Amphibious PrandtlPlane: Preliminary Design Aspects Including Propellers Integration and Ground...

for Challenges in the Design of Joined Wings Special Session

Amphibious PrandtlPlane: Preliminary DesignAspects Including Propellers Integration and Ground

EffectRauno Cavallaro,∗ Massimiliano Nardini††, Luciano Demasi‡‡

In 2011 a joint team led by University of Pisa begun the design of IDINTOS, an am-phibious aircraft featuring a PrandtlPlane joined-wing layout. The vehicle falls within theLight Sport Aicraft (LSA) category, and a prototype was officially presented in 2014.

In PrandtlPlane configurations the wings have (frontally) a box-shape, as historicallysuggested by eminent German scientist Ludwig Prandtl with the concept of Best WingSystem (BWS) concept, which achieves the minimum induced drag condition for a givenwing span and lift.

Design of such aircraft presents exceptional challenges due to the innovative solutionmixed also with the amphibious nature. Aerodynamic early stage design was pursued withad-hoc and consolidated approaches based on the hypothesis of potential flows. Resultswere later validated with the aid of advanced CFD codes, wind tunnel tests, and scaledmodels flight tests. The hydrodynamic design was pursued by CFD air-water free surfacesimulations and a water tunnel campaign.

The authors collaborated with the Aerospace Engineering Department of Universityof Pisa in the creation of an aerodynamic analysis tool based on the Boundary ElementMethod (BEM), with advanced capabilities aimed to tackle some specific problems con-cerning design of IDINTOS. Some distinctive traits of the code are the advanced kinematicmodule, the capability of exploiting multi-symmetry planes, the possibility of simultane-ously handling thick and thin body, the analytical surface sensitivities. Moreover, body-wake impingements can be efficiently modeled.

This paper will show some preliminary applications of this BEM code for studyingspecific problems regarding IDINTOS. One of the topic concerns propellers integration.Their presence changes the aerodynamic fields in proximity of the aircraft, leading to aredistribution of the aerodynamic actions. It is important to predict the impact on static(and dynamic) flight stability, both in the longitudinal and later-directional mechanics.Results will offer physical insight in this regard, which is of foremost importance in theearly design stages, especially due to the highly integrated concept this layout promotes.

Low speed operations in proximity of the ground will be studied. The ground effect,not always intuitive to be predicted, will be examined showing the variations of lift andpitching moment as the distance between the wing and the ground is reduced.

I. Introduction

There is currently great interest in innovative aircraft configurations. Among them, joined-wing con-cept [1,2] has captured the attention as a possible candidate for the airplane of the future. Last decades

have been characterized by an increasing number of studies carried out both in the US and in Europe.These efforts mainly addressed the conceptual/preliminary design with an analytical and/or experimentalapproach [1, 3, 4], with only a few examples of scaled flying vehicles (among them some recent examplesare found in [5, 6]) realized in practice. To the best of authors’ knowledge, the first two-seater (or larger)

∗PhD Candidate, Department of Aerospace Engineering, San Diego State University and Department of Structural Engi-neering, University of California San Diego, AIAA Member

†Visiting Graduate Student, San Diego State University, MS Candidate at the Dipartimento di Ingegneria Aerospaziale,Università di Pisa.

‡Associate Professor, Department of Aerospace Engineering, San Diego State University, Lifelong AIAA Member

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American Institute of Aeronautics and Astronautics

56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

5-9 January 2015, Kissimmee, Florida

AIAA 2015-1185

Copyright © 2015 by Rauno Cavallaro, Massimiliano Nardini, Luciano Demasi. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA SciTech

https://www.researchgate.net/publication/272026508_Joined_Wing_Aircraft?el=1_x_8&enrichId=rgreq-8fa1b24b-5627-4d29-a014-4cfb75d34589&enrichSource=Y292ZXJQYWdlOzI3MDYxNDcyODtBUzoxOTExMTAzMzQ3Mzg0MzdAMTQyMjU3NTY2MjcyNg==


amphibious project that led to a full scale prototype manufacturing is IDINTOS [7]: by means of a grant ofTuscany regional government, a joint team led by University of Pisa designed and realized an Ultralight (theaircraft falls within the Light Sport Aicraft LSA category) Amphibian PrandtlPlane joined-wing configura-tion. The final prototype was officially presented in November 2013 in Pontedera (Italy) (on the occasion ofCrea@tivity Exposition), and on April 2014 at the Aeroexpo in Friedichschafen (Germany).

Some aspects of design of IDINTOS are outlined in [7–9], ranging from the earlier stages based on lowerfidelity computational tools (see also works [5, 10]) to later phases, where higher accuracy approaches, aswind and water tunnel campaigns, were pursued.

The design and realization of a real Joined Wing is a unique opportunity from a scientific point of view.In fact, previous studies have shown results pointing to several different directions and with contradictoryconclusions regarding the potential advantages of Joined Wings. As remarked in [1, 11], a thorough designand an alternative approach is to be sought in order to exploit potential advantages.

For Joined Wings, this has not always been the case. For example, some claims regarding the aerodynamicbenefits [12,13] not being observed were actually consequence of separated flow [12]. In other cases [13], theassessment of the aerodynamic efficiency of a Box Wing with respect to a bi-plane was conducted withoutcomparing the necessarily different optimal conditions (see [14–16]) of the two systems.

A true assessment of the benefits of different configurations should be pursued on optimized systemsunder the same types of constraints. To illustrate this concept, suppose that the induced drag advantages ofa boxwing with respect to a biplane need to be investigated. Connecting the tips of the biplane to obtain aboxwing (see [15, 16]) is a methodological error because the resulting configuration would in general not beoptimized even if the biplane, from which the Joined Wing is obtained, performes under optimal conditions.

Achieving a meaningful study on the actual benefits of Joined Wings when compared with classicalcantilevered wings (or with alternative designs such as the blended wing body), is a formidable task due tothe inherently strongly connected disciplines. To see this point, consider the aerodynamics and the flightmechanics properties of an airplane: if these two disciplines are not taken simultaneously into account, anoptimal design in terms of drag may, for example, be not even trimmed or stable. On the other hand,designing in order to reach stability and trim, without considering aerodynamic efficiency, may lead to far-from-optimum performances. A Multidisciplinary Design Optimization (MDO) is then necessary since theearly design stages. Efforts in this direction are shown in [17], although a sequential approach was adopted,in which aerodynamic and structural analysis were not carried out simultaneously. Partial MDO, in whichthe structural side was not considered, was carried out in [10,18] on PrandtlPlane (box-wing) configuration(see [19, 20] for details about this configuration). In these efforts, however, the optimization process was asimultaneous and not a sequential one, leading to an exploration of a wider design space. Other interestingefforts [21], although presenting advanced framework, give results and trends that are not directly applicable(being only aerodynamics considered).

MDO, however, often does not provide a complete scenario: some parameters and choices have to bedone at early stages, restricting the design space. These preliminary choices are of foremost importance,and need insight and experience, consequences of a more analytical and isolated approach. Moreover, somepractical constraints are difficult to be translated in mathematical formulae.

A very important issue regards the use of lower fidelity tools as a reasonably accurate mean of analysis.In particular, in light of the fact that higher fidelity (CFD) and experimental results were accessible, itwas possible to evaluate the level of precision given by these tools for the specific requested task. Thisapproach was pursued with a Vortex Lattice Method (VLM), which favors a relatively rapid evaluation ofthe aerodynamic properties, and is an invaluable capability to be combined within an optimization process.

Compared to VLM, a step forward in the early/preliminary aerodynamic and flight mechanics/dynamicsdesign is represented by the panel methods, where thickness of the aerodynamic surfaces is taken intoaccount. There are not many work in literature about what can be expected from this tool when appliedto PrandtlPlane configurations in terms of precision and reliability. Moreover, there is a lack of comparisonof the performances of different modeling within the panel method. These modeling options concern, forexample, the wake.

Panel methods are also valuable design tool to study problems such as engine integration: effects of apropeller from both an aerodynamic and flight mechanics perspective can be evaluated in a relative fast way.They can also be used to assess the effects of ground vicinity to the trim of the aircraft, or, for example, tostudy the response of the rigid aircraft to gusts.

Current flying tests performed on (1 to 4) scaled model have underlined the importance of the early

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assessment of such problems, suggesting that the possibility of having qualitative and quantitative results inrelatively short time and reduced computational resources strongly impact the design process.

II. Contribution of the Present Study

Aerodynamic design of IDINTOS has been pursued both by analytical and experimental approach [7–9, 22]. Considering the computational efforts, both low and high fidelity tools have been used to assess theperformances. In particular, a VLM integrated with analytical models was used as the aerodynamic black boxto solve an optimization problem, capable of giving a trimmed optimal configuration [7, 18]. Higher fidelityCFD tools were adopted to fine-tune the previous results (deflection of control surfaces was calculated tocorrect the trim, and low-speed performances and design of the high-lift devices including front and rearwings flap was accomplished) and also to study the take-off from water condition [22].

Experimental investigations were carried out in a water tunnel [9] and a wind tunnel [8]. Water tunneltests were necessary for the design of the hull, especially considering the take-off run. The aerodynamiccampaign was a comprehensive session in which both aerodynamic final performances and aerodynamicderivatives were evaluated on a 1 to 4 scaled model.

Although low speed conditions were tested in a wind tunnel and with CFD (and also in the early stageswith a VLM), with a reasonable correlation, ground effects have not been fully investigated yet.

One of the open issues regards proper consideration of the engine integration, i.e., how the aerodynamicfield distortion due to the propeller would affect the design. Considering the framework of preliminary designstages of an amphibious PrandtlPlane, this work will address the following open questions:

• What can be learned in terms of specific submodeling strategies, e.g. wake modeling, applied to thespecific case?Very fast tools as VLM or Panel Method require wake modeling. The most popular assumption is theone that employs a rigid wake aligned with the freestream velocity. However, this may give rise toinaccurate predictions, considering that, due to the particular arrangement, the wake shape plays animportant role.

• How does the propeller change the aerodynamic distribution, the trim and the aerodynamic derivatives?A three-blade propeller is considered to be placed on the fuselage, immediately after the cockpit. Thewake shed by the propeller will pass not far from the vertical empennage and the inner part of therear/upper wing. How is propeller presence affecting the whole aircraft mechanics? Could it be usedto enhance stability on the latero-directional and longitudinal plane?

• How does ground effect impact the PrandtlPlane?Compared to the traditional layout, now there are two wings sharing the overall lift. When the aircraftis close to the ground the interference of the two wings, leading to a up/downwash on the front/rearwing, changes. How does this affect the overall maneuverability close to the ground?

III. Theoretical Highlights Regarding the Present Computational Tool

The in-house capability is here briefly outlined. It consists of a Boundary Element Method (BEM)formulation of the differential problem regulating the incompressible potential flow around an aerodynamicbody. More in detail, the differential problem is expressed by:

∇2φ = 0 on V∂φ

∂n= −V ∞ · n on SB

(1)

where V and SB are the domain of definition and the boundary represented by the aerodynamic body, re-spectively, n the normal-to-the-surface unit vector (pointing in the direction of the domain), φ represents theperturbation (velocity) potential, such that the velocity in a generic point in the domain is the superpositionof the undisturbed flow (V ∞), and the perturbation velocity (∇φ):

v = V ∞ + ∇φ (2)

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Moreover, with ∂φ∂n it is intended the derivative of the perturbation potential in respect of the coordinate in

the direction of n, i.e. ∇φ · n. This equation thus, represents the wall tangency boundary condition.To close the problem, a singularity surface containing the vorticity shed by the body, i.e. the potential

wake SW , has to be defined. This is a discontinuity surface for φ, and this jump has to be related to thepotentials on the trailing edge of the aerodynamic body (see [23]).

A. Boundary Element Method Model

Following the classic boundary element approach, the linear partial differential equation is written as aboundary integral equation. Thus, the perturbation potential in the whole field is expressed as a boundaryintegral in which the unknowns are the values of the perturbation potential and its derivative across thenormal to the surface direction:

E(x)φ(x) =∫

SB

(G

∂φ

∂n− φ(y)∂G

∂n

)dSB(y) −

∫SW

(∆φ(y)∂G

∂n

)dSW(y) (3)

where G(x, y) is the Green function ([23,24], for 3D case it holds that: G(x, y) = − 14π

1∥y−x∥ ), and E(x) is

defined as follows:

E(x) =

1 if x ∈ V

1/2 if x ∈ SB ∪ SW

0 if x ∈ R3\V(4)

Considering the linearity of the problem, the solution can be obtained as a superposition of elementarysolutions. Source and doublet singularity surface distributions are then defined. Observing the first integralon the Right Hand Side of eq.(3), the two terms represent the perturbation potential induced by a surfacesource distribution of intensity σ = ∂φ

∂n , and a surface doublet distribution of intensity µ = φ, respectively(for the wake it is µW = ∆φ).

The integral equation (see eq.(3)) is then discretized by a mesh of the surface SB and the wake SW . Oneach element of the mesh (panel), the values of singularities intensity is considered to be constant. Moreover,for the body’s doublets, these constant values are unknown. Enforcing the boundary conditions (usually walltangency, which immediately sets the source intensity to value of the normal component of the undisturbedflow V ∞) at an appropriate number of collation points, eq.(3) becomes a linear system. Actually, in orderto close the problem the wake doublets’ intensities have to be related to the body ones thorough physicalmodeling .

B. Steady and Unsteady Capabilities

The equations presented in the previous section, are valid both for the steady and unsteady cases. Unsteadi-ness enters the problem through the wake evolution, and the Bernoulli equation.

For the potential wake, the material (substantial) derivative of ∆φ is equal to zero:

D∆φ

Dt= 0 (5)

Thus, for the unsteady case, the wake material points are convected downstream without changing theassociated jump ∆φ [23,24]. In the (time and space) discretized setting, the shed wake panels maintain their∆φ values, even though they are convected (and distorted) according with the local flow speed. However,generally, two wake panels shed at different times from the same trailing edge segment do not have the samejump in the perturbation potential.

In the steady case, the vorticity shed at a fixed trailing edge point remains constant. Thus, all the wakematerial points that have been shed by the same trailing edge point have the same associated jump ∆φ.Thus, in the discretized setting, all the wake panels shed by the same trailing edge segment have the samedoublet intensity µw.

The Bernoulli equation for the unsteady case reads:

∂φ

∂t

∣∣∣∣o

+ p

ρ+ ∥∇φ∥2

2= po

ρ(6)

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where p is the pressure, ρ the (constant) density, po is the pressure of the undisturbed medium and the timederivative subscript o refers to the frame of reference fixed with the undisturbed air. Thus, a variation in timeof the aerodynamic field has per-se an effect on the aerodynamic forces on the body: whereas aerodynamicfield is (expect for the wake which carries information about the history evolution) completely determined bythe instantaneous conditions (geometry, undisturbed flow direction), the aerodynamic forces depend directlyon the rate of variation of perturbation potential. In the steady case, this dependence on the rate of variationis trivially zero.

C. First and Second Order Kutta Condition

As previously mentioned, a condition relating the jump ∆φ on the shed wake to the potential φ on theshedding trailing edge has to be defined. The classic way of closing this problem is to use the Kutta-Joukowsky condition [24,25]. It is usually achieved enforcing

∆φ = φupte − φdown

te (7)

where the subscript te refers to the potential of trailing edge point where the wake is shed, and the superscriptsup and down denote the different sides from which the trailing edge is approached (upper surface and lowerssurfaces respectively). Actually, this condition originates from the Joukowsky condition, which states thatno concentrated vortex exists at the trailing edge [23, 25]. This condition can be thought as a first orderapproximation and, depending on the implementation, may lead to some inaccurate results [26].

The German scientist Kutta postulated also that no jump in pressure between the upper and lower partsof the trailing edge has to be registered [25]. Use of the approach described above in eq.(7), may give ∆p ̸= 0at the trailing edge (especially when employing lower order panel methods), even when refining the grid[23,26,27]. This is particularly important in the case of rotatory wing, where strong cross-flow is observed.

In order to drive to zero the pressure jump, an iterative process is then established. Parameters of theiterations are the values of the last shed wake doublet intensities µte

w . Sensitivity of ∆pte in respect of µtew has

to be found: in this effort an analytical approach was pursued. This process requires two distinct steps. Inthe first one, the sensitivity of ∆pte in respect of µ is determined: this is accomplished starting from eq.(6)noticing that the surface pressure distribution depends on the surface perturbation velocity (on the bodysurface φ = µ). In the second step, a relation through the body (µ) and near wake (µte

w ) doublet intensity isfound: during the iterative process, the satisfaction of the linear system representing the discretized integro-differential problem should always be guaranteed. Thus, for a variation of δµte

w a corresponding incrementδµ is found.

Once the sensitivity is built, the Newton iteration can be carried out. Having the new values of thesingularities, the pressures on the trailing edge can be tested, and, if does not vanish to a negligible value,the basic iterative step can be repeated.

D. Wake/Body Interference

When wake passes very close to body or impinges on it, instability is observed. This is consequence of thesingularity of the terms inside the integral of eq.(3), when y approaches x. A novel formulation to avoidsuch problems was presented in [28,29]. The basis of the method consists in decomposing the perturbationvelocity potential in two contributions: an incident potential φI generated by the doublets of the far wakeand a scattered potential φS generated by the singularities over the body and near wake surfaces (doublet andsources for the body, doublets for the near wake). The perturbation potential can be written as φ = φI +φS .Following the treatise outlined in [28], the same formal integral equation as the one introduced before is foundagain, but for the scattered potential φS and considering only the near wake portion SN

W :

E(x)φS(x) =∫

SB

(G

∂φS

∂n− φS(y)∂G

∂n

)dSB(y) −

∫SN

W

(∆φS(y)∂G

∂n

)dSN

W(y) (8)

The incident potential φI enters the problem redefining the source intensity:

σ̃ = −V ∞ · n − ∇φI · n (9)

Thanks to this formulation, it is possible to use the well known analogy between doublets and vortexrings [28], and, introducing a regularization function, ∇φI remains bounded even when the collocation pointis very close to the inducing panel, that is, even when the wake impinges on the body surface.

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E. Advanced Kinematics Module

One advanced feature of the in-house capability is the treatment of kinematic conditions. It is possible toattach different parts of the whole configuration to user-defined reference systems. The kinematic evolutionin time of each reference system is given by the user in terms of translation of the origin and rotation ofthe axes, in respect to other reference systems (also a global one). As a trivial example, it is possible tostudy the aerodynamic field of an aircraft translating at constant speed and its propeller rotating at fixedrate. In order to describe the motion of the propeller in terms of global coordinate system, one can define anauxiliary reference system attached to the aircraft, and a further one attached to the propeller. Then, theuser should give as an input the initial position and orientation, as well as the evolution law (linear velocityof the origin and angular velocity) of the propeller coordinate system in respect of the aircraft’s one: it isstraightforward then to described the rotation of the propeller as seen in the aircraft reference system.

One important capability is the treatment of the rotations with Hamilton’s quaternion [30] to avoidsingularities arising when using Euler’s angles (a phenomenon known as gimbal lock, see [31]).

F. Zero-thickness Bodies

The boundary integral formulation of eq.(3) holds for bodies with non-negligible thickness and it provides anexpression for the velocity potential inside and outside the body. A thin body can be represented as a zero-thickness surface in order to reduce the number of panels used to represent the geometry and, consequently,the computational cost of the simulation. In case of zero-thickness surfaces, eq.(10) can still be written asthe sum of the contribution of singularities over the body surface and the wake; however, the induction willbe evaluated in terms of perturbation velocity rather than perturbation potential.

∇φ · n = −V ∞ · n (10)

The present code offers the possibility to represent both thick and zero-thickness bodies in the same model.This is achieved considering the wall tangency condition in terms of perturbation potential or velocity if theconsidered collocation point lies on a thick or thin body, respectively.

G. Surface Sensitivity

As future applications towards advacend aeroelastic analyses, the code is given a surface sensitivity capability.Force variations consequence of a perturbation of the aerodynamic shape is achieved with an analyticalapproach. Details of the implementation are described in reference [32]. Part of the sensitivity of pressuredistribution to surface displacements is evaluated as product of the sensitivity to the doublet intensities andsensitivity of the doublet strength to surface displacements. The first term of this product is needed also inthe iterative Kutta condition (see section C).

Within the same framework, is also possible to extract informations needed for the evaluation of aerody-namic derivatives, needed for the study of static and dynamic flight stability.

IV. Validation of the Present Capability

In this section validation of the present in-house capability, referred to as UPM (Unsteady Panel Method),is carried out. The three selected test cases cover different scenarios in which the panel method is required toperform. The first one is a classic unsteady problem, for which an analytical solution was found. It consistsof an oscillating fixed wing (airfoil). The second test case concerns a rotatory wing problem.

The last test case is again a rotatory wing problem, where the shed wake is impacted by the blades. Itis thus designed to validate the capability discussed in section III.D.

A. Theodorsen

One of the features of an unsteady panel code is the ability to predict unsteady loads due to the motion of abody in a uniform free-stream. The problem of an oscillating airfoil is a good example to test the kinematicmodule and to validate the predictivity of the code, comparing the results of lift and pitching moment withthose provided by the classical theory.

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1. Theodorsen’s theory: brief outline

The problem of an oscillating symmetrical airfoil in an uncompressible, inviscid flow was studied by Theodorsenwho, starting from the thin-airfoil theory, was able to provide an analytical expression for lift and pitchingmoment. The hypothesis behind the classical thin-airfoil theory and all the details about the procedureadopted by Theodorsen can be found in [33]. In those calculations, effects of thickness were neglected andthe airfoil was represented by a continuous distribution of vortices along its mean line (a flat plate in case ofsymmetrical airfoil). The motion of the airfoil produced a distribution of perturbation velocities normal tothe chord, which were taken into account to enforce the flow tangency condition to the flat plate. Also thewake was represented by vortices and the Kutta condition was enforced at the flat plate trailing edge. Thewake was considered to be flat: the vortices were projected on a wake mean line, as shown in Fig. 1.

x

y

Body vorticity projected onairfoil’s mean line

Wake vortices projected on wake’s mean line

Fig. 1. Summary of Theodorsen’s classical vortex theory. Body and wake were represented by a distributionof vortices projected on body’s and wake’s mean lines

To characterize the unsteadiness of motion, reduced frequency k is introduced:

k = ωb

V∞= ωc

2V∞(11)

where ω is the frequency of the oscillation, V∞ the wind speed and c the chord of the airfoil.For k = 0 the flow is steady, while for 0 ≤ k ≤ 0.05 it can be considered quasi-steady (the unsteady

terms of the governing equations can be neglected). For values of the reduced frequency larger than 0.05the flow is considered unsteady. In particular, for values greater than 0.2 the flow is highly unsteady and theaerodynamic loads are dominated by the unsteady terms.

For the validations, a rectangular untapered NACA 0012 wing of aspect ratio AR = 12 is considered. Forthe sake of brevity, only the set of simulations concerning oscillations along the vertical axis (pure heaving)at different reduced frequencies are here presented. The amplitude of the oscillations is 0.05 · c.

The results from the unsteady panel code are compared to the analytical solution obtained by Theodorsen,in terms of lift coefficient and pitching moment coefficient about mid-chord. For all the simulations the wakeis considered rigid (to better correlate with the assumptions of the Theodorsen’s model) and the iterativeKutta condition is enforced. Table 1 shows the details of the simulations.

Mesh Reduced frequency Dimensionless time intervaldetails k V∞·∆T

c

30 panels spanwise

π 1/60

40 panels chordwise

π/2 2/60π/4 3/60π/16 16/60π/40 30/60

Table 1. Details of the different simulations: mesh, reduced frequencies and employed time-steps.

2. Pure heaving

Figs. 2 and 3 show the comparison between the panel code and Theodorsen results in terms of lift coefficientand pitching moment. They are in excellent agreement and, as expected, they tend to be closer as the

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reduced frequency decreases.

0 5 10 15 20 25 30 35 40

-0.08

-0.04

0

0.04

0.08

0 1 2 3 4 5 6 7 8-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-0.8

-0.4

0

0.4

0.8

0 0.5 1 1.5 2 2.5-4

-3

-2

-1

0

1

2

3

4

t

AR = 12NACA0012

π

UPMtheory

0 10 20 30 40 50 60 70 80

-0.04

-0.02

0

0.02

0.04

CL Heavingk =

AR = 12NACA0012

UPMtheory

π/2

Heavingk =

CL

t

t

CL

π/4

Heavingk =

π/16

Heavingk =

t

π/40

Heavingk =

t

CL

CL

Fig. 2. CL comparison between Theodorsen and in-housce capability (UPM) results for a heaving wing atdifferent reduced frequencies.

B. Propeller - Biermann and Gray 1942 NACA Report

In this second test case, a rotatory wing problem is considered. More in detail, the in-house capabilityis validated against results described in NACA Wartime report [34]. The case examined is a three-bladesingle-rotating pusher propeller with a 10-foot diameter, mounted at the rear end of a streamlined bodywhich covers the hubs. The experimental results were obtained in a 20-foot propeller research wind tunnel.

In the numerical simulation performed by the panel code, only the blades have been simulated and thepresence of the spinner has been omitted, assuming its effects to be negligible for the purposes of codevalidation. Fig. 4 shows the geometry of the propeller, the disposition of the blades and the surface mesh.Thrust and power of the propeller are expressed in terms of dimensionless coefficients:

CT = T

ρn2D4 Thrust coefficient

CP = 2πnQ

ρn3D5 Power coefficient

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0 0.5 1 1.5 2 2.5-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 1 2 3 4 5 6 7 8-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 5 10 15 20 25 30 35 40

-0.02

-0.01

0

0.01

0.02

0 10 20 30 40 50 60 70 80

-0.01

-0.005

0

0.005

0.01

0.015

t

AR = 12NACA0012

π

UPMtheory

CM Heavingk =

CM

t

π/2

Heavingk =

π/4

Heavingk =

t

CM CM

t

π/16

Heavingk =

π/40

Heavingk =

CM

t

Fig. 3. CM about mid-chord comparison between Theodorsen and in-housce capability (UPM) results for aheaving wing at different reduced frequencies.

O

Fig. 4. Front view of geometry and surface mesh of Biermann and Gray 1942 NACA Report [34]. The rotationaxis passes through point O and is parallel to the wind speed.

whereT = thrust [N ]Q = torque [N · m]ρ = air density

[Kg/m3]

n = revolutions per second [1/s]D = propeller diameter [m]

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Also, the advance ratio J is defined as the ratio between the distance the propeller moves forward throughthe fluid during one revolution, and the diameter of the propeller.

In Fig. 5 results are compared. Excellent agreement for some advance ratios is observed, whereas thecorrelation is not as good as the advanced ratio decreases. This is due to the flow separation, whose effectsare not taken into account in the present capability. It is interesting to notice that the power coefficient isless influenced by the separation; a possible explanation could be that the separation occurs near the rootof the blades, which gives a smaller contribution to the total torque.

0 0.5 1 1.5 2 2.5

0

0.05

0.1

0.15

0.2

0.25

J

CT Exp - = 20°b

Exp - = 30°b

Exp - = 40°b

UPM - = 20°b

UPM - = 30°b

UPM - = 40°b

0 0.5 1 1.5 2 2.5

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

J

CP

Fig. 5. Comparison between experimental (Biermann and Gray 1942 NACA Report [34]) data and numericalresults. Thrust and power coefficient (ordinate) curves versus advance ratio for the three-blade single rotationpropeller.

C. Caradonna-Tung Experiment

This validation includes a wake-on-body impingement case. As already stated (see section III.D), in allcases in which a wake comes too close or impinges on a body, the BEM formulation has to be modified: thewake will be considered composed of vortex rings, thanks to the analogy between vortex rings and doublets.This allows to introduce a regularization in the vortex inductions and even in those cases in which a wakepenetrates a body, the induced potential remains bounded.

Fig. 6. Details of the Caradonna-Tung experiment, wind tunnel set-up. Taken from [35]

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A classical test found in literature, known as Caradonna-Tung experiment [35], involves a two-blade rotorcomposed of two rectangular untapered NACA 0012 wings. Fig. 6 shows the set-up of the experiment. Therotor was tested in a wind tunnel and, through pressure probes placed on the wing surface, the chordwisepressure distributions were obtained at specific sections. The rotor starts from rest and there is no wind,

UPM

Exp

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1.5

1

0.5

0

-0.5

-1

-1.5

x c/

CSection / = 0.68r R

UPM

Exp

1

0.5

0

-0.5

-1

-1.5

x/c

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

1.5

1

0.5

0

-0.5

-1

-1.5

Section = 0.96r/R

x/c

Section = 0.80r/Rp Cp

Cp

Fig. 7. Comparison between experimental data and numerical results for three different spanwise sections.

thus, during the first revolutions the wake is not convected downstream, but stays close to the blades. Whilethis fact has no consequences in a real experiment, in the panel code represents a problem because the wakeimpinges on the blades several times in the first revolution; without the alternative vortex ring formulation,this would lead to instabilities, resulting in completely inaccurate results.

For a rotational speed of 1200 rpm, a collective pitch θ = 8◦ and a tip Mach number M = 0.52,the comparison between experimental results and numerical simulation in terms of pressure coefficients ispresented in Fig. 7. The three considered sections are, respectively, r/R = 0.68, r/R = 0.80 and r/R = 0.96,where R is the blade radius and r is the span-wise coordinate. The code results and the experimental dataare in excellent agreement and the main trend of the Cp distribution is well captured. It has to be underlinesthat no iterative Kutta condition has been applied (this can be seen in observing the pressure coefficientson trailing edge), resulting in possible inaccuracies of the Cp towards the trailing edge. Fig. 8 offers arepresentation of the developed wake in the numerical simulation.

V. IDINTOS Model

A. Models’ Description

The aerodynamic surface of the amphibious aircraft was kindly provided by the Aerospace EngineeringDepartment of University of Pisa, which was leading the IDINTOS project in terms of design and manu-facturing of the configuration. The external surfaces included also propellers and shrouds. A picture of anearly version of the prototype model is offered in Fig. 9. The CAD model is shown in Fig. 10.

Four different configurations were then considered starting from the prototype. In the first one, the

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Fig. 8. Developed wake of the Caradonna-Tung simulation.

Fig. 9. First prototype of IDINTOS as presented at the technological fair Cre@ctivity in November 2013.

fuselage was not modeled. To obtain the classical box, the root of the front wing was extended to meetits symmetric counterpart in a direction normal to the longitudinal plane. In this process, the airfoil wasmaintained the same as the wing root’s one. The wing surface has been cleaned of the tip tank and otherdevices on the surface. In the following of the paper, the authors will refer to this configuration with thename of wingsystem. The modeled (meshed) aerodynamic surface is represented in Fig. 11. As for the theother cases, a convergence test on the lift coefficient was carried out for the particular flow condition. Thisled to a chord-wise subdivision with 25 elements on each side (upper and lower). More refined models, werenot changing the physical sense of the results, and actually, were computationally more demanding: typicallyBEM linear system dimensions scale with the square of the number of (body) panels.

The second configuration, called wingprop, adds the propeller. Two variants are possible: the unductedand the ducted propeller, as shown in Fig. 12. However, in the present effort, only the unducted case isconsidered. Moreover, propeller’s surface is modeled either with thick body (actual external surface) or thinbody (only the mean plane). Propeller meshing, on the other hand, is not driven to convergence since forceson the blades are not investigated, however, a refined grid is employed in order to describe the wake shapeevolution with sufficient precision.

In the third configuration, called wingbody, the fuselage, vertical fin and the real wing surfaces aremodeled. Compared to the actual fuselage shape, presenting a step in the lower part of the hull, the modeledaerodynamic surface has been smoothed in those areas to avoid unphysical results. The area on the fuselage

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Fig. 10. CAD model of the IDINTOS external surface.

y

x

z

V

x

Fig. 11. Aeordynamic model of the wing system.

downstream of the front wing trailing edge was refined to appropriately enforce the boundary conditionwhen the free wake was modeled. The wake shedding from the inboard part of the front wing passes veryclose to the fuselage, and, with a coarser mesh, it can cross it, with consequent meaningless results. This isexacerbated when sideslip angle is given to the aircraft.

The fourth and last configuration adds the propeller, and is called complete. It is shown in Fig. 13.

B. Operative Conditions

The different analyses are performed at different operative conditions. Nominal cruise condition is a speedof V cr = 49 m/s, at the altitude of hcr = 1000 m (which sets the air density). The nominal angle of attackis αcr = 1◦. As far as propeller rotational speed is concerned, at the cruise condition it is 3000 revolutionsper minute (rpm).

Although a sensitivity capability is inherently implemented in the code, to evaluate the aerodynamicderivatives a small increment is given in order to pursue a numerical differentiation. With engineeringinsight, this choice revealed to be an acceptable one.

For the ground effect investigations, a low speed condition is set: V low = 25 m/s and the angle of attackis such that the nominal cruise lift is attained (αlow ≃ 8.5◦). Wind tunnel investigations (described in [8])show that for this angle of attack response is still linear, thus, no major separations are in place.

The longitudinal force and moment coefficients are normalized considering the planform wing surface Sref

and aerodynamic mean chord cref. For the latero-directional coefficients, the surface of fuselage,joints andfin projection on the lateral plane is selected as reference value, whereas the semispan of the model is thereference length.

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y

x

z

Fig. 12. Aerodynamic model of the wing system and (ducted) propeller. Blades and (shroud) actual surface ishere modeled. Only one half of the model is shown (the configuration is symmetric with respect of xz-plane).

y

x

z

Fig. 13. Aerodynamic model of the fuselage, wing system and (ducted) propeller (referred to as complete).Only one half of the model is shown (the configuration is symmetric with respect of xz-plane).

VI. Panel Methods as a Modeling Tool

A. Free-wake modeling effects

With the free wake modeling, the wake is forced to be parallel with the velocity field. Considering anisolated wing, to model the wake considering or not its roll up and deformation does not usually providesignificant differences in terms of forces on the wing. However, when a full configuration is considered, notaccurately modeling the actual wake’s shape may lead to relevant discrepancies. Especially for a PrandtlPlaneconfiguration, this may have a strong impact: not only a small variation in the local-to-the-rear wingaerodynamic field has non-negligible effects due to the distance from the center of gravity, but also theeffects on the lift are enhanced because of the large surface. Considering the strong integrated design neededfor this layout, there is no much room for fine-tuning without affecting the overall design.

With reference to Table 2, effects on the total lift is not very relevant if a free-wake of rigid-wake modelingis used. This is generally true for all the tested cases and can be better appreciated comparing the outcomeswith all the other parameters fixed, and varying the wake modeling option. For example, for the wingsystemcase (fuselage and propeller not modelled), the relative difference in the lift coefficient is negligible (about0.5%). However, when the pitching moment coefficient is considered, the differences are more substantial (10to 20%). It is useful, in order to gain insight, to reproduce the results graphically and earn physical sense.

With the aid of Fig. 14, the lift distribution in terms of normalized sectional lift C2dl · c (being c the

sectional chord) and lift coefficient C2dl along the wingspan is studied in the two cases. The main difference

is concentrated on the tip of the rear wing, where the tip vortex directly influences the aerodynamic fields

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Simulation CL Cm

Wingsystem-IKC-Free 3.05E-01 -2.01E-02Wingsystem-LKC-Free 3.18E-01 -3.28E-02Wingsystem-IKC-Rigid 3.07E-01 -2.37E-02Wingsystem-LKC-Rigid 3.20E-01 -3.62E-02

Wingprop-IKC-Free 3.04E-01 1.20E-03Wingprop-LKC-Free 3.17E-01 -8.10E-03Wingprop-IKC-Rigid 3.10E-01 -1.01E-02Wingprop-LKC-Rigid 3.23E-01 -2.05E-02

Wingbody-IKC-Free 2.54E-01 -1.59E-02Wingbody-LKC-Free 2.64E-01 -3.39E-02Wingbody-IKC-Rigid 2.52E-01 -3.30E-02Wingbody-LKC-Rigid 2.63E-01 -5.20E-02

Complete-IKC-Free 2.52E-01 4.96E-03Complete-LKC-Free 2.62E-01 -9.79E-03Complete-IKC-Rigid 2.54E-01 -1.85E-02Complete-LKC-Rigid 2.65E-01 -3.57E-02

Table 2. Steady lift and pitching moment coefficients for nominal cruise condition and different modelingapproaches (LKC and IKC refer to the regular and iterative Kutta condition, Rigid/Free indicate the adoptedwake modeling).

Front Wing

rigid wake

C c [ ]m lC

y [m] y [m]

Front Wing

Rear Wing Rear Wing

free wake

rigid wake

free wake

Wingsystem - No IKC

l •

0 0.5 1 1.5 2 2.5 3 3.5 4

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.5 1 1.5 2 2.5 3 3.5 4

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2d 2d

Fig. 14. Sectional semi-normalized lift (C2dl · c) and lift coefficient (Cl) along the wing span for the wingystem

case when rigid or free wake is modeled. The regular (linear) Kutta condition is enforced.

in a sensible way. With the free wake modeling, those regions slightly experience a drop in the sectional liftand bidimensional lift coefficient C2d

l .Plotting the pressure coefficient along the chord for the sections of the rear wing shows how near the root

sections the different wake modeling does not lead to any difference, whereas, a slight larger peak suction(which is on the lower side of the leading edge) is responsible for the smaller airfoil lift on the rear wing tip.This is shown in Fig. 15.

15 of 27


Rear Wing y = 0.76 m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1.5

-1

-0.5

0

0.5

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1.5

-1

-0.5

0

0.5

1

rigid wake

free wake

Wingsystem - No IKC

t/ct/c

cp cp Rear Wing y = 3.75 m

Fig. 15. Pressure coefficient (cp) distribution at different rear wing sections. Wingsystem case when rigid orfree wake is modeled. The regular Kutta condition is enforced.

In previous efforts, as references [1, 23, 36–38], free wake model was observed to change lift distribution(and aeroelastic properties) and induced drag coefficients when compared to a rigid wake case. For thisparticular configuration at the cruise condition, the difference in the induced drag is slightly larger than 1%,being lower for the free-wake case. Other studies showed even a larger decrease in drag [23,36,37].

Adding the propeller (wingprop) slightly increases the discrepancy in the lift and moment coefficientswhen the different wake models are adopted. This may be partially understood noticing that propeller wakeshape has a direct influence on the aerodynamic field, particularly on the rear wing (the wake is developingand passing not far from it). Moreover, the wing and propeller wake interact in a nonlinear way. Fig. 16shows the lift distribution (in terms of C2d

l · c and C2dl ) along the wingspan between the two cases. The rear

Front Wing

rigid wake

y [m] y [m]

Front Wing

Rear Wing Rear Wing

free wake

rigid wake

free wake

Wingprop. - No IKC

0 1 2 3 4

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

C c [ ]ml •

2d

lC2d

Fig. 16. Sectional semi-normalized lift (C2dl · c) and lift coefficients (C2d

l ) along the wing span for the Wingpropcase when rigid or free wake is modeled. The regular Kutta condition is enforced.

wing experiences a localized drop in lift, especially near the root area, close to where the propeller wake is

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passing. Thus, it is directly related to a different shape of the wake of the propeller. It can be speculatedthat, when free to warp, the propeller wake has a tendency to slightly enlarge its helix radius, with theconsequence that it passes closer to lower part of the rear wing. This redistribution of loads on the rear winghas large effects on the moment, thus, a more realistic wake modeling gives a nose pitch-up contribution(especially when the propeller is considered).

Ideally, a (slightly) non-trimmed situation can be fixed with small deflections of the control, however,what is important to control is how the flight mechanics stability is affected when the different modeling areemployed. One important parameter in this regard is the static margin of stability (the ratio between pitchingmoment slope and lift slope coefficients normalized by the mean aerodynamic chord, i.e. Cmα/(CLα ·cmean)).Considering the wing-only (wingsystem) cases, it is observed a decrease of the margin of stability when

Simulation − Cmα

cmean·CLα(%)

Wingsystem-IKC-Free 16.60 %Wingsystem-LKC-Free 18.95 %Wingsystem-IKC-Rigid 18.95 %Wingsystem-LKC-Rigid 20.34 %

Wingprop-IKC-Free 17.11%Wingprop-LKC-Free 18.44%Wingprop-IKC-Rigid 17.23%Wingprop-LKC-Rigid 18.90%

Table 3. Static margin of longitudinal stability at nominal cruise condition and different modeling approaches(LKC and IKC refer to the regular and iterative Kutta condition, Rigid/Free indicate the adopted wakemodeling).

accurately modeling the wake, see Table 3. This might lead to important consequences if a preliminarydesign with the rigid wake was already in the lower end of the admissible margin of stability. Interestingly,what observed above holds to a much smaller extent (the gap almost disappears) when the propeller too aremodeled (wingprop).

Cases and comparisons when fuselage and complete aircraft are also included in the model are currentlyunder investigation.

B. Iterative Kutta Condition Enforcement

It is well known among BEM applied-to-aerodynamic practitioners, that enforcement of the Kutta conditioncan be achieved with different approaches, see section III.C. With low-order BEM approaches an iterativeprocess (iterative Kutta condition) was suggested in [26,27] to guarantee a zero jump pressure at the trailingedge.

Historically, this condition was applied to rotatory wings or unsteady simulations, since, in cases wherestrong cross-flow was measured, the classic Kutta condition was leading to large pressure jumps at the trailingedge. Thus, this condition would be definitely employed when simulating the propeller wake. However, itsimportance is here assessed within the fixed wing case (airplane configuration without propellers).

The isolated wing system (wingsystem) is considered, and for a fixed set of parameters the simulationsis run with the classic and iterative enforcement of the Kutta condition. The differences on the CL are inthe order of 5% (see Table 2), being lower values associated with the iterative Kutta condition. In Fig. 17is depicted the pressure distribution at a section close of the tip of the rear wing. It can be appreciated thedifference in the distribution: when the Kutta condition is iteratively enforced there is no pressure jumpacross the trailing edge. However, the distribution in the upstream area is also (very) slightly affected,resulting in a smaller bidimensional lift.

Consequence of the redistribution of pressures lead to a decreased margin of stability, see Table 3. It isinteresting to notice how, employing lower order (and faster) modeling as the rigid wake and linear Kuttacondition simulation does give larger coefficient predictions (higher lift and higher nose-up pitching moment)and non-conservative results in terms of stability (larger margin of stability).

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No IKC

IKC

Wingsystem - Rigid Wake

t/c

cp Rear Wing y = 3.75 m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-1.5

-1

-0.5

0

0.5

1

0.9 0.92 0.94 0.96 0.98 1

-0.2

0

0.2

0.4

Fig. 17. Pressure coefficient (cp) distribution at rear wing section y = 3.75 m(15/16 b) for Wingsystem case andrigid wake modeling. Regular and iterative Kutta condition results are compared.

Aerodynamic forces seem to be very sensitive to the trailing edge treatment, even if traditionally thiswas observed mainly for problems concerning rotatory wing. It can be speculated that this is consequence ofeffects of different trailing edge conditions on the wake evolution (doublet’s intensity and eventually shape).This topic is currently under investigation.

VII. Propellers Integration

A. Longitudinal Mechanics

Due to the particular configuration having the propellers mounted on the fuselage, it is expected non negli-gible effects on the aerodynamic performances. In fact, the variation of aerodynamic flow will particularlyaffect areas in the neighborhood of wings, fin and fuselage. The direct contribution of the propeller to thetotal forces is not considered.

1. Effects on load redistribution

Considering the wingsystem and wingprop, effects of propeller on lift coefficients is small (regardless of thetype of wake and Kutta condition modeling, as it could be appreciated in Table 2). On the contrary, effectson the pitching moment are larger, and contribute with a nose pitch-up tendency. This is well explainedin Fig. 18. The propeller’s wake, passing under the rear wing, creates a complicated redistribution of theloading which decreases its lift production capability. This is especially located in the region where the wakeis physically developing. In fact, at the tip of the wings, there is no change in the lift production betweenthe propelled and un-propelled cases. Interestingly enough, this action is almost balanced (in terms of totallift) by an increase of the lift in the front/lower wing: here the aerodynamic field is modified by the propelleraccelerating the air more uniformly than what happens for the rear wing. As a consequence, the upper sideexperiences a pressure drop. This can be clearly inferred from Fig. 19, where the pressure coefficient is shownon front- and rear-wing root sections (inside the cylinder formed by the propeller disk translated along x-axisdirection) and also tip sections. Considering the front wing, it can be recognized a drop in pressure on theupper surface, which contributes to a larger lift. For the rear wing, the situation is more complicated, evenif, as expected, a smaller drop on the pressure on the lower surface of the wing can be recognized.

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Front Wing

wing system

y [m] y [m]

Front Wing

Rear Wing

Rear Wing

wing system +propeller

IKC, Free Wake

0 0.5 1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.5 1 1.5 2 2.5 3 3.5 40.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

PROPELLERCYLINDER

PROPELLERCYLINDER

C c [ ]ml •

2d

lC2d

Fig. 18. Sectional semi-normalized lift (C2dl · c) and lift coefficients (C2d

l ) along the wing span for the wingsystem (wingsystem) and wingsystem plus propeller (wingprop) cases. Free wake and iterative Kutta conditionenforcement are considered.

2. Effects on trim and stability

This lift redistribution increases the pitch-up moment, as Table 2 clearly shows. Thus, the design should befine-tuned to have a balance at the sought cruise operative condition.

In terms of static margin of stability, with a rough modeling of the wake (rigid) the propeller induces adecrease, whereas with a free wake modeling and iterative Kutta condition a slight increase is observed.

B. Latero-Directional Mechanics

For the latero-directional mechanics, the wingbody and complete configurations are considered. The values

Simulation CY β Clβ Cnβ Wake

Wingbody: Joint 0.11 −0.047 0.013 FreeWingbody: Fin 0.16 −0.025 0.083 FreeWingbody: All (no fuselage) 0.29 −0.135 0.092 Free

Complete: Joint 0.11 −0.047 0.013 FreeComplete: Fin 0.12 −0.018 0.062 FreeComplete: All (no fuselage) 0.24 −0.129 0.07 Free

Wingbody: Joint 0.11 −0.047 0.016 RigidWingbody: Fin 0.15 −0.022 0.083 RigidWingbody: All (no fuselage) 0.29 −0.128 0.093 Rigid

Complete: Joint 0.11 −0.047 0.015 RigidComplete: Fin 0.14 −0.020 0.075 RigidComplete: All (no fuselage) 0.28 −0.132 0.086 Rigid

Table 4. Contribution to the value of some aerodynamic derivatives with or without propellers. Cl (Cn) isthe rolling (yawing) moment coefficient, positive along the wind (vertical) direction. β is the sideslip angle,positive when pointing to the right side of the aircraft.

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Rear Wing y = 0.76 m

Front Wing y = 0.86 m Front Wing y = 3.75 m

wingsystem

wingprop

IKC, Free Wake

t/c

t/c

cp cp

cp cp Rear Wing y = 3.75 m

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1-2

-1

0

1

0 0.2 0.4 0.6 0.8 1-2

-1

0

1

t/c

t/c

Fig. 19. Pressure coefficient (cp) distribution at front and rear wing root and tip sections, for wingsystem(wing-only) and wingprop (wing+propeller) cases. Free wake and iterative Kutta condition enforcement areconsidered.

of some aerodynamic derivatives is shown in Table 4, where CY , Cl and Cn refer to the lateral force, rollingand yawing moment coefficients (measured in wind-axis). β is the sideslip angle, positive when pointing toy direction. The separate contribution of the lateral joints and vertical fin to the value of the derivatives(evaluated not considering the forces on the fuselage) are given. Before further commenting, it is importantto notice the values above have been obtained using as normalization parameters the projection of fuselage,fin and joints on the lateral plane (xz), and the wing semispan. Moreover, considering the unsteady flavourof the configuration with propeller, an average value is chosen.

Figs. 20 and 21 show the pressure coefficient distribution and the wake shape for the nominal cruisecondition, when a slight sideslip angle is considered β = 0.1◦. The value of CY β slightly decreases whenpropellers are modeled. It can be speculated that this is consequence of the propeller’s wake convected fromthe sideslip angle closer to the “higher pressure” side of the vertical fin, counterbalancing then the angle ofattack created by the undisturbed flow. This is supported by the fact that the contribution of the fin to CY β

decreases. It is also interesting to notice effects of the joints, which contribute almost as the fin does. If thewake is modeled as rigid, the drop of CY β due to propellers is slightly smaller.

When Clβ (dihedral effect) is considered, the contribution of fin (and also joint) to the derivative is not aslarge. This indicates that the wings play a prominent role. For this reason, since propellers seem to mostlyimpact fin force production, overall effect on the derivative are negligible.

Focusing on Cnβ (weathercock stability), as expected the major contribution is given by the verticalempennage. Although the joints produce a comparable amount of lateral force, the contribution to theyawing moment coefficient is smaller because, from a lateral view, the center of gravity is approximatelylocated at the average streamwise coordinate of the joint. Overall, presence of propeller reduce the value ofthis coefficient to a non negligible extent.

Extending this investigations also to other aerodynamic derivatives can be very useful insight in the

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a=1

b=0.1

Fig. 20. Wingbody configuration. Pressure coefficient distribution and wake shape, for α = 1◦, β = 0.1◦.

a=1

b=0.1

Fig. 21. Complete configuration. Pressure coefficient distribution and wake shape, for α = 1◦, β = 0.1◦.

design or also fine tuning of a flying model. For example, they can suggest why a smaller than expecteddutch roll stability can be found when design was not considering interference with propellers.

Contribution of the fuselage has been not considered above due to the very high sensitivity to a correctmodeling. For example, withe the modeling proposed above the contribution to the CY β and Clβ arenegligible, whereas, the one to Cnβ is large and opposite, promoting an overall unstable configuration. Thesituation is even more complicated noting that, in a real situation, flow around fuselage may have separations.

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Thus, higher fidelity approaches are probably necessary for assessing latero-directional performances withan higher confidence.

VIII. Ground Effect

Low-speed performances of IDINTOS have been investigated with high fidelity means, see for example [8].However, the presence of ground has never been taken into account.

With panel method, this is easily done (using a perfectly symmetric-to-the-ground configuration). How-ever, the use panel method in high-lift situations may be questionable, at least without any mean for con-sidering the occurring separations. This section, thus, focuses more on the conceptual effects of the groundproximity, not necessarily in a very-low speed operative condition. Redistribution of loads and change inaerodynamic derivatives, trim and stability are studied, with the idea that many results will qualitativelycarry-over in a real low-speed close to the ground condition. Considering the amphibious nature of thesystem, study of ground effect is relevant also when landing is on the water, not only ground.

Investigations are carried out on the wingsystem configuration, flight conditions are the ones specified insection V.B for the low speed case. Distance from the ground h, measured from the nose of the aircraft, isvaried and aerodynamic forces and distributions are computed.

A. Importance of the Alternative Formulation

Alternative formulation presented in section III.D finds the majority of its application in the topics concerninghelicopters. However, unexpectedly, it was found to be of fundamental importance also for this case. Infact, with reference to Fig. 22, the wake developing for the wingsystem (at 2m from the ground), encounterssome instabilities. These are consequence of the strong distortion of the wake in the tip regions, leadingto wake impingement on the joint’s surface. This interaction causes numerical instabilities inherent to the

Fig. 22. Wake instabilities when the “classic” formulation is employed. Due to the intense circulation, tipvortices at the lower wing-joint and upper-wing joint intersections tend to impinge on the aerodynamic surface.

singularities equations (potential induction), and is not treatable with desingularization techniques based onvortex-core methods (which actually have direct effect on velocity induction).

Whether this behaviour could be avoided with smaller time steps or different time integration schemesother than explicit one here employed has not been investigated. In fact, the time step is already very smallconsidering that the wake evolution strategy is used to determine its shape at steady state, and not to studythe transient. Moreover, although localized, these instabilities profoundly impact the loads on the wings,with unreliable results.

For this reasons, the alternative formulation presented in section III.D is employed for this investigations.Fig. 23 shows the same condition above when the alternative formulations is used. It can be observed thesmooth structure of the vortices, in particular the very interesting interaction of starting vortices unique tothe PrandtlPlane configuration.

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starting vorticesinteraction

Fig. 23. Wake when the “alternative” formulation is employed.

B. Changes in lift and moment coefficients

Fig. 24 summarizes results of preliminary investigations. As the distance between aircraft nose and ground(h) is varied, lift and moment coefficients are measured and (percentage) differences with the nominal lowspeed case (in which the ground is very far) are depicted.

From a lift point of view, in the closest-to-the-ground configuration (h = 2 m), an increment of approx-imately 8% has been registered. Studying the lift distribution along the wingspan (box on the top of theplot), it may be noticed that lift increment is more pronounced on the rear/upper wing. At first glance, thisrepresents an unexpected result, since the lower front wing was thought to have the largest increase in liftdue to its closer proximity to the ground. However, the complicate up/downwash system characterizing thelayout, for which front (rear) wing experiences an upwash (downwash), may have been partially modifiedand reduced by the ground presence. This is a possible explanation of the results. Experimental wind tunnelresults simulating the ground effects would be relevant to confirm and understand this mechanism.

One of the consequences of this redistribution is that front-to-aft wing lift ratio decreases from a valueof 1.36 to 1.25. This is responsible also of an increase in the pitch down moment of the configuration: thepicture also depicts the variation in pitching moment (positive when pitching up) coefficient. In the closest-to-the-ground configuration, there is a decrease in the pitching moment of 10.5% (when normalized with thereference lift and chord).

This aspects need to be taken into consideration in the low speed design of the configuration. Of course,these results should not be taken from a quantitative point of view, due to the inherent limitations of BEMand the complicated low speed regime exacerbated by the ground proximity. However, they give a qualitativeinsight for a successful, efficient and robust design.

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DC

CL

L

DC

CL

M

h/b

0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4

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1.25 12.5

-10

-5

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h=2 m

h=100 m

0

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1.25 12.50.25

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FW

Fig. 24. Change of lift and pitching coefficients, lift distribution and repartition as function of distance fromthe ground (x-axis has a logarithmic scale).

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IX. Conclusions

This contribution shows preliminary applications of an in-house aerodynamic solver based on BEM tothe design of an amphibious PrandtlPlane. The code comes with some features ad-hoc thought to studyparticular problems, like operations in the vicinity to the ground, or propeller integration. In particular, thecode has embedded a formulation that enables to avoid numerical instabilities caused by situations in whichwake impinges on body. Moreover, surface sensitivity are also implemented giving this code more flexibilityfor pursuing aeroelastic analyses: different coupling approaches are then possible (implicit or explicit).

One of the shown applications regards sensitivity to wake’s shape when investigating PrandtlPlane (or,in general, nonplanar) configurations. Load redistribution are found on the tip regions, with effects on thetrim and static stability.

A second shown case is the integration of propellers. Their effect on the flow are studied for the lon-gitudinal and latero-directional planes. In the first case, there is a lift redistribution leading to a pitch-upmoment. When flight mechanics is concerned, results on margin of stability depend on the wake modeling.Thus, more in depth analyses are needed to verify which approach better correlates with real behavior. Thelatero-directional properties are modified by the presence of propellers mainly in the weathercock stability,with a tendency to destabilize the aircraft. On the contrary, dihedral effect is not very sensitive. Fuselagedestabilizing contributions are large. However, as a general note, these results are very sensitive to a correctwake shape and also fuselage modeling, able to reproduce the real scenario.

A final application is towards the study of ground effect. In particular, the alternative formulationis necessary to avoid numerical instabilities consequence of the wake impingements on the joint’s surface.Moreover, ground proximity interferes with the typical downwash/upwash pattern inherent to PrandtlPlane,and, unexpectedly, a nose pitch-down moment is found to take place.

X. Acknowledgements

The authors acknowledge the support by San Diego State University (College of Engineering) and Univer-sity of California San Diego (Graduate Student Association). They also like to warmly thank Professor AldoFrediani, Vittorio Cipolla, Fabrizio Oliviero and Emanuele Rizzo of the Aerospace Engineering Departmentof Università di Pisa for the fruitful collaboration, and for providing us IDINTOS model.

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