Simulation with Virtual Reality Visualization of Wing in Surface Effect Craft during Takeoff ManeuverSinggih S. Wibowo1, Hari Muhammad2 and Said D. Jenie3 Research Assistant Department of Aeronautics and Astronautics Insitut Teknologi Bandung e-mail:
[email protected],
[email protected] Associate Professor Department of Aeronautics and Astronautics Insitut Teknologi Bandung e-mail:
[email protected] Professor Department of Aeronautics and Astronautics Insitut Teknologi Bandung 3 Chairman Agency for Assessment and Application of Technology e-mail:
[email protected] 3 2 1 Abstract The takeoff maneuver of Wing in Surface Effect (WiSE) craft is very important to be considered and analyzed because it has significant influence to overall flight performance. The analysis of the take off maneuver is not an easy task since it needs the understanding of both aerodynamic and hydrodynamic characteristics of the craft. The proper model of its aero and hydrodynamic characteristics is a major requirement for the analysis. This paper describes the mathematical modeling of aero-hydro characteristics of WiSE craft which is suitable for simulating takeoff maneuver. The aerodynamics coefficients were calculated and predicted using Digital DATCOM, while the hydrodynamic properties were modeled for transitional and planing modes. The simulation is carried out by solving the equation of motion which was derived based on Newton-Euler approach. MATLAB/Simulink is used for the simulation, and combined with Virtual Reality (VR) toolbox for visualization of the motion to give real illustration. Keywords – aerodynamics, hydrodynamics, takeoff maneuver, mathematical model, simulation, virtual reality Nomenclature u, w θ,q Fx , Fz FN , FA CN , C A CD CL Cm FB I yy g M m α pitch angle and pitch rate total external forces components in x and z-axes respectively aerodynamics normal and axial forces aerodynamics normal and axial force coefficients aerodynamics drag coefficient aerodynamics lift coefficient aerodynamics pitching moment coefficient buoyant force inertia of the vehicle about the y-body axes system gravity constant total moment due to thrust, aero and hydrodynamic mass of the vehicle angle of attack 1 Introduction T ,T x z velocity components in x and z-body axes system respectively thrust components in x and z-body axes system respectively The Wing-in-Surface-Effect craft is an air vehicle which operates at very low-altitude to gain an improved aerodynamic lift-drag ratio. The phenomenon is known as ground effect. This effect appears at about one wing chord distance from the ground. This phenomenon leads to fuel efficiency and finally reducing the flight cost. The usage of this effect has been discovered in nature where birds and flying fish spend less energy moving in the vicinity of water surface [1]. The other advantage of the craft is its amphibious capability. The crafts can takeoff and land from any flat surfaces such as water, snow, and ground, and therefore eliminate the need for building expensive airports. Its speed is much higher than that of ships, with operational expenses much lower than those of airplanes. These advantages make the WiSE craft a promising transportation means of the near future. The present work deals with the dynamics of WiSE craft. This dynamic model of the vehicle is a nonlinear model based on Newton-Euler equation of motion. The WiSE craft which will be considered here is takeoff and land on water. Therefore, the mathematical model of vehicle motion during takeoff maneuver includes hydrodynamic modeling, besides aerodynamic and propulsion modeling. Numerical integration is used for examining the equation of motion. Virtual Reality visualization was developed to give real illustration of the motion. The modeling and simulation of the WiSE craft is performed for the purpose of analyzing the takeoff maneuver of the vehicle. Figure 2: Radio Control model of WiSE 18 pax during low altitude cruise [2] 2 Dynamic of WiSE Craft Table 1: Radio control (RC) model parameters of WiSE 18 pax [2] Parameter Take Off Weight, kg Cruising speed, kts CL cruise Wing area, m2 Aspect Ratio Wing Span, m Engine power, hp Remote Control (RC) Model 40 40 0.6 2.52 3 2.75 11 Full Scale 7800 100 0.5 100 3 17.32 975 The dynamics of WiSE is the same with the aircraft. Its motion actually is 6-DOF (six degree of freedom) motion. It consists three translational and three rotational motions. The 6-DOF motions of aircraft commonly divide into two groups, longitudinal and lateral-directional modes. The first mode, longitudinal motion, describes the motion in longitudinal plane, OX b Z b . The second mode describes the motion in lateral, OYb Z b and directional plane OX bYb . In this paper, we will only consider the longitudinal motion of WiSE. It consist two translational and one rotational motion, and therefore, this motion also called 3-DOF (three degree of freedom) motion. 2.1 The Equation of Longitudinal Motion Using the Newton-Euler equations, the translational and angular motions of the vehicle, in body axis, can be derived as the following set equations: Tx + Fx − qw − g sin θ m T + Fz + qu + g cos θ w= z m M q= I yy u= In this paper, the WiSE craft that will be considered is a RC model of WiSE 18 pax having parameters as shown in Table 1. Figure 1 and Figure 2 show the RC model of the WiSE craft during flight test. (1) θ =q where u is velocity in x -axis, w is velocity in z -axis, q is pitch rate, Tx is thrust component in x -axis, Tz is thrust component in z -axis, Fx is total external (aerodynamic and hydrodynamic) force in x -axis, Fz is total external force in z -axis, M is total moment (moment due to thrust, aero, and hydro), g is gravity constant, m is mass of the aircraft, I yy is inertia of the aircraft, θ is pitch angle. Figure 1: Radio Control model of WiSE 18 pax during planing motion on the water [2] 2.2 Aerodynamics Aerodynamic characteristics of WiSE were calculated and predicted using Digital DATCOM, a computer program that predicts the stability and control derivatives of airplane. The software commonly used for aircraft design for its accuracy and fast calculation. We present the aerodynamic characteristics of the aircraft in Figure 4, Figure 5, and Figure 6. The data is taken from Ref. [4]. CD Aerodynamic Drag Coefficients 0.12 0.1 0.08 0.06 0.04 0.02 H=0 H = 0.17 m H = 0.33 m Free Air 0 1 2 3 4 5 6 0 -3 -2 -1 Alpha [deg] Figure 5: Aerodynamic drag coefficient as function of angle of attack at various altitudes [6] Figure 3: Aerodynamic lift and drag, and thrust vectors [6] The lift and drag coefficients then transformed to the axial and normal force coefficients, to accommodate the simulation. Note that the simulation will be done in body axis. Using Figure 3, Figure 7 and transformation procedures explained in [5], [6], and [8], the transformation of lift and drag coefficients to axial and normal force coefficients can be expressed as C A (α , h ) = CL sin α − CD cos α CN (α , h ) = −CL cos α − CD sin α Aerodynamic Pitching Moment Coefficients 0.15 0.1 0.05 Cm 0 -3 -2 -1 -0.05 H=0 H = 0.17 m H = 0.33 m Free Air Alpha [deg] 0 1 2 3 4 5 6 (2) (3) -0.1 -0.15 The aerodynamic force then expressed as FAx = ρV SC A (α , h, δ e ) 1 2 2 (4) (5) Figure 6: Aerodynamic pitching moment coefficient as function of angle of attack at various altitudes [6] FAz = ρV SCN (α , h, δ e ) 1 2 2 where V = u 2 + w2 denotes the speed of vehicle and S denotes reference area. Aerodynamic pitching moment is defined as M A = 1 ρV 2 ScCm (α , h, δ e , q ) 2 (6) Aerodynamic Lift Coefficients 2 1.8 1.6 1.4 1.2 CL 1 0.8 0.6 0.4 0.2 0 -3 -2 -1 0 1 2 3 4 5 6 Alpha [deg] H=0 H = 0.17 m H = 0.33 m Free Air Figure 7: Transformation of lift and drag into normal and axial force 2.3 Hydrodynamics Determination of hydrodynamic of a WiSE is very important since it is the dominant external force and moment acting on the vehicle, before the take-off and after landing maneuver. During takeoff, the motion of a WiSE can be divided into two stages, see Ref. [1]: Figure 4: Aerodynamic lift coefficient as function of angle of attack at various altitudes [6] • Transitional Fr = Cv = V mode, gD 13 when the Froude number < 3, where V is the vehicle speed 10, and Figure 11 show the hydrostatic characteristic of the RC model of WiSE 18 pax craft. The buoyancy force then transformed to the normal and axial force as FBx = FB sin θ FBz = − FB cos θ and D is displacement of the vehicle, • Planing mode with aerodynamic unloading, when Fr > 3. The value, Fr = Cv = 3 is then called critical Froude number. In the two stages above, it is difficult to determine the displacement because it is change with time which cause the difficulty in determining the Froude number. So, we will use another approach by using Cv = V gb as reference Froude number in which the beam b is used as the characteristic length. We then define the critical Froude number is 3. It follows from Ref. [9], which stated the planing condition happen when Cv > 3, and pure planning occur at Cv > 3.6. The complicated stepped form of the fuselage bottom of WiSE, see Figure 8 and Figure 12, cause difficulties in determining its hydrodynamic characteristics, and it will be more difficult during the take-off and landing since the attitude and its displacement change rapidly, see Ref. [10]. Since the hydrodynamic characteristics of the stepped bottom depend essentially on the step geometry and its arrangement, there are not any universal experimental data applicable in design. Practically, the laborious hydrodynamic tests in high speed towing tanks should be carried out for each WiSE project separately, but this is both time consuming and costly. That is why we need proper mathematical modeling for hydrodynamic determination, see Ref. [10]. For this purpose, we will explain here the simple mathematical model that can be use to determine the hydrodynamic characteristics of WiSE, by assuming the stepped bottom as vee-planing surface (hull). We will consider the hydrodynamic in two stages, transitional mode and planing mode. Hydrodynamics in transitional mode: In the transitional mode, the speed of vehicle is still low. Therefore we will consider in this mode, the force acting on the vehicle is only buoyancy force. This force is also known as hydrostatic force. The buoyant force can be expressed in the following relation, see Ref. [11], FB = ρ w gD (8) (9) We define the center of buoyant force is ( x fb , z fb ) in body axis. The moment produced by the force then can be determined using the following relation, M B = FBx z fb − FBz x fb (10) Figure 8: Buoyancy force diagram Buoyancy Force 120 100 Buoyant Force (Kg) 80 60 40 20 0 0.00 theta = -10 theta = -6 theta = 0 theta = 6 theta = 10 deg -0.10 -0.05 0.05 Altitude, H (m) 0.10 0.15 0.20 Figure 9: Buoyant force as function of H and θ (7) Center of Buoyant Force 2.0 theta = -10 theta = -6 theta = 0 theta = 6 theta = 10 deg where ρ w is water density, g is gravity constant, and D is immersed volume or also called displacement. The presence of the buoyancy force FB is a consequence of gravity, because an identifiable volume of fluid has weight. The buoyant force always acts in the opposite direction to OZ h (upward) in order to support the weight of displaced fluid. It follows that FB acts through the centre of gravity of the displaced fluid and consequently for a fluid of constant density it must act through the geometric centre (or ’centroid’) of the volume D , see Figure 8. Figure 9, Figure 1.5 1.0 xfg (m) 0.5 0.0 0.00 -0.5 -1.0 -1.5 Altitude, H (m) -0.10 -0.05 0.05 0.10 0.15 0.20 Figure 10: Center of Buoyant Force, x fb Center of Buoyant Force 0.25 acts in the horizontal direction as shown in Figure 14. Hydrodynamic lift of vee-planing surface is expressed as LH = 1 ρ wV 2 b 2 CLβ 2 (11) 0.20 zfg (m) 0.15 where ρ w is water density, b is beam length, V is vehicle speed, and CLβ is the lift coefficient of vee-planing surface theta = -10 theta = -6 theta = 0 theta = 6 theta = 10 deg 0.10 having dead-rise angle β , that can be calculate using the following empirical formula 0.6 CLβ = CL − 0.0065β CL 0 0 0.05 (12) -0.10 -0.05 0.00 0.00 0.05 Altitude, H (m) 0.10 0.15 0.20 The term CL0 in Equation (12) is the lift coefficient of flat planing surface that can be expressed as ⎛ 0.0095λ 2 ⎞ CL = θ b1.1 ⎜ 0.012 λ + ⎟ Cv2 ⎝ ⎠ 0 Figure 11: Center of Buoyant Force, z fb Hydrodynamics in planing mode: The WiSE hull in front of step differs from the after step. The front step hull has veebottom surface while the the aft-step hull has flat one. The hydrodynamic characteristic of the surfaces are different, so it can be consider as two planning surface, see Figure 13 and Figure 14. (13) where θ b = θ + θ b 0 is the bottom surface trim-angle (in gb is degree), see Figure 13. Here, θ b0 denotes the bottom surface angle at θ = 0, which has value of 2 degree. Cv = V the well-known Froude number in which the beam b is used as the characteristic length, and λ is the ratio between mean wetted length lm and hull-span defined as λ= lm b (14) Equation (13) is not completely empirical but actually has physical significance since, as discussed in Refs. [3] and [12], the first term of the equation represents the dynamics component of the planing load, while the second term corresponds to the buoyant component of the load. Figure 16 shows the hydro lift as function of Cv and λ . The mean wetted length lm is defined as, see again Figure 13, Figure 12: WiSE nomenclature lm = lk + lc 2 (15) where lk is wetted keel length and lc is wetted chine length, both measured from tail tip. Figure 13: Definition of lc , lk , and lm for planing surface The mathematical model of hydrodynamic force of planing surface has been derived in Refs. [3] and [12]. The formula has good agreement with wide range of tank-tests. So we choose this mathematical model for WiSE planing motion. The hydrodynamic force of planing surface can be divided into two form, lift and drag which acting on the center of pressure. The hydrodynamic lift is defined to be acts in the vertical direction, and the hydrodynamic drag is defined to be Figure 14: Hydrodynamic of double planing surface Here, Vw denotes the average fluid velocity along the bottom, and C f is friction coefficient of water. The relation between V , Vw and trim angle θ b , has been defined by Sottorf as shown in Table 2. Using the data in Table 2, we get the following empirical formula Vw = −0.0002θ b3 + 0.0021θ b2 − 0.01θ b + 1 V (19) Figure 15: Definition of hydrodynamic center of pressure Table 2: Average Water Velocity Hydrodynamic Lift Coefficient 0.40 0.35 0.30 0.25 λ=5 λ=6 θb (deg) 0 2 4 6 8 10 12 0.20 0.15 0.10 0.05 0.00 0 λ=4 λ=3 λ=2 λ=1 Vw V 1.00 0.99 0.98 0.96 0.93 0.87 0.76 CL* We define the center of pressure in body axis is ( xcp , zcp ), 2 4 Cv 6 8 10 * Figure 16: Hydrodynamic lift coefficient, CL = CL0 1.1 θb relative to c.g. The center is defined to be lies on the keel line, see Figure 15. It can be determined using the following empirical formula, derived by Savitsky in Ref. [12]: ⎛ ⎞ 1 lcp = ⎜ 0.75 − ⎟ λb ⎜ 3.06 λC + 2.42 ⎟ ⎝ ⎠ 2 v 32 Hydrodynamic Friction Coefficient Using Schoenherr Equation 7 6 5 CF*1000 (20) Using Figure 14 and Figure 15, it follows that xcp = lcp − xcg , while zcp is function of xcp , which determined manually using the figure. The friction coefficient is calculated using Schoenherr equation; see Ref. [13], log ( Re⋅ C f ) = 5 9 13 Log(Re) 17 21 4 3 2 1 0 0.242 Cf (21) where Re is Reynolds number, defined by Re = V λb Figure 17: Friction coefficient υ (22) The difference between wetted keel and chine length is defined by the following empirical formula: lk − lc = b tan β π tan θb here, υ denotes water viscosity. Using Eqn. (21) the friction coefficient can be plotted as Figure 17. The hydrodynamic lift and drag then transformed to the axial and normal force as FHx = LH sin θ − DH cos θ FHz = − LH cos θ − DH sin θ (16) The hydrodynamics drag of vee-planing surface is defined by the following formula (23) (24) DH = D f + LH sin θ b cos θ b (17) Finally, the hydrodynamic moment produced by the hydrodynamic force can be derived as follow M H = FHx zcp − FHz xcp And Df is the friction drag, defined by Df = 1 λb2 2 ρw Vw C f 2 cos β (25) (18) 2.4 Thrust Modeling Another important thing to consider for simulation is the thrust model. Here we will use standard model of propeller engine as explained in Ref. [8]. The model is divided into two modes, the first is static thrust, i.e. the thrust produced by engine from standstill until the velocity reach the minimum velocity ( V = Vstall ), and the second is dynamic thrust i.e. the thrust produced when the vehicle moving at velocity greater than the minimum velocity ( V > Vstall ). In the mathematical form, the thrust model is written as ⎧η V P = constant, for 0 ≤ V < Vstall T =⎨ P for V ≥ Vstall ⎩η V stall In this work, the simulation is carried out using parameter as shown in Table 3. Other parameters such as aerodynamic and hydrodynamic which are also used, have been shown in previous figures, see again section 2.2 and 2.3. The first and second methods were successfully carried out, but the third method was failed. The erroneous result was occurred at the transition point, i.e. at Cv = 3 when the hydrostatic mode is changed instantaneously into hydroplaning mode. (26) Where η denotes propeller efficiency, P is engine power, and Vstall is stalling speed. The thrust direction is assumed to be parallel to xb , which yields Tx = T and Tz = 0 . Using Eqn. (26) the thrust profile can be plotted as shown in Figure 18. Thrust of WiSE 18 pax RC model 700 600 500 400 300 P = 40 % P = 100 % = 11 hp Table 3: Parameter used in simulation Parameter m I yy V0 Value 40 7.7440 Unit Kg Kg.m2 0 5 0 See Figure 26 -4, m/s deg m % deg α 0 ,θ0 P = 80 % H0 Power Setting T (N) P = 60 % δe 200 P = 20 % 100 P=0 0 0 5 10 15 V (m/s) 20 25 30 Figure 19, Figure 20 and Figure 21 show the VR reality visualization of the simulation. This visualization gives real perspective of the motion which help the analyst to understand the motion. Figure 22 trough Figure 25 show the simulation results for the first method. Power or thrust setting for all simulation is shown by Figure 26. Simulation results for the second method are shown in Figure 27 to Figure 29. The last two figures, Figure 30 and Figure 31 show the simulation results for the third method. Figure 18: Thrust profile of WiSE RC model 3 Simulation Procedures and Results The simulation is carried out using MATLAB/Simulink. The virtual reality toolbox is used to develop a visualization of the WiSE craft motion with adequate fidelity. The simulation of the WiSE craft’s motion on the water surface will be performed using the following approaches: (i) Full hydrostatic plus hydrodynamic drag, where the hydrodynamic forces and moments acting on WiSE craft are modeled as hydrostatic forces and moments including hydrodynamic drag. In another word, the motion on the water surface is considered as a transition mode during on water motion. (ii) Hydrodynamic planning, where the hydrodynamic forces and moments acting on WiSE craft are modeled as combination of hydrostatic and hydrodynamic planing, with constant attitude angle as proposed in [7]. The hydrostatic mode is applied for 0 ≤ Cv < 3 and then continued by hydroplaning mode for Cv ≥ 3. (iii) Hydrodynamic planning with free attitude angle. This method is similar to method (ii), but the attitude angle is free which mean that it can be oscillated. This method is more realistic than method (ii) since in the real motion the attitude angle can oscillate easily. Figure 19: VR visualization of WiSE motion, viewed from right observer Incidence and Attitude 20 Alpha Theta 15 10 5 α,θ (deg) 0 -5 -10 -15 -20 0 1 2 3 4 5 6 7 8 9 10 11 Time (s) Figure 20: VR visualization of WiSE motion, viewed from pilot observer Figure 23: Incidence and attitude angle, simulation using first method, δ e = -4 deg Velocity 30 25 20 V (m/s) 15 10 5 0 0 2 4 6 8 10 12 Time (s) Figure 24: Velocity history, simulation using first method, Figure 21: VR visualization of WiSE motion, viewed from right-front observer Motion Path 6 5 4 3 2 1 0 -1 0 δ e = -4 deg H (m) Hydrodynamic Axial Force 200 (N) X (m) Horizontal Path History F 25 50 75 100 125 150 175 200 225 0 -200 -400 0 2 4 6 8 10 12 Xh Time (s) Vertical Path History 6 5 4 3 2 1 0 -1 0 F Zh 250 200 150 100 50 0 0 X (m) Time (s) Hydrodynamic Normal Force 0 (N) 1 2 3 4 5 6 7 8 9 10 11 12 -500 -1000 0 2 4 6 8 10 12 H (m) Time (s) Hydrodynamic Moment 200 M (Nm) 100 0 -100 0 2 4 6 8 10 12 1 2 3 4 5 6 7 8 9 10 11 12 Time (s) h Time (s) Figure 22: Motion path, simulation using first method, δ e = -4 deg Figure 25: Hydro force and moment, simulation using first method, δ e = -4 deg Thrust vs Velocity Thrust (N) 250 200 150 100 0 5 10 15 20 25 30 35 50 Hydrodynamic Axial Force (N) F -50 0 Xh 0 1 2 3 4 5 6 7 8 Velocity (m/s) Thrust History Thrust (N) 300 0 Time (s) Hydrodynamic Normal Force (N) Zh -200 -400 0 1 2 3 4 5 6 7 8 200 100 0 2 4 6 8 10 12 Time (s) Power Setting 100 50 1 F Time (s) Hydrodynamic Moment M (Nm) (%) set 0 P 0 0 h -1 0 2 4 6 8 10 12 1 2 3 4 5 6 7 8 Time (s) Time (s) Figure 26: Thrust history, used for all simulation methods Figure 29: Hydro force and moment, simulation using second method, δ e = -4 deg Hydrodynamic Axial Force 500 Motion Path 5 4 3 2 1 0 0 H (m) (N) Xh 0 -500 -1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 20 40 60 80 100 120 X (m) Horizontal Path History 125 100 75 50 25 0 0 F Time (s) Hydrodynamic Normal Force 0 X (m) (N) F 1 2 3 4 5 6 7 8 Zh -2000 -4000 0 Time (s) Vertical Path History 5 4 3 2 1 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) Hydrodynamic Moment 1000 M (Nm) 1 2 3 4 5 6 7 8 H (m) 500 0 -500 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (s) h Time (s) Figure 27: Motion path, simulation using second method, δ e = -4 deg Incidence and Attitude 20 Alpha Theta 15 Figure 30: Hydro force and moment, simulation using third method Froude Number 3.5 3 2.5 10 5 2 α,θ (deg) 0 C 1.5 -5 v 1 -10 0.5 -15 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -20 0 1 2 3 4 5 6 7 8 Time (s) Time (s) Figure 28: Incidence and attitude angle, simulation using second method, δ e = -4 deg Figure 31: Velocity coefficient, simulation using third method 4 Discussion on Results Pengkajian dan Penerapan Teknologi, BPPT) under contract number 17/KONTRAK/P2TMRB/BPPT/VII/2004. References The simulation results demonstrate the feasibility of the full hydrostatic plus hydrodynamic drag model. This new approach is presented to conduct WiSE craft motion during on water motion, i.e. during take off maneuver. The approach is a simplified model which excludes hydroplaning lift. Hydrodynamic drag is included since in the real condition, the force is always acting on the craft during on-water motion. Therefore it can not be excluded from the dynamic model. An important parameter for evaluating take off performance is the take off distance, sTO . The take off distance for this RC model is defined as the distance from stand still to position where the craft achieved the altitude of 1 meter. Using this model, the take off distance can be determined, i.e. sTO = 180 m as shown in Figure 22. This result is agreed with flight test result, i.e. approximately 200 m. Simulation using the second method is also successfully carried out. Using this model, the take off distance can be determined as sTO = 40 m as shown in Figure 27. This method although can be simulated successfully but have disadvantage, i.e. the assumption of constant attitude angle which are not agreed with the real motion. The third simulation method can not be simulated successfully. This simulation is stopped at transition point ( Cv = 3) where the hydrostatic mode change instantaneously into hydroplaning mode. The erroneous result comes from the discontinuity of hydrodynamic force and moment, see Figure 30. 5 Concluding Remarks [1] N. Kornev and K. Matveev, Complex numerical modeling of dynamics and crashes of wing-in-ground vehicles, AIAA, 2003. [2] H. Muhammad, et. al., Design and development of WIGE 10-20 passengers RC model, tech. rep., ITB and BPPT, 2004. [3] B. V. Korvin-Kroukovsky, D. Savitsky, and W. F. Lehman, Wetted area and center of pressure of planing surfaces, Technical Report SIT-DL-49-9-360, 1949. [4] H. Muhammad, T. Indriyanto, U. Muhdy, and J. Sembiring, Study of perfomance and control of WIGE 10-20 passengers, tech. rep., BPPT-ITB, 2004. [5] S. S. Wibowo, Calculation of aerodynamic characterisitics and analysis of dynamics and stability of rocket RX 250 LAPAN’s two dimensional motion, Undergraduate Thesis, Aeronautics and Astronautics Department, Bandung Institute of Technology, 2002. [6] S. D. Jenie and H. Muhammad, Lecture Notes PN3233 Flight Dynamics, Aeronautic and Astronautic Department, Bandung Institute of Technology, 2004. [7] S. D. Jenie, Analysis of winged ship craft take off maneuver, Technical Report LAGG.TR.06.0004.R, 2006. (in Bahasa Indonesia) [8] G. Ruijgrok, Elements of Airplane Performance, Delft University Press, 1994. [9] G. Fridsma, A systematic study of the rough-water performance of planing boats (irregular waves-part 2), Report SIT-DL-71-1495, 1971. [10] K. Benedict, N. Kornev, M. Meyer, and J. Ebert, Complex mathematical model of the WIG motion including the take-off mode, Ocean Engineering, pp. 315—357, 2002. [11] B. R. Clayton and R. E. D. Bishop, Mechanics of Marine Vehicles, EFN Spoon, Ltd, 1982. [12] D. Savitsky, Wetted length and center of pressure of veestep planing surfaces, Report SIT-DL-51-9-378, 1951. [13] E. J. Mottard and J. D. Loposer, Average skin-friction drag coefficients from tank tests of a parabolic body of revolution (NACA RM-10), NACA Report, 1952. The modeling and simulation method for WiSE craft dynamics during take off maneuver is presented. In this phase, hydrodynamic force and moment is modeled by hydrostatic and Savitsky hydroplaning approach. This modeling is successfully implemented with assumption of constant attitude angle. A new approach was also introduced, i.e. combining full hydrostatic and hydrodynamic drag. This new approach is also successfully implemented with free attitude angle (attitude angle can oscillate freely). The third method, which combine hydrostatic and hydroplaning, with free attitude angle, lead to erroneous result. This erroneous result is occurred due to the limitation of Savitsky hydroplaning method, i.e. only valid for positive pitch angle ( θ > 0). While in realistic simulation, the pitch angle can be easily oscillating from positive to negative. Another source of problem for this method is the discontinuity of hydrodynamic force and moment at the transition point, i.e. at Cv = 3. Acknowledgment This research is fully supported by The Agency for Assessment and Application of Technology (Badan