Armin Troesch: Dynamics and hydrodynamics of high speed craft - PASI

PASI 2010 in Dynamics and Control of Manned and UnmannedMarine VehiclesDynamics and Hydrodynamics of High Speed Craft1400-1545, June 29, 2010Barranquilla, ColombiaArmin TroeschNaval Architecture and Marine EngineeringUniversity of MichiganArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

OUTLINE• Planing Hull Hydrodynamics and DynamicsSelected experiments and theorieswith practical applications• Nonlinear Dynamics Analysis Applied to Planing Hulls• Stochastic Vibro-Impact Model for Extreme PlaningCraft Acceleration EstimationArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

With a little help from friends:Recently Active UM Graduates:Dr. Lixin XuDr. Carolyn Frank JudgeWayne Arguin (USCG)Timothy Conners (USCG)Dr. Richard RoyceTony DanielsDr. Kevin MakiDr. Brant SavanderOscar Tuscan (Dr. to-be)Fredy ZarateAnd many more…….Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Planing and Impact Research at UMKang, K.G. (1988) Non-linear Impact Hydrodynamics. Ph.D. Thesis.Talmor, A. (1991) Non-linear Slender-Body Approach for Predicting Planing Performance, Ph.D. Thesis.Hicks, J.D. (1993) Analysis Method for Planing Hull Vertical Motions. Professional Degree Thesis.Lai, C. (1994) Hydrodynamic and Dynamic Analysis of High Speed Planing, Ph.D. Thesis.Akers, R.H. (1995) Planing Hull Design Environment. Professional Degree Thesis.Wang, M. (1995) A Study on Non-linear Free Surface Flows. Ph.D. Thesis.Savander, B.R. (1997) Planing Hull Steady Hydrodynamics. Ph.D. Thesis.Xu, L. (1998) A Theory for Asymmetric Vessel Impact and Steady Planing. Ph.D. Thesis.Judge, C.F. (2000) Impact of Wedges with Horizontal and Vertical Velocities. Ph.D. Thesis.Arguin, W. (2001) Simulation of Planing Hull Dynamics in the Transverse Plane. MSE Thesis.Conners, T. (2001) Coupled Surge, Sway, Roll, and Yaw Hydrodynamic Coefficients for High Speed Planing Craft.MSE Thesis.Royce, R.A. (2001) Impact Theory Extended to Planing Craft with Experimental Comparisons. Ph.D. Thesis.Daniels, A.S. (2002) Design and Construction of the Stepped Planing Hull Dynamometer. Professional Degree Thesis.Maki, K. (2005) Transom Stern Hydrodynamics, Ph.D. Thesis.Tascon, O. (2010) Numerical Computation of the Hydrodynamic Forces Acting on a Maneuvering Planing Hull via Slender BodyTheory - SBT and 2-D CFD Impact Theory. Ph.D. ThesisRose, C. J. (2010) Marine Systems Application of Extreme Value Prediction of a Vibro-Impact System Subject to StochasticExcitation, MSE ThesisZarate, F. (2010) CFD Modeling of Yawed and Heeled High Speed Planing Hulls, MSE ThesisArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Planing Craft Resistance and DynamicsArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Planing Craft Resistance and DynamicsStepsArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Planing Hull DesigngivenHull Particulars (target)Propulsion CharacteristicsEnvironment?AnalysisSteadyPerformance?UnsteadyPerformancePrototypeArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Physics of Planing - Some DefinitionsJetJet headCalmwaterlineJetedgeWetted chineDry chineArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Physics of Planing - Some definitions and idealizationsSlender, low aspect ratio, prismatic hulls:Wagner (1931, 1932), von Karman (1929)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Physics of Planing - Some definitions and idealizationsHigh aspect ratio, flat hulls:Green (1936)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Physics of Planing - Some definitions and idealizationsSlender, low aspect ratio, flat hulls:Tulin (1957)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Physics of Planing - Force and moment balanceRef: Experiments of prismatic planing hulls, Savitsky (1964)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Relationship between planingand impact hydrodynamics• Low order approximation• Coordinate transformation betweentime and longitudinal coordinateX = U t• Transverse plane is equivalent to 2-Dimpact or strip theory approximation ofplaningArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Seminal Work in Impact Hydrodynamics, Wagner (1932) Model:Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Reduction of physical model to 2-D impactsolution spaceyZ ch( x)Hull Cross Section Geometryβ( xz , )hxz ( , ) h o( xz , )y wl( x)zyFlow Physicsvwz c( x )v n( z)C p( z)v s( z)v jetv s( z)y wl( x) zV( x)z b( x)ApproximationPlaning surface passing through earth-fixed planev=∂φ∂yw=∂φ∂zyv n body ,=v n fluid ,C p( z) = 0vz ( )zSlender Body Theory Planing Model, Savander, et al. (2002)γ( z) = 2w( z) ≠ 0γ = w = 0Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

The Boundary Value Problem• Nonlinear dynamic free surface boundary condition( V s − z cτ ζ) ∂V s∂ζ + z dV scdτ = 0• Body kinematic boundary conditionγ c ( ζ, τ) =−2cosβ ( ζ,τ)ζκ ( ζ, τ )⎡⎢1 −ζ 2 ⎢ V()+ τ1⎢ π⎣+ ζ2 −1πb( τ)∫s=1γ s ( s,τ)dsκ( s, τ) s 2 −11≤ζ≤b()τb( τ)∫s=1( )( s 2 −ζ 2 )γ s ( s,τ)ds( )κ( s, τ) s 2 − 1⎤⎥⎥⎥⎦+0 ≤ z ≤ z c ( τ)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

The Boundary Value Problem, con’t.• Velocity continuity condition (i.e. Kutta condition)V()+ τ1 πbγ s ( s,τ)ds∫ at z = zc(z = 1)s=1 κ( s, τ) s 2 = 0−1( )Total Pressure Coefficient• Displacement continuity condition9.08.0Y wl ( τ)= 2 π1∫s=0cos β ( s,τ)h c ( s, τ)dsκ( s, τ) 1 − s 20.8y/Z ch 0.60.40.20-1-0.500.51-1.00.01.02.03.04.0Y6.05.0x/Z chXZ7.0C p0.0500.0450.0400.0350.0300.0250.0200.0150.0100.0050.000z/Z chArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

3-D Pressure Distribution and Spray SheetBrown&Martin Vorus&Lai Usaero z=0Spray RootKeelC L (Savitsky) 0.091C L (USAERO) 0.053oθ 0 (z=0) 23.29oθ (USAERO) 29.17oθ (Vorus&Lai) 32.88oθ (Brown&Martin) 39.47λ = 0.913, τ = 9 , β = 20ooVariable deadrise 40 mph skiboatCalculations based on 3-Dboundary integral method(Savander, 1997)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

FLUENT 6.1 (CFD) Analysis: Straight Line RunningBass BoatDown Angle Lifting Strake IncludedFLUENT 6.02d, Segregated, VOFLam, Unsteady30Time = 0.150 secU=50mphτ =1.74degx=11.0ft25Transverse Flow @ Transom:50 mphEngine Trim ¼ OutStraight Liney(inches)20151050-50 5 10 15 20 25 30 35 40 45 50x (inches)Starboard Transom of Bass BoatSection Bottom Pressure Comparison1.51.0Ideal FlowSolutionPressure(psI)0.5β = 12 deg0.0FLUENT-0.50 5 10 15 20 25 30 35 40 45 50x (inches)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Conclusions of planing modeling analysis(the more significant ones?)• Modeling the jet separation point (line) is critical toaccurate planing predictions.• Prediction of the correct wetted surface is critical toaccurate planing predictions.• There may be significant non-slender effects for large θ.• The reduction to the z=0 plane works well in the chinesdry regime but less so in the chines wet regime.• Both slender body theory and 3-D Models have thepotential to predict steady lift and drag accuratelyenough for design purposes.Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Validation and Application of TechnologyExtension of 2-D Planing Theory to Innovative Hull Form Design(a) High pressure region in chines dry impact(b) Low pressure region in chines wet impactCalculated variation of deadrise to achieve maximum lift to drag ratioPlan Viewhigh pressurelow pressureArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Validation and Application of TechnologySOLAR SPLASH: Intercollegiate Solar/Electric Boat Regatta featuringThe University of Michigan’s Inverted “V” Planing HullArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

OUTLINE• Planing Hull Hydrodynamics and DynamicsSelected experiments and theorieswith practical applications• Nonlinear Dynamics Analysis Applied to Planing Hulls• Stochastic Vibro-Impact Model for Extreme PlaningCraft Acceleration EstimationArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

RATIONALE FOR DYNAMIC ANALYSIS:Identification of design parameters that arecritical to performance.TitleExample: “A Case Study of Dynamic Instability in aPlaning Hull”, Codega and Lewis. Marine Tech., April,1987Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Problem Definition : Steady Symmetric Planingattached chines drypressure distributionseparated chines wetArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Problem Definition : Steady Asymmetric Planing -Type “A”attached chines dryseparated chines dry/wetArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Problem Definition : Steady Asymmetric Planing -Type “B”keel separation/attached keel separation/chines dryArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Transition to Steady Asymmetric Planing -Type “B”Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Steady Transverse Planing Modeling:Asymmetric Impact TheoryU ( t)≡ V2DW ( t)≡ W2D( x)( x)Type B (U/W = 0.4)Type A (U/W = 0.4)Critical angle β2 versus the corresponding β1 at whichventilation occurs off the keel for different ratios of impactvelocities(Judge et al, 1999Xu et al, 1998, 1999)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Steady Transition to asymmetric planing - Type “B”35 deg deadrise heeled 20 deg 35 deg deadrise heeled 29 degArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Jet RootKeelJet RootJet RootKeelJet RootV/U = 0.52V/U = 1.30V/U = 2.08Jet RootKeelJet RootOnset of SeparationDue to TransverseVelocityDirection of VArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Steady Asymmetric planing due to horizontalvelocityWEstimate of the horizontal velocityrequired for separation:VVW ≅ V jV jβ j β 1W sinβ j− tanβ 1cosβ jtanβ 1β 1 V/W20 o 4.2-4.535 o 2.0-2.5Ref: Xu, Troesch, 1999 and Judge, et al. 2002Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

The Synergy of Experimentsand TheoryExperiments with prismatic hull forms• Steady planing• Unsteady planing - vertical planemotionsFor example: Savitsky (1964), Altman (1968),Fridsma (1969, 1971), De Zwaan (1976), Savitsky &Brown (1976), Troesch (1992), and others…….Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

On the Hydrodynamics of VerticallyOscillating Planing HullsArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Z = m ˙ ˙ η 3 (t)M = I 55 ˙ ˙ η 5 (t)May be Modeled as[ m + A(η;ω) ]{ ˙ η (t)}+ B(η;ω)[ ] ˙[ ] η(t){ η (t)}+ C(η) { }= { F(t) }Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry: Dynamic wetted lengthL(t) = lcg +( ) − ( z wl +η 3 (t))sin( τ−η 5 (t))vcgtan τ−η 5 (t)λ ave = ( λ k +λ c ) 2 + 0.03λ ˆk = λ ˆave + 0.5( 0.57 + 0.001β) ( tan β (2 tan(τ−η 5 )) − 0.006β)− 0.03λ ˆc = λ ˆk − ( 0.57 + 0.001β )( tanβ (2tan(τ−η 5 )) − 0.006β) for λ ˆc ≥ 1Steady mean wetted length from Savitsky (1964)and Savitsky &Brown (1976) modified for motions (Troesch 1992)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry: Dynamic wetted length in heaveWetted keelWetted chineTop of strokeWetted keelBottom of strokeArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry: Dynamic wetted length in heaveTop of strokeBottom of strokeArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry: Dynamic wetted lengthWetted length6Forced static heave Forced static pitch5x 4x3xx2 xx 1x0-0.15 -0.1 -0.05 0 0.05 0.1 0.15η 3 BWetted length6543 xx xxx xx2-2 -1 0 1 2η 5 (deg)Wetted length versus constant heave and pitch displacement. -■-, λave;- - - , Eq. (5); -●-, λk; ––, Eq. (6); -✕-, λc ; - - -, Eq. (7).Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry Dynamic wetted lengthForced heave Forced pitchWetted lengthWetted length2π tT2π tTWetted length during one cycle of heave and pitch oscillation.ξ 3 /B = 0.036, ω Bg= 1.13. + , λ c ; - - -, Eq. (4); ● , λ k ; ––, Eq. (4).Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry: Dynamic wetted lengthForced heave46Chine Wetted length321 xxxxx xx0 0.05 0.1 0.15ζ 3 BKeel Wetted length5432 xxxxx xx0 0.05 0.1 0.15ζ 3 BWetted maximum and minimum chine and keel lengths as a function ofheave amplitude. -●- , λ max; ––, Eq. (4); -✕-, λ min; - - -, Eq. (4); -■-,λaveArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Geometry: Dynamic wetted lengthForced pitch47Chine Wetted length3.532.52x xxx x xxxxxKeel Wetted length6543xxx x xx x x1.50 0.5 1 1.5 2 2.5ζ 5 (deg)20 0.5 1 1.5 2 2.5ζ 5 (deg)Wetted maximum and minimum chine and keel lengths as a function ofpitch amplitude. -●- , λ max; ––, Eq. (4); -✕-, λ min; - - -, Eq. (4); -■-,λave .Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Hydrodynamic stiffness, C 55 and C 33Forced pitch Forced heave0.10.4F 5 ρ V 2 B 30.05 ◆◆◆◆-0.050 ▲ ▲ ▲ ▲◆◆▲ ▲▲ ◆-0.1-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5η 5 (deg)F 3 ρ V 2 B 20.3◆0.2◆◆▲0.1▲ ◆▲▲ ◆▲▲◆◆ ▲0-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15η 3 B: Total vertical force and moment versus constant linear heave and pitchdisplacement. L/B = 3.0 , τ = 4.0 deg. Cv = 1.5; -◆-, exp; ––; Savitsky[14]. Cv = 2.5; -▲-, exp; - - -, Savitsky [14].Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Hydrodynamic stiffness, C 35 and C 53Forced pitch Forced heaveF 3 ρ V 2 B 20.140.120.10.080.060.04◆▲◆▲◆▲◆▲◆▲◆▲◆▲F 5 ρ V 2 B 30.050-0.05-0.1-0.15-0.2▲◆▲◆◆▲◆▲◆▲◆▲◆ ▲0.02-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5η 5 (deg)-0.25-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15η 3 B: Total vertical force and moment versus constant linear heave and pitchdisplacement. L/B = 3.0 , τ = 4.0 deg. Cv = 1.5; -◆-, exp; ––; Savitsky[14]. Cv = 2.5; -▲-, exp; - - -, Savitsky [14].Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Added mass and damping, A 33 and B 33−ω 2 ( m + A 33 )+ iωB 33 + C 33 = f 1 + f 2( ) ζ 3 => ∑ F = m˙ ˙−ω 2 ( −mx cg + A 53 )+ iωB 53 + C 53 = ( f 1 − f 2 )L ζ 3 => ∑ M = 0ζ 3Which reduce toA 33 =( )1 ⎡ mag f 1 + f 2−ω 2 ⎢⎣ mag( ζ 3 )⎤cos( arg( f 1 + f 2 )− arg( ζ 3 ))− C 33 ⎥ − m⎦B 33 = 1 ω( )⎡ mag f 1 + f 2⎢⎣ mag( ζ 3 )( ( ))sin arg( f 1 + f 2 )− arg ζ 3⎤⎥⎦Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Added mass and damping, A 33 and B 33Heave Damping due to HeaveHeave Added Mass due to HeaveωB gωB gAdded mass and damping coefficients in heave versus frequency L/B = 4.0;τ = 6 deg. -▲-, Cv = 1.5; -◆-, Cv = 2.0; -●-, Cv = 2.5 .Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Conclusions of forced motion experimentsWetted length: The wetted length and equivalentlythe wetted surface of an oscillating planing hull isstrongly time dependent. For low to moderateamplitudes of motion, the keel wetted length can betreated kinematically as the intersection between thekeel and a stationary free surface. The chine wettedlength is influenced by spray jet dynamics.Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Conclusions of forced motion experiments(con’t.)Restoring force matrix, C. The restoring force matrixis amplitude dependent. A good approximation forprismatic hulls can be found by applying the resultsof Savitsky [14] with the mean wetted, λ, andeffective trim expressed as functions of the heave andpitch motions.Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Conclusions of forced motion experiments(con’t.)Added mass and damping matrices, A and B. Forlow to moderate planing speeds, Cv=1.5 - 2.5, theadded mass coefficient, and to a lesser extent thedamping coefficient, can be frequency dependent.When the experimental results were analyzed using aconstant restoring force matrix, the added mass anddamping in heave, Aj3 and Bj3, j=3,5 showedrelatively little amplitude dependency compared tothe added mass and damping in pitch, Aj5 and Bj5,j=3,5.Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Planing Hull DesigngivenHull Particulars (target)Propulsion CharacteristicsEnvironment?AnalysisSteadyPerformance?UnsteadyPerformancePrototypeArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

RATIONALE FOR DYNAMIC ANALYSIS:Identification of design parameters that arecritical to performance.TitleExample: “A Case Study of Dynamic Instability in aPlaning Hull”, Codega and Lewis. Marine Tech., April,1987Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

THE ROLE OF SIMULATION IN DESIGNWith regards to the new computer simulators... "Ifyou choose the right parameters, your simulatedexperiment will normally work just like thecorresponding real-world experiment. (However,)there are some edges to this simulated world, and ifyou step over the simulation breaks downbadly..." (Swaine, 1992)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Analysis and Simulation ofNonlinear Planing Hull Dynamics• General description of methods of modernnonlinear systems analysis• Examples of analysisRef: Troesch and Falzarano (1993),Troesch and Hicks (1994)Hicks, Troesch and Jiang (1995)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Analysis and Simulation of NonlinearPlaning Hull DynamicsSimple Model - Complex DynamicsRef: Savitsky (1964)Guckenheimer and Holmes (1983)Thompson and Stewart (1986)Seydel (1988)Troesch (1992)Troesch and Falzarano (1993)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Analysis and Simulation of NonlinearPlaning Hull DynamicsComplex Model - ComplexDynamicsRef: Zarnick (1978)Guckenheimer and Holmes (1983)Seydel (1988)Akers et al. (1999, etc.)Hicks et al. (1994, 1995)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

VERTICAL PLANE EQUATIONS OF MOTIONLinear (unforced) (Martin, 1978)[ A] { ˙ η (t)}+ BEquivalent nonlinear model (unforced) (Hicks et al, 1994)[ A] { ˙ η (t)}+ B[ ] ˙[ ] ˙Equivalent nonlinear model (forced) (Hicks et al, 1994)[ A] { ˙ η (t)}+ B{ η (t)}+ C{ η (t)}+ C (η (t))[ ] ˙[ ] η (t){ }= 0[ ] η (t){ η (t)}+ C (η (t)){ }= 0[ ] η (t){ }= F(t){ }Fully nonlinear simulation (forced) (Zarnick, 1978, Akers, 1994)[ M] { ˙ η (t)}= F(t){ }{}{}Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

SIMULATION:TRANSITIONTOPORPOISINGlcg/B (a) 2.09(b) 2.03(c) 1.98C v = 4.5(Troesch and Hicks, 1994)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

EQUATIONS OF MOTIONLinear (unforced) (Martin, 1978)[ A] { ˙ η (t)}+ BEquivalent nonlinear model (unforced) (Hicks et al, 1994)[ A] { ˙ η (t)}+ B[ ] ˙[ ] ˙Equivalent nonlinear model (forced) (Hicks et al, 1994)[ A] { ˙ η (t)}+ B{ η (t)}+ C{ η (t)}+ C (η (t))[ ] ˙[ ] η (t){ }= 0[ ] η (t){ η (t)}+ C (η (t)){ }= 0[ ] η (t){ }= F(t){ }Fully nonlinear simulation (forced) (Zarnick, 1978, and Akers, 1999, etc.)[ M] { ˙ η (t)}= F(t){ }{}{}Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

η 3(t)BSIMULATEDFORCED RESPONSE2T e(Troesch and Hicks, 1994)t T et T eη 5(t)(deg)2T eC v =4.5ς o B =0.15λ L =2.40ω e B g =2.29Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

OUTLINE• Planing Hull Hydrodynamics and DynamicsSelected experiments and theorieswith practical applications• Nonlinear Dynamics Analysis Applied to Planing Hulls• Stochastic Vibro-Impact Model for Extreme PlaningCraft Acceleration EstimationArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Full Scale MARK V Acceleration Time HistoriesMARK V deck & seat frame acceleration datacollected January 10, 2003 by NSWC-PC.Sea Trial conditions: 3.0 ft significant wave height,8.3 second wave periodArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Extreme Responses in Stochastic Design EnvironmentsStatistics of ImpactSimulated Mark V Acceleration at Bow and Bending Moment(Sea State 2)2Bow Acceleration(G)10-12E+06-2Bending Mo ment (P owerS E A)Bending Mo ment: Calm Water (SHIPMO)Bending Mo ment: Calm Water + RMS (SHIPMO)Bending M oment (lbs- ft)1E+060 100 200 300Time (sec)0-1E +060 100 200 300Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Stochastic Vibro-Impact Model for ExtremePlaning Craft Acceleration EstimationArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Stochastic Vibro-Impact ModelParametric Hardening SpringArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Ensemble of Band-limited ForcingArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Extreme Value Statistics BackgroundElevation PDFMaxima PDFQuantile-Quantile Plot(Weibull Space)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringQ x = log 10 (ξ)( )Q y = log 10 −log 10 ( 1 − P(ξ) )Dynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Stochastic Vibro-Impact Modelζ=0.5, η=0.5, γ=1.0, ε=0.5Quantile-Quantile Plot(Weibull Space)ζ=0.5 (damping ratio), η=0.5(central forcing freq.), γ=1.0(wall stiffness)Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Stochastic Vibro-Impact Model for Extreme PlaningCraft Acceleration Estimation - ApplicationArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Stochastic Vibro-Impact Model for Extreme PlaningCraft Acceleration EstimationQuantile-Quantile Plot(Weibull Space)Extreme Acceleration EstimatesH 1/3 11.5 g 50 g 20” 2’30”2 ft 95’ 600 yr 2.1 g 4.9 g4 ft 19.3” 2’18” 11.8 g 52 g6 ft 8.5” 23” 42 g 254 gArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Summary• Planing Hull Hydrodynamics and DynamicsSelected experiments and theories with practicalapplications- Complex coupled hydrodynamics and dynamics- Appendages play large role in assessingperformance- Steady hydrodynamics relatively mature. Bigchallenge is resolving jet kinematics and geometry- Linear theory can be of use in assessing stabilityboundariesArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Summary• Nonlinear Dynamics Analysis Applied to Planing Hulls- Problem is rich in interesting dynamics andhydrodynamics- Reduced order nonlinear modeling required tounderstand global dynamics- Need to understand underlying physics to supportbrute force Monte Carlo simulations- Role that high fidelity simulators play in design anddesign optimization is not clearArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

Summary• Stochastic Vibro-Impact Model for Extreme Planing CraftAcceleration Estimation- Traditional stochastic analysis assumptions for planingdynamics may be invalid- Extreme values of planing dynamics are the result of highlynonlinear, non-Gaussian processes- Reduced order models have important place in understandingextreme valuesArmin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia

QUESTIONS ???Armin TroeschUniversity of MichiganDepartment of Naval Architecture and Marine EngineeringDynamics and Hydrodynamics of High Speed CraftJune 29, 2010Barranquilla, Colombia