FINAL YEAR BENG PROJECT REPORT ME30227

Jason Newton, June 9, 2015

Project title: Genetic algorithm optimisation of a UAV using vortex lattice method

Supervisor: Michael CarleyAssessor: David Cleaver

I certify that I have read and understood the entry in the Student Handbookfor the Department of Mechanical Engineering on Cheating and Plagiarismand that all material in this assignment is my own work, except where I haveindicated with appropriate references. I agree that, in line with Regulation15.3(e), if requested I will submit an electronic copy of this work for submis-sion to a Plagiarism Detection Service for quality assurance purposes.

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Abstract

The aim of this project is to optimise a UAV designed to deliver aid for maxi-mum range. These objectives were acheived by using a multidisciplinary ap-proach of combining GA optimisation with aerodynamics, structural weightestimations and stability. Sensitivity analysis and comparison to the existingUAV is performed to explain why the best UAV found performs better andwhat implications this may have for UAV design in general.

It was found that the effect of the lift distribution on the span efficiency is toosmall for this to be of significant concern when trying to minimise drag hencethe requirement of an inboard loaded wing must either be forced or come fromaccurate structural estimates. The lowest drag wings produced tend to have avery low CP over the upper surface throughout the entire chord length witha low taper ratio on the outer partitions. The best solutions are founds whenthe population size per generation is increased. The maximum increased rangeof the UAV was 55% although with an increase in wing area for TO and land-ing purposes a 50% increase is still acheivable. Small UAV wings can acheivemuch higher AR than large aircraft due to the low bending moments on thewing and the high strength of CFRP. It was from this that it was concluded thatlong range UAV flight is best acheived with a small amount of batteries and alarge AR low drag wing.

Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Boundary layer transition at low reynolds numbers . . . 32.2 Aerodynamic GA optimisation . . . . . . . . . . . . . . . 42.3 Airfoil parameterisation . . . . . . . . . . . . . . . . . . . 4

3 Computational methods . . . . . . . . . . . . . . . . . . . . . . . 53.1 Airfoil .dat files . . . . . . . . . . . . . . . . . . . . . . . . 53.2 Determining number of Chord and Span wise panels to

use . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63.3 Re-estimating viscous drag . . . . . . . . . . . . . . . . . 73.4 Initial simplified Flying Wing Problem . . . . . . . . . . 73.5 Revised flying wing . . . . . . . . . . . . . . . . . . . . . 93.6 Estimating fuselage drag . . . . . . . . . . . . . . . . . . 103.7 Full model . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164.1 Number of panels . . . . . . . . . . . . . . . . . . . . . . 164.2 Initial flying wing experiment . . . . . . . . . . . . . . . 174.3 Improved flying wing experiment . . . . . . . . . . . . . 194.4 Full model results . . . . . . . . . . . . . . . . . . . . . . . 22

5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.1 Initial flying wing experiment . . . . . . . . . . . . . . . 265.2 Improved flying wing experiment . . . . . . . . . . . . . 275.3 Full model . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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Glossary and notation

AR - Aspect ratiob - SpanC - Chord lengthCr - Root chord lengthCD - Drag coefficientCM - Pitching moment coefficientCFD - Computational fluid dynamicsC.G - Centre of GravityCP - Pressure coefficientD - Dragh0 - Aerodynamic centeriw - Wing settingGA - Genetic AlgorithmKn - Stick fixed static marginHm - Stick fixed maneuvre marginMAC - Mean Aerodynamic ChordMTOW - Maximum take off weightnbatt - Number of Batteriespop - Population sizePPLR - Project Plan and Literature ReviewRe - Reynolds numberS - Wing areaTE - Trailing edgeTO - Take offUAV - Unmanned Aerial VehicleV - VelocityVS - Stall velocityVSf - Stall velocity with flapsV - Tail volume coefficientVLM - Vortex Lattice MethodW = WeightWwing - Wing WeightXFLR5 - XFOIL program designed for aerodynamic performance estimates atlow reynolds numbers - Angle of Attackt - Geometric twist angle - Taper ratio - Dihedral angle

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1 Introduction

There is increasing interest within Aerospace Engineering in regards to UAVsand their applications. One such application is using drones for delivery. AUAV being designed by an MEng project team is intended to deliver aid toareas afflicted by a humanitarian disaster. A typical mission scenario will in-volve:

-Launch from a pneumatic cannon from a position as close as possible to theaffected area at a MTOW of 7kg.- Drop two 1kg payloads (with 0.3kg parachute) in the target area.-Return home at a weight of approximately 4.4kg-Perform a net landing. (1)

Strict laws encapsulated in CAP 722 and the ANO (2) mean that it is desiredfor the UAV to remain under 7kg. In order to maximise the business poten-tial of this project it is desired that the UAV is optimised for maximum rangewhile still meeting basic criteria such as TO, landing and maneuvre. Since thereis a high degree of non-linearity in the problem due to aircraft being multi-disciplinary it is difficult to find a true global optimum for such a problem.Historically these kinds of non-linear problems have been solved with greatsuccess using genetic algorithms hence it will be useful to see if they can beapplied to this scenario.

The aim of this report is hence to use a GA to optimise a UAV for maximumrange. The objectives to acheive these aims are:

Combine an aerodynamic model with structural and stability estimatesto create a full model of any reasonably sized UAV.

Perform sensitivity analysis to make sure that a global optimum is beingacheived

Comparison with the existing UAV to see why it performs better.The layout of the report will consist of reviewing revelant literature to thestudy, the computational methods and design assumptions assumed, the salientresults from the intermediary and main experiments and then finally a discus-sion on the interesting features of the results and how they have improvedupon the existing UAV.

2 Literature review

2.1 Boundary layer transition at low reynolds numbers

It is very difficult to predict when boundary layer transition will occur and thisis a topic with a lot of literature surrounding it. The UAVs of the size beingdiscussed are well into the transition region so it is an important considera-tion for the estimation of viscous drag. Since it is not a principal aim at themoment only a small amount of research was conducted however a highly rel-evant piece of research was found in (3). An airfoil similar to the RG15 being

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used was tested to find the transition point at various Reynolds numbers andangles of attack. Based on an extrapolation of the data given in Table 1 of thestudy, transition will occur at around an Re of 55000-75000 on both the upperand lower surface at chord reynolds numbers of 150000-350000 for an AOA of5 degrees, about the same as the wing incidence of the UAV in cruise based offthe current design.

2.2 Aerodynamic GA optimisation

As discussed in the PPLR (1), GAs have been shown to provide better solutionsthan the gradient method and simulated annealing (4) which is the reason whyit was chosen to use this method for the UAV optimisation.

Some studies that have been on aerodynamic optimisation using GAs include(5-8). The flaws with these studies when compared to the work undertaken isthreefold. Firstly the aircraft are typically much larger so many of the variablesas will be shown e.g. the effect of aspect ratio on wing weight are not applicableto this study. Secondly, they are very constrained in that these studies specifya cruise speed and AOA and sometimes even wing area. These are unknownsin the work undertaken since the UAV works towards a weight limit to deter-mine maximum range i.e. what is the optimal number of batteries, wing sizeand tailplane configuration so that the UAV does not exceed a MTOW of 7kg?Finally they typically only consider the wing on its own without any consider-ation for the effect on the whole design of the aircraft.

A more relevant study was performed in (9) which is similar to the full modeloptimisation intended to be performed where the wholistic effects such as tailplane sizing and wing position are considered. This study still suffers from thesame problem where variables such as cruise AOA are fixed and that the UAVis on the order of four times bigger than the one being considered.

The only directly comparable study performed was found in (10) which at-tempts to do a full configuration optimisation of a similarly designed UAVthat weighs about 1kg. The only major difference is that this UAV is optimisedfor endurance and maneuverability rather than range however some of the pa-rameters are comparable to the model produced by the GA in this report.

GAs have also been used with airfoil design (11-13), however this requirescomplex parameterisation as discussed in Section 2.3.

2.3 Airfoil parameterisation

The following is from the PPLR written for this project (1). It is included toexplain some of the decisions for the future work on airfoil optimisation whichwas unable to be undertaken due to the time constraints of the project.

One of the main problems with optimising the airfoil is how to parameterisethe profile. Using vertices to define the profile means that the algorithm willhave too many degrees of freedom, mostly likely on the order of 100, and willconsider many unfeasible designs meaning that the solution will take too long

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to converge. Using polynomials to define the airfoil surface will reduce thedegrees of freedom (6) but also has the inherent flaw of considering too manyunfeasible designs and will also most likely not converge since the parametersused to define the surface will not be based on the aerodynamics and hence thesurface will be varied all at once rather than trying to refine specific qualitiesof the airfoil such as leading edge radius or trailing edge slope.

This can be resolved by using Bezier curves and B-Splines (14). With an 8thdegree Bezier curve the approximate relative error between the original airfoiland the airfoil represented with Bezier curves was around 0.3% and airfoilssuch as NACA 0012 were succesfully optimised using this parameterisation byreducing the drag at allCLs by generally at least 1% with up to 35% in one case.The B-Spline method was advised against due to having a case to case posi-tive or negative effect compared to Bezier curves while having higher compu-tational burden. Bezier curves still have the problem where the optimiser getsstuck in a local minimum due to modifying the whole curve for any change incoefficients.

The Bezier-PARSEC method (15) improves upon this fundemental flaw andwas shown to have accelerated convergence for aerodynamic optimizationusing Differential Evolution. It is proposed that the BP-3333 method from thepaper is best for the GA airfoil optimisation of the UAV.

3 Computational methods

Most of the work performed is done by creating a specific batch script for theproblem. This batch script is based off an example given in the program calledstudentbatch.m (16).

3.1 Airfoil .dat files

The airfoils used for the project have their geometry defined by a .dat file whichcan be obtained from (insert coord database link). These need to be modifiedfor the program so that they can be read correctly as shown in Figure 1:

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Figure 1: An example with the NACA 0008 airfoil. Any non-geometry dataneeds to be commented out, the number of upper and lower surface pointsneeds to be stated in the beginning of the file and the coordinates must be inascending order.

This was performed for the RG15, NACA0008 and S8025 airfoils used inthe original UAVs wing, fin and tail.

3.2 Determining number of Chord and Span wise panels touse

It is necessary to determine the number of chord and span wise panels to usesince the optimisation will be useless if the answer is inaccurate and extremelytime consuming for an answer that is too accurate. This will be determinedby performing a fully factorial analysis where each combination of chord andspan wise panels from one to ten each will be used to find the induced drag ofthe wing and tailplane of the current UAV during trimmed cruise flight as:

Drag is the most important output since this determines the potentialrange of the UAV

The skin friction drag and fuselage drag estimates are not based on thenumber of panels

These calculations take longer to computeA 3D scatter plot of induced drag - no. of chord wise panels - no. span wisepanels will graphically show where a good value will lie.

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3.3 Re-estimating viscous drag

The current viscous drag calculation used by tornado implicitly assumes bound-ary layer transition at 10% chord. Given that the Re of the flow over the wingsof a UAV this size is around 200000-300000 this would suggest a pessimistictransition at Re = 20000-30000. zeroliftdragpred.m was changed so that bound-ary layer transition occurs according to the research conducted in Section 2.1.Figure 2 shows the changes.

Figure 2: Changes to the Tornado viscous drag estimation for the purposes ofthis analysis.

An if statement was used to preserve the programs original function for Reoutside of the ones being examined.

3.4 Initial simplified Flying Wing Problem

In order to verify and tweak the program before creating a full model, a simpli-fied flying wing problem is contrived that removes much of the complexityand contraints of the full model. The goal is simply to have maximum cruiserange with the following constraints, assumptions and limitations:

The wing is producing maximum lift of (or close to) 68.67 N i.e. thisignores the payload drop element to the problem

The wing size does not have any effect on the amount of batteries thatcan be carried.

The UAV is electrically powered and the combination of wing and bat-teries weighs no more than 2.5kg. This is equal to the weight of the wingand batteries in the current UAV and allowing anymore weight wouldmean an unfeasible design since the other weight is required for fuse-lage, electronics, payload etc.

The choice of battery and motor is not affected so much by the designchanges that the correlations used are inadequate.

Stability is ignored for now The weight of the wing and batteries does not significantly affect the re-

quired fuselage weight in order to support the shear and bending mo-ments. This is reasonable since the fuselage is already overdesigned witha minimum number of composite layers (17)

TO, landing and maneuvre requirements are ignored Trim drag is ignored for now and so solverloop5.m, a simple steady

state analysis, is used instead of fTrimCLconst.m for the drag estima-tion. This will change when a Tailplane is added in the full model.

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The Cm Re relationship is ignored for now since it is very hard topredict unless a solver such as XFOIL is used and is not a core aim of thestudy. An average CM0 of -0.05 will be used for the RG15 airfoil for theanalysis (18)

For structural estimates an overall average taper ratio will be used inorder to avoid spending time modifying existing programs. The structureestimates also assume negligible dihedral and no sweep although in thiscase the sweep will not be optimised due to the propeller positioning.The wing weight also estimates that the lift in each chordwise step isproportional to the wing weight of that strip.

The fitness function was determined as follows:

Range = Energy/Drag since this is equivalent to Distance = Work done/Force.Based on the propulsion expert in the UAV team the LiPo batteries provide555000J/kg of energy (19). The electrical efficiency of these batteries is approx-imately 0.6 and the combined efficiency of the other components (e.g. motor,propeller, ESC etc) was approximated at about 0.56. This gives a usable energyof 186460J/kg and given that the batteries used are 252g each, this means themaximum range is given by:

R = ED =0.252nbatt186460

D (=(2.5Wwing)186460

D )

Where 0 < nbatt < 10 and takes integer values and 2.5 0.252 nbatt +Wwing .

The problem with this fitness function is that keeping the lift at 68.67N (ormore accurately equal to the weight) will need to be a included as a constraint.The lift depends on many variables and will cause very slow convergence asthe program tries to find correct values that satisfy it. This was found by trialand error when trying to use the lift as an inequality constraint as the programtook about 90 minutes to just go through 10 generations with only 3 variables.This can be overcome by incorporating a term into the fitness function thatgravitates the solutions to the correct lift. The term (1 + (W L)2) was mul-tiplied to D so that a penalty is applied to solutions which deviate away fromhaving L = W . Since MATLABs GA attempts to minimise the fitness function,the final equation is given by:

Fitness = D(1+(WL))2

46988nbatt ( 1R )

The code for the wing weight comes from the structures leader (17) in whicha specific MATLAB script is written that accurately calculates the wing weightfor this specific UAV. This needs to be looped so that the optimum number ofribs is found. For the design decisions such as the material, number of com-posite layers, load factor etc it is recommended that this document is read toexplain the reasoning behind the code. For simplicity the code is left unalteredand so the program will be assuming a straight overall taper.

The variables to be optimised are shown in Table 1 with the bounds.The program was run with a population size of 200 and was ended at 26 gen-erations.

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Lower bound Upper Bound NotesV (m/s) 10 36 70kt is CAP 722 maximum speedCr (m) 0.04 0.61,2,3 0.5 1 (Rad) 0 0.174 0.192 Rad is theoretical stall angle of airfoilb1,2,3 (m) 0 2t1,2,3,4(Rad) -0.1047 0 t1 refers to root chord1,2,3 (Rad) 0 0.785

Table 1: Variables optimised in the problem. Other variable bounds were justestimated starting points. Numbered subscripts refer to the partition of thevariable.

3.5 Revised flying wing

Based on the results of the initial flying wing model there were two changes tobe investigated:

Should twist be kept in as a variable but be forced to change linearly? Revamping the fitness function to acheive an elliptical lift distribution.

This is needed so that the ailerons dont stall at high angles of attack, thedownwash is constant over the span, and so that the wing spar designand weight estimations are much easier.

It is proposed to do this in a similar way to keeping the lift constant by apply-ing a term which puts a penalty against values which deviate from the ideal.Since squaring the residuals worked well for lift, this method was used for thistask.

The program evaluates the localCL at typically up to 9 points along each semis-pan. These points can be used to calculate how close the curve is to elliptical byfinding out the ratio of their local CL at specific coordinates as shown in Figure3:

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Figure 3: Ideal ellipse geometry shown with example values. This will be per-formed at all points in the program.

The fitness function will be given by:

Fitness = KD(1+(WL)2))

46988nbatt

Where K =n=ystationlengthn=1 (1 + 10 (CLn CLidealn)2) and CLidealn =

CLroot Cos(yn/yystationlength)

The extra factor of 10 on the residuals of the local lift coefficients is to makethe factor K of roughly the same magnitude as the lift, meaning the programwill put equal weight on this criteria as keeping L = W . This fitness functionhas the advantage of retaining the main goal of range when the lift and lift dis-tribution criteria are met while accelerating the convergence when they are not.The finalised batch script used is given in the appendix under flyingwing.m.This has the executable command written in the description. The experimentwas run with 200 population size linear twist, 300 population linear twist and300 population no twist each for 50 generations.

3.6 Estimating fuselage drag

An approximate value for the fuselage drag was based off (20) as follows:

CDof = Cf fLD fM SwetfSWhere fLD is a function of the fineness ratio defined as the fuselage length,L, over the diameter, D, and fM is a function of the mach number, neglectedsince M < 0.1. The fuselage length and max diameter is 0.714m and 0.258mrespectively (Figure 4). The approximate reynolds number over the fuselagewas calculated as:

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Re = V L =V 0.7140.0000146

The transition point from laminar to turbulent flow was estimated as simplybeing at Re = 200000. This may be inaccurate but it should suffice for the pur-poses of the program.

Cf = Cf,lam xltr + Cf,turb (1 xltr )

Where

Cf,lam =1.327Re

Cf,turb =0.455

(log10(Re))2.58

fLD = 1+60

(L/D)3 +0.0025 (L/D) = 1+ 60(0.714/0.258)3 +0.0025 (0.714/0.258) =3.84

The estimated wetted area of the fuselage came from ME30219 performancenotes (21).

SWet = 0.8 pi Dmax L = 0.8 3.1415 0.258 0.714 = 0.463m2

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Figure 4: Fuselage geometry (22).

3.7 Full model

The full model includes the effects of the drag from the fuselage and the dragand weight of the tailplane and boom. The tailplane and boom size will bebased off stability criteria to find the minimum weight necessary. The effect ofthe payload drop and trim drag will also be included when analysing cruise.There are several assumptions and constraints that are made to try to simplifythe problem:

The propeller positioning does not significantly affect the aerodynamics The fuselage shape will not be optimised. Since iw is fixed and changing the angle of attack to increase/reduce lift

will cause extra drag from the fuselage not being horizontal, the speed

after payload drop can be inferred as

4.47 Vfullpayload.

Any amount of batteries over six is placed in f4 (Figure 5) which is locatedat 554mm from the nose. See the appendix for weights and C.G positions

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of various components of the current UAV.

The TE of the wing is always in front of the propeller (Figure 5). It wasalso decided that sweep shouldnt be investigated since the stability op-timisation is already quite computationally intensive.

The downwash is constant across the wing span. This is to simplify theproblem since the downwash calculated by the program varies in accor-dance with the lift distribution and creates a downwash matrix that isdifficult to integrate with simple stability calculations. The downwashwas estimated as dd =

35api180AR (23)

It was calculated that a minimum wing area of 0.455 m2 was needed andthat with flaps spanning 60% of the span with 20% of the chord CM0 atfull deflection was -0.19 (24). Plain flaps were estimated to give a CL of1.0 at full deflection and. CLmax was conservatively used as 1.05 whichis slightly below the CLmax of the airfoil data.

The aspect ratio and taper ratio of the vertical and horizontal tails is 1.8and 23 ARW , 1 and 0.7 respectively based on recommendations used in(25). The fin volume coefficient is assumed to be the same as the currentUAV based on the design considerations from the same reference.

The fin and boom weights are simply correlated to volume since they areoverdesigned with the current minimum amount of fibre layers used e.g.boom has safety factor of 6.5.

Figure 5: Sideview of aircraft geometry (17). The propeller is mounted on theback of the fuselage hence the wing is limited to being in front of it.

To reduce the complexity of the problem it was decided that the weight estima-tion for the aerodynamic solver will be approximated rather than exact. Sincethe program inevitably gravitates towards having the most weight possible theweight was estimated as just being 68.67N and 43.2N for full and no payloadrespectively. This is since it is preferred that the tailplane is a consequence ofthe aircraft rather than simply another input variable as this would mean thatthe tailplane weight would need to be found simultaneously with the wingand battery weight meaning many unfeasible designs will be considered in theprocess.

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Another problem is that the tailplane and boom move the C.G position aft-wards due to the extra weight so that in effect h0 h becomes smaller as thetailplane effectiveness increases. It was decided the best way to deal with this isto assume that the program gravitates towards the original tailplane and boomsizes (since the program prefers a main wing with minimum area) to give aninitial C.G position and then loop to refine the value.

V was defined by the minimum value which satisfies Kn= 0.05, Hm = 0.08(25) as well as the cruise, climb and descent maneuvre conditions which arebased off the trim equation CM = CM0 (h0 h)CL V CLT .

The lift curve slope of the tailplane is estimated to be around 3.7 based onthe current UAV. In further work it is suggested that this be more accuratelypredicted using ESDU sheets 89029 and 70011 (26-27).

The total weight of the combined wing, batteries, fin, tail and boom was up-dated to 2837g. This is like the same as the 2.5kg used for the wing and bat-tery weight in the flying wing experiment except now since stability is takenaccount of, the program should now gravitate towards a small tailplane for re-duced drag and weight.

The initial full model experiment will have no constraint on wing area sinceit is desired to find out what the true optimum is if TO and landing had no ef-fect. Three experiments consisting of a population size of 400, population sizeof 400 with the current UAV as the initial population, and a population sizeof 500 were performed. The program was altered such that fTrimCLconst.mthe program converges when CL = 0.01 rather than 0.001 as otherwise thenumber of iterations needed makes the program far too slow. A block diagramof the program is given in Figure 6:

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Figure 6: Simplified block diagram of the program.15

4 Results

4.1 Number of panels

It was found that in order to do a trimmed analysis, some of the combinationsof chord and span wise did not give a converged solution for this wing withinthe default 10 iterations in fTrimCLconst.m. For the purposes of analysis thiswas increased to twenty.

The results of the batch script are shown in Figure 7. The aircraft was assumedto be at max payload for reference. The batch script used with the referencedata inputted is given in the appendix.

Figure 7: Accuracy of analysis on the current UAV with varying numbers ofchord and span wise panels.

It was seen that the accuracy of the analysis did not depend much on thenumber of span wise panels in comparison to the number of chord wise panels.Based on Figure 7 an appropriate number of chord and span wise panels toacheive sufficient accuracy are eight and three respectively.

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4.2 Initial flying wing experiment

Figure 8: Geometric results of the analysis

Figure 9: Lift distribution in cruise.

The geometry of the initial flying wing optimisation is shown in Figure 8.

It was seen that the (1 + (W L)2) factor performed as intended and causedthe algorithm to incline towards solutions where L = W (Table 2) without be-ing as time consuming as including this as a constraint in the program. Table2 also shows that the program used geometric twist in such a manner to make

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V (m/s) 34.7Cr (m) 0.1031,2,3 0.52, 0.78, 0.54 (Rad) 0.162b1,2,3 (m) 0.25, 0.63, 0.40t1,2,3,4 (Rad) -0.0959, -0.0743, -0.0844, -0.04791,2,3 (Rad) 0.187, 0.213, 0.0075Weight (N) 67.63Lift (N) 67.04CL 0.721D (N) 1.457Re 130650S (m2) 0.1241b (m) 2.56Wing Weight (kg) 0.561Number of batteries 8Fitness 3.876 106

Table 2: The optimum variables decided by the algorithm along with the salientoutputs.

the wing difficult if not impossible to manufacture. It was proposed to try ei-ther forcing a linear twist or to remove this as a variable not just for programand manufacturing simplicity but also since it may not be necessary if the othervariables are optimised correctly as shown in (28).

It was originally assumed that the program would tend towards inboard loadedwings for minimum induced drag, however it not perform as intended as thelift distribution turned out to be no where near elliptical suggesting that a newapproach will be needed when creating the fitness function (Figure 9).

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4.3 Improved flying wing experiment

Figure 10: Pressure plots for each of the wings produced in the second iteration.

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Figure 11: Lift distribution in cruise for each wing produced in the seconditeration.

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Experiment 200 pop no twist 300 pop no twist 300 pop linear twistV (m/s) 25.5 32.6 28.3Cr (m) 0.128 0.066 0.1191,2,3 0.82, 0.85, 0.76 0.91, 0.58, 0.47 0.60, 0.79, 0.52 (Rad) 0.069 0.096 0.112b1,2,3 (m) 0.65, 0.28, 0.84 0.50, 0.59, 0.45 0.53, 0.68, 0.421,2,3 (Rad) 0.20, 0.51, 0.75 0.18, 0.47, 0.75 0.15, 0.52, 0.74t - - -0.0455Weight (N) 67.50 68.60 67.96Lift (N) 67.65 68.55 67.93CL 0.57 0.74 0.62D (N) 1.7 1.42 1.71Re 162500 116000 147000S (m2) 0.3 0.143 0.225b (m) 3.54 3.07 3.27Wing Weight (kg) 0.869 0.477 0.663Number of batteries 6 8 7Fitness 6.433 105 3.99 105 4.79 105

Table 3: The optimum variables decided by the algorithm along with the salientoutputs.

Although the algorithm was heavily weighted to produce a perfect ellipti-cal lift distribution it only produced a rough approximation as seen with thesharp rise in CL midspan (Figure 11). This is sufficient for the aircraft since it ismostly about avoiding tip stall at high angles of attack. The program was alsoseen to prefer much more dihedral than the original run.

It was seen in Figure 10 that the lowest drag wing had a very low value ofCP across the entire area which would explain why the GA chose this wingto have a high cruise speed in replacement of wing area since this wing is de-signed more for high speed flight. This also explains the wing had a muchbetter value of L/D than the other wings.

It was found that introducing a bigger population size led to a much betterend design with having enough weight for 2 extra batteries, a 20% reductionin cruise drag while still having a greater cruise speed in the 300 pop no twistcase although this likely due to the fact that the wing is around 2.5 times assmall. The lift distribution shape of the 300 pop no twist case (11) was inter-estingly similar to the 200 population experiment with a slight improvementin the midspan. It was seen however when linear twist was introduced that aninferior design was produced which was in between the 200 population andthe 300 population with no twist as demonstrated in Table 3.

However when looking at the lift distributions it is clear that introducing twisthas significantly improved this aspect of the design. From this it was con-cluded that it is worth keeping twist to improve the aerodynamic performancehowever it will be necessary to have at least a population size of 400-500 tohave a likely chance of finding a global optimum in the full model. Unfortu-

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nately this meant that few analyses on the full model could be performed sincethis requires tremendous computational effort.

4.4 Full model results

Figure 12: Full geometry for the three full model runs.

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Figure 13: Convergence plots for the three full model runs.

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Figure 14: Lift distribution in cruise for the three full model runs.

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Figure 15: Pressure distribution plots in cruise for the three full model runs. Itwas found that there is a bug within Tornado VLM which means sometimesthe tailplane is not plotted in the pressure plot graphs.

The geometry of each design is given in Figure 12. All designs tended to con-verge within about 25 generations so they were stopped here (Figure 13) sincethey take 2-3 days to run. The 400 pop group had the best lift distribution shape

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Experiment 400 pop 500 pop 400 pop initial pop CurrentV (m/s) Full & no payload 18.1, 14.4 18.8, 14.9 23.2, 18.4 21, 16.65Cr (m) 0.175 0.172 0.187 0.261,2,3 0.85, 0.95, 0.5 0.63, 0.77, 0.66 0.97, 0.69, 0.50 0.928, 0.928, 0.928 (Rad) 0.152 0.1458 0.13 0.096b1,2,3 (m) 0.31, 0.74, 0.25 0.73, 0.53, 0.39 0.35, 0.26, 0.31 0.327, 0.327, 0.3051,2,3 (Rad) 0.16, 0.22, 0.53 0.10, 0.48, 0.47 0.20, 0.24, 0.66 0, 0, 0.17t -0.056 -0.069 -0.044 -0.0279Wing TE position (m) 0.691 0.522 0.568 0.6Boom length (m) 1.618 1.29 1.75 0.95CL 0.91 0.88 0.76 0.57Average Drag (N) 2.59 2.36 3.53 3.65S (m2) 0.37 0.36 0.27 0.455Sfin (m2) 0.017 0.0272 0.0081 0.045Stail (m2) 0.0947 0.0302 0.0232 0.046V 3.19 0.946 1.04 0.4b (m) 2.60 3.30 1.83 1.94Wing Weight (kg) 0.88 0.96 0.53 1.03Number of batteries 6 6 8 6Range (m) 109000 119500 106500 77300

Table 4: The optimum variables decided by the algorithm along with the salientoutputs.

(Figure 14). The 500 pop group had the lowest drag and was shown in Figure15 that CP was typically much lower towards the TE of the wing planform aswell as the LE suggesting that the wing is good at producing lift and avoidingboundary layer separation. This aircraft had around 55% extra range than thecurrent UAV. It was found that the 400 and 500 pop experiments were converg-ing towards a similar point suggesting that a global optimum may have beenfound (Table 4). The main difference between the two is that the 500 pop sizefound a much better stability solution than the 400 pop experiment meaningthat a larger aspect ratio wing could be afforded leading to reduced drag andextra range. The 400 pop experiment with the initial population interestinglyconverged towards a completely different solution albeit one that has nearlythe same performance as the other 400 pop experiment. This utilised having2 extra batteries at the expense of a low weight low aspect ratio wing. In the-ory this could be the best design since it will have a similar range to the othersexcept it will be much more maneuvarable and faster however all of these de-signs ignore the wing area component to the problem (for TO and landing)hence it will be very unlikely that the 8 battery design could be feasible.

5 Discussion

5.1 Initial flying wing experiment

There are a couple of interesting points to note about the results of the initialflying wing experiment.

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Firstly due to the low stresses in the wings, much higher aspect ratios can beacheived compared to large aircraft such as passenger aircraft as the weight ismore affected by the total volume of the wing rather than the aspect ratio caus-ing the design for a wing that can withstand high bending moments. A wingaspect ratio of around 52.5 was produced whilst only weighing 0.581kg witha reference area of 0.1241 m2. This is in contrast to the wing that the currentUAV has where an aspect ratio of 8.25 has a 1.03kg wing with a reference areaof 0.455 m2. This means the current UAV wing has around 3.7 times the area ofthe flying wing whilst only weighing 1.84 times more however the aspect ratiois far lower which suggests that low Re UAVs should be designed to have assmall wing area as possible with a larger aspect ratio than might be expected.According to Raymer the correlation of wing weight to surface area and aspectratio is S0.758 and AR0.6 and 0.04 (29) which would suggest that:

Current UAV wing weight =k 0.4550.758 8.250.6 = 1.95k, initial flywing wingweight =k0.12410.758 52.50.6 = 2.21k i.e. the wing should weigh more due tothe bending moment that it needs to be designed to resist (Assuming 0.04 1).

Although theoretically an elliptical lift distribution will give the lowest in-duced drag this was not even close to being seen despite the main target ofthe program being to reduce drag. There are several possible explanations forthis result:

The algorithm didnt have enough variation or enough generations toconverge to an elliptical distribution and got stuck in local minima.

Due to the finite number of ways the wing was allowed to be changedthe algorithm had difficulty finding correlations which would lead to anelliptical distribution

The effect of an elliptical lift distribution on drag is small and hencethe traits of a high AR and lots of batteries on range outweighed thisconsideration.(30-31)

It was also interesting to note the similarities in the results of this experimentwith the one performed by (5). The program also used geometric twist in sucha way to make difficult shapes (t1,2,3,4 = 0, 0.4691,3,4.9685). Anotherwas that the program also preferred a variety of solutions rather than a singleregion of wing geometries as was shown in the improved wing experiments.This has been suggested as being due to the fact that nature prefers diversesolutions to a solitary optimum. Similar types of results were found in (32)where a diverse range was the outcome of the experiment.

5.2 Improved flying wing experiment

It was seen that the high amounts of dihedral compared to the initial wingexperiment could be explained by observing the wings without any dihedral.Despite the increase in lift the drag remains at a similar value of 1.78N and Fig-ure 16 shows that the lift distribution has changed dramatically suggesting thatdihedral is being used to change the lift distribution whilst having a negativeimpact on L/D.

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Figure 16: Lift distribution of the wing without dihedral.

5.3 Full model

The results for the full model experiments are similar to the UAV optimised in(10) in that a large AR ratio wing was considered optimum by the program.However the UAV optimised for endurance has an AR of 10 rather than 30.This is likely due to the fact that the wings for this UAV are made out of justfoam hence they would not be strong enough for such high ARs. The UAV alsoneeded to weigh around 1kg so having an excessively large wing could not beconsidered as it would weigh too much. Since the UAV needs to TO and landon a runway the wing area was greater in proportion to the designs in section4.4 which is the reason why the UAV from this study has a calculated cruiseCL of 0.5.

Due to time constraints on the project a full model with a fixed wing area wasnot performed. However the 500 pop answer gives the most likely candidateof being used for as the new design. This is because it has the best combina-tion of being able to meet the wing area requirements whilst having the largestrange out of the experiments due to having a low drag wing whilst still havinga reasonable number of batteries. Parameters were changed in a trial and er-ror method to create a UAV with S = 0.455m2 based off the 500 pop solution.This is given in FIGURE 17:

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Figure 17: Modified optimum UAV results.

As shown in Table 5 the UAV still gives around 50% extra range than thecurrent UAV due to its low drag performance although interestingly it sacri-fices a battery in order to acheive this. A wing aspect ratio of about 32.5 isproduced which explains why the drag is 81% lower and how this is worth the17% decrease in availible energy. This again demonstrates how strong CFRP

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V (m/s) Full & no payload 16.7, 13.24Cr (m) 0.191,2,3 0.63, 0.77, 0.66 (Rad) 0.1458b1,2,3 (m) 0.68, 0.8, 0.451,2,3 (Rad) 0.097, 0.48, 0.47t -0.069Wing TE position (m) 0.522Boom length (m) 1.29CL 0.86Average Drag (N) 2.02S (m2) 0.455Sfin (m2) 0.039Stail (m2) 0.0175V 0.427b (m) 3.86Wing Weight (kg) 1.26Number of batteries 5Range (m) 116300

Table 5: The revised values to increase the wing area.

is for the skin of the wing. In reality this may be lower or even significantlyhigher since the current wing weight estimation fails to take into account thefact that only multiple layers of composite are possible rather than a continousthickness.

There are a few errors and uncertainties that havent been looked into withthis design:

The boom is 1.29m long and the stiffness has not been looked into so itmay be that this needs to be limited if the elasticity decreases the effec-tiveness of the tailplane during maneuvres.

Dynamic stability hasnt been looked into so it may well be that the dihe-dral will need to change.

Since the span is nearly 4m long it may be that this is too large for ma-neuverability purposes.

So far it has been seen that the GA prefers solutions with rather highvalue of CLcruise. This suggests that a significant reduction in drag willbe acheivable with changing or optimising the airfoil for minimum dragat around CL = 0.9. For the current airfoil this gives nearly double theestimated drag coefficient at CL = 0.6 (33), the cruise CL of the currentUAV. This will also have a twofold effect since many high lift airfoilshave a high CLmax meaning that the wing area could be reduced to theS = 0.36m2 optimum point which was found.

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6 Conclusions

It was found that 8 chord wise and 3 span wise panels are needed for sufficientaccuracy in analysing a UAV. Dihedral can be used advantageously to refinethe lift distribution of a wing. The effect of span efficiency is very small incomparison to the effect of AR and the number of batteries. The lowest dragwings produced tend to have a very lowCP over the upper surface throughoutthe entire chord length. Better solutions are founds when the population sizeper generation is increased. A combination of linear twist and dihedral pro-duces the best lift distributions for the program however it appears to increasethe chances of finding local minima leading to an overall higher drag wing.The optimal design for cruise was produced by the 500 pop group which con-verged to a similar yet overall best design to the 400 pop group. Introducingan initial population appears to increase the chances of finding a local minimawith this type of problem as shown with the other 400 pop group. The maxi-mum increased range of the UAV was 55% although with an increase in wingarea a 50% increase is still acheivable. Small UAV wings can acheive muchhigher AR than large aircraft due to the low bending moments on the wingand the high strength of CFRP. It was because of this that a lower amount ofbatteries with a large AR low drag wing appears to be the optimum for longrange flight whilst being able to acheive reasonable TO and landing speeds.

7 Future work

Firstly, it is desired to have more sensitivity analysis performed as well as someresearch into interesting areas of the experiment. Some potential areas include:

Complete the experiment with a fixed wing area of 0.455m2

If it is still necessary to force an elliptical lift distribution, what effect doeschanging the weighting have on the final results?

Would squaring the number of batteries and drag in the fitness functionlead to better convergence as the program will equally favour minimumdrag from the start of each run to the other criteria?

What is the effect of including stability in the calculations? How wouldthe results differ if the original tailplane and boom were used?

Secondly the results should be grealty improved if the wing weight calcula-tions to take into account lift distribution and discrete layers of thickness. Thisshould eliminate the need for forcing an elliptical lift distribution since wingwill weigh much more which is likely to have a much bigger effect than thespan efficiency.

Thirdly there is a lot of potential to reduce the drag further by creating a sep-arate airfoil optimiser that runs in a loop with the configuration optimiser e.g.shown in diagram below:

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Figure 18: How the program should include an airfoil optimiser.

This should make the program more stable than optimising simultaneouslysince it would not only mean having half of the variables but it will allow re-lationships to be more easily found by the program i.e. it would be undesiredif the wing airfoil is affecting the size of the tailplane. Fourthly, the currentfuselage drag estimates are approximate and assume a drag similar to that of awell designed passenger aircraft. Considering how much the fuselage reducesthe ideal cruise velocity (by nearly a factor of 2!) it would be beneficial to havea more accurate value. This may also have the potential to create a third opti-mising stage for the fuselage.

And lastly, it would be desired to have a better estimatation of the lift curveslope of the tailplane based on (26-27) and to use the full downwash matrixprovided by the program.

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Appendix

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