Dynamic Aircraft Simulation Model Covering Local Icing Effects · code LEWICE, Version 2.2 [22]. A...

DYNAMIC AIRCRAFT SIMULATION MODEL COVERINGLOCAL ICING EFFECTS

C. Deiler, DLR (German Aerospace Center),Institute of Flight Systems

T. Kilian, DLR (German Aerospace Center),Institute of Aerodynamics and Flow Technology

Lilienthalplatz 7, 38108 Braunschweig, Germany

Abstract

A novel ∆-model approach to characterize the changes in longitudinal and lateral aircraft dy-namics due to local icing is analytically derived. This model extension is formulated as a separatemodule in the aircraft flight mechanics simulation and can be used in existing simulation mod-els. Using the example of the former DLR research aircraft VFW 614 ATTAS, the base informationabout the aircraft’s iced aerodynamics is obtained by 3D CFD calculations with numerically gen-erated ice shapes. With the resulting data ∆-model parameters describing a local aerodynamicdegradation are estimated. Simulation of the local ice influences on the dynamic aircraft be-havior show the ∆-model’s capabilities to cover aerodynamic changes during a de-icing process.

NOMENCLATURE

Symbols

a model parameter

α angle of attack rad

αmax angle of attack at CLmax rad

C(·) aerodynamic coefficient

c1, α? flow separation function parameters

D drag force N

d ∆-model offset

e Oswald factor

ε downwash angle rad

η elevator deflection rad

ηy iW non-dimensional wing coordinate

F force N

f function

g acceleration due to gravity m/s2

H altitude m

i segment index

iH horizontal tail plane deflection rad

Ixx, Iyy, Izz, Ixz moments of inertia Nm2

k ∆-model factor

k1, k2 drag coefficient factors

L lift force N

Λ wing aspect ratio -

L, M, N body fixed momentsabout x ,y ,z axis Nm

lµ mean aerodynamic chord m

mAC aicraft mass kg

Ma Mach number

N number of surface segments

~Ω rotational speed vector rad/s

P model parameter

ptot total pressure N/m2

Φ, Θ, Ψ Euler angles rad

Deutscher Luft- und Raumfahrtkongress 2016DocumentID: 420031

1©2016

p,q,r rotational velocities rad/s

Re Reynolds number

rH, r ?H, z?H horizontal tail lever arms m

~r position vector m

S surface area m2

t time

Ttot total temperature C,K

τ2 time constant 1/s

Tb inertia tensor

∆t time delay s

u,v ,w translational velocitiesalong x ,y ,z axis m/s

VIAS indicated airspeed m/s

VTAS true airspeed m/s

~V speed vector m/s

X wing flow separation point

X, Y , Z body fixed forces along x ,y ,z axis N

x , y , z axes coordinates

Subscripts

A aerodynamic

b body-fixed

Base base model part

E engine

H horizontal tail

Ice ∆-model icing part

ID System Identification

l rolling moment

m pitching moment

n yawing moment

Ref. reference

Sim Simulation

W wing

WB wing/body

Abbreviations

CFD Computational Fluid Dynamics

LWC Liquid Water Content

MVD Median Volume Diameter

SLD Supercooled Large Droplets

1 INTRODUCTION

Aerodynamic icing can have hazardous effects onaircraft performance characteristics. It can also bea limiting factor of the safe flight envelope. Ic-ing induced dynamic behavior change and poten-tial premature stall raise the need for pilot situa-tional awareness and an adaption of any aircraftcontrol strategy. During the last decades, variousaccidents worldwide have shown the severity of ic-ing related degradations as well as pilot’s difficul-ties to cope with changes in aircraft behavior [1–3].For a better understanding of aerodynamic icingeffects on aircraft performance and for enhancingfuture pilot training concerning icing hazards, newaerodynamic models for aircraft simulation shouldbe developed, which is part of the HGF foundedjoint DLR & TU-Braunschweig research project “Su-percooled Large Droplet Icing” (SulaDI).

During the flight through icing conditions, icecan accumulate on airframe parts facing the inflowe.g. wing or stabilizer leading edges, aircraft noseor engine intakes. The main aerodynamic degra-dation is expected to be caused by wing ice accre-tions and manifests itself in a reduced stall angleof attack and increased drag. These accumulationsmanifest in different shapes, depending on e.g. at-mospheric conditions and aircraft geometry. Thegeneral aerodynamic influence is outlined for ex-ample in the “AGARD Report 344” [4] and given inFig. 1. In the past, these effects of the icing phe-nomena for different airfoils and icing cases (e.g.[4–6]) as well as for complete aircraft (e.g. [7–10])had been investigated in various studies.

From a scientific point of view different aspectsof the aircraft icing phenomena are of interest. Forexample:

1. aircraft operational limitations and behaviorwith accumulated ice on different surfaces,

2. flight performance, dynamic behavior andhandling quality changes during ice accretion,

3. aircraft behavior with variable accumulationseverity on different surfaces,

4. aircraft behavior during de-icing and ice shed-ding,

5. pilot’s situational awareness concerning icingand ability to detect a degradation due to icecontamination.

The challenge in describing aerodynamic degrada-tions mathematically is to combine points 1-4 inone model formulation to extend the aerodynam-ics within the simulation. For dynamic simulationanalysis or training in a flight simulator the modelmust be capable of accumulating ice on certain air-craft parts and/or de-icing the aircraft if e.g the air-

Deutscher Luft- und Raumfahrtkongress 2016

2©2016

clean

iced

Angle of Attack α

Lift

Co

effi

cien

tCL

clean

iced

Drag Coefficient CDLi

ftC

oef

fici

entCL

Figure 1: Expected aerodynamic degradation dueto icing [4] (lift curve and drag polar)

craft leaves atmospheric icing conditions or coun-termeasures are activated.

This paper mainly addresses to item 1, 3 and 4of describing the aircraft operational limitationsand behavior for symmetric and asymmetric icingcases. In several attempts, the aircraft icing degra-dation problem had been faced based on data col-lected from flight test with the NASA Twin Otterat the beginning of the last decade [11–15]. Withnotable success, the aerodynamic model formula-tions had been changed and extended for reliablyconsidering icing effects and this built-in approachwas used to develop a special icing training simula-tor [14,16]. Another way for accounting the degra-dation in the simulation model is to extend anavailable basic aircraft model with an additionalpart (∆-model in Fig. 2) in the aerodynamics mod-ule [17].

After a basic aircraft simulation model is formu-lated and validated for a specific aircraft, exten-sions for covering aerodynamic icing effects arederived to estimate and afterwards simulate per-formance changes. This approach gives the ad-vantage that existing aerodynamic models do nothave to be altered and the module parameterscan be independently determined from the datasource. Using data of flights with artificial iceshapes such an ∆-model for the fundamental ef-fects of icing on the aircraft’s longitudinal motionis presented in [18] and for all six degrees of free-dom in [19].

The herein presented new ∆-model extensioncovers ice related changes of the longitudinal andlateral motion aerodynamics in lift, drag as well asrolling and yawing moment. Changes contribut-ing the basic stall model formulation and the dragpolar curvature are necessary to cover icing ef-fects. The wing surface is divided into individ-ual segments allowing the consideration of localicing effects and their consequences on the air-craft’s lateral dynamics. The fundamental ∆-modelformulation for icing effects is comparable to themodel proposed in [11], where model parameters

Base

∆-Model

+ Forces &Moments

Parameters

Aircraft Motion

Controls

Environment

Derivatives

Aerodynamic Model

Figure 2: Illustration of aerodynamic model with∆-model extension [18]

are linearly altered to include icing related aero-dynamic degradations. To demonstrate the ca-pability of the proposed ∆-model to reproduceaerodynamic local icing effects in the aircraft sim-ulation, the necessary model parameters are ob-tained using an aerodynamics database generatedby 3D CFD calculations. These calculations for theformer DLR research aircraft VFW 614 ATTAS (seeFig. 3) are performed for a clean aircraft case anda case with additional attached ice shapes gener-ated with LEWICE [20]. With the developed modelthe dynamic aircraft behavior during asymmetricde-icing is simulated.

2 AERODYNAMIC DATABASE OF AIR-CRAFT ICING EFFECTS

A CFD study has been conducted in order to quan-tify the effects of leading edge icing on an air-craft’s wing and horizontal tailplane (HTP) on theaerodynamic performance.

2.1 AIRCRAFT AND ICING GEOMETRYDEFINITION

The basic aircraft geometry was derived from theVFW 614 ATTAS. Its aerodynamic performance iswell known and DLR pilots are well accustomedto its flight behavior. This becomes of special im-portance when proceeding towards an assessment

Figure 3: DLR research aircraft VFW 614 ATTAS


3©2016

Figure 4: Overview of VFW 614 geometry with additional leading edge ice shapes

freestream velocity V = 200 kt= (103 m/s)

total temperature Tt = −10 Cmedian volume diameter MVD = 119µm

liquid water content LWC = 0.7 g/m3

icing time t = 10 minangle of attack α = 2

Table 1: Expected icing conditions in typical hold-ing pattern for CFD calculations

of in-flight icing effects in a flight-simulator study.For simplification reasons and since no absolutebut delta-values (iced / non-iced) are of interest,the aircraft geometry has been smoothed, cleanedof any extruding details and also the engines areneglected for CFD computations.

The leading edge ice shapes of choice had to ful-fill the need for a potentially high aerodynamic im-pact and at the same time the corresponding icingconditions should match those of an airliner’s typi-cal holding pattern. NASA has created a public ex-perimental database [21] of 2D Supercooled LargeDroplets (SLD) ice shapes, which are known toseverely influence the aerodynamic performance.Out of a set of icing conditions, which relate to aholding pattern at 200 kt, test case 7575 was cho-sen. It features a large leading edge horn ice shapein upward and downward direction, creating a po-tentially large aerodynamic performance degrada-tion. An overview of the icing conditions is givenin Tab. 1.

The chosen ice geometries were applied to theVFW 614 utilizing a technique commonly used inthe process of aircraft certification: 2D ice shapes

are generated on several airfoil sections of thewing and the horizontal tailplane using the icingcode LEWICE, Version 2.2 [22]. A repositioning andconnection of the 2D shapes results in a 3D icingstructure, which can be attached to the existingclean leading edge. An overview of the iced air-craft geometry is given in Fig. 4. Section cuts illus-trate the change in relative ice thickness depend-ing on the local chord length.

2.2 NUMERICAL SETUP

Steady flow computations were performed withthe TAU code, Version 2014.2, a Reynolds-averaged Navier-Stokes (RANS) solver developedby DLR [23] using unstructured hybrid meshes. De-spite local flow detachments previous numericalstudies on iced aircraft geometries have shown anoverall steady behavior and thus proven the con-cept of steady computations. The two-equationShear-Stress-Transport turbulence model (SST) byMenter [24] was applied including an extension toaccount for wall roughness [25].

Half-model meshes were generated with thehybrid mesh generator CENTAUR, a commercialsoftware package developed by CentaurSoft [26].The surface was discretized with triangles, semi-structured prism cells were stacked above to cap-ture boundary-layer effects and the far field wasfilled with tetrahedral elements. The leading edgeicing regions were heavily refined to capture smallscale flow features. The final mesh consists of 14million nodes for the clean and 20 million nodesfor the iced case.


4©2016

Figure 5: Surface pressure distribution and streamlines on upper wing and HTP for clean and iced con-figuration

2.3 DATABASE GENERATION

The simulations of the clean and iced configura-tion cover a wide range of angles of attack fromα = −6 to beyond αCLmax . The boundary condi-tions summarized in Tab. 2 correspond to icing con-ditions in a holding pattern. The ice roughness wasset to 3.967 mm on the wing and 2.665 mm on theHTP following an empirical correlation in [20].

Surface streamlines on the upper side of wingand HTP in Fig. 5 illustrate the gradual degrada-tion effect leading edge icing has on the aerody-namic performance towards higher angles of at-tack. In the case of a clean wing the flow is fullyattached throughout the depicted angle of attackregime. The iced case on the other hand shows, asexpected, areas of detached flow around the lead-ing and trailing edge at α = 6 and at α = 8 thewings upper surface is predominantly detached.

Mach number Ma = 0.3

Reynolds number Re = 21.7 milliontotal pressure pt = 88644 Pa

total temperature Tt = 263 K

Table 2: Boundary conditions for CFD calculation

The significant icing effect on overall lift and dragcoefficients is highlighted in Fig. 6. The maximumlift coefficient CL,max is reduced by 50 % from 1.2

to 0.6 and the corresponding angle of attack is re-duced by 5.5 . The zero-lift drag coefficient risesnoticeably by 25 %, half of this increase can be ac-counted to ice roughness effects. Through theintegration of local surface pressure data the span-wise distribution of forces dF/dy and momentsdM/dy can be derived. The distribution of theforce component in z-direction for three differentangles of attack in Fig. 7 illustrates a result of this

−5 0 5 10 15

−0.5

0

0.5

1

Angle of Attack α []

Lift

Co

effi

cien

tCL

[-]

0 0.02 0.04 0.06 0.08 0.1 0.12

−0.5

0

0.5

1

Drag Coefficient CD [-]

Lift

Co

effi

cien

tCL

[-]

cleaniced

Figure 6: Coefficients of lift and drag for clean and iced configuration


5©2016

Figure 7: Spanwise distribution of local force in z-direction along wing and HTP

procedure. The implementation of icing effectsinto the kinematic model described in this paperis primarily based on this local evaluation of forcesand moments. It allows simulation of not only sym-metrical icing through mirroring the half-modelbut also non-symmetric conditions, e.g. throughpartial de-icing failure.

3 MODEL FORMULATION

The basic aircraft motion is represented by a sixdegree-of-freedom kinematic model. The equa-tions of the translational motion are given by

u = −q · w + r · v − g · sin Θ +XE +XAmAC

,

v = −r · u + p · w + g · cos Θ · sin Φ +YE + YAmAC

,

w = −p · v + q · u + g · cos Θ · cos Φ +ZE + ZAmAC

(1)

with the engine forces XE , YE , ZE . The unsteadynonlinear aerodynamics are modeled by the forcesXA, YA, ZA in the corresponding direction. The ro-tational motion equations are given byp

q

r

b

=T−1b

LE + LAME +MANE + NA

b

−

qr(Izz − Iyy)− pqIxzrp(Ixx − Izz) + (p2 − r2)Ixzpq(Iyy − Ixx) + qr Ixz

b

(2)

including the engine induced body fixed momentsLE, ME, NE, the aerodynamic moments LA, MA, NA,and the inverse inertia tensor

T−1b =

Ixx 0 −Ixz0 Iyy 0

−Ixz 0 Izz

−1

b

. (3)

The necessary forces and moments for the aircraftmotion simulation result form the base aircraft

aerodynamic model (section 3.1) and additional ∆-model formulation in section 3.2.

3.1 BASE AIRCRAFT AERODYNAMICS

The base aircraft aerodynamic model is formulatedas a two-point model, splitting wing and horizon-tal tailplane influences (see Fig. 8). For the wingaerodynamics, a nonlinear,unsteady lift curve isconsidered, which allows to simulate flow sepa-ration and reattachment effects [28]. The com-plete aerodynamic model of the VFW 614 ATTASis given in [29] as a system identification processresult. Several equations of the longitudinal aero-dynamics model are outlined hereafter as a basisfor the later on derived ∆-model formulation. Thelateral aerodynamics model formulation – a stateof the art derivative model – can be found in [29].Furthermore, the base aircraft model formulationsimilar to the herein used ATTAS-model is outlinedin [18, 19], where comparable approaches to ac-count for icing effects in the dynamic simulationare presented.

The non-dimensional steady wing flow separa-tion point X is given by [30]

X =1

2·(

1− tanh (c1 · (α− α?))), (4)

whereas α? denotes the angle of attack for whichthe wing flow is half separated. The simplifiedwing/body lift coefficient equation including stall– considering Kirchhoff’s theory of flow separationfrom the trailing edge – results in

CL,WB = CL0 + CLα,WB ·(

1 +√X

2

)2α. (5)

The basic drag equation is dominated by zero, liftinduced and stall dependent drag and can be ex-pressed by

CD = CD0 +1

eπΛC2L+

∂CD

∂X

(1− X

). (6)


6©2016

x

z

xA α

xA,HxA

iH αH

εH

r ?H

z?H

rH

LW

DW

M0W

LH

DH

M0H

Wing Neutral Point

HT Neutral Point

Center of Gravity

Figure 8: Illustration wing and horizontal tail geometry for the two-point model formulation [27]

3.2 ∆-MODEL EXTENSION

The necessary equations to implement a ∆-modelapproach (as given in Fig. 2) to consider local ic-ing effects are derived hereafter. The basic idea isto use linear altered parameters for icing inducedaerodynamic changes in aircraft simulation, whichwas introduced by Bragg [11]. Hence, a model pa-rameter P is assumed to consist of a basic modelpart PBase and an additional ∆-model part ∆PIce de-scribing the icing induced changes:

P = (1 + kP ) · PBase + dP = PBase + ∆PIce (7)

The additional factor kP and the offset dP areused to model the degraded aircraft aerodynam-ics. As a result, an aerodynamic model coefficientC(·) which depends on an extended parameter Pcan be expressed as:

C(·)(P ) = C(·) (PBase + ∆PIce)

=(C(·) (PBase)

)Base

+ ∆(C(·) (PBase + ∆PIce)

)Ice.

(8)

At this stage of model development only the ic-ing influence on the aircraft’s wing is considered.

3.3 LOCAL WING SEGMENT EQUATIONS

The aircraft wing is divided span-wise in N seg-ments with the same wing segment width y iW butconsequently different cord length and surfacearea. This segmentation is shown for example inFig. 9 for N = 20 segments.

With the distance vector ~r i of the ith segmentto CG the local segment inflow velocities (withoutwind) are given by

~V ?i = ~V + ~Ω× ~r i ,with ~V ?i =

[u?i , v ?i , w ?i

]T, ~Ω i = [p, q, r ]T

and ~r i =[x iW,CG, y

iW,CG, y

iW,CG

]T.

(9)

10987

11121314

654321

151617181920

Figure 9: Illustration of ∆-model wing segmenta-tion (N = 20)

Considering modern aircraft’s swept angle ϕ anddihedral ν the local velocities u?i , v ?i and w ?i resultin ui , v i and w i , which are the local inflow velocitiesrectangular to the local 25 % chord line. With thelocal true airspeed

V iTAS =

√(ui)2

+(v i)2

+(w i)2

(10)

the local angle of attack of the i -th segment resultsin

αi = arctan

(w i

ui

). (11)

To determine the aerodynamic influence of each∆-model segment, an additional lift and drag coef-ficient as a local change towards the base aircraftaerodynamic is calculated. The changes of the lat-eral aerodynamics further result from the summa-tion of all these segments influences and their cor-responding lever arms

(~r i). The following equa-

tions are the results of splitting the aerodynamicmodel formulations in [29] into their base and ic-ing parts using the parameter extension accordingto equation (8).


7©2016

With the extension given in equation (7), the pa-rameters of the non-dimensional separation pointwithout hysteresis effects according to [30]

c i1 =(

1 + k ic1)· c1Base

α?i =(

1 + k iα?)· α?Base

(12)

lead to a separation of the hyperbolic tangensterm of each segment i into its base part

ai1Base = c1Base ·(αi − α?

)(13)

and its icing induced part

ai1Ice = c1Base ·[k ic1α−α?

(k ic1 + k iα?

(1 + k ic1

)) ]. (14)

This analytic separation results in the local non-dimensional flow separation point of the base air-craft

X iBase = 0.5 ·(

1− tanh(ai1Base))

(15)

and its icing induced adaption ∆X iIce

∆X iIce =tanh(ai1Ice)− tanh2(ai1Base) tanh(ai1Ice)

−2 ·(

1 + tanh(ai1Base) tanh(ai1Ice)) . (16)

With the parameter extensions for the i -th seg-ment

C iL0 =(

1 + k iCL0)· CL0Base

C iLα,WB =(

1 + k iCLα,WB

)· CLα,WBBase

(17)

and the separated influences of the local flow sep-aration

ai2Base = 0.25 ·(

1 + 2

√X iBase + X iBase

)(18)

ai2Ice = 0.25 ·(

2

√X iBase + ∆X iIce

− 2

√X iBase + ∆X iIce

) (19)

the local lift coefficient change ∆C?iL,WBIce results in

∆C?iL,WBIce = k iCL0CL0Base

+(ai2Base + ai2Ice)kiCLα,WB

CLα,WBBaseαi

+ai2IceCLα,WBBaseαi .

(20)

This coefficient change is related to each segment’swing surface area SiW. Consequently the local liftcoefficient change ∆C?iL,WBIce must be transferredto a general value ∆C iL,WBIce by

∆C iL,WBIce = ∆C?iL,WBIceSiWSW

. (21)

To calculate the local drag coefficient changenecessitates to approximate the local change of

-1.0 -0.5 0.5 1.0

0.2

0.4

0.6

0.8

ηy iW

√1− η2

y iW

local segment position

Figure 10: Elliptic distribution including the span-wise positions of 20 wing segments

the lift induced drag for each segment. An el-liptic wing lift distribution based on the non-dimensional wing coordinate

ηy iW =y iWs

(22)

of each segment is assumed for the base aircraftaerodynamics (see Fig. 10). The local base liftcoefficient C?iL,WBBase is approximated as a functionof the general base lift coefficient, local and com-plete wing surface area and the non-dimensionalwing coordinate ηy iW :

C?iL,WBBase = f(CL,WBBase, SW, ηy iW , S

iW

)(23)

Hence, the local ice induced drag coefficientchange is formulated as

∆C?iD,WBIce = k iCD0CD0Base

+∆C?iL,WB2

Ice

1

eπΛ

+2 · ∆C?iL,WBIceC?iL,WBBase

1

eπΛ

+(

∆C?iL,WBIce + C?iL,WBBase)· d ik1

+(

∆C?iL,WBIce + C?iL,WBBase)2 · k

ik2

eπΛ

+k i∂CD∂X

∂CD

∂X

(1−

(X iBase + ∆X iIce

))

−∂CD∂X

∆X iIce

(24)

using the parameter extensions

C iD0 =(

1 + k iCD0)· CD0Base

k i2 =

(1 + k ik2

)

eπΛ(∂CD

∂X

)i=

(1 + k i∂CD

∂X

)· ∂CD∂X Base

,

(25)

The linear lift depended drag coefficient is intro-duced in the ∆-model as an offset d ik1 , because


8©2016

there is no part of the base model which could belinear extended. The general additional segmentdrag coefficient ∆C iD,WBIce can be calculated ana-log equation (21). The local force coefficients re-sult from ∆C iX,WIce and ∆C iZ,WIce result from equa-tions (21) and (24) by turning the aerodynamic co-efficients around the local angle of attack αi

∆C iX,WIce = ∆C iLIce sin(αi)− ∆C iD Ice cos

(αi)

∆C iZ,WIce = −∆C iLIce cos(αi)− ∆C iD Ice sin

(αi).

(26)

Further the rolling and yawing moment contribu-tions of the i -th wing segment are given by

∆C il ,WIce = ∆C iZ,WIce ·y iWs

∆C in,WIce = −∆C iX,WIce ·y iWs.

(27)

In this version of the ∆-model, no wing pitchingmoment or side force change is considered, butcould also be added by suitable model formula-tions. It is assumed that the aerodynamics changesintroduced by the herein presented ∆-model coverthe primary icing effects on aircraft dynamics.

3.4 GLOBAL ICING INFLUENCE

The above derived equations to determine the lo-cal icing induced aerodynamic changes in a dy-namic aircraft simulation model allow to calculatethe new global force coefficients by summing upthe influence of each segment i . The new forcecoefficient result in

CX = CXBase +∑

i

∆C iX,WIce

CZ = CZBase +∑

i

∆C iZ,WIce,(28)

and the new moment coefficients are given by

Cl = ClBase +∑

i

∆C il ,WIce

Cn = CnBase +∑

i

∆C in,WIce.(29)

4 ∆-MODEL PARAMETER ESTIMATION

The parameters of the above derived ∆-model areobtained from the CFD results in section 2 byan automated process using system identificationtechniques. First, the lift and drag coefficients ofeach wing segment are calculated by summing upthe n local discrete forces FX,n and FZ,n given by

Separation: α?i c i1

Lift: C iL0 C iLα,WB

Drag: C iD0 k i1 k i2

(∂CD∂X

)i

Table 3: Estimated parameters of the local seg-ment reference aerodynamics

the force distributions dF/dy for the different an-gles of attack:

C iD,CFD(α) =∑

n

( FX,n cos (α) + FZ,n sin (α))

qSiW

C iL,CFD(α) =∑

n

(−FX,n sin (α) + FZ,n cos (α))

qSiW

(30)

The necessary information for the parameter esti-mation is available1 after the application of equa-tion (30) to the clean aircraft and iced CFD data.Before the ∆-model parameters can be estimated,corresponding base model parameters for eachstrip are needed. Using these parameters, the for-mulations derived in section 3.3 can be applied onthe iced aircraft CFD results. Therefore a nonlin-ear regression technique to determine the baseaircraft lift and drag coefficients is performed, us-ing a model formulation similar to the equationsin section 3.1, with initial parameter values forzero lift, lift slope, zero lift drag and lift depen-dent drag previously obtained by a simple linearregression. For the nonlinear regression the DLRMatlab R© toolbox Fitlab [31] is used, providing aset of algorithms to optimize model parameters indifferent domains. The corresponding base modelsegment parameters are listed in Tab. 3. These pa-rameters are segment related and therefore com-parable to the e. g. lift coefficient in equation (23).

With the base segment model available, thedesired local wing segment ∆-model parametersare estimated also by using a nonlinear regressiontechnique. The resulting fit of lift and drag coef-ficient is shown in Fig. 11 for one example wingsegment.

The CFD results are well matched using the basemodel formulation. Furthermore, the combinationof base and ∆-model to cover the icing degrada-tion does not show significant deviations from theCFD results. Consequently it is assumed, that the∆-model structure and its parameter estimates re-liably cover the aerodynamic changes of each wingsegment due to ice accretion. The local segmentcoefficients are related to the complete wing sur-face area (see for example equation (21)), which

1Note that the data are clipped for further processing to anangle of attack range without unreliable post-stall behavior


9©2016

−5 0 5 10

−0.2

0

0.2

0.4

0.6

0.8


Seg

men

tLi

ftC

oef

fici

entCi L

[-]

0 0.02 0.04

−0.2

0

0.2

0.4

0.6

0.8

Segment Drag Coefficient C iD [-]

Seg

men

tLi

ftC

oef

fici

entCi L

[-]

CFDRef.modelRef.

CFDIcemodelIce

Figure 11: Comparision of wing segment lift and drag coefficient, i = 6, N = 20

−5 0 5 10

−0.2

0

0.2

0.4

0.6

0.8


Lift

Co

effi

cien

tCL

[-]

0 0.02 0.04 0.06

−0.2

0

0.2

0.4

0.6

0.8


Lift

Co

effi

cien

tCL

[-]

CFDRef.CFDIce

modelRef.,∑N

modelIce,∑N

Figure 12: Comparision of complete aircraft lift and drag coefficient, N = 20

allows the direct summation of all individual wingsegment ∆ model results to the complete icing in-fluence. Figure 12 shows a comparison of lift anddrag curves for local summed influences (after pa-rameter estimation) and complete aircraft CFD re-sults. The good matches of the results indicate thatthe proposed method to cover local aerodynamicicing effects is well applicable.

The final step is to transfer the obtained ∆-model parameter estimates to values usable in theATTAS simulation model. The available simula-tion model identified from flight data contains dif-ferent parameter values than the parameter es-timates obtained for the clean basic model fromthe CFD results. These results are calculated with-out engine pylons, which have an influence onthe wing flow and consequently on the completeaircraft drag. Therefore the herein estimated ∆-model parameters are linearly transformed for theusages with the identified aircraft model. The cor-responding segment parameter estimates of the ∆-model (N = 20 wing segments) are given in Tab. 5.

5 LOCAL ICING INFLUENCE ON AIRCRAFTBEHAVIOR

For the aircraft simulation it is suitable to allowa fading between the base aircraft and the icingdegradation, instead of suddenly switching on theicing influence. An additional fading factor k iIce,which describes the icing severity [11], is used toscale each segment’s ∆-model parameters duringthe simulation:

k i(·),Sim(t) = k iIce(t) · k i(·). (31)

If k iIce is set to zero for all segments, the aircraft be-havior is only influenced by the base aerodynam-ics. For all other values of k iIce, the aircraft’s aero-dynamic behavior is degraded due to the icing ef-fects activated in the simulation by the ∆-model.This allows to simulate ice accretion by slowly in-creasing k iIce as well as de-icing using a sudden k iIcedecrease. The changes in lift curve and drag po-lar between the base and icing degraded aircraftfor different values of k1−20Ice (symmetric ice case) is


10©2016

−5 0 5 10 15

−0.5

0

0.5

1

1.5


Lift

Co

effi

cien

tCL

[-]

0.05 0.1 0.15 0.2 0.25

−0.5

0

0.5

1

1.5


Lift

Co

effi

cien

tCL

[-]

k1−20Ice = 0.0

k1−20Ice = 0.25

k1−20Ice = 0.5

k1−20Ice = 0.75

k1−20Ice = 1.0

Figure 13: Adaption of ATTAS aerodynamic characteristics for wing icing by the ∆-model (N = 20)

given in Fig. 13, using the transfered segment pa-rameters given in Tab. 5.

The herein developed ∆-model provides the ca-pability to only degrade the aerodynamics of cer-tain wing parts represented by the individual seg-ments. This provides the possibility to simulateasymmetric icing effects on an aircraft’s dynamicmotion. To demonstrate this capability, the aero-dynamic model is evaluated for different anglesof attack between −5 and 17 and a flight in10000 ft with Mach 0.3, which corresponds to thecase used for the CFD calculation.

The additional rolling moment coefficient∆C il ,WIce generated by each segment i ∈ [11, 20]

(k iIce = 1.0, k1−10Ice = 0.0) on the right wing are givenin Fig. 14 to analyze each wing segment’s degrad-ing influence on the lateral aircraft aerodynamics.The maximum rolling influence for high angles of

attack α > 12 result from segments # 17 and # 18

in Fig. 9. The significant lift degradation for thesesegments in combination with the large lever armcause the large rolling moments. The additionalrolling moments of segments # 19 and # 20 aresmaller because of the smaller corresponding liftdegradation due to small segment surfaces. Forangles of attack between 0 and 10 the outer seg-ments show the strongest influence because thelarge lever arms and the gradual degrading effectsof the wing span. Similar results are obtained forthe individual yawing moment coefficient ∆C in,WIceof each right wing segment given in Fig. 14.For lower angles of attack up to 10, the outerwing segments gradually influence the additionalyawing moment. But with α > 10 the segments# 17 and # 18 show the most significant effectbecause of the combination of drag increase andlarge lever arm.

−5 0 5 10 15

0

0.005

0.01

0.015


add

.ro

llin

gm

om

ent

coef

fici

ent

∆Ci l,WIce

[-]

#11 #12

#13 #14

#15 #16

#17 #18

#19 #20

−5 0 5 10 15

0

0.002

0.004

0.006

0.008


add

.ya

win

gm

om

ent

coef

fici

ent

∆Ci n,WIce

[-]

#11 #12

#13 #14

#15 #16

#17 #18

#19 #20

Figure 14: Additional single rolling and yawing moment coefficients due to individually iced right wingsegments (k1−10Ice = 0.0, N = 20)


11©2016

−5 0 5 10 15−0.15

−0.1

−0.05

0


add

.ro

llin

gm

om

ent

coef

fici

ent

∑i

∆Ci l,WIce

[-]

case 1 case 2case 3 case 4case 5 case 6case 7 case 8case 9 case 10case 11

−5 0 5 10 15

−0.06

−0.04

−0.02

0


add

.ya

win

gm

om

ent

coef

fici

ent

∑i

∆Ci n,WIce

[-]

case 1 case 2case 3 case 4case 5 case 6case 7 case 8case 9 case 10case 11

Figure 15: Additional complete rolling and yawing moment coefficients due to several iced/ de-iced rightwing segments (k1−10Ice = 1.0)

case k11Ice k12Ice k

13Ice k

14Ice k

15Ice k

16Ice k

17Ice k

18Ice k

19Ice k

20Ice

1 1 1 1 1 1 1 1 1 1 1

2 1 1 1 1 0 1 1 1 1 1

3 1 1 1 1 0 1 1 0 1 1

4 1 0 1 1 0 1 1 0 1 1

5 1 0 1 1 0 0 1 0 1 1

6 1 0 1 1 0 0 1 0 1 0

7 1 0 1 0 0 0 1 0 1 0

8 1 0 1 0 0 0 1 0 0 0

9 0 0 1 0 0 0 1 0 0 0

10 0 0 1 0 0 0 0 0 0 0

11 0 0 0 0 0 0 0 0 0 0

Table 4: Example random de-icing pattern forright wing segments

To further demonstrate the model’s capability ofcovering asymmetric icing effects, model simula-tion results including variable segment icing sever-ity are provided. In Tab. 4 a set of 11 cases is givendescribing a random de-icing pattern for the rightwing segments, which is similar to a distinct acti-vation of certain de-icing installations (like electroimpuls de-icing [32]), whereas the left wing stayscontaminated (k1−10Ice = 1.0). This could be seen asa left side de-icing system malfunction. The firstcase contains a complete iced wing (k11−20Ice = 1.0)and case 11 a fully de-iced right wing (k11−20Ice = 0.0).The additional rolling moment coefficient as a sumof each segments individual influence is given inFig. 15 versus the angle of attack. Because of thede-icing cases all moments are opposed to the in-dividual moment coefficients in Fig. 14. Similarto the individual icing analysis the influence in-creases with the angle of attack and beginning

wing separation. With all right wing segments de-iced the additional rolling moment

∑i ∆C il ,WIce also

shows a strong increase of icing influence over 10

and reaches almost a value of −0.136 at an an-gle of attack of 15, which corresponds to about118 % of the clean aircraft roll control authority.Hence, the aircraft would be uncontrollable in thatcase. Comparable results are obtained for the ad-ditional yawing moments coefficient

∑i ∆C in,WIce,

which reaches a maximum value of about −0.062

for the asymmetric ice case (k11−20Ice = 0.0) at α =

15.

Using the in Tab. 4 given pattern for the rightwing, the aircraft motion for an asymmetric wingde-icing case can be simulated with the developedmodel. The pattern is therefore transfered to ade-icing command for each individual segment i ,changing the corresponding state of the severityfactor k iIce linearly from 1 to 0 within 0.2 s. Af-ter one segment is fully de-iced the process is trig-gered for the next segment according to the pre-defined pattern. To demonstrate these model ca-pabilities a de-icing example case beginning witha trimmed steady horizontal flight in 10000 ft withan indicated airspeed of 160 kt is simulated, withthe de-icing process starting after 6 s of simulationtime. The resulting time histories of several aircraftstates and outputs are given in Fig. 16 illustratingthe aircraft’s behavior during and after the rightwing is de-iced. No counteracting pilot inputs areapplied, which results in an uncontrolled flight af-ter the aircraft is asymmetrically de-iced. The de-icing starts with segment # 15, which is located inthe mid part of the wing, followed by the furtheroutboard segment # 18. The aircraft starts to roll


12©2016

0 2 4 6 8 10 12 14−0.03

−0.02

−0.01

00

t [s]

∑i

∆Ci l ,WIce

[-]

∑i ∆C

il ,WIce∑

i ∆Cin,WIce −0.01

−0.005

00

∑i

∆Ci n,WIce

[-]

−15

−10

−5

00

p[

/s]

pr −5

00

r[

/s]

−100

−50

00

Φ[

]

Φα

6

7

8

α[

]

160

170

180

VIAS

[kt]

VIASH 9 800

10 000

H[f

t]

0

0.5

1

0

ki Ice

[-]

k11Ice k12Ice k13Ice k14Ice k15Icek16Ice k17Ice k18Ice k19Ice k20Ice

Figure 16: Dynamic aircraft behavior for right wing de-icing with random pattern (k1−10Ice = 1.0)

and yaw to the left resulting in a spiral motion.With all segments de-iced the aircraft’s rolling rateexceeds 15/s and due to the spiral motion the air-speed increases with a loss of altitude.

According to Fig. 14 each segment has a differ-ent influence on the lateral moments and henceresulting aircraft motion, which also manifests inthe dynamic aircraft simulation. A detailed timehistory plot of the resulting additional lateral mo-ments and the rotational accelerations p & r forthe simulated de-icing process between t = 6 and8 s is given in Fig. 17. Depending on the positionand the aerodynamic influence of each segment,the resulting contribution to the additional lateralmoments is different during de-icing. The inboardsegments # 11 to # 14 have a small additional in-fluence on the rolling motion at medium angles ofattack – as given in Fig. 14 – which means, that theadditional rolling moment caused by the de-icingis also small. The removal of the ice influence ofsegment # 12 beginning at 6.4 s or segment # 11

beginning at 7.4 s results in only a small additionalvalue of ∆C il ,WIce. During the de-icing of segment# 12, the roll damping influence of the wing dom-inates the roll acceleration and eliminates the ad-ditional de-icing influence. For de-icing of seg-ment # 11, the damping influence exceeds the ad-

ditional roll influences, and the aircraft’s roll ac-celeration is reduced. In contrast, the removal ofthe ice influence at the outboard segment # 19 att = 7.2 s significantly increases the roll accelera-tion although the aircraft encounters a large rolldamping influence due to the established rollingmotion. A similar behavior with reduced effects isvisible for the yaw influence given also in Fig. 17.

With these first results, it can be stated, thatthe new ∆-model formulation allows to reliably ac-count for local wing icing effects and consequentlythe behavior during and after icing removal.

6 CONCLUSION

In this paper a methodology to formulate the lo-cal degrading effects of icing on aircraft aerody-namics in a dynamic simulation is presented. Thedeveloped ∆-model formulation allows to use anarbitrary number of segments distributed over thecomplete wing span which are individually respon-sible for the local aerodynamic degradation. Withinformation of the iced aerodynamics availablethrough various different sources, the correspond-ing model parameters of each segment can be de-termined.


13©2016

6 7 8−0.03

−0.02

−0.01

00

t [s]

∑i

∆Ci l,WIce

[-]

∑i ∆C

il ,WIce

−0.01

−0.005

00∑i

∆Ci n,WIce

[-]∑

i ∆Cin,WIce

−10

−5

00

p[/s2

]

pr −1.5

−1

−0.5

00

r[/s2

]

0

0.5

1

0

ki Ice

[-]

k11Ice k12Ice k13Ice k14Ice k15Icek16Ice k17Ice k18Ice k19Ice k20Ice

Figure 17: Additional lateral moments during rightwing de-icing with random pattern(k1−10Ice = 1.0, detailed plot of Fig. 16)

In the given example, the ∆-model is used to ac-count for icing effects on the former DLR researchaircraft VFW 614 ATTAS. The results of CFD calcu-lations of a three-dimensional ATTAS aircraft ge-ometry with and without attached ice shapes arethe base for the ∆-model parameter estimation.With the resulting new aerodynamic model the air-craft behavior for different icing cases was eval-uated. The simulation of an asymmetric de-icingcase where a random pattern is used to segment-wise remove the right wing degradation shows themodel capabilities and allows to evaluate the air-craft behavior in this special case as a first result.

With the herein developed model further eval-uations concerning the flight performance, flight

dynamic changes, altered handling qualities willbe conducted. Also an additional formulation forthe degradation of the horizontal tailplane will bedeveloped similar to the wing ∆-model and de-grading effects of icing on control surfaces will betaken into account to analyze the aircraft control-lability. New results of CFD calculation for differ-ent ice shapes – generated with the new DLR icingcode TAUICE [33] – attached to the ATTAS aircraftwill result in different parameter sets and there-fore further analysis. Hence, the differences be-tween ice shapes with distinct degrading aerody-namic influences on the aircraft will be evaluated.

References

[1] Bundesstelle für Flugunfalluntersuchung, FinalReport (BFU 5X011-0/98). April, 2001, Braun-schweig, DE.

[2] Green, Steven D.: A Study of U. S. Inflight Ic-ing Accidents and Incidents, 1978 to 2002. 44thAIAA Aerospace Sciences Meeting and Exhibit,Reno, Nevada, USA, January 9th - 12th, 2006.American Institute of Aeronautics and Astro-nautics, Inc. (AIAA), Paper No. AIAA 2006-82.

[3] National Transportation Safety Board (NTSB),Aircraft Accident Report (NTSB/AAR-96/01,DCA95MA001), Safety Board Report. July 9th,1996, Washington, DC, USA.

[4] Advisory Group for Aerospace Research & De-velopment (AGARD): Ice Accretion Simulation.AGARD Advisory Report 344, Fluid DynamicsPanel Working Group 20, North Atlantic TreatyOrganization (NATO), Neuilly-Sur-Seine, France,December, 1997.

[5] Gray, Vernon H.: Prediction of aerodynamicpenalties caused by ice formations on variousairfoils. Technical Note D-2166, National Aero-

Segment i1 / 20 2 / 19 3 / 18 4 / 17 5 / 16 6 / 15 7 / 14 8 / 13 9 / 12 10 / 11

k iCL0 0.21201 0.19140 0.04382 −0.05401 −0.08956 −0.11607 −0.12817 −0.13397 −0.14374 −0.05904k iCLα,WB −0.24934 −0.26912 −0.24910 −0.21078 −0.17369 −0.16700 −0.16903 −0.15869 −0.12378 −0.05569k iCD0 0.52586 0.47511 0.35921 0.24237 0.15032 0.09803 0.06483 0.03718 0.01488 0.04313

d ik1 −0.05730 −0.05288 −0.03536 −0.02347 −0.00928 −0.00505 −0.00419 −0.00714 −0.00244 0.02295

k ik2 4.14728 1.81220 1.74388 1.14707 0.62762 0.63235 0.67946 0.72906 0.89423 0.32086

k i∂CD∂X

−0.48488 0.30413 0.20761 0.20098 0.22990 0.23328 0.33554 0.56470 0.21009 −0.02237

k iα? −0.27097 −0.29210 −0.31879 −0.32208 −0.32543 −0.32986 −0.33705 −0.34259 −0.36263 −0.34640k ic1 0.37557 0.00000 0.94870 0.93992 0.62499 1.07812 2.40925 4.01841 4.34672 1.57112

Table 5: Estimated ∆-model parameters (N = 20)


14©2016

nautics and Space Administration (NASA), Wash-ington, D.C., USA, Februar, 1964.

[6] Broeren, Andy P.; Whalen, Edward A.; Busch,G. T. and Bragg, Michael B.: Aerodynamic Sim-ulation of Runback Ice Accretion. Journal ofAircraft, Vol. 47, No. 3, pp. 924–939, May-June,2010.

[7] Ranuado, Richard J.; Batterson, J. G.; Reehorst,A. L.; Bond, T.H. and O’Mara, T. M.: Determi-nation Of Longitudinal Aerodynamic DerivativesUsing Flight Data From An Icing Research Air-craft. 27th AIAA Aerospace Science Meeting,Reno, Nevada, USA, January 9th - 12th, 1989.American Institute of Aeronautics and Astro-nautics, Inc. (AIAA), Paper No. AIAA 89-0754.

[8] Ratvasky, Thomas P. and Ranuado, Richard J.:Icing Effects on Aircraft Stability and Control De-termined from Flight Data. Preliminary Results.31st AIAA Aerospace Science Meeting and Ex-hibit, Reno, Nevada, USA, January 11th - 14th,1993. American Institute of Aeronautics and As-tronautics, Inc. (AIAA), Paper No. AIAA 93-0398.

[9] Lee, Sam; Barnhart, Billy P. and Ratvasky,Thomas P.: Dynamic Wind-Tunnel Testing of aSub-Scale Iced S-3B Viking. AIAA Atmosphericand Space Environments Conference, Toronto,Ontario Canada, August 2th - 5th, 2010. Amer-ican Institute of Aeronautics and Astronautics,Inc. (AIAA), Paper No. AIAA 2010-7986.

[10] Gingras, David R.: Requirements and Model-ing of In-flight Icing Effects for Flight Training.AIAA Modeling And Simulation Technologies(MST) Conference, Boston, Massachusetts, USA,August 19th - 22th, 2013. American Institute ofAeronautics and Astronautics, Inc. (AIAA), PaperNo. AIAA 2013-5075.

[11] Bragg, Michael B.; Hutchison, Tim; Merret,Jason; Oltman, R. and Pokhariyal, Davesh: Ef-fect of Ice Accretion on Aircraft Flight Dynam-ics. 38th AIAA Aerospace Science Meeting andExhibit, Reno, Nevada, USA, January 10th - 13th,2000. American Institute of Aeronautics and As-tronautics, Inc. (AIAA), Paper No. AIAA 2000-0360.

[12] Brown, Anthony P.: Negative Speed Stabil-ity, a Factor in Transport Airplane Icing Upsets.20th AIAA Applied Aerodynamics Conference,St. Louis, Missouri, USA, June 24th - 26th, 2002.American Institute of Aeronautics and Astro-nautics, Inc. (AIAA), Paper No. AIAA 2002-3051.

[13] Whalen, Edward A.; Lee, Sam; Bragg,Michael B. and Ratvasky, Thomas P.: Charac-terizing the Effect of Ice on Aircraft Perfor-mance and Control from Flight Data. 40th AIAAAerospace Sciences Meetings and Exhibit, Reno,Nevada, USA, January 14th - 17th, 2002. Amer-ican Institute of Aeronautics and Astronautics,Inc. (AIAA), Paper No. AIAA 2002-0816.

[14] Deters, Robert W.; Dimock, Glen A. and Selig,Michael S.: Icing Encounter Flight Simulator.Journal of Aircraft, Vol. 43, No. 5, pp. 1528–1537, September, 2006.

[15] Lampton, Amanda and Valasek, John: Predic-tion of Icing Effects on the Dynamic Response ofLight Airplanes. Journal of Guidance, Control,and Dynamics, Vol. 30, No. 3, pp. 722–732, May-June, 2007.

[16] Ratvasky, Thomas P.; Barnhart, Billy P.; Lee,Sam and Cooper, Jon: Flight Testing an Iced Busi-ness Jet for Flight Simulation Model Validation.45st AIAA Aerospace Science Meeting and Ex-hibit, Reno, Nevada, USA, January 8th - 11th,2007. American Institute of Aeronautics and As-tronautics, Inc. (AIAA), Paper No. AIAA-2007-0089.

[17] Jategaonkar, Ravindra V.: Flight Vehicle Sys-tem Identification - A Time Domain Methodol-ogy: Second Edition, volume 245 of Progress inAstronautics and Aeronautics. American Insti-tute of Aeronautics and Astronautics, Inc., 1801Alexander Bell Drive, Reston, Virginia 20191,USA, 2015.

[18] Deiler, Christoph: Time Domain OutputError System Identification of Iced AircraftAerodynamics. Deutscher Luft- und Raum-fahrtkongress, Rostock, September 22th - 24th,2015. Deutsche Gesellschaft für Luft- und Raum-fahrt (DGLR).

[19] Deiler, Christoph: Aerodynamic Modeling,System Identification and Analysis of Iced Air-craft Configurations. AIAA Aviation Forum andExibition, Washington D.C., USA, June 13th -17th, 2016. American Institute of Aeronauticsand Astronautics, Inc. (AIAA).

[20] Ruff, G.A. and Berkowitz, B.M.: Users Man-ual for the NASA Lewis Ice Accretion Predic-tion Code (LEWICE). Technical Report NASA CR-185129, NASA, 1990.

[21] Foss Van Zante, J.: A Database of SupercooledLarge Droplets Ice Accretions. Technical ReportNASA/CR – 2007-215020, NASA, 2007.


15©2016

[22] Ghenai, C and Gin, C. X.: Verification and Vali-dation of NASA LEWICE 2.2 Icing Software Code.Journal of Aircraft, Vol. 43, No. 5, pp. 1253–1258, September-Oktober, 2006.

[23] Gerhold, Thomas: Overview of the HybridRANS Code TAU, MEGAFLOW - Numerical FlowSimulation for Aircraft Design. Notes on Numer-ical Fluid Mechanics and Multidisciplinary De-sign, Vol. 89, pp. 81–92, 2005.

[24] Menter, F. R.: Two-Equation Eddy-ViscosityTurbulence Models for Engineering Applica-tions. AIAA-Journal, Vol. 32, No. 8, pp. 1598–1605, August, 1994.

[25] Knopp, Tobias; Eisfeld, Bernhard and Bar-tolome Calvo, Javier: A new extension for k-ωturbulence models to account for wall rough-ness. International Journal of Heat and FluidFlow, Vol. 30, No. 1, pp. 54–65, February, 2009.

[26] CentaurSoft, CENTAUR Software. retrievedJune, 2016, http://www.centaursoft.com.

[27] Mönnich, Wulf: Ein 2-Punkt-Aerodynamikmodell für die Identifizierung.Symposium ’Systemidentifizierung in derFahrzeugdynamik’. DFVLR Mitteilung 87-22,Paper No. 3.1, 1987, in German.

[28] Fischenberg, Dietrich and Jategaonkar, Ravin-dra V.: Identification of Aircraft Stall Behaviorfrom Flight Test Data. RTO - MP - 11. Paper No.17, March, 1999.

[29] Jategaonkar, Ravindra: ldentification of theAerodynamic Model of the DLR Research Air-craft ATTAS from Flight Test Data. DeutscheForschungsanstalt für Luft- und Raumfahrt e. V.(DLR), Köln, September, 1990.

[30] Fischenberg, Dietrich: Identification of an un-steady aerodynamic stall model from flight testdata. AIAA Atmospheric Flight Mechanics Con-ference, pages 138–146, Baltimore, Maryland,USA, August 7th - 10th, 1995. American Instituteof Aeronautics and Astronautics, Inc. (AIAA), Pa-per No. AIAA 95-3438-CP.

[31] Seher-Weiß, Susanne: FitlabGui - A VersatileTool for Data Analysis, System Identification andHelicopter Handling Qualities Analysis. 42nd Eu-ropean Rotorcraft Forum, Lille, France, 5th - 8thSeptember, 2016.

[32] Sommerwerk, Hannah; Horst, Peter and Bans-mer, Stephan: Studies on Electro Impulse De-Icing of a Leading Edge Structure in an Icing

Wind Tunnel. AIAA Aviation Forum and Exibi-tion, Washington D.C., USA, June 13th - 17th,2016. American Institute of Aeronautics and As-tronautics, Inc. (AIAA).

[33] Steiner, Jan: Development of a 2D ice ac-cretion computational method. DeutscherLuft- und Raumfahrtkongress, Braunschweig,September 13th - 15th, 2016. DeutscheGesellschaft für Luft- und Raumfahrt (DGLR).


16©2016

http://www.centaursoft.com

Dynamic Aircraft Simulation Model Covering Local Icing Effects · code LEWICE, Version 2.2 [22]. A...

Documents

Transcript of Dynamic Aircraft Simulation Model Covering Local Icing Effects · code LEWICE, Version 2.2 [22]. A...