Development of a Preliminary Design Tool For Conventional,

Co-Axial and Tandem Helicopter Configuration

Miguel Pontemiguel.s.m.ponte@tecnico.ulisboa.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

November 2016

Abstract

This work will present the development and implementation of a computational tool with the maingoal of aiding the preliminary design, of a given helicopter with conventional, co-axial or tandemconfiguration. The user will have the ability to choose between a wide variety of key design parameters(ranging from the airfoil at each blade section to the main rotor radius value, main rotor blade chordat blade root and tip, blade twist distribution, to the power plant installed), between the 2 mostknown theories developed for rotorcraft (Momentum Theory and Blade Element Theory) and obtainthe corresponding power requirements curve. Analyzing the results obtained, the maximum range,maximum range speed, endurance and maximum endurance speed can be computed, which are keyaspects for the preliminary design of any new rotorcraft.

Keywords: tool, preliminary design, design parameters, momentum theory, blade element theory

1. Introduction

In the past few years, several computational toolswith the goal of predicting the preliminary designfor different rotorcraft were developed, varying inthe code complexity, progamming language, acessi-bility and cost. The most relevant tools will now beindividually adressed.

Starting with the RAPID/RaTE: RotorcraftAnalysis for Preliminary Design Rand Technolo-gies & Engineering [1], this is the most complexand accurate tool for helicopter project. However,the paid access and difficult accessibility, presentsa barrier for students or casual users, who wish todevelop a basic rotorcraft design and study the per-formance of their design choices.

Another very complete design tool is the CAM-RAD II [2]. This tool provides an aeromechani-cal analysis of helicopters and rotorcraft that in-corporates a combination of advanced technology,including multibody dynamics, nonlinear finite el-ements, structural dynamics, and rotorcraft aero-dynamics. The design, testing, and evaluation ofrotors and rotorcraft at all the stages is included,together with the research, conceptual design, de-tailed design, and development. However, besidesbeing an expensive tool, it can be too complex forthe basic user and/or student, presenting an highlearning curve and requiring an advanced knowl-edge of rotorcraft design.

When searching for a simpler, less expensive butcapable tool, the Preliminary Helicopter DesignProgram Ver.1 [3], is a valid option. In this pro-gram build in C++ progamming language, the usercan input engine characteristics and missions pro-files and obtain the sizing points for engine, rotorradius, weight and power required for various per-formance conditions. However, the fact that thisprogram can only be applied for the conventionalconfiguration with a single main rotor, tail rotorand engine, presents an obstacle to the user whodesires a more refined study of the rotorcraft pre-liminary design and a variety in the configurationselection options.

Still in the range of simple, but powerful prelimi-nary design software, are the tools developed by Ro-man Vasyliovych Rutskyy [4] and Anatol Cojocari[5] of Instituto Superior Tecnico. These tools arebased on the application of Momentum and BladeElement Theories , that joined with a database ofempirical data produce fast and relatively accurateresults. However, some design parameters requiredfor a more refined preliminary design, such as thepossibility to vary the airfoil section along the bladespanwise direction are not included. It should bementioned that several concepts, approaches andmethodologies used in these tools, will be applied,expanded and further developed in the context ofthis work.

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2. Theoretical Background2.1. Momentum Theory in Hovering Flight

Figure 1: Measurements of the velocity field in adiametric plane near the rotor in hover ([6], pg. 59)

According to [6], the flow near a hovering rotorpresents a unique behavior, since the rotor haszero forward and vertical speed, and produces anazimuthally axisymmetric flow field, as depictedin Figure 1. As the flow approaches and passesthrough the rotor disk plane there is a contractionin wake diameter and, consequently, a smooth in-crease in its velocity. It should be noted that thereis no discontinuity in the velocity across the rotordisk plane but since thrust is being produced, theremust be a discontinuity in pressure.

The mathematical solution of this problem will bebased in the application of the three conservationlaws: conservation of mass, momentum and energyof the rotor and its flow field.

These conservation laws will be applied in a one-dimensional integral formulation to a control vol-ume surrounding the rotor and its wake, which willenable an analysis of the rotor performance (specif-ically, its thrust and power) without having to con-sider what is happening locally at each blade sec-tion. This approach is referred as MomentumTheory which was first developed by [7] to ana-lyze marine propellers and further developed by [8],[9], [10] and formally generalized by [11].

The fundamental assumption of this theory isthat the rotor is idealized as an infinitesimally smallthin actuator disk which creates a difference in pres-sure though the actuator disk. The work done onthe rotor leads to a gain in the kinetic energy of therotor wake and is an unavoidable energy loss thatis commonly referred as induced power. Accordingto this theory, the general equation for the totalpower coefficient, in hovering flight, of a given con-ventional configuration helicopter with a rotor ofradius R, comprised of Nb blades, and a sectionalzero-lift drag coefficient of Cd0 , in hover flight, willbe given by:

CP =kCT

3/2

√2

+1

8σCd0 (1)

where k is the induced power correction factor andaccounts for the non-ideal effects, where the quan-tity σ, is known as the rotor solidity, and representsthe ratio between the rotor blade area and the rotordisk area (Nbc/πR). The most-right term is relatedwith the profile power losses estimation.

2.2. Momentum Theory in Forward FlightIn the forward flight regime, the rotor movesthrough the air with an edgewise component of ve-locity that is parallel to the plane of the rotor disk.Under this conditions, in order to produce both apropulsive force (to propel the helicopter forwarddirection) and a lifting force (to overcome the heli-copter weight), the rotor disk must be tilted forwardto create an angle of attack relative to the incomingflow and the axisymmetry of the flow through therotor is lost. Rather, the aerodynamic environmentvaries periodically as the blade rotates with respectto the direction of flight.

Figure 2: Glauert’s flow model for the MomentumTheory analysis in forward flight ([6], pg. 93)

The first approach to model the rotor performanceunder forward flight conditions was derived by [11],in which the analysis is performed with respect toan axis aligned with the rotor disk.

According to this theory, the general equation forthe total power coefficient, in forward flight, of aconventional helicopter will be given by:

CP =k C2

T

2√µ2 + λ2

+σCd0

8(1 +Kµ2) (2)

where µ is the tip speed ratio or advance ratio,defined by µ = V∞ cosα/ΩR , and λ, the in-flow ratio for the forward flight regime, given by

λ = (V∞ sinα+vi)ΩR = µ tanα + λi, where α is the

angle of attack of the rotor and vi, the induced ve-locity.

Regarding the profile power generated by the ro-tor, since in the forward flight regime there is an ad-ditional translational component of velocity (V∞),its effects must be accounted in the profile drag es-timation, through the use of the K parameter.

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2.3. Extension of Momentum Theory to other Ro-tor Systems

Co-Axial SystemsThe advantage of using an helicopter with a coaxialrotor configuration is that the net size of the rotorsis reduced, since each rotor now produces verticalthrust. However, since the wake of the two rotorsinterfere with each other, this flow interaction willresult in a loss of the net rotor system aerodynamicefficiency. This effect can be accounted by consid-ering that the coaxial rotor can be analyzed as tworotors operating isolatedly but with an interferenceeffect, accounted by kint. With this in considerationand based on [6], the non-dimensionalized form ofthe total power requirements, for forward flight, canbe written as:

CP =2kintkCT

3/2

√2

+2σCd0

8(3)

Regarding the forward flight regime, an identicalanalysis will be considered. Applying the conceptof the interference factor (where the same value ofkint is assumed for both rotors and is independentof the forward velocity), the non-dimensionalizedform of the total power requirements, for forwardflight, can be written as:

CP =2kintk C

2T

2√µ2 + λ2

+2σCd0

8(1 +Kµ2) (4)

Tandem SystemsTandem rotor designs are used most commonly usedfor heavy-lift helicopters because, like the coaxialdesign, all of the rotor power is used to generateuseful lift. However the induced power of a partlyoverlapping tandem rotor system is higher than thatof the two isolated rotors, since one of the rotorswill operate in the slipstream of the other rotor,resulting in a higher induced power, for the samethrust produced.

Figure 3: Model used for tandem configurationanalysis ([6], pg. 107)

So, based on [6] and defining the interferencepower factor, kov, similarly to what was done forthe co-axial case, the total power coefficient, in hov-

ering flight, will be given by:

CP =2kovkCT

3/2

√2

+2σCd0

8(5)

[12] suggested the following approximation based ongeometric parameters, for the kov, where d is thedistance between rotorshafts and D the diameter ofthe main rotors:

kov ≈

[√

2−√

2

2

d

D+

(1−√

2

2

)(d

D

)2]

(6)

Regarding the forward flight regime, an identicalanalysis will be considered. Applying the conceptof the overlapping factor (where the same value ofkov is assumed for both rotors and is independentof the forward velocity) and recalling equation (2),the non-dimensionalized form of the total power re-quirements, for forward flight, can be written as:

CP =2kovk C

2T

2√µ2 + λ2

+2σCd0

8(1 +Kµ2) (7)

However, the analysis of measured data of the for-ward flight performance obtained shows that forµ > 0.1, the performance of the the front rotorwas almost identical of that of a single isolated ro-tor, suggesting that in this case there is little or nointerference produced on the forward rotor by therear rotor. With this considerations and applyingthe overlapping factor, kov, the induced power forthe tandem configuration is:

Pi = Tfvif + kovTrvir = Tfvi + kovTrvi (8)

So the total rotor power of a tandem configurationsystem, in the non dimensionalized form, throughMomentum Theory analysis, in the forward flightregime for which µ > 0.1 can be written as:

CP =k C2

T

2√µ2 + λ2

+kovk C

2T

2√µ2 + λ2

+2σCd0

8(1+Kµ2)

(9)

2.4. Blade Element Analysis in Hovering FlightThe Blade Element Theory (BET) forms the ba-sis of the most modern analysis of helicopter rotoraerodynamics because it provides an estimation ofthe local radial and azimuthal distributions of theblade aerodynamic loading over the rotor disk, [6].The overall rotor performance can be obtained byintegrating the sectional aerodynamics forces (andmoments), at each blade element over the lengthof the blade and averaging the result over a rotorrevolution.

Figure 4 depicts the flow environment and aero-dynamic forces at a representative blade element-According to [6], the resultant local flow velocity

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Figure 4: Incident velocties and aerodynamic envi-ronment at a typical blade element([6], pg. 116)

at any blade element at a radial distance y fromthe rotational axis, has an out-of plane componentUP = Vc + vi, which is normal to the rotor, due tothe induced inflow and the climb velocity and anin-plane component UT = Ωy, parallel to the ro-tor due to blade rotation. Therefore, the resultantvelocity at a blade element can be written as:

U =√U2T + U2

P (10)

and the relative inflow angle:

φ = tan−1

(UPUT

)(11)

In helicopter aerodynamics the out of plane ve-locity Up can be considered to be much smallerthat the in-plane velocity, UT , so one can writeU =

√U2T + U2

P ≈ UT . Using this assumption,and according to [6] the following is obtained, inthe non dimensionalized form, for the incrementalthrust and power coefficients:

dCT =1

2σ [Cl cos (φ)− Cd sin (φ)] r2dr (12)

dCP =1

2σ [Cl sin (φ) + Cd cos (φ)] r3dr (13)

To obtain the total CT and CP , the incrementalthrust and power coefficients must be integratedalong the the blade, in the spanwise direction, yield-ing:

CT =1

2

∫ 1

0

σ(r) [Cl cos (φ(r))− Cd sin (φ(r))] r2dr

(14)and:

CP =1

2

∫ 1

0

σ [Cl sin (φ(r)) + Cd cos (φ(r))] r3dr

(15)

where the limits of integrating are r = 0 and r = 1,corresponding to the blade root and tip, respec-tively. It should be noted that in order to evalu-ate CT and CP it is necessary to predict the span-

wise variation of the inflow angle, φ(r) = λ(r)r ,

the sectional aerodynamic force coefficients, Cl andCd, and also the spanwise chord distribuition since,

σ(r) = Nbc(r)πR . If 2-D aerodynamics are assumed,

then the sectional lift and drag coefficients willbe a function of the local effective angle of at-tack and of the local Reynolds and Mach numbers(Cl = Cl(α,Re,M) and Cd = Cd(α,Re,M)). Sincethese effects cannot, in general, be explicitly ex-pressed in an analytic form, it will be necessary tonumerically solve the integrals for CT and CP .

2.5. Blade Element Analysis in Forward FlightAccording to [6], the same blade element assump-tions and approximations previously used for thehovering flight can also be considered valid for for-ward flight. As before, the velocity at a bladeelement is decomposed in an perpendicular veloc-ity component, UP and a tangential component,UT , perpendicular to the leading edge of the blade.However, in forward flight, the velocity componentsare periodic at the the rotor rotational frequencyand depend on the blade azimuthal position (ψ).

Figure 5: Perturbation velocities on the blade re-sulting from blade flapping velocity and rotor con-ing ([6], pg. 157)

For the in-plane velocity, and comparing with thehover case, there is now a further free stream (trans-lational) velocity component, such that:

UT = Ωy + V∞ sinψ (16)

Regarding the out-of-plane component there is nowtwo more terms that result from perturbations pro-duced by the flapping motion of the blade. Theterm yβ is result of the blade flapping velocity andµΩRβ(ψ) cos(ψ) is produced due to the blade flap-ping displacements (see Figure 5). So, the velocityperpendicular to the rotor disk, can be written as:

UP = (Vc + vi) + yβ(ψ) + V∞β(ψ) cos(ψ) (17)

In forward flight, there is also a radial velocity com-ponent, parallel to the span axis of the blade, whichis given by:

UR = µRΩ cosψ (18)

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However, in BET, the aerodynamics effects pro-duced by the radial velocity component and by theterms depending on the coning angle and on theconing angle time variation, are neglected and willnot be considered in the context of this work.Hence, for the forward flight regime, with the con-siderations made above and following the same pro-cedure applied in the hover case, the total thrustand power coefficients will be given by:

CT =1

2

∫ 1

0

σ [Cl sin (φ(r))

+Cd cos (φ(r))] (r + µ sinψ)2dr.(19)

and:

CP =1

2

∫ 1

0

σ [Cl sin (φ(r))

+Cd cos (φ(r))] (r + µ sinψ)3dr.(20)

where φ(r) = tan−1(UP

UT

)= tan−1

(λ(r)

r+µ sinψ

).

2.6. Extension of Blade Element Theory to otherRotor Systems

It has been been previously discussed in the Mo-mentum Theory section, that accounting the in-duced interference effects between the rotors, by ap-plying an interference factor on the induced powerequations for each configuration, will yield consid-erably good results. The same procedure will beused in the Blade Element Theory analysis for theco-axial and tandem rotor system configuration.

2.7. Parasitic Power in Forward FlightAccording to [6] and considering that the powerto propel the helicopter forward is given byTV∞ sin (αTPP ), using the small angle approxima-tions, the following equation is obtained:

PP = TV∞ sin (αTPP ) ≈ DV∞ (21)

This power term is known as Parasitic Power andrepresents the energy lost due to viscous effects.Because helicopter airframes are much less aero-dynamic that their fixed-wing counterparts, thissource of drag can be very significant and cannotbe disregarded.

2.8. Climb PerformanceThe climb power requirements are equal to the timerate of increase of potential energy of the helicopter.Based on [6] and denoting the potential energy asE = Wh, the rate of increase of potential energy isWh = TVc = WVc, where W is the aircraft weightand Vc is the climb velocity.Assuming that Pinst is the total power installed inthe helicopter, the general power equation in thedimensional form can be written as:

Pinst = Pi + P0 + Pp + Pother + Pc (22)

where Pc = TVc, and where Pother includes thepower terms that depend of the helicopter configu-ration. Rearranging and solving in terms of Vc, thefollowing equation is obtained:

Vc =(Pinst − Pi + P0 + Pp + Pother)

T(23)

2.9. Maximum EnduranceEndurance is defined as the time that an helicopteris able to fly without refueling. To obtain the max-imum endurance, the fuel burn per unit time mustbe a minimum. According to [6], the maximum en-durance can be accurately approximated by:

E ≈WF

[1

P · SFC

]WGTOW−Wf/2

(24)

where the above equation is evaluated at the pointin cruise in which the aircraft weight is equal tothe initial gross weight minus half the initial fuelweight, WF . Since the SFC curve is fairly flat overthe power spectrum analyzed in the context of thiswork, the endurance will be inversely proportionalto the power required for flight. Therefore the speedfor maximum endurance coincides with the speedfor minimum power, which will be found by com-puting the minimum value of the total power curveobtained for each theory and configuration.

2.10. Maximum RangeThe range of the helicopter is the maximum dis-tance it can fly for a given takeoff weight and for agiven amount of fuel. According to [6], the maxi-mum range can be accurately approximated by:

Ra ≈WF

[V

P · SFC

]WGTOW−Wf/2

(25)

where the evaluation point of the above equation isthe same as for the endurance calculation. Analyz-ing the above equation a first crude approximationto the speed of maximum range is obtained whenthe ratio P/V is minimum, which can be computedby finding numerically the minimum of the curvedefined by the ratio between the total power re-quirements curve and the forward speed.

2.11. Compressiblity AnalysisVery often, in helicopter rotors, when operating inhigh speed forward flight, the speed of the tip ofthe advancing blade exceeds the drag divergenceMach number of the airfoil section, changing theflow characteristics and the overall rotor perfor-mance. Therefore, for an accurate power require-ments prediction, an analysis of this effects cannotbe disregarded.The region of the rotor disk affected by compress-ibility effects is represented in Figure 6 and can be

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Figure 6: Compressibility affected region and re-verse flow region ([6], pg. 221)

defined by finding where the incident Mach numberof the flow exceeds the drag divergence Mach num-ber, Mdd. For an unswept blade, the incident Machis given by:

Mr,ψ =ΩR

a(r+ µ sinψ) = MΩR (r+ µ sinψ) (26)

where a is the sonic velocity and MΩR is the Machnumber of the blade tip in hover. Therefore theregion of the disk affected by compresibility effectscan be defined by:

r + µ sinψ ≥ Mdd

MΩR(27)

Based on [6] and using Blade Element theory con-siderations, the increment in profile power associ-ated with this region, will be given by:

∆CPσ

=1

4π

∫ ψ2

ψ1

∫ 1

rdd

(r + µ sinψ)3 ∆Cd r dr dψ

(28)where ∆Cd is the extra drag on the blade sectionwhen it exceeds the drag divergence Mach number,Mdd. However, an effective solution to reduce thecompressibility problems, is found by sweeping backthe blade tip, since the lift and drag generation ismainly affected by the velocity component that isnormal to the leading edge of the blade. DefiningΛ as the local sweep angle, the velocity componentnormal to the leading edge, Un, is given by:

Un = ΩR(r + µ sinψ) cos Λ (29)

The incident mach number Mr,ψ can then be writ-ten as:

Mr,ψ = MΩR(r + µ sinψ) cos Λ (30)

If, for a certain rotor, the design goal is to maintainthe local Mach number below the drag divergenceMach number of the blade tip airfoil section, thesweep angle required to avoid any compressibilityissue will be given by:

Λ = cos−1

(Mdd

MΩR(r + µ)

)(31)

2.12. Reverse Flow AnalysisAt higher rotor advance ratios, a considerableamount of reverse flow will exist on the retreatingside of the rotor disk, meaning that the blade sec-tions operate with the trailing edge into the relativewind. Based on [6] and starting by defining that thefrontier of this region is given by the locus of pointsthat satisfy UT = 0, the following equation is ob-tained:

UT = 0 = ΩR(r + µ sinψ) (32)

The solution to this equation is given by r =−µ sinψ. Therefore the region of reverse flow whereUT ≤ 0 is defined by a circular shaped region cen-tered at (r, ψ) = (µ/2, 270) with diameter µ. Us-ing the procedure defined on the Blade ElementTheory section, the effects of reverse flow can beincluded by writing the profile power equation asfollowing:

CP =

∫ 2π

0

∫ 1

0

σ(r)

4πCd cos (φ) (r + µ sinψ)3 dr dψ

−∫ 2π

π

∫ −µ sinψ

0

σ(r)

2πCd cos (φ) (r + µ sinψ)3 dr dψ.

(33)If the drag coefficient is assumed to be unchangedin the reverse flow region, then after integration theprofile power coefficient becomes:

CP0 =σCd0

8

(1 +Kµ2 +

3

8µ4

)(34)

3. Graphical User Interface PresentationWhen initiating the graphical user interface (GUI)file, the Configuration and Theory Selection Menuwill appear, enabling the user to choose the desiredhelicopter configuration and theory.

Figure 7: GUI Configuraton and Theory SelectionMenu

Starting with the interface for Momentum The-ory, and selecting the conventional configuration,the input variables and design parameters depictedin the figure above can be chosen by the user.

After having selected all the design input val-ues, clicking on the Compute Power Curve buttonwill initiate the computation of total power require-ments as a function of the forward velocity curve,

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Figure 8: GUI Conventional Configuration - Mo-mentum Theory Menu

following a MATLAB routine based on the Momen-tum Theory formulas.

Figure 9: GUI Configuration and Theory SelectionMenu - Power Curve Results

The user can now select several options in the Vi-sualization Panel. The Show Power Componentsoption, will plot the individual contribution of eachpower term to the total power curve.

Figure 10: GUI Configuration and Theory SelectionMenu - Show Maximum Climb Velocity option

Regarding the Show Maximum Climb Velocitybutton, selecting this option will perform the cal-culation of the maximum climb velocity whilethe Show Maximum Endurance Velocity and ShowMaximum Endurance Velocity buttons, will com-pute the maximum endurance/range value and thepower and velocity values for which the maximum

endurance/range is attainable:

Figure 11: GUI Configuration and Theory SelectionMenu - Show Maximum Endurance Velocity option

Analyzing the Show Helicopter Preliminary Designbutton, selecting this option will open a new panel,with the preliminary dimensional design of the he-licopter. The dimensional design values are thefollowing: Helicopter Height (Hh), Length (Lh),Width (Wh), Tip-to-Tip Length (Th), which wereobtained by using the empirical formulas developedin [2].

Figure 12: GUI Helicopter Prelininary DesignPanel

When compared to the Momentum Theory, theBlade Element Theory GUI is far more complex andcomplete, providing the user with more functional-ities, dedicated menus, input variables and designchoices. A crucial difference is the presence of theB.E.T. Parameters panel. This option will definethe integration steps for the radial and azimuthalpositions, when integrating numerically the powerequations. In the context of this work and afteranalyzing the influence of the number of radial andazimuthal discretizations steps on the accuracy ofthe results and on the computational time requiredto perform the computations, the number of ra-dial and azimuthal segments, chosen to launch thesimulations will be 30, due to a low computationaltime required and a low loss of accuracy when com-pared with 70 radial and azimuthal segments, whichwould increase the computational time required in80 times and improve the accuracy in only 2.9 %,as depicted in Figure 13.

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Figure 13: Influence of the number of azimuthaland radial discretization steps on the computationaltime required and on the relative error obtained atV∞ = 60 m/s

Regarding the additional dedicated panels, start-ing with the Power Plant Menu, in this panel thereis the possibility to select a wide range of enginesalong with the desired quantity, and obtain realtime information about the total power installed,weight and specific fuel consumption of the totalengine system. Moving to the Blade Planform Se-lection menu, this panel is dedicated to the rotordesign. Here the values of the rotor radius, num-ber of blades and root chord length can be cho-sen. Additionally, there is the option to chose thechord length at the tip (which will define the ta-per ratio), the root-cut-out and the chord distri-bution model, and to have a visual representationof the designed rotor. Moving forward to the Air-foil Selection Menu, this menu is mainly focusedon the aerodynamic design of the blades. The userhas the option to divide the blade in 3 differentsections named root, middle and tip sections. Foreach section the user will have the possibility toselect the airfoil shape, the section length and thetwist at the root and end of each section, while ob-taining the first 3D representation of the designedblade. This menu will also integrate a compress-bility and reverse flow preliminary analysis, wherethe user can start to test the aerodynamic behav-ior/characteristics of the designed rotor individu-ally, by increasing the forward velocity value andobtain real time visual information about the com-pressibility and reverse flow regions, together withnumeric information about the characteristics ofthis regions. Furthermore, the option to introducetip shape modifications in the rotor design is alsopossible, in order to reduce the effects of the com-pressibility issues, by applying a sweep back angleon the blade tip.

Extension of the GUI for Tandem and Co-axial configurationsThe Blade Element Theory and Momentum The-ory graphical user interface for tandem and co-axialconfigurations are identical to the conventional con-figuration interfaces. All the key functionalitiesand design parameters are available, and addition-

Figure 14: GUI Blade Planform Selection Menu -Visualize Main Rotor option

Figure 15: GUI Compute 3D Aerodynamics charac-teristics option - Visualization Panel

Figure 16: GUI Compressibility Analysis option -Results window for V∞ = 120.75m/s

Figure 17: GUI Reverse Flow Analysis option - Re-sults window for V∞ = 120.75m/s

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Figure 18: GUI Implement tip shape modificationsoption

ally, for the tandem configuration there is the RotorPlacement Panel, for which the user can chose thetandem rotor system position. while having realtime information about the value of kov and of theoverlapping area.

4. ResultsThe main goal of this section is to evaluate if thetool developed is producing accurate results, forthe three different rotorcraft configurations and twotheories implemented. The most effective way toaccomplish this evaluation is to select a known con-figuration of an already developed rotorcraft, in-put all its available design parameters in the tool,compute the power curve, maximum endurance andmaximum range characteristics and compare the re-sults obtained with the specifications of the manu-facturer. The chosen helicopters, for each configu-ration, to launch the simulation, are the following:

• Conventional Configuration: Bell 429

• Tandem Configuration: Boeing CH-47

• Co-axial Configuration: Kamov Ka-27

For each model selected, the relative error obtainedwith Momentum and Blade Element Theory, for themaximum climb velocity, maximum range, maxi-mum endurance and preliminary dimensional de-sign, were the following:

Model Range Endurance VcBell 429 10.7 % 7.4 % 12.9 %Boeing CH-47 11.1 % 5.5 % 145.5 %Kamov Ka-27 35.3 % 11.3 % 4.6 %

Table 1: Relative errors obtained with Blade Ele-ment Theory

4.1. Discussion of ResultsAnalyzing the results obtained, it is possible to con-clude that the tool is predicting accurately many of

Model Vc Range EnduranceBell 429 16.4 % 6.2 % 9.8 %Boeing CH-47 29.9 % 25.0 % 158.0 %Kamov Ka-27 34.8 % 57.5 % 18.7 %

Table 2: Relative errors obtained with MomentumTheory

Model 429 CH-47 Ka-27Hh 8.33 % 15.9 % 23.1 %Lh 9.85 % 14.59 % 33.2 %Wh 13.48 % 20.4 % 19.1 %Th 1.9 % - 23.1 %

Table 3: Relative errors obtained emprical formu-las developed in [2], which are independent of thetheory used

the general preliminary design characteristics, fora given set of the desired design parameters. Al-though the 3 models chosen to test the tool accu-racy, had several input parameters available, therewas still some key information that was lacking,such as the airfoil shape, or the sweep back angleof the blades. However, even with this lack of in-formation, the results obtained showed good agree-ment for each configuration and for each theory.The only exception was the maximum climb veloc-ity obtained for the tandem configuration. For thisheavy configuration (WGTOW > 20000 Kg), the re-sults were not satisfactory. The explanation for thisdeviance can be related to the fact that the onlyconstraint implemented in the tool for the maxi-mum rate of climb is the power available, for eachforward velocity value. In a heavy rotorcraft, otherconstraints can play a role such as the ones comingfrom aerodynamic, structural or engine transmis-sion issues, that impose a limit in the maximumrate of climb.Regarding the empirical formulas for dimensionaldeisgn developed by [2], they produced relatively ac-curate results for the 3 configurations, even thoughthey were just developed for the conventional con-figuration. Another issue that must be mentionedis the comparison between the results obtained withthe two different theories. The Blade Element The-ory shows a global tendency for producing more ac-curate results. This is expected, since this theorypresents much more complexity and an higher num-ber of input variables. However, in some cases, thegain in accuracy does not compensate the increasein the computational time required to perform thecalculations, when compared with Momentum The-ory. For instance, the computational time requiredfor Momentum Theory never exceeds the value of

9

10 seconds, as opposed to Blade Element Theory,which for a high number (> 60) of azimuthal andradial discretization segments, can reach up to the36000 seconds. Therefore, if the user desires a veryfast and basic analysis, the choice should be theMomentum Theory interface. If the user wishesa more refined analysis, but still with fast results,the choice should be the Blade Element Theory in-terface, but with a relatively small number of az-imuthal and radial discretization segments (<30).For a very accurate analysis the user should referto the Blade Element Theory interface but know-ing that a high number of radial and azimuthal dis-cretization segments, can push the computationaltime value to several hours.In a general analysis, the tool has accurately pre-dicted the characteristics of the 3 known designs(one for each configuration) even though there werea wide variability of design parameters and charac-teristics. This fact increases the confidence that thetool is able to produce accurate and trustworthy re-sults for any new and experimental design that theuser wishes to study/analyze.

5. Conclusions

The main goal of this work was to develop a com-plete, user-friendly and trustworthy computationaltool that would aid the student, researcher or curi-ous in the preliminary design of any new rotorcraft.With this purpose, it was developed a MATLABgraphical user interface, simply to use and, at thesame time, able to incorporate a wide variety of in-put parameters. To evaluate if the tool was predict-ing accuratetly the rotorcraft characteristics, for agiven set of input parameters, three helicopter mod-els already developed were selected (one for eachconfiguration). Using the design parameters val-ues provided by the manufacturers, the simulationswere launched. The results obtained showed a rel-atively good agreement between the predictions ofthe tool and the real performance characteristics ofthe selected models. This fact increases the confi-dence that the tool developed is able to predict cor-rectly any new design desired by the user, for the3 different configurations. However, some improve-ments should be made. The computational timerequired for the Blade Element Theory calculationswhen the number of discretization segments is high,must be decreased. Even if the increase in accuracyis not worth the increase in the total required timefor the computations, the user should have the pos-sibility to refine the results as he wishes withouthaving to wait for several hours. Regarding thetool functionalities, more airfoils and airfoil datashould be incorporated, and the possibility to se-lect between several linear inflow models should beincluded together with the option to choose between

different numerical integration schemes. Also, thepossibility to perform preliminary structural anal-ysis and stability studies should be included. Fur-thermore, to make the tool developed a reference forany rotorcraft design, it should be also expanded forpreliminary multi-rotor drone design.

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Sizing by Statistics, Faculty of Aerospace En-gineering, Technion Israel Institute of Tech-nology, Haifa, 2002.

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