above cruise velocity; however the wings must still be designed to

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take this loading. Also, it is apparent that gust loadings during normal flight are of minimal load

impact, which is partly due to the lower speeds the aircraft is flying at.

3.4 Trim Diagrams

The V-n diagrams only give the maximum g-loading for the aircraft though; in order to

calculate the actual normal and axial loads, corresponding to the lift and drag, expected on the

wing one needs to look at the aerodynamic values versus angle of attack. This is done by

manipulating the lift, drag and moment coefficients in order to find the force coefficients on the

wing during normal flight, which is done by the code in Appendix Y. These force coefficients

versus angle of attack for each aircraft variant are shown in the figures below. These diagrams

are also made under the simplifying assumption that the horizontal tail is parallel with the wing

as further design, specifically tail airfoil selection, is needed to do more realistic calculations.

Figure 3.5 Monoplane variant trim diagram.

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Figure 3.6 Biplane variant trim diagram.

These force coefficient values can in turn be multiplied by the appropriate max load

factor as given by the V-n diagram and design values to find the maximum force that the wing

structure must be able to withstand. However, doing this design and calculation was outside the

scope of current efforts. Further, the difficulty of attempting to calculate what the distribution of

lift over the blended wing body would be, given the limited number of design tools available,

made doing a similar trim diagram for the blended wing variant time prohibitive.

3.5 Material Trade Study

The main trade study that could be performed at this stage of design was in choosing the

materials to be used in the structure of the aircraft. Because of increasing use of composite

materials in all types of aircraft design, it was necessary to compare modern fiberglass and

carbon fiber composites against more traditional material choices such as aluminum and steel.

Looking at the most relevant mechanical properties in Table 3.1 of elastic and shear modulus (E

and G respectively), even when taking density into account, it becomes apparent that fiberglass

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cannot offer the same performance as aluminum in the structure of the aircraft. Only continuous

carbon-fiber composites offer specific properties that can rival steel and aluminum. However,

this is highly dependent on the ply orientations and therefore one does not get the same

combination of elastic and shear modulus as with the bulk metals. Furthermore, the much higher

costs of carbon composite versus metal and the greater complexity in utilizing it means that it is

unsuited for this design as it is supposed to be simple and cost effective. Therefore aluminum

and steel are the materials of choice for this aircraft. Carbon composites would only be used if

aircraft weight became a serious problem later on in development.

Table 3.2 Material Mechanical Properties Ref. [2]

Material E (GPa) G (GPa) density (kg/m3) Fiber fraction Ply Orientation Aluminum 2024 75 28 2800 n/a n/a

Steel (AISI 4130) 210 81 8000 n/a n/a Discontinuous Fiberglass 13.8 3 1760 0.4 n/a

18.5 3 2050 0.6 n/a 23.1 3 2320 0.8 n/a

Continuous Fiberglass 28.7 4.6 2040 0.6 0/90 5x5 14.1 12.8 2040 0.6 +/-45 5x5 33 7.8 2040 0.6 0/45 6x4

Continuous Carbon Fiber 99 13 1560 0.6 0/45 7x3 63 22 1560 0.6 0/45 4x6

3.6 Future Work

After deciding upon which aircraft variant to use, there is much more structural work to

do. After a more detailed lift profile for the wing design is obtained, it will be possible to

thoroughly calculate the forces and moments along the wing structure and fix the internal

structure accordingly to sustain those loads with the desired margin of safety. Further, these

values can be used to design the wing and ring frame interface at the wing root to properly

transfer the loads across the fuselage and support the weight of the fuselage itself. Further, once

26

the center of gravity and therefore location of the internal payloads is fixed, the fuselage

structure dimensions can be calculated in detail as well. After this is done, and one has fixed the

weight of the aircraft structure and the rest of the craft, the loads the landing gear must sustain

can then be analyzed in detail for each different configuration, from which the most appropriate

selection can be made.

4.  Sizing Analysis and Concept Selection (TF)  4.1 Mission Profile The mission profile was well documented and was even included in the RFP. However,

there were a few modifications that could be made to the mission profile in the RFP. For

example, it was up to the team to determine if the aircraft would have to travel back to the

airstrip after its’ payload drop or if the mission would end close enough to the runway where this

was not a consideration. Our team decided to go with the worst case scenario where the aircraft

would have to travel some distance before reaching the runway. Another assumption that was

made was that the airplane would retain its’ payload during the flight. This assumption would

also represent the worst case scenario and gave the team an idea of what the very upper weight

limit would be for the aircraft. This mission profile can be seen in Fig. 4.1

0 1

2 3

4

5 6

7

8

Figure 4.1 Payload delivery mission profile.

27

The RFP also mentioned another mission profile that would act as a “ferry” flight where

the plane could be transferred between missions. The distance for this mission was specified in

the RFP to be one to two miles, so the team decided on the two mile range to account for the

worst case scenario. The mission profile for the ferry flight can be seen in Fig. 4.2

0 1

2 3

4 5

Figure 4.2 Short ferry flight mission profile.

4.2 Initial Sizing

Initial sizing calculations were conducted using Raymer (Ref [1]). The initial sizing

method presented in these references allows the design team to achieve an estimate of the take

off gross weight (W0 or TOGW) so that further analysis can be done on different aspects of the

aircraft. If additional weight is added over the initial estimate it is likely that the plane will still

fly, but not up to specifications.

For this analysis, the TOGW was split up into three categories: fuel weight, payload

weight, and empty weight. The payload weight comes from the RFP and depends on what kind

of cargo the plane is carrying. The analysis was done for both types of payloads; however the

design team is going to use the heavier payload in its design considerations because that is the

maximum weight.

The initial sizing depends a lot on the selected mission profile and how it is broken up.

The team used the same mission profile as described in section 4.1 and used each leg to perform

weight fraction analysis. Once each segment’s weight fraction was found, they were multiplied

28

together to get the final weight fraction. From this the fuel fraction can be found and a safety

factor of 1.06 was applied to account for reserve and trapped fuel. Takeoff, climb and landing

fractions were taken from historical data in Table 3.2 of Ref [1]. The descent portions of the

flight were considered part of the cruise leg, so their weight fractions were assumed to be one.

The cruise portion distance was calculated using data from the RFP and some simplifying

assumptions. The RFP specified a field size of 1000 ft by 0.5 mi. For the initial sizing, the

design team decided to estimate the distance to spray the field by taking the area sprayed per

pass and adding the turn distance times the number of passes. A second cruise portion was

added after the spraying mission to account for the aircraft returning to the landing strip and to

give the maximum possible distance that the aircraft would have to travel. This distance was

estimated to be around 1000 ft, or the width of the field. The weight fraction for both cruise

segments was calculated using the Breguet range equation in Ref [1].

The empty weight fraction was found using the equation found in Table 3.1 of Ref [1].

Historical values are given for different parameters and then using an initial guess for the

TOGW, the empty weight fraction can be found. To be thorough, a survey of historical

agricultural aircraft was also taken and the results were compared to what was obtained using

Raymer (Ref [1]). The results, along with what the empty weight fraction for our proposed

design (based on the TOGW determined later) are presented in Fig 4.3 and Table 4.1.

29

y = -5E-10x2 + 5E-06x + 0.4953

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0 2000 4000 6000 8000 10000 12000 14000 16000 18000TOGW (lbs)

We/W

0

Figure 4.3 Plot to compare empty weight ratios.

Table 4.1 Data for the Comparison of Empty Weight Ratios Plane TOGW (lb) Empty Weight (lb) We/W0

AT-401B 7860 4244 0.540 AT-402A/B 8600 4100 0.477 AT-502A/B 9400 4297 0.457 AT-602 12500 5600 0.448 AT-802A 16000 6505 0.407 AT-802F 16000 7210 0.451 PAC Cresco 8250 2950 0.358 An-2 12000 7300 0.608 An-3 13000 7000 0.538 M-18 Dromader 11700 5975 0.511 PZL-106 Kruk 6600 3674 0.557 PA-25 Pawnee 2900 1288 0.444 PA-36 Pawnee Brave 4400 2180 0.495 GA200 Fatman 4400 1914 0.435 Cessna 188 3300 2160 0.655 G-164 Ag Cat 7020 3150 0.449 Ayres Thrush 6000 3700 0.617 CallAir A-9 3800 1800 0.474 Design Point 1120 559.97 0.500

30

The weight fractions were then used to calculate the fuel fraction that each configuration

needed and then the TOGW was guess iteratively until the guess approximately equaled the

result from the equation based on the empty weight fraction. A number of design parameters

were chosen based on the airplan configuration and those are presented below in Table 4.2. Each

configuration had many parameters in common, such as CD0, SFC, and propeller efficiency. The

spray distance is different for each configuration because of the wingspan that is required to

produce the desired performance and this seems to be the biggest difference between the

configurations. A summary of the iterated TOGW and weight fractions are also tabulated in

Table 4.3. Finally, a summary of the mission segments and their weight fractions are presented

in Table 4.4.

Table 4.2 Input Data for Initial Sizing

Parameter Conventional Biplane Blended Wing

Body Operating Altitude (ft) 20 20 20

Operating Speed (ft/s {mi/hr}) 168 {114.5} 168 {114.5} 168 {114.5}

Operations Distance (ft {mi}) 132000 {25} 264000 {50} 264000 {50}

Turning Speed (ft/s {mi/hr}) 168 {114.5} 168 {114.5} 168 {114.5} Minimum Turning Radius (ft) 327.6 327.6 327.6

Turn Distance (ft {mi}) 18064 {3.42} 18064 {3.42} 18064 {3.42} Return Distance (ft) 1000 1000 1000

Spray Time (seconds {minutes}) 893 {14.89} 1678.95 {27.98} 1678.95 {27.98}

CD0 0.03 0.03 0.03

e0 0.85 0.85 0.85 AR 6.67 13.33 3.33

SFC (cruise) (lb/hr/bhp) 0.1527 0.1527 0.1527 Prop Efficiency (cruise) 0.8 0.8 0.8

(L/D)max 12 13 11

CL,max 1.44 1.44 1.44 Solids Payload Weight (lb) 350 350 350

Liquids Payload Weight (lb) 285 285 285

31

Table 4.3 Initial Sizing Results for Input Data

Parameter Conventional Biplane Blended Wing Body TOGW solids (lb) 1121 1126 1130

TOGW liquids (lb) 933 938 941

We/W0 0.6 0.6 0.6

Wf/W0 0.070 0.072 0.073 Solids Mission Fuel Weight (lb) 78.7 81.6 83.0

Liquids Mission Fuel Weight (lb) 65.5 68.0 69.1 Max Fuel Capacity Needed (gal) 13.13 13.63 13.85

Table 4.4 Summary of Mission Segment and Weight Fractions

Leg Segment Height

(ft) Range (miles) (L/D)

V (ft/s)

SFC (lb/hr/lb) Assume Wi/Wi-1 Wi/W0

0

Warm up and

taxi 0 NA NA NA NA Included in Takeoff 1.000 1 Takeoff 0 NA NA NA NA Historical fuel fraction 0.970 0.970 2 Climb variable NA NA NA NA Historical fuel fraction 0.985 0.955

3 Descend variable NA NA NA NA Descent is part of

cruise 1.000 0.955

4 Cruise 20 25 12 168 0.12 (L/D)=(L/D)max 0.997 0.953 5 Climb variable NA NA NA NA Historical fuel fraction 0.985 0.939

6 Cruise 50 0.19 12 168 0.12 (L/D)=(L/D)max 0.99998 0.938

7 Descend variable NA NA NA NA Descent is part of

cruise 1.000 0.938 8 Land 0 NA NA NA NA Historical fuel fraction 0.995 0.934

4.3 Constraint Analysis

The next step in preliminary analysis was the Constraint Analysis, which is used to

determine wing loading and power to weight ratios. The Constraint Analysis was performed

assuming that the plane was in the conventional configuration, but the constraint diagrams

should be similar for all of the different designs.

The Constraint Analysis was done using the results and assumptions from the initial

sizing. The assumptions and conditions that were used in the Constraint Analysis are

32

summarized below in Table 4.5. The equations for conducting the Constraint Analysis are

located in Anderson and Raymer (Refs [3] and [1]). The design team decided to perform the

Constraint Analysis on the most important parts of the aircraft’s flight, which include the takeoff,

landing, turning, and cruise. The plot resulting from the constraints is shown in Fig 4.4.

Table 4.5 Summary of Constraint and Assumptions Constraint Assumptions

Takeoff 750 feet, standard sea level (SSL) conditions, thrust(power) is much greater than the drag and ground friction

Landing 750 feet, standard sea level (SSL) conditions, CL,max,L is greater than CL,max

Sustained Turn

Load factor of 2.5, turn velocity equals operating velocity, SSL conditions, CD0=0.03

Cruise SSL conditions, velocity>1.3vstall, CD0=0.03, e0=0.85

4.4.1 Selection of a Design Point

From Fig 4.4, it is easy to see that the design space will be constrained by the sustained

turn and landing constraints. The design point that the team selected is located at a wing loading

of 16 lb/ft2 and a power to weight ratio of 0.095 bhp/lb. The design point was selected here so

that even if the plane changes, the constaints will not be violated. This design point also decides

a number of design parameters which are summarized below in Table 4.6. The results from the

design parameters also influenced the choice of design point because if the wing loading were

lower there would be less thrust required, but the wings would have to be very large. The

parameters were tabulated for both payload cases, however the heavier TOGW is more important

because that is the maximum.

Table 4.6 Summary of Design Parameters Given by Constraint Analysis

TOGW (lbs) Power Required (bhp) Sref Wingspan (ft) Chord Length (ft) 1121 106.50 70.06 21.62 3.24 933 88.64 58.31 19.72 2.96

33

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0 5 10 15 20 25Wing Loading (W/S)

Pow

er to

Wei

ght R

atio

(P/W

)

Cruise Constraint

Takeoff Constraint

Sustained CruiseConstraintLanding Constraint

Design Point

Figure 4.4 Constraint analysis diagram with design point selected.

 

5. Performance (TF) 

5.1 RFP and Other Requirements

The RFP specified a number of performance values that must be met in order for the

design to be considered successful. There were a number of other parameters that were not

specified by the RFP so those were chosen so that the other design team members could create a

workable design. These specifications are outlined below in Table 5.1.

Table 5.1 Summary of Performance Requirements Requirement Value Source

Operating Speed 1.3*Vstall RFP Takeoff Distance (ft) 750 RFP Landing Distance (ft) 750 RFP Operational Altitude (ft) 20 RFP Ferry Altitude (ft) 1000 RFP Ferry Distance(mi) 2 RFP

Turning Radius (ft) < 250 Design Team

34

As was discussed in section 4 the three important requirements that must be met are the

takeoff and landing distance and the cruise distance to cover the fields. The other parameters

would be derived from what the plane could do based on the other performance characteristics.

The ferry mission could also be easily met if the three main specifications were because the

weight for the ferry mission is much lighter and the distance is also less than a regular payload

drop mission.

The only requirement that the design team felt the need to specify was a turning radius.

The value of 250 ft was chosen because of the width of the field. If the plane didn’t meet this

requirement it would not jeopardize the success of the payload dropping mission, however a

more maneuverable plane would make this mission easier and quicker to accomplish.

5.2 Design Parameters Investigated

To meet the requirements the most important parameters of the airplane are the

aerodynamics and structures. The structures portion will deal mainly with the wing loading and

the load factor that is applied during the turn. The aerodynamics performance parameters that

affect the critical performance requirements of the plane are CL,max, CD0, and AR.

The amount of wing loading is critical to almost every aspect of how the aircraft

performs, but is particularly important in the case of takeoff and landing. A higher wing loading

means that it is harder for the airplane to get off of the ground and also makes it harder to land in

a set distance. Because of the requirements in the RFP, our vehicle will need to have a low wing

loading. The load factor is important in determining turning radii and speeds. To achieve the

desired performance the load factor will have to be in the medium range.

For the cruise portion of the mission, it is critical to have a high lift to drag ratio (L/D),

which stems from a high CL,max and CD0 according to the equations in Raymer (Ref. [1]). When

35

CD0 is increased it decreases the maximum speed and range of the aircraft. CL,max has a big effect

on the stall speed of the aircraft as well as the takeoff and landing distances. When CL,max is

increased, the landing distance and takeoff distance decrease and the stall speed decreases as

well. Overall it is good to have a higher CL,max because the airplane will be more efficient and

less likely to stall. However one downside to having a high CL,max is that the cruise speed is

decreased. The cruise effects of a high CL,max can be offset by increasing the aspect ratio (AR) of

the wing to reduce the drag due to lift (induced drag or CDi).

5.3 Takeoff and Landing Performance

The equations that were used to determine the takeoff and landing performance came

from Raymer and Anderson (Refs. [1] and [3]). The equation accounts for the effects of wing

loading, ground friction, thrust, induced drag, and zero-lift drag. A spreadsheet was created in

Excel that took the values for each parameter and plugged them in to give the takeoff distance

for a given set of values. Different values were chosen for the velocity until a reasonable CL,max

was obtained. The analysis was done using the weight buildup values from Configuration and

the aerodynamics data from Aerodynamics.

The values for the takeoff and landing distances were then compared to what they were

with the chosen design point from the Constraint Analysis. A summary of this comparison can

be found in Table 5.2.

Table 5.2 Summary of Takeoff and Landing Distances

Configuration

Initial Weight (lbs)

Build-up Weight (lbs)

Initial takeoff distance (ft)

Revised takeoff distance (ft)

Initial landing distance (ft)

Revised landing distance (ft)

Conventional 1121 1361 468.86 1063.84 739.88 705.30 Bi-Plane 1126 1358 468.86 Not Available 739.88 406.34 Blended Wing Body 1130 1384 468.86 956.49 739.88 965.76

36

5.4 Sustained Turn Performance

Throughout the payload drop portion of the mission, the aircraft will be turning after

every pass, which makes the turning performance crucial to how well it will complete the

mission. The analysis used to determine the performance come from Anderson (Ref [3]). The

maximum load factor allowable by the thrust of the engine was calculated and from that the

turning stall speed, minimum turning radius, and turning velocity were calculated. Results from

this analysis are presented in Table 5.3 below.

Table 5.3 Summary of Turn Performance Based on Maximum Thrust Configuration nmax, thrust Vstall (ft/s) Turning Radius (ft) Conventional 2.22 164.62 446.25 Bi-Plane 1.18 94.56 1394.18 Blended Wing Body 1.05 112.60 2742.54

5.5 Other Miscellaneous Performance Parameters

Several other performance parameters were also specified in the RFP, but do not merit

their own section. Those parameters include the operating speed, the total mission time, and

drag for the segments of flight. The operating speed was specified in the RFP and was calculated

using an equation from Anderson (Ref [3]). Drag for each segment was based on the classic drag

equation using the dynamic pressure, wing area, and drag coefficient. These are all tabulated

below in Table 5.4 and 5.5.

Table 5.4 Summary of Miscellaneous Performance Parameters

Configuration Mission Time

(min) Vstall (ft/s) Minimum Operating

Speed (ft/s) Turn Rate

(rad/s) Conventional 20.50 110.61 143.79 0.352 Bi-Plane 32.30 86.93 113.01 0.352 Blended Wing Body 32.30 109.86 142.82 0.352

37

Table 5.5 Summary of Drag for each Segment Configuration Cruise Drag (lbs) Turn Drag (lbs) Takeoff Drag (lbs) Landing Drag (lbs)

Conventional 98.72 242.95 130.02 116.51 Bi-Plane 268.29 852.85 649.36 570.76 Blended Wing Body 400.63 1510.42 670.27 586.91

5.6 Trade Studies

Two trade studies were performed in an attempt to shed light on the cause of the

shortcomings of the designs, particularly with the takeoff and turning radius specifications. The

takeoff trade study had CL,max altered to gauge the effect that it would have on the takeoff

distance. From the trade study it can be concluded that a lower CL,max is beneficial to the takeoff

distance. The results can be seen in Fig 5.1. For the turning radius study, CD0 was altered so that

its effect on the loading factor, and therefore the turning radius could be seen. The effect of CD0

was not as profound as the results for CL,max however the study still shows that the lower the CD0

is the smaller the radius can be. This makes sense because if less thrust is being nullified by drag

it can then be used to power through a turn. The results of that trade study can be seen in Fig

5.2. Both trade studies were performed for the conventional configuration.

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 0.5 1 1.5 2 2.5

CL

Take

off D

istan

ce (f

3

t

Figure 5.1 CL trade study for the takeoff distance.

38

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

0.000 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090

CD0

Turn

Rad

ius (

ft

Figure 5.2 CD0 trade study for the turning radius.

5.7. Future Work

Since the takeoff and turning requirements for the RFP were not met it is essential that

those are the first specifications that are looked into further so that they can become optimized

and fall within the desired range. The mission profile has been somewhat simple so far and

therefore in the future a better estimate of the performance can be obtained by discretizing the

mission profile further.

Other performance characteristics that should be looked at in the future include power

available, and by extension, climb rate. While these parameters are not essential to the RFP, the

fuel consumption and overall mission time could depend greatly on these parameters.

6. Aerodynamics (TL) 

6.1 RFP Requirements, Initial Sizing, and Constraint Analysis While the RFP requirements do not immediately constrain the aerodynamic design in any

fundamental way, the previously completed initial sizing and constraint analyses provided basic

estimates of the wing geometry for the monoplane. The large span of the monoplane’s wings

39

requires a folding-wing design to ensure that the monoplane will fit on standard roads (a

requirement of the RFP). The only other RFP requirement with aerodynamic consequences is

the 750 ft takeoff/landing distance specification, which affects the design through performance

considerations.

6.2 Airfoil Selection

Before making additional design choices for any of the variants, the NACA 2412 airfoil

was selected for the wing of the monoplane, both wings of the biplane, and the “wing” portion of

the BWB. This airfoil was chosen for its relative simplicity, and its reasonable and well-

documented performance characteristics at the flight conditions specified by the RFP.

Additionally, a single airfoil section was chosen for the wing sections of all three variants in

order to standardize the basis for comparing their aerodynamic performance. The airfoil chosen

for both the horizontal and vertical tail sections of all three aircraft was the NACA 0012. This

airfoil was also chosen due to its relative simplicity, well-known performance characteristics,

and symmetric shape.

6.3 Wing/Fuselage Geometry In addition to the initial sizes determined by the Constraint Analysis, several wing design

choices were made for the monoplane to improve both aerodynamic performance and overall

stability. A gradual geometric twist of 3 deg was added to each wing, such that the tip airfoil

sections are angled downwards with respect to the root airfoil sections. This ensures that the root

of the wing will stall before the tip during a high angle of attack maneuver, allowing outboard

control surfaces to function even if a portion of the inboard wing has stalled. A positive dihedral

of 3 deg was also added to the wings to ensure roll stability (Ref [1]). This dihedral also helps

ensure that the wingtips of the low-mounted wings will not strike the ground during a less than

40

ideal landing. The angle of incidence of the wing was set to 3 deg, in order to achieve a

reasonable attitude orientation at cruise. Finally, sharp-cornered wingtips were used to prohibit

the free flow of air around the wingtip, weakening any wingtip vortices formed, hence reducing

induced drag without the need for heavier and more complicated winglets.

6.4 Aerodynamic Characteristics

6.4.1. Monoplane Variant

The required CL for the monoplane variant can be determined at the various flight

conditions in the mission profile by using equation A.4.1. For this equation, the required lift is

assumed to be roughly equal to the weight of the airplane (as supplied by Configuration), and

approximate velocities supplied by Performance are used. For a cambered airfoil, the

relationship between CD and CL can be determined via Equation 6.1.

CD = CDmin + K(CL - CLmin drag)2 (6.1)

Solving for the unknown variables in this equation is a lengthy process, involving many

of the equations in Ref [1] Chapter 12, and briefly summarized here. K is determined using

Equation A.4.2 and A.4.3. CLmin drag is determined using equations A.4.4-A.4.7 and NACA 2412

experimental airfoil data (Ref [3]). CDmin in Equation 6.1 is equal to CD0, and was first estimated

using Equation A.4.8, and then analytically determined using the component build-up method

outlined in Ref [1], and corresponding to Equations A.4.9-A.4.21. The component breakdown of

CD0 for the monoplane is shown below in Table 6.1.

Table 6.1 Component Drag Buildup for Monoplane Component CD0 % CD0 Total

Fuselage 0.0037 11.52

Wing 0.0082 25.36

V-Tail 0.0009 2.68

H-Tail 0.0022 6.63

Cowlings 0.0004 1.10

41

Landing Gear 0.0020 6.16

Sprayers 0.0105 32.21

Propeller 0.0018 5.46

Flaps 0.0029 8.87

Total 0.0325 100.00

After initial analysis was completed assuming that flaps were not installed on the TE of

the monoplane, performance considerations necessitated the addition of flaps to the design.

These flaps were sized according to equation A.4.22 and Chapter 16 of Ref [1]. The effect of

these flaps on CD0 and CDi is accounted for through equations A.4.23-A.4.24. Additionally,

ground effect was accounted for at takeoff and landing via equation A.4.25. The results of this

analysis yield the aerodynamic characteristics listed below in Table 6.2 for all RFP flight

conditions.

Table 6.2 Aerodynamic Characteristics for Monoplane Flight Condition Velocity (ft/s) Lift Required (lb) CL CD0 CD L/D

Take-Off 116 1500 1.461 0.034 0.126 11.613 Payload Drop 168 1400 0.646 0.031 0.044 14.616 Turn 168 2940 1.357 0.031 0.111 12.180

Cruise 168 1400 0.665 0.031 0.045 14.695

Landing 116 1400 1.364 0.034 0.113 12.095

6.4.2 Biplane Variant

Analysis of the biplane aerodynamic performance is similar to the analysis undertaken for

the monoplane. However, a simpler form of the relationship between CD and CL is used, shown

below in equation 6.2. This was done because it serves as a reasonable approximation of

equation 6.1 during the conceptual design process.

CD = CD0 + KCL2 (6.2)

42

CD0 for the biplane is calculated in the same manner as it was for the monoplane, and the

component values are below in Table 6.3. The wing combination unsurprisingly results in an

increased CD0 when compared with the monoplane. However, CD0 for the biplane is only 4%

larger than for the monoplane, this small difference is due to the lack of flaps on the biplane

configuration, as flaps comprised approximately 9% of CD0 for the monoplane.

Table 6.3 Component Drag Buildup for Biplane Component CD0 % CD0 Total

Fuselage 0.0035 10.35Top Wing 0.0060 17.77Bottom Wing 0.0046 13.73

V-Tail 0.0008 2.41

H-Tail 0.0024 7.00

Cowlings 0.0003 0.99

Landing Gear 0.0020 5.91Sprayers 0.0098 28.93

Propeller 0.0017 4.91

Wing Supports 0.0027 7.99

Total 0.0338 100.00

K can theoretically be calculated using equations A.4.2 and A.4.26 from Ref [1].

However, using equation A.4.26 with the geometry of the biplane yields an Oswald’s efficiency

factor of >1. This is theoretically impossible, and thus an estimated e value of .75 was used

instead. This value is suitably lower than e for the monoplane, however it is purely an estimate,

and thus the CDi calculated for the biplane is likely subject to non-trivial flaws. The aerodynamic

characteristics at the various flight conditions are below in Table 6.4 for comparison.

Table 6.4 Aerodynamic Characteristics for Biplane Flight Condition Velocity (ft/s) Lift Required (lb) CL CD0 CD L/D

Take-Off 105 1500 1.659 0.036 0.583 2.844 Payload Drop 168 1400 0.605 0.036 0.110 5.509 Turn 168 2940 1.270 0.036 0.363 3.498

43

Cruise 168 1400 0.623 0.036 0.114 5.451

Landing 105 1400 1.549 0.036 0.513 3.020

As is apparent from the table, CD is significantly larger than for the monoplane. This is

partially explained by the decrease in e relative to the monoplane. However, the much smaller

aspect ratio for the biplane is the larger cause behind the higher CDi it experiences.

6.4.3 Blended Wing Body

For the analysis of the BWB, the airframe was simply treated as three airfoils molded

together. Equation 6.2 was used again to represent the relationship between CD and CL for the

BWB. The tabulation of CD0 is shown below in Table 6.5

Table 6.5 Component Drag Buildup for Blended Wing Body Component CD0 % CD0 Total

Fuselage Wing 0.0036 8.49Wing 0.0029 6.90V-Tail 0.0007 1.56

Landing Gear 0.0020 4.76

Sprayers 0.0102 24.19

Propeller 0.0017 4.10

Total 0.0210 100.00

As expected for such a streamlined shape, CD0 is lower than both the monoplane and

biplane, yielding a value that is 36% lower than CD0 for the monoplane.

Aerodynamic characteristics for the BWB are tabulated below in Table 6.6. Despite the

BWB’s smaller CD0, the aircraft’s total CD quickly grows larger than that for both the biplane and

monoplane at equivalent CL values. This is due in largely to the small span of the craft, which

results in small equivalent aspect ratios for both the main wing section and the fuselage wing

section. This small aspect ratio results in a large induced drag for the craft.

44

Table 6.6 Aerodynamic Characteristics for Biplane Flight Condition Velocity (ft/s) Lift Required (lb) CL CD0 CD L/D

Take-Off 105 1500 1.659 0.036 0.583 2.844 Payload Drop 168 1400 0.605 0.036 0.110 5.509 Turn 168 2940 1.270 0.036 0.363 3.498

Cruise 168 1400 0.623 0.036 0.114 5.451

Landing 105 1400 1.549 0.036 0.513 3.020

As is apparent from the table, CD is significantly larger than for the monoplane. This is

partially explained by the decrease in e relative to the monoplane. However, the much smaller

aspect ratio for the biplane is the larger cause behind the higher CDi it experiences.

6.4.3 Blended Wing Body

For the analysis of the BWB, the airframe was simply treated as three airfoils molded

together. Equation 6.2 was used again to represent the relationship between CD and CL for the

BWB. The tabulation of CD0 is shown below in Table 6.5

Table 6.7 Component Drag Buildup for Blended Wing Body Component CD0 % CD0 Total

Fuselage Wing 0.0036 8.49Wing 0.0029 6.90V-Tail 0.0007 1.56

Landing Gear 0.0020 4.76

Sprayers 0.0102 24.19

Propeller 0.0017 4.10

Total 0.0210 100.00

As expected for such a streamlined shape, CD0 is lower than both the monoplane and

biplane, yielding a value that is 36% lower than CD0 for the monoplane.

Aerodynamic characteristics for the BWB are tabulated below in Table 6.6. Despite the

BWB’s smaller CD0, the aircraft’s total CD quickly grows larger than that for both the biplane and

monoplane at equivalent CL values. This is due in largely to the small span of the craft, which

45

results in small equivalent aspect ratios for both the main wing section and the fuselage wing

section. This small aspect ratio results in a large induced drag for the craft.

Table 6.8 Aerodynamic Characteristics for Blended Wing Body

Flight Condition Velocity (ft/s) Lift Required (lb) CL CD0 CD L/D

Take-Off 122 1500 1.275 0.022 0.629 2.026 Payload Drop 168 1400 0.628 0.022 0.169 3.708 Turn 168 2940 1.319 0.022 0.672 1.963

Cruise 168 1400 0.647 0.022 0.178 3.628

Landing 122 1400 1.190 0.022 0.551 2.160

6.5 Drag Polar and Final Aerodynamic Selection

The CL versus CD plots for all three variants are plotted below in Figure 6.1.

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.05 0.1 0.15 0.2 0.25 0.3

CD

CL

Conventional Bi-Plane Blended Wing Body

Figure 6.1 Drag polar for all three variants.

As expected from the previously discussed data, the monoplane has the greatest L/D ratio

at almost all CD values. Only when CL is vey low does the BWB have a better L/D ratio. This is

the expected behavior, because the majority of the BWB’s drag is due to induced drag. The

46

biplane experiences marginally better performance at high CD values over the BWB, however it

is never outperforms the monoplane.

Thus from an aerodynamic standpoint, the monoplane variant is the performs best, easily

surpassing both the BWB and biplane. The results indicate that the aspect ratio for both the

BWB and biplane are far too small to achieve a reasonable level of performance. Increasing the

span of both aircraft to a value similar to that for the monoplane would likely decrease the

aerodynamic performance gap that currently exists between them.

6.6 Aspect Ratio Trade Study

The effect of small aspect ratio on the biplane and BWB variants was made obvious in

the previous analysis, and a trade study examining the effect of aspect ratio on the performance

of the monoplane is a natural extension of this discovery.

As aspect ratio is varied from 6.65 to 1.7 for the monoplane, CD0 stays constant while CDi

steadily increases. Figure 6.2 below makes this readily apparent; as aspect ratio is decreased

from 6.65 to 3 the drag polar curve “squeezes inward” as L/D decreases at all values of CD.

Further reducing A to 1.7 causes CD to increase again for equivalent CL values, and at A=1.7 the

monoplane CL v. CD curve looks very similar to that for the BWB.

47

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0.05 0.1 0.15 0.2 0.25 0.3

C D

Monoplane, A=6.65 Blended Wing Body Monoplane, A=1.7 Monoplane, A=3

Figure 6.2 Drag polar for varying monoplane aspect ratio.

6.7 Future Work

The actual lift created by the wing at a given Reynolds number for the monoplane should

be determined to ensure the airplane will takeoff when expected. Additionally, optimization of

the wing span should be performed, as the added cost and complexity of a folded wing is

undesirable. Also, enhancement of the sprayer bar to reduce separation behind the cylinder

should be considered, as this would greatly decrease CD0. Finally, optimization of the take-off

and landing speeds with the ultimate goal of removing the flaps should be explored in order to

reduce the drag, weight, and cost penalty associated with these devices.

 

 

48

7. Propulsion (KP) 

7.1 RFP and Other Requirements

The RFP simply states that the engine requirements are that it be a widely available “off

the shelf” engine that, based on technology available today, is best for the design. The process

of selecting an engine was affected by other requirements in the RFP such as the need to carry

the extra weight of the expendable payload. A wide range of studies were done to determine

which engine would be best for the design.

7.2 Engine Selection

Before actually selecting the engine type, a range of crop dusting and other light aircraft

were looked at in terms of what engines they used with respect to their weights. Using the data

from the initial sizing analysis and historical data from the aforementioned research, it was found

that an engine with approximately 100 horsepower would be needed to support the design. Since

all of the design configurations are light weight, the use of multiple engines or jets was dismissed

immediately due to lack of need and impracticality. The engine types that were researched were

internal combustion and electric.

Research was done on the Sonex Electric Airplane concept, which has a fully electric

engine that has a 24 hour charge cycle that gives one hour of flight. This system provides the

approximate equivalent of 80 horsepower. This would be a very good selection for this mission

profile if it were more widely available and slightly more powerful. An area for future work in

this project would be looking into using an electric motor such as this one. Since the Sonex

engine is still a concept model however, it was best for this design to choose a different engine.

Electric propulsion was therefore dismissed due to a lack of availability.

49

Several internal combustion engines with a power output close to the required value were

researched, and the Jabiru 3300 was chosen from the following list of candidates.

Table 7.1 Candidate Engines Ref [6] Maker Model Horsepower Cruise RPM Weight (lbf) P/W (hp/lbf) Rotax 912 UL 80 5500 134.2 0.596

912 ULS 100 5500 140.6 0.711 Aeroconversions AeroVee 2.0 80 3400 158 0.506

Lycoming O-235-C 115 2800 245 0.469 O-320-A 150 2700 275 0.545

Jabiru 2200 85 3300 132 0.644 3300 100 2750 178 0.562

Wankel LCR-814 TGti 75 6000 120 0.625

Table 7.2 Jabiru 3300 Specifications Ref [5] Maker Jabiru Model 3300 Cylinders 6 Displacement 200 cubic inches Bore 3.84 inches Stroke 2.91 inches Weight 180 lbf Power 100hp @ 2750rpm Fuel Cons. 5 US gal/hr @ 75%

7.2.1 Engine Power

The Jabiru 3300 aircraft engine puts out 100 horsepower at 2750 rpm, and is capable of a

maximum power output of 120 horsepower at 3300 rpm. One of the prime reasons it was chosen

over the other candidate engines is the extra power that it can produce.

7.2.2 Engine Power to Weight

The Jabiru 3300’s power to weight ratio is 0.562, which is comparable to most of the

others that it was compared to. The Rotax 912 ULS has a better ratio, but the high rpm and the

lack of ability to produce more power than the required minimum of 100 horsepower made it a

50

less suitable candidate than the Jabiru. The power to weight ratio that the Jabiru engine provides

for the entire aircraft is approximately 0.091.

7.2.3 Engine Cbhp

The Cbhp of the Jabiru 3300 engine is 0.46 lbf/hp/hr. This value is very close to other

engines with similar power ratings that were researched. The Jabiru uses approximately 5.0 US

gallons per hour at cruise and around 7.0 US gallons at 100% throttle.

7.3 Propeller Selection

The options for propeller selection are fixed pitch and constant speed variable pitch. The

number of blades to be used must be chosen as well. Beyond that, a radius has to be chosen that,

along with consideration of the horsepower of the engine, keeps the speed of the tips of the

blades below Mach 1. This is necessary to keep the noise level of the propeller to a minimum.

In researching different propellers, the number of blades was the first area that was

analyzed. The first consideration in choosing a propeller is that this aircraft will be taking off

and landing on improvised airstrips, which means that a good amount of clearance between the

propeller and the ground must be maintained. This fact pointed toward the use of a three blade

propeller due to the fact that a three blade prop can have a smaller radius than a two blade

propeller. Historical data was also looked into and it was found that many current crop dusters

use a three-blade propeller configuration.

A propeller radius that would both clear the ground and have a tip speed of less than

Mach 1 is the next requirement. The available clearance on all three design configurations is just

over 5 feet, so to ensure proper ground clearance during take off or landing, a radius of 4.5 feet

was chosen. This radius puts the helical tip speed of the propeller at 661 feet per second, which

is far less than Mach 1, and is a very good value in terms of noise reduction.

51

The next consideration to take into account is whether or not the propeller will be

constant pitch or constant speed with a variable pitch. The main advantage of a variable pitch

propeller is that it can change the engine’s thrust without having to change the engine power or

the speed of the propeller. It can also be used to create reverse thrust to decrease the landing

distance of the aircraft. Due to these advantages, a variable pitch propeller was chosen for this

design. The analysis of such a propeller, however, is more complicated than that of a fixed pitch

propeller. Due to this complication, this concept design’s propeller is treated as a fixed pitch

propeller of the same radius. An area for future work in this area is to be a study into whether or

not the variable pitch propeller would actually perform better than the fixed pitch prop in this

setting.

The propeller that was chosen for this design is the Airmaster AP332 fully feathering

propeller, which comes with a controller that can be preset with propeller speeds for each

segment of a flight, which in the case of an unmanned aircraft, would be ideal. This propeller

was designed specifically for the Jabiru 3300 engine, which also makes it a prime candidate for

use in the design.

7.3.1 Propeller Efficiency

The efficiency of this propeller was found to be approximately 0.75, which is a

reasonable value for this mission.

Table 7.3 Propeller Specifications Ref [4] Maker Airmaster Model AP332 Diameter 4.5 feet Hub Diameter 10 inches Blade Length 22 inches Blade Chord 2.5 inches Helical Tip Speed 661 feet/second Efficiency 0.75 Static Thrust 380 lbf

7.3.2 Propeller Thrust

52

The AP332 propeller with a 4.5 foot diameter generates a static thrust of approximately

380 lbf. The thrust required for takeoff and landing, and cruise are 356.68 lbf and 245.5 lbf

respectively, and thus the engine and propeller meet these requirements for each leg of the

mission.

7.4 Fuel and Fuel Storage

Table 7.4 Thrust and Fuel Consumption Mission Leg Time

(min) Power Required

(%) Fuel Cons.

(gph) Velocity

(ft/s) Thrust

(lbf) Fuel Used

(gal) TSFC

(lb/h/lbf) Takeoff 2 100 7 115.65 356.68 0.23 0.120 Climb 3 100 7 145 284.50 0.35 0.148 Cruise 12 75 5 168 245.50 1.00 0.122 Turns 3 75 5 168 245.50 0.25 0.122

Descent 3 100 7 125 330.00 0.35 0.128 Landing 2 100 7 115.65 356.68 0.23 0.120

Ferry 6 75 5 168 245.50 0.50 0.122 Reserve 20 100 7 168 245.50 2.33 0.172

Total 51 ----- ----- ----- ----- 5.24 -----

The current fuel tank setup has room enough for 15.12 gallons of fuel in all three design

configurations. This is so that the airplane can spray multiple fields on one tank of fuel and

saves the customer from having to refuel the aircraft before each field is done. The fuel that the

Jabiru 3300 uses is Avgas 100/130, which has a density of 6.02 lb/gal.

7.5 Trade Study on Propeller Diameter

A trade study was conducted on the effects of different propeller diameters. The

boldfaced values in Table 7.5 are those that are to be used in the design. As shown in Figure 7.1,

propeller efficiency increases as a function of diameter. A 1.25 foot increase in propeller

diameter increases the efficiency of said propeller by 22%. The trade off here is that the

propeller cannot be so large that it becomes too heavy or impacts the ground during takeoff or

landing.

Table 7.5 Effects of Propeller Diameter

53

Diameter (ft) Advance Ratio Corrected Advance Ratio

Cp Ct/Cp Propeller Efficiency

Static Thrust (lbf)

4.5 0.8146 0.7706 0.1346 1.3 0.75 381.3 4 0.9164 0.8537 0.2426 0.8 0.63 264

4.25 0.8625 0.8103 0.1792 1 0.72 310.6 4.75 0.7717 0.7343 0.1027 1.71 0.79 475.2

5 0.7331 0.7011 0.0795 2.2 0.83 580.8 5.25 0.6982 0.6705 0.0623 2.4 0.85 603.4

0

0.2

0.4

0.6

0.8

1

4 4.25 4.5 4.75 5 5.25

Propeller Diameter (ft)

Prop

elle

r E

ffici

ency

Figure 7.1 Propeller diameter vs. propeller efficiency.

0100200300400500600700

4 4.25 4.5 4.75 5 5.25

Propeller Diameter (ft)

Stat

ic T

hrus

t (lb

)

Figure 7.2 Propeller diameter vs. static thrust.

54

As shown in Figure 7.2, thrust also increases as a function of propeller diameter. The

trade off here is whether or not the extra thrust that a larger propeller diameter provides is

needed. In the case of the crop duster design, the considerations that need to be taken into

account are how large the propeller can be in order for it to be clear of the ground on an

improvised airstrip, and an approximation of how much thrust will be needed. As shown in the

figures, a larger propeller would be better in terms of efficiency, but due to the takeoff and

landing conditions, the required thrust has to be the limiting factor. The propeller in this case

should be as small as possible while still maintaining the required thrust for the airplane. Since

the takeoff thrust, which is the maximum required thrust, is 356.68 lbf, and the 4.5 foot diameter

propeller provides enough thrust to cover that requirement, it is the ideal choice. If the

conditions of the flight were different, such as a smooth paved runway for takeoff and landing, a

larger propeller could be considered to increase efficiency.

7.6 Future Work

Some areas that will require work in the future are the engine type, propeller type, and the

effects of aerodynamic forces on the propulsion system. A more thorough study of alternative

engine types, including ethanol fuel engines and a fully electric engine needs to be done in the

future. Research into the effects of having a variable pitch propeller as opposed to a fixed pitch

propeller will also be done. Once a thorough study of the aerodynamics and performance of the

final design is completed, it will be possible to get more accurate data regarding the propulsion

system’s losses.

 

55

8. Stability and Control (CK) 

8.1 RFP Requirements

The most basic requirement for static stability of an aircraft is ensuring that the center of

gravity is ahead of the neutral point (location where 0MC =α

∂∂

) as specified in the data

requirement of the RFP. This guarantees that disturbances to the aircraft pitch will create a

restoring force proportional to the perturbed angle of attack thus return the aircraft to steady,

level flight. This will ensure our aircraft will handle without any stability augmentation system

or computer controlled flight surfaces. This lack of complicated stability augmentation devices

aligns well with the RFP requirement that our agricultural aircraft be both affordable to

underdeveloped countries and made from inexpensive off the shelf parts. First, however, to find

an aircraft's neutral point it is first necessary to find proper control surface sizes.

8.2 Tail Sizing

With the Constraint Analysis from the performance person, enough information is known

to do a preliminary stability and control analysis. This provides the necessary information in

finding the reference area and aspect ratios of an aircraft's horizontal and vertical tail which is

based primarily on the historic quantities known as tail volume ratios. For both the biplane and

our monoplane configuration the horizontal tail volume coefficient of 0.5 was used [Ref. 1], and

the vertical tail volume coefficient of 0.05 [Ref. 9] was used assumed to provide sufficient yaw

stiffness. From these tail volume coefficients, the reference area of the vertical tail ( vS ) and the

reference area of the horizontal tail ( hS ) were found. Also the aspect ratio of the horizontal tail

( hAR ) and the aspect ratio of the vertical tail ( vAR ) are generally around 4.5 and 2.75

respectively [Ref. 8]. The results of these calculations are tabulated here.

56

Table 8.1 TailGeometry Aircraft Type Monoplane Biplane Blended Wing Body

Sh (ft2) = 15.1857 16.4923 N/A Sv (ft2) = 10.1287 11.7204 9.5514

ARh = 4.5000 4.5000 N/A ARv = 2.7500 2.7500 2.7500

It should be noted that the third aircraft concept that X-Duster team is considering is the

blended wing body but calculation of tail areas using tail volume ratios does not apply because

tail volume ratios are based on historic data for more conventional configurations, not blended

wing bodies. For blended wing bodies directional control and the necessary vertical tail are quite

small. For example, the YB-49 only needed small vertical tails [Ref. 1]. Since no exact

calculations for tail sizing are available, a comparison to similar sized flying wings (such as

mentioned YB-49) and other blended wing bodies such as Boeing-Blended-Wing Concept was

used as historic data to estimate our vertical tail size.

The length of the fuselage was chosen to be a minimum in order to reduce hollow

sections on the inside of the structure. This reduces both the excess weight while also reducing

wetted area with respect to the fuselage even though this did lead to larger elevators. A future

trade study will be necessary to compare aircraft weight gains or losses for various tail volume

ratios.

8.3 Static Margin

Static margin is the distance (as a percentage) between the center of gravity and the

neutral point of the aircraft normalized by the main wing's mean chord. This is defined as

positive when the center of gravity is ahead of the neutral point and negative for a neutral point

ahead of the center of gravity. These neutral points were calculated with the goal of having a

static margin between positive 5% and 19% [Ref. 1]. This ensured static stability of each design

which implies the airplane will return to steady and level flight upon any turbulence without any

57

flight control inputs. This stability would make for easy implementation of the autonomous flight

control program.

In order to find the static margins, various data from both the Constraint Analysis and

historical values from Raymer were used. Now of course, having the specified range of static

margin (5% - 19%) implies that the aircraft center of gravity be oriented 5% - 19% ahead the

aircraft's neutral point. Thus considerable coordination with the Configuration's person was

involved in adjusting the configuration of the aircraft until the center of gravity did indeed ensure

a static margin between 0.05 and 0.19. The formula for calculating neutral point is based on

parameters like the lift curve slopes of the main wing's airfoil, distance between aerodynamic

centers, reference areas, etc. Most importantly the neutral point is only a function of the

geometry which for each configuration is constant throughout the entire flight. So the neutral

point remains fixed and independent of c.g. shift. These neutral point locations, Xnp, are

tabulated as follows.

Table 8.2 Neutral Point Locations Aircraft Type

Monoplane Biplane Blended Wing Body Xnp = 0.3540 0.2573 0.4352

For the monoplane the neutral point is the distance behind the main wing's leading edge

as a percentage of the mean chord. For the biplane the neutral point location is the distance

behind the lower wing leading edge as a percentage of the lower wing mean chord. And the

blended wing body's neutral is with respect to the nose of the aircraft as a percentage of the entire

aircraft's length.

For the blended wing body the same formula could not be used. Since the blended wing

body in our design is very nearly a flying wing, the neutral point of a wing is the aerodynamic

center. And in low speed subsonic flight the aerodynamic center is most nearly the quarter chord.

58

So the mean quarter chord was found, which gives a good estimate of the neutral point in a very

complex blended wing body.

The center of gravity evolves during the mission profile. So to ensure static stability in

the acceptable range over the entire flight profile, the center of gravity as a function of time was

found for these cases: empty aircraft c.g. location, fueled aircraft c.g. location, liquid payload and

fueled c.g. location, and solid payload and fueled c.g. location with linear variation due to fuel

burn and payload drops. These four configurations represent the extreme c.g. locations, thus in

preliminary stability and control design the static margin was calculated for each c.g. locations

with the above calculated neutral points.

Table 8.3 Static Margin Evolution Static Margin (%c) Mission Profile Segment Monoplane Biplane BWB Empty 15.020 14.514 7.762 Fueled (No Payload) 18.200 16.957 10.067 Fully Fueled with Full Liquid Payload 3.290 2.492 7.414 Fully Fueled with Full Solid Payload 1.010 0.338 7.007

As seen in the previous table the monoplane, biplane, and blended wing body remain

statically stable over the entire mission, although one issue that may need resolved in further

design is the large static margin shift. For example in the monoplane the static margin changes

from 1% to 18%. However since the aircraft is trimmable it will still be able to maintain steady

level flight.

8.4 Control Surface Sizing

In very much the same manner that tail sizes were found, initial estimates of control

surface areas are also based on historic data. Typically both the elevator and the rudder are 25%

59

of their respective tail sizes. This applies well for both the monoplane and the biplane [Ref. 7].

The results of this calculation, rudder area rS and elevator area eS , are tabulated in the following

table.

Table 8.4 Control Surface Area Aircraft Type Monoplane Biplane Blended Wing Body

Sr (ft2) 2.5322 2.9301 2.3878 Se (ft2) 3.7964 4.1231 N/A

Again, the blended wing body tends to be an exception as it does not have an elevator.

Elevons would have to be used on the blended wing body because they would control both the

roll and pitch of the aircraft with a lack of tail. Elevon reference areas are likely beyond the

scope of this course, so if blended wing body proves to be the most viable option, future research

would be done of how to size elevons.

8.5 Trim Analysis

An aircraft does not necessarily have to be stable in order to fly even if it lacks stability

augmentation. For example the Wright Flyer was mildly unstable, but because it was trimmable

the Wrights could keep it in the air. Thus ensuring our aircraft is both statically stable (as above

from positive static margin) and trimmable yields a very well behaved aircraft. Trim ensures that

the tails and control surfaces can produce enough torque to cancel any pitching moment from the

main wings and the aircraft can recover from maneuvers to steady level flight.

A trim plot is the best graphical way to see both the results of trim analysis and

simultaneously shows the aircraft static stability. The plot simply shows the moment coefficient

( MC ) as a function of LC (or equivalently angle of attack) for various static margins. The slope

of this plot ignoring propulsion effects is the negative of the static margin which implies the

aircraft is statically stable. And the MC intercept is the zero lift pitching moment coefficient.

60

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

-0.20 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80

CL

CM

Monoplane EmptyMonoplane Payload and FueledBiplane EmptyBiplane Payload and FueledBWB EmptyBWB Payload and Fueled

Figure 8.2 Required 'LC s for various configurations to be in trim.

The results here most importantly show the required 'LC s for our aircraft to be trimmed.

And from the aerodynamicist it is known that these 'LC s are obtainable because NACA 2412

does not stall until . Thus the monoplane, biplane, and blended wing body are all

trimmable and statically stable for all portions of our mission profile which makes them all

viable options from a static stability viewpoint.

1.6LC =

8.6 Trade Study – Static Margin's Effect on Trim

A trade study was performed on how the trimmed LC was affected by changing the static

margin. This analysis is a graphical way of seeing how a configuration change (thus c.g. location

change or similarly static margin change) would influence the necessary LC for trim. This shows

whether or not it is possible to trim the monoplane aircraft at various static margin values. In a

61

sense this also demonstrates how much the aircraft’s center of gravity can be changed while still

having a trimmable aircraft.

-0.15

-0.13

-0.11

-0.09

-0.07

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

CL

CM

SM = 0 SM = .025 SM = .05 SM = .10 SM = .15

Figure 8.2 Trim analysis with varying static margins.

The most important result here is that for the monoplane design, with our current airfoil with a

maximum LC = 1.6 ( LC stall) the static margin must remain above 1.5% which is where the

static margin would intersect 0MC = .

8.7 Future Considerations

A few considerations will be necessary when a more detailed design takes place. One

issue as previously mentioned was the large center of gravity shift throughout the mission. While

the monoplane, biplane, and blended-wing-body all remain statically stable, their static margins

change significantly during flight. This is due to the fact that the payload hopper/tank is quite far

from the empty aircraft’s c.g. It will be wise to consider alternative payload locations closer to

the empty c.g. in future, more detailed design.

62

If the blended-wing-body does prove to be the most viable option, more technical data

and design philosophy for blended-wing-bodies should be found. The current neutral point

approximation may prove to not to be precise. Also elevons tend to be more trade secrets since

they are primarily used on military aircraft like the B-2 so sizing of them may prove difficult.

Finally and most importantly, static stability is only the beginning in determining how the

aircraft design will fly. Yaw and roll stability in addition to longitudinal dynamic stability will

further complicate the design but yield more precise handling characteristics. For example, the

blended-wing-body concept may be statically stable, but when it enters a turn it could spiral out

of control, or go into a Dutch roll. These are examples of multiple axes of rotation coupled

together and will be necessary stability and control analysis outputs in future work.

 

 

9. Cost Analysis (WH) 

9.1 Development of Cost Model

The DAPCA IV Cost Estimation Relation, developed by the Rand Company, and

presented in Raymer, was used for preliminary cost estimation for the aircraft. Unfortunately the

DAPCA IV CER does not apply well to the aircraft because it is modeled primarily for tactical

fighter aircraft and commercial transport aircraft. With this in mind it was decided to use a

modified version of the DAPCA IV model that would help to alleviate the problem associated

with applying it to this aircraft. This modified version included using engine cost data from the

engine manufacturing company, selecting appropriate avionics components and creating a total

avionics cost from the cost of each component. The preliminary idea is for an autonomous

63

aircraft; to account for this the avionics cost includes advanced computer hardware and software

for the aircraft to run autonomously. The modified DAPCA IV model was modified further for

the blended wing body configuration. This modification primarily was a modification in the

manufacturing and avionics cost. The blended wing body configuration has inherent

manufacturing obstacles that produce a high cost; the manufacturing cost would increase for the

blended wing body because of the structure’s complexity. As a way to counteract the high

manufacturing cost, a possible solution of composites was proposed. However, the combined

material cost for composites along with no structural advantage gained using composites,

deemed composites unnecessary. The DAPCA IV model uses the calculated empty weight and

maximum velocity and the number of aircraft produced in a five year production run. The

modified DAPCA IV model output a total research, development, engineering, testing and

flyaway cost that varied with the production run number.

To calculate a preliminary operating a cost, a cost estimation relation was created for the

aircraft application. The operating cost used fuel data from the engine manufacturing company

and current costs for the operational fuel required by the selected engine. An annual insurance

cost was estimated from historical data of similar aircraft. An hourly maintenance cost was

estimated considering the fact that most farmers will attempt self repairs on the aircraft. A

training cost was estimated with the preliminary idea that the aircraft would be autonomous with

manual back up and over-ride and the operator would need to be trained mostly in the use of the

software to set up the flight path. The lifespan of the aircraft was estimated from historical data

of agricultural aircraft and historical data of hourly usage for a year. The operating cost model

output a cost per year, cost per hour heavily dependent on the number of hours that the aircraft

was used in a calendar year.

64

9.2 Cost Breakdown

The flyaway cost produced by the modified DAPCA IV CER allows for calculation of

the cost for certain specialized technical areas. The percentage of total flyaway cost for each

aircraft production area was calculated and is shown in Figure 9.1.

9%

1%

48%

15%

7%

10% 0% 7%1%

2%Avionics

Spray System

Manufacturing

Materials

Qualtiy Control

Tooling

Training

Propulsion

Flight Testing

Development Support

Figure 9.1 Production cost breakdown.

Figure 9.1 shows that the flyaway cost of the aircraft relies heavily on the manufacturing cost.

The next influential component is the materials and following that is the avionics.

Manufacturing’s heavy influence on a production price is indicative of the large amount of time

devoted to building an aircraft. Even though the aircraft is designed to be composed of mostly

“off the shelf” parts, the main material of the air aluminum is not readily available in the

preformed parts of a fuselage, wing structure and empennage. This explains why the materials

cost is an influential part of the aircraft even with “off the shelf” parts. Using the preliminary

design of an autonomous aircraft the avionics cost includes the ground support software and

hardware and the advanced aircraft software for monitoring the flight, weather and spray pattern.

9.3 Cost vs. Production Run

65

As shown in Figure 9.2 the flyaway cost decreases exponentially with the number of

aircraft produced in five years.

$0

$1,000,000

$2,000,000

$3,000,000

$4,000,000

$5,000,000

$6,000,000

$7,000,000

$8,000,000

$9,000,000

$10,000,000

0 100 200 300 400 500

Production Run in 5 Years

Cost

($)/A

irpl

ane

Figure 9.2 Cost vs. production.

The flyaway cost per airplane decreased as expected because many aspects of the production are

reused, and the modified DAPCA IV model accounts for a learning curve of the manufacturing

and tooling laborers. The high cost for a single aircraft production run is explained by the high

cost for the tooling, manufacturing, and materials is entirely devoted to one aircraft. Shown

below in Table 9.1 is the flyaway cost for production runs of 50, 100 and 500 aircraft.

Table 9.1 Production Run and Cost/Airplane($) Production Run Amount Cost/Aircraft($)

50 $850,000.00 100 $630,000.00

500 $350,000.00

9.3 Cost vs. Fuel Cost

66

As shown in Figure 9.3 as the cost of the required fuel increases the cost per hour of

usage increases linearly.

$0.00

$10.00

$20.00

$30.00

$40.00

$50.00

$60.00

$70.00

$80.00

$3.00 $3.50 $4.00 $4.50 $5.00 $5.50 $6.00 $6.50 $7.00

Fuel Cost($)

Oper

atio

n Co

st/H

our($

)

Figure 9.3 Cost vs. fuel cost.

Considering that the general national trend is a rise in fuel cost per gallon the operating cost was

studied for increasing fuel costs. The linear increase in operation cost per fuel cost per gallon is

as expected because the operating cost relies heavily on the amount of fuel used per hour.

Possible remedies to the problem of high operating costs due to a rise in fuel is researching

alternative fuel sources, or researching a different, more fuel efficient engine.

9.4 Future Cost Analysis Work

In the future more historical data needs to be investigated to create a proper cost model

for the aircraft application. More trade studies can be done to investigate the operational cost

and flight time cost. The propulsion systems need to be studied to see if any modification can be

made to find a more fuel efficient engine, or an engine that uses different fuel. Since the main

driving factor of the flyaway cost was the manufacturing time, trade studies in reducing

67

manufacturing time need to conducted to reduce the flyaway cost. The material needed for the

aircraft were a considerable percentage of the flyaway cost, to investigate possible flyaway cost

reductions trade studies in reducing the materials cost need to be conducted. These include

researching less expensive materials or decreasing the weight, and therefore using less material

which will in turn decrease the flyaway cost. An analysis of cost effectiveness of cost per acre of

sprayed crop needs to be completed to be compared to other aerial application solutions.

 10. Ground Operations 

10.1 Aircraft Control

As a preliminary judgment the optimum operation of the aircraft is a completely

autonomous aircraft with a manual back-up/over-ride. The reasoning behind this is that if a pilot

is required the operating costs will climb significantly from the baseline operating costs

presented in this report. While the individual farmer could be trained as the pilot, his time is

better served as doing other work while the aircraft performs the aerial application on its own.

Due to the autonomous aspect the avionics cost was increased for an advanced software and

computer that would be needed to monitor the aircraft’s airspeed and the wind speed and

direction as well as the flow rate of the product being applied.

10.2 Ground Control Components

The ground station includes advanced software for piloting the aircraft, determining the

optimum flight path around the field of operation, monitoring the flow rate and the coverage of

the product over the field. The ground control would consist of the computer which will be the

user interface with the aircraft, on the computer display during flight there will be flight data as

can be seen in manned aircraft. The computer will also have a joystick for a manual back-

68

up/over-ride. The ground control station will also consist of two of its own weather stations that

can be stationed at user specified locations to monitor the weather in the vicinity of the field.

The computer interface would require a certain amount of training, this is included in the

flyaway cost at approximately $1000.00 and would take approximately one day to complete.

10.3 Future Work in Ground Operations

The ground operations will be totally designed in the future. Studies will be done to

determine which components are entirely necessary for the ground operations. Design ideas for

the ground control station will include an integrated design station on the tow trailer or a ground

control container that will contain all of the ground hardware and can be loaded on to a pick up

truck and towed along with the aircraft to the desired location.

Conclusion  

After going through the first stages of analysis on all three aircraft variants, it was

apparent that the monoplane was the better choice for fulfilling the RFP. The monoplane itself

had the benefits of simplicity in both design and manufacturing, which is one of the main goals

of the RFP in order to allow for export. The only real drawback was in transport of the aircraft

given its larger wingspan, but this can be overcome by giving it folding wings that are simple to

deal with as the fuel tanks take up only half the wing span.

The other variants on the other hand have numerous significant design problems

compared to the monoplane design. The biplane variant, while still relatively conventional and

low cost as the monoplane was, ended up being at best neutrally stable. This would render it

harder to control in flight, putting greater demands on the control systems. Additionally, the

69

smaller wingspan which would aid in transport of the craft actually hindered the design in that it

reduced the effective spray area on each pass; in effect doubling the number of passes to cover a

given area versus the monoplane. This, coupled with a much higher turning radius, made the

biplane a much less efficient crop duster compared to the monoplane even with the slight weight

and size benefits.

The main problem that arose with the blended wing body was the innate complexity in

the design that hindered analysis. However, what analysis that could be done indicated that it

also was not a viable option when compared to the conventional monoplane. The blended wing

shared the same problem as the biplane in that the effective spray area was half the monoplane;

however its turning radius was not as large as the biplane, making it slightly more efficient. In

this and other areas the blended wing performed better or at least on par with the biplane. There

was one main problem though that would arise for the blended wing body that would discount it

regardless of performance, and that was the cost of each unit. To manufacture a blended wing

body aircraft would require much more complex, and therefore expensive, manufacturing

processes than either of the more conventional variants. This ends up going against the

affordability requirements of the RFP. Additionally, the simple fact that it is an unconventional

design irregardless of cost makes it less likely to be adopted by any group of consumers.

In light of all of these reasons, it is clear that the variant of choice with which to continue

on to a detailed design is the conventional monoplane. This variant was able to best fulfill by far

out of the three the RFP requirements for the Agricultural Unmanned Aircraft System.

 

 

70

References 

[1] Raymer, D., Aircraft Design: A Conceptual Approach Third Edition, AIAA Education Series, Reston, VA, 1999. [2] Gay, Daniel, Hoa, Suong V. and Tsai, Stephen, “Conception and Design,” Composite Materials: Designs and Applications, CRC Press, New York, 2003, pp. 87-101. [3] Anderson, Jr., John D., Aircraft Performance and Design, WCB/McGraw-Hill, Boston, MA, 1999. [4] “Airmaster Products – AP332”, 2001, http://www.airmasterpropellers.com/wa.asp?idWebPage=3454 [5] “Jabiru 3300 120 hp Engine”, http://www.usjabiru.com/jabiru_3300.htm [6] “Ultralight Engines”, http://www.ultralightnews.com/engineinfo/index.html [7] Chevalier, Howard, Model Airplane Design and Performance for the Modeler, ChallengeEngineering, Inc., New Baden, TX, 1993. [8] Lennon, Andy, R/C Model Aircraft Design, Air Age Inc., Ridgefield, CT, 1996. [9] Jones, Dave, "Fins and Rudders". Quiet Flight International, No. 17, Traplet Publications, Severn, England, Oct./Nov. 1995.

71

Appendix A.1 Structures V‐n & Trim Diagram MATLAB Code function AE440_Trim_Diagram_Mono() % Michael Duffy AE440 Conceptual Design Report % ----- % Monoplane Trim Diagram % ----- % Airfoil data; row vector of values in order [col1, col2, col3, col4] = textread('NACA2412.data','%f%f%f%f%*[^\n]','delimiter',' '); alpha = [col1].'; C_l = [col2].'; C_d = [col3].'; C_m_w = [col4].'; % Calculate wing force values based on angle of attack C_z_w = zeros(1,length(alpha)); C_x_w = zeros(1,length(alpha)); for i = 1:length(alpha) if alpha(i) > 0 C_z_w(i) = C_l(i)*cosd(alpha(i))-C_d(i)*sind(alpha(i)); C_x_w(i) = C_d(i)*cosd(alpha(i))+C_l(i)*sind(alpha(i)); elseif alpha(i) == 0 C_z_w(i) = C_l(i)*cosd(alpha(i)); C_x_w(i) = C_d(i)*cosd(alpha(i)); else alpha(i) < 0; C_z_w(i) = C_l(i)*cosd(alpha(i))+C_d(i)*sind(alpha(i)); C_x_w(i) = C_d(i)*cosd(alpha(i))-C_l(i)*sind(alpha(i)); end end % Calculate tail force values c_w_mac = 3.115; % wing mean aerodynamic chord (feet) l_t = 5.906; % horizontal distance of tail AC BEHIND plane CG (feet) l_wb = -.312; % horizontal distance of wing AC BEHIND plane CG (feet) C_z_t = (c_w_mac./l_t).*C_m_w - (l_wb./l_t).*C_z_w; %h_t = -.594; % vertical distance of tail AC BELOW plane CG (feet) %h_wb = .147; % vertical distance of wing AC BELOW plane CG (feet) %C_x_t = (c_w_mac./h_t).*C_m_w - (h_wb./h_t).*C_x_w; C_x_t = 0; % Assume for early models that the tail is parallel with the wing % Calculate total force values C_z_total = [C_z_w + C_z_t]; C_x_total = [C_x_w + C_x_t]; % Plot all the values versus angle of attack figure plot(alpha,C_z_total,'k-','linewidth',2) hold on grid on plot(alpha,C_x_total,'k--','linewidth',2) plot(alpha,C_z_w,'r-','linewidth',2) plot(alpha,C_x_w,'r--','linewidth',2) plot(alpha,C_z_t,'b-','linewidth',2) % plot(alpha,C_x_t,'g--','linewidth',2) plot(alpha,C_m_w,'g-','linewidth',2) legend('C_ztotal','C_xtotal','C_zw','C_xw','C_zt','C_mw','location','eastoutside') title('Monoplane Wing Trim Curves') xlabel('Angle of Attack Alpha (degrees)') ylabel('Coeffecient Value')

72

function AE440_Vn_Diagram_Mono() % Michael Duffy AE440 Conceptual Design Report % ----- % Monoplane V-n Diagram % ----- % Design values rho = 0.002378; % density (slug/ft^3) W_o = 1360.4; % gross weight (lbf) S_w = 64.46; % wing planform area (ft^2) V_c = 168; % cruise velocity (ft/s) V_d = 1.3*V_c; % dive velocity (ft/s) c_w_mac = 3.115; % mean aerodynamic chord (feet) C_l_alpha = 6.2069; % Lift slope coefficient l_t = 5.906; % horizontal distance of tail AC BEHIND plane CG (feet) l_wb = -.312; % horizontal distance of wing AC BEHIND plane CG (feet) U = 30; % Vertical gust velocity (ft/s) [raymer 395] mu = 2*(W_o/S_w)/(rho*32.7*c_w_mac*C_l_alpha); K = .88*mu/(5.3+mu); KU = K*U; % effective gust velocity (ft/s) n_max = 4.4; % max load factor - utility aircraft [raymer 392] n_min = -1.8; % min load factor - utility aircraft [raymer 392] % Airfoil data [col1, col2, col3, col4] = textread('NACA2412.data','%f%f%f%f%*[^\n]','delimiter',' '); alpha = [col1].'; C_l = [col2].'; C_d = [col3].'; C_m_w = [col4].'; % Calculate wing force values C_z_w = C_l.*cosd(alpha)+ C_d.*sind(alpha); % Calculate tail force values C_z_t = (c_w_mac./l_t).*C_m_w - (l_wb./l_t).*C_z_w; % Calculate total force values C_z_total = [C_z_w + C_z_t]; % Calculate limiting velocity values V_a = (n_max/(1.25*max(C_z_total)*rho/(2*(W_o/S_w))))^.5; V_g = (-n_min/(max(C_z_total)*rho/(2*(W_o/S_w))))^.5; % Create velocity function matrices V_upper = linspace(0,V_a,100); V_lower = linspace(0,V_g,100); n_upper = (1.25*max(C_z_total)*rho/(2*(W_o/S_w))).*V_upper.^2; n_lower = -(max(C_z_total)*rho/(2*(W_o/S_w))).*V_lower.^2; % Create gust function matrices i = max(size(C_z_total)); a = (C_z_total(i)-C_z_total(i-1))/((alpha(i)-alpha(i-1))*pi/180); V_range = linspace(0,V_d,150); n_g_upper = 1 + rho.*KU.*a.*V_range./(2*(W_o./S_w)); n_g_lower = 1 - rho.*KU.*a.*V_range./(2*(W_o./S_w)); % Plot the Vn Diagram figure plot(V_upper,n_upper,'r-','linewidth',2) plot([0,1.1*V_d],[0,0],'k-','linewidth',2) hold on grid on plot(V_upper,n_upper,'r-','linewidth',2) plot(V_lower,n_lower,'r-','linewidth',2) plot([V_g,V_c],[n_min,n_min],'r-','linewidth',2)

73

plot([V_c,V_d],[n_min,-1],'r-','linewidth',2) plot([V_a,V_d],[n_max,n_max],'r-','linewidth',2) plot([V_d,V_d],[-1,n_max],'r','linewidth',2) plot(V_range,n_g_upper,'b--','linewidth',2) plot(V_range,n_g_lower,'b--','linewidth',2) plot([V_d,V_d],[min(n_g_lower),max(n_g_upper)],'b--','linewidth',2) plot([V_c,V_c],[n_min,0],'g-','linewidth',2) plot(V_d,n_max,'ko','linewidth',2) plot(V_a,n_max,'ko','linewidth',2) plot(V_g,n_min,'ko','linewidth',2) axis([0,1.1*V_d,-3,5]) title('Monoplane V-n Diagram') xlabel('Velocity, V (ft/s)') ylabel('Load Factor, n') text(V_a,n_max,[' V_a = ',num2str(V_a)],'VerticalAlignment','bottom','HorizontalAlignment','right') text(V_g,n_min,[' V_g = ',num2str(V_g)],'VerticalAlignment','top','HorizontalAlignment','right') text(V_d,n_max,[' V_d = ',num2str(V_d)],'VerticalAlignment','bottom','HorizontalAlignment','left') text(V_c,0,[' V_c = ',num2str(V_c)],'VerticalAlignment','bottom','HorizontalAlignment','center') text(V_a,n_max,[' High AoA '],'VerticalAlignment','top','HorizontalAlignment','right') text(V_d,n_max,[' Max q '],'VerticalAlignment','top','HorizontalAlignment','left') text(max(V_range),max(n_g_upper),[' + Dive Gust '],'VerticalAlignment','middle','HorizontalAlignment','left') text(max(V_range),min(n_g_lower),[' - Dive Gust '],'VerticalAlignment','middle','HorizontalAlignment','left')

74

Appendix A.2 Stability and Control: Equations Used A.2.1 Tail volume ratios to find vertical tail and horizontal tail reference areas

.05.05

.5.5

v vvt v

v

h hht h

h

S l S bc = = S =Sb lS l S cc = = S =Sc l

⋅ ⋅⇒

⋅ ⋅⇒

(A.2.1)

A.2.2 Neutral Point Calculation ignoring propeller effects since thrust line almost goes through c.g. Assuming aerodynamic center at quarter chord:

14acw

x = c⋅ , 0.90hη = , 2F FFMα fus

K W LC =

cS ,

4ac hh

cx = l + , 1hα ε=α α

∂ ∂−

∂ ∂ (A.2.2-6)

h hL ac M h L acα w α α hfus h

nph h

L h Lα αh

S αC x C +η C xS αx = S αC +η C

S α

∂⋅ −

∂∂∂

(A.2.7)

A.2.3 Blended Wing Body Neutral Point Sample Calculation Weighted average of fuselage neutral point and wing neutral point:

np, fus fus np,w wnp

fus w

x S + x Sx =

S + S, np

np

xx =

l (A.2.8-9)

A.2.4 Static Margin Calculation

S . M .=�xnp− �xcg

�c (A.2.10)

A.2.5 Trim Analysis

0 w t

t tM M L o

S lC C CScα α

α ε= +o

, M L MM C CC S− ⋅ + (A.2.11-12) =

        

75

Appendix A.3 Thrust vs. Velocity Curve and Propeller           

Figure A.1 Thrust vs. velocity for Jabiru 3300.

Figure A.3.1 Thrust vs. velocity curve.

Figure A.3.2 Airmaster AP332 fully feathering propeller.

   

76

Appendix A.4 Aerodynamics Equations L=qSCL,

1KAeπ

= , ,0.681.78(1 0.045* ) 0.64e A= − − max max 0.250.9 cosL lC C c= Λ (A.4.1-4)

exposed

22 2refmax

2 2

2 ( )tan2 4 1

L

t

SAC FSA

απ

βη β

⎛ ⎞= ⎜ ⎟

⎛ ⎞ ⎝ ⎠Λ+ + +⎜ ⎟

⎝ ⎠

(A.4.5)

2 21 Mβ = − , 2 /

lC αηπ β

= , 0wet

D feref

SC CS

= (A.4.6-8)

( ) ( )c

misc L&P

f0 subsonic

C * * * cc c wetD D

ref

FF Q SC C

S= + DC+∑ (A.4.9)

laminar 1.328 /fC R= , turbulent 2.58 2 0.6510

0.455(log ) (1 0.144* )fC

R M=

+, VlR ρ

μ= (A.4.10-12)

1.053cutoff 38.21( / )R l= k (A.4.13)

40.18 0.280.61 100 1.34* (cos )

( / ) mm

t tFF Mx c c c

⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎡= + + Λ⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎣⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦⎤⎦ for Wing, Tail, Strut, Pylon (A.4.14)

3

601400

fFFf

⎛ ⎞= + +⎜⎝ ⎠

⎟ for Fuselage, 1 (0.35 / )FF f= + for Nacelle (A.4.15-16)

max(4 / )l lfd Aπ

= = , for Nacelle, 1 (0.35 / )FF f= +max(4 / )

l lfd Aπ

= = (A.4.17-19)

fuselage wing vtail htail cowlings1.0, 1.1, 1.03, 1.08, 1.5Q Q Q Q Q= = = = = (A.4.20)

feathered prop propeller disk( / ) .1D q Aσ= , max max

flappedH.L.

ref

0.9 cosL l

SC C

S⎛ ⎞

Δ = Δ Λ⎜ ⎟⎝ ⎠

(A.4.21-22)

flap0 flap flapped ref flap( / )( / )( 10)D fC F C C S S δΔ = − , 2 2flap / 4( ) cosDi f L cC k CΔ = Δ Λ (A.4.23-24)

1.5effective

1.5

33( / )1 33( / )

K h bK h b

=+

2 2

2

(1 )2

rer r

μμ σμ

+= 2+ +

(A.4.25-26)

77