Dear Jonkman,

For a fixed cylinder with only irregular waves in the environment, I use potential flow theory and Morrison equation to provide Cd, using HydroDyn for calculation, as shown below

```
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
1025 WtrDens - Water density (kg/m^3)
250 WtrDpth - Water depth (meters)
0 MSL2SWL - Offset between still-water level and mean sea level (meters) [positive upward; unused when WaveMod = 6; must be zero if PotMod=1 or 2]
---------------------- WAVES ---------------------------------------------------
2 WaveMod - Incident wave kinematics model {0: none=still water, 1: regular (periodic), 1P#: regular with user-specified phase, 2: JONSWAP/Pierson-Moskowitz spectrum (irregular), 3: White noise spectrum (irregular), 4: user-defined spectrum from routine UserWaveSpctrm (irregular), 5: Externally generated wave-elevation time series, 6: Externally generated full wave-kinematics time series [option 6 is invalid for PotMod/=0]} (switch)
0 WaveStMod - Model for stretching incident wave kinematics to instantaneous free surface {0: none=no stretching, 1: vertical stretching, 2: extrapolation stretching, 3: Wheeler stretching} (switch) [unused when WaveMod=0 or when PotMod/=0]
13630 WaveTMax - Analysis time for incident wave calculations (sec) [unused when WaveMod=0; determines WaveDOmega=2Pi/WaveTMax in the IFFT]
0.25 WaveDT - Time step for incident wave calculations (sec) [unused when WaveMod=0; 0.1<=WaveDT<=1.0 recommended; determines WaveOmegaMax=Pi/WaveDT in the IFFT]
7 WaveHs - Significant wave height of incident waves (meters) [used only when WaveMod=1, 2, or 3]
11.9 WaveTp - Peak-spectral period of incident waves (sec) [used only when WaveMod=1 or 2]
3.3 WavePkShp - Peak-shape parameter of incident wave spectrum (-) or DEFAULT (string) [used only when WaveMod=2; use 1.0 for Pierson-Moskowitz]
0.31 WvLowCOff - Low cut-off frequency or lower frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
2.378 WvHiCOff - High cut-off frequency or upper frequency limit of the wave spectrum beyond which the wave spectrum is zeroed (rad/s) [unused when WaveMod=0, 1, or 6]
0 WaveDir - Incident wave propagation heading direction (degrees) [unused when WaveMod=0 or 6]
0 WaveDirMod - Directional spreading function {0: none, 1: COS2S} (-) [only used when WaveMod=2,3, or 4]
1 WaveDirSpread - Wave direction spreading coefficient ( > 0 ) (-) [only used when WaveMod=2,3, or 4 and WaveDirMod=1]
1 WaveNDir - Number of wave directions (-) [only used when WaveMod=2,3, or 4 and WaveDirMod=1; odd number only]
90 WaveDirRange - Range of wave directions (full range: WaveDir +/- 1/2*WaveDirRange) (degrees) [only used when WaveMod=2,3,or 4 and WaveDirMod=1]
123456789 WaveSeed(1) - First random seed of incident waves [-2147483648 to 2147483647] (-) [unused when WaveMod=0, 5, or 6]
RANLUX WaveSeed(2) - Second random seed of incident waves [-2147483648 to 2147483647] for intrinsic pRNG, or an alternative pRNG: "RanLux" (-) [unused when WaveMod=0, 5, or 6]
TRUE WaveNDAmp - Flag for normally distributed amplitudes (flag) [only used when WaveMod=2, 3, or 4]
"" WvKinFile - Root name of externally generated wave data file(s) (quoted string) [used only when WaveMod=5 or 6]
1 NWaveElev - Number of points where the incident wave elevations can be computed (-) [maximum of 9 output locations]
0 WaveElevxi - List of xi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
0 WaveElevyi - List of yi-coordinates for points where the incident wave elevations can be output (meters) [NWaveElev points, separated by commas or white space; usused if NWaveElev = 0]
---------------------- 2ND-ORDER WAVES ----------------------------------------- [unused with WaveMod=0 or 6]
False WvDiffQTF - Full difference-frequency 2nd-order wave kinematics (flag)
False WvSumQTF - Full summation-frequency 2nd-order wave kinematics (flag)
0 WvLowCOffD - Low frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
3.5 WvHiCOffD - High frequency cutoff used in the difference-frequencies (rad/s) [Only used with a difference-frequency method]
0.1 WvLowCOffS - Low frequency cutoff used in the summation-frequencies (rad/s) [Only used with a summation-frequency method]
3.5 WvHiCOffS - High frequency cutoff used in the summation-frequencies (rad/s) [Only used with a summation-frequency method]
---------------------- CURRENT ------------------------------------------------- [unused with WaveMod=6]
0 CurrMod - Current profile model {0: none=no current, 1: standard, 2: user-defined from routine UserCurrent} (switch)
0 CurrSSV0 - Sub-surface current velocity at still water level (m/s) [used only when CurrMod=1]
"DEFAULT" CurrSSDir - Sub-surface current heading direction (degrees) or DEFAULT (string) [used only when CurrMod=1]
20 CurrNSRef - Near-surface current reference depth (meters) [used only when CurrMod=1]
0 CurrNSV0 - Near-surface current velocity at still water level (m/s) [used only when CurrMod=1]
0 CurrNSDir - Near-surface current heading direction (degrees) [used only when CurrMod=1]
0 CurrDIV - Depth-independent current velocity (m/s) [used only when CurrMod=1]
0 CurrDIDir - Depth-independent current heading direction (degrees) [used only when CurrMod=1]
---------------------- FLOATING PLATFORM --------------------------------------- [unused with WaveMod=6]
1 PotMod - Potential-flow model {0: none=no potential flow, 1: frequency-to-time-domain transforms based on WAMIT output, 2: fluid-impulse theory (FIT)} (switch)
1 ExctnMod - Wave-excitation model {0: no wave-excitation calculation, 1: DFT, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES *.ssexctn INPUT FILE]
1 RdtnMod - Radiation memory-effect model {0: no memory-effect calculation, 1: convolution, 2: state-space} (switch) [only used when PotMod=1; STATE-SPACE REQUIRES *.ss INPUT FILE]
60 RdtnTMax - Analysis time for wave radiation kernel calculations (sec) [only used when PotMod=1 and RdtnMod>0; determines RdtnDOmega=Pi/RdtnTMax in the cosine transform; MAKE SURE THIS IS LONG ENOUGH FOR THE RADIATION IMPULSE RESPONSE FUNCTIONS TO DECAY TO NEAR-ZERO FOR THE GIVEN PLATFORM!]
0.1 RdtnDT - Time step for wave radiation kernel calculations (sec) [only used when PotMod=1 and ExctnMod>0 or RdtnMod>0; DT<=RdtnDT<=0.1 recommended; determines RdtnOmegaMax=Pi/RdtnDT in the cosine transform]
1 NBody - Number of WAMIT bodies to be used (-) [>=1; only used when PotMod=1. If NBodyMod=1, the WAMIT data contains a vector of size 6*NBody x 1 and matrices of size 6*NBody x 6*NBody; if NBodyMod>1, there are NBody sets of WAMIT data each with a vector of size 6 x 1 and matrices of size 6 x 6]
1 NBodyMod - Body coupling model {1: include coupling terms between each body and NBody in HydroDyn equals NBODY in WAMIT, 2: neglect coupling terms between each body and NBODY=1 with XBODY=0 in WAMIT, 3: Neglect coupling terms between each body and NBODY=1 with XBODY=/0 in WAMIT} (switch) [only used when PotMod=1]
"HydroData/ConfigC" PotFile - Root name of potential-flow model data; WAMIT output files containing the linear, nondimensionalized, hydrostatic restoring matrix (.hst), frequency-dependent hydrodynamic added mass matrix and damping matrix (.1), and frequency- and direction-dependent wave excitation force vector per unit wave amplitude (.3) (quoted string) [1 to NBody if NBodyMod>1] [MAKE SURE THE FREQUENCIES INHERENT IN THESE WAMIT FILES SPAN THE PHYSICALLY-SIGNIFICANT RANGE OF FREQUENCIES FOR THE GIVEN PLATFORM; THEY MUST CONTAIN THE ZERO- AND INFINITE-FREQUENCY LIMITS!]
1 WAMITULEN - Characteristic body length scale used to redimensionalize WAMIT output (meters) [1 to NBody if NBodyMod>1] [only used when PotMod=1]
0.0 PtfmRefxt - The xt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1]
0.0 PtfmRefyt - The yt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1]
0.0 PtfmRefzt - The zt offset of the body reference point(s) from (0,0,0) (meters) [1 to NBody] [only used when PotMod=1. If NBodyMod=2,PtfmRefzt=0.0]
0.0 PtfmRefztRot - The rotation about zt of the body reference frame(s) from xt/yt (degrees) [1 to NBody] [only used when PotMod=1]
1583.36 PtfmVol0 - Displaced volume of water when the body is in its undisplaced position (m^3) [1 to NBody] [only used when PotMod=1; USE THE SAME VALUE COMPUTED BY WAMIT AS OUTPUT IN THE .OUT FILE!]
0.0 PtfmCOBxt - The xt offset of the center of buoyancy (COB) from (0,0) (meters) [1 to NBody] [only used when PotMod=1]
0.0 PtfmCOByt - The yt offset of the center of buoyancy (COB) from (0,0) (meters) [1 to NBody] [only used when PotMod=1]
---------------------- 2ND-ORDER FLOATING PLATFORM FORCES ---------------------- [unused with WaveMod=0 or 6, or PotMod=0 or 2]
0 MnDrift - Mean-drift 2nd-order forces computed {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero. If NBody>1, MnDrift /=8]
0 NewmanApp - Mean- and slow-drift 2nd-order forces computed with Newman's approximation {0: None; [7, 8, 9, 10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero. If NBody>1, NewmanApp/=8. Used only when WaveDirMod=0]
12 DiffQTF - Full difference-frequency 2nd-order forces computed with full QTF {0: None; [10, 11, or 12]: WAMIT file to use} [Only one of MnDrift, NewmanApp, or DiffQTF can be non-zero]
0 SumQTF - Full summation -frequency 2nd-order forces computed with full QTF {0: None; [10, 11, or 12]: WAMIT file to use}
---------------------- PLATFORM ADDITIONAL STIFFNESS AND DAMPING -------------- [unused with PotMod=0 or 2]
0 AddF0 - Additional preload (N, N-m) [If NBodyMod=1, one size 6*NBody x 1 vector; if NBodyMod>1, NBody size 6 x 1 vectors]
0
0
0
0
0
0 0 0 0 0 0 AddCLin - Additional linear stiffness (N/m, N/rad, N-m/m, N-m/rad) [If NBodyMod=1, one size 6*NBody x 6*NBody matrix; if NBodyMod>1, NBody size 6 x 6 matrices]
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0 AddBLin - Additional linear damping(N/(m/s), N/(rad/s), N-m/(m/s), N-m/(rad/s)) [If NBodyMod=1, one size 6*NBody x 6*NBody matrix; if NBodyMod>1, NBody size 6 x 6 matrices]
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0 AddBQuad - Additional quadratic drag(N/(m/s)^2, N/(rad/s)^2, N-m(m/s)^2, N-m/(rad/s)^2) [If NBodyMod=1, one size 6*NBody x 6*NBody matrix; if NBodyMod>1, NBody size 6 x 6 matrices]
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
---------------------- AXIAL COEFFICIENTS --------------------------------------
2 NAxCoef - Number of axial coefficients (-)
AxCoefID AxCd AxCa AxCp
(-) (-) (-) (-)
1 0.00 0.00 1.00
2 9.60 0.00 1.00
---------------------- MEMBER JOINTS -------------------------------------------
2 NJoints - Number of joints (-) [must be exactly 0 or at least 2]
JointID Jointxi Jointyi Jointzi JointAxID JointOvrlp [JointOvrlp= 0: do nothing at joint, 1: eliminate overlaps by calculating super member]
(-) (m) (m) (m) (-) (switch)
1 -28.8675 0.00000 -14.00000 1 0
2 -28.8675 0.00000 0.00000 1 0
---------------------- MEMBER CROSS-SECTION PROPERTIES -------------------------
3 NPropSets - Number of member property sets (-)
PropSetID PropD PropThck
(-) (m) (m)
1 6.50000 0.03000 ! Main Column
2 12.00000 0.06000 ! Upper Columns
3 24.00000 0.06000 ! Base Columns
---------------------- SIMPLE HYDRODYNAMIC COEFFICIENTS (model 1) --------------
SimplCd SimplCdMG SimplCa SimplCaMG SimplCp SimplCpMG SimplAxCd SimplAxCdMG SimplAxCa SimplAxCaMG SimplAxCp SimplAxCpMG
(-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
0.60 0.60 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00
---------------------- DEPTH-BASED HYDRODYNAMIC COEFFICIENTS (model 2) ---------
0 NCoefDpth - Number of depth-dependent coefficients (-)
Dpth DpthCd DpthCdMG DpthCa DpthCaMG DpthCp DpthCpMG DpthAxCd DpthAxCdMG DpthAxCa DpthAxCaMG DpthAxCp DpthAxCpMG
(m) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
---------------------- MEMBER-BASED HYDRODYNAMIC COEFFICIENTS (model 3) --------
1 NCoefMembers - Number of member-based coefficients (-)
MemberID MemberCd1 MemberCd2 MemberCdMG1 MemberCdMG2 MemberCa1 MemberCa2 MemberCaMG1 MemberCaMG2 MemberCp1 MemberCp2 MemberCpMG1 MemberCpMG2 MemberAxCd1 MemberAxCd2 MemberAxCdMG1 MemberAxCdMG2 MemberAxCa1 MemberAxCa2 MemberAxCaMG1 MemberAxCaMG2 MemberAxCp1 MemberAxCp2 MemberAxCpMG1 MemberAxCpMG2
(-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-) (-)
1 0.88 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 ! Upper Column 1
-------------------- MEMBERS -------------------------------------------------
1 NMembers - Number of members (-)
MemberID MJointID1 MJointID2 MPropSetID1 MPropSetID2 MDivSize MCoefMod PropPot [MCoefMod=1: use simple coeff table, 2: use depth-based coeff table, 3: use member-based coeff table] [ PropPot/=0 if member is modeled with potential-flow theory]
(-) (-) (-) (-) (-) (m) (switch) (flag)
1 1 2 2 2 1.0000 3 TRUE ! Upper Column 1
---------------------- FILLED MEMBERS ------------------------------------------
0 NFillGroups - Number of filled member groups (-) [If FillDens = DEFAULT, then FillDens = WtrDens; FillFSLoc is related to MSL2SWL]
FillNumM FillMList FillFSLoc FillDens
(-) (-) (m) (kg/m^3)
---------------------- MARINE GROWTH -------------------------------------------
0 NMGDepths - Number of marine-growth depths specified (-)
MGDpth MGThck MGDens
(m) (m) (kg/m^3)
---------------------- MEMBER OUTPUT LIST --------------------------------------
0 NMOutputs - Number of member outputs (-) [must be < 10]
MemberID NOutLoc NodeLocs [NOutLoc < 10; node locations are normalized distance from the start of the member, and must be >=0 and <= 1] [unused if NMOutputs=0]
(-) (-) (-)
---------------------- JOINT OUTPUT LIST ---------------------------------------
0 NJOutputs - Number of joint outputs [Must be < 10]
0 JOutLst - List of JointIDs which are to be output (-)[unused if NJOutputs=0]
---------------------- OUTPUT --------------------------------------------------
True HDSum - Output a summary file [flag]
False OutAll - Output all user-specified member and joint loads (only at each member end, not interior locations) [flag]
3 OutSwtch - Output requested channels to: [1=Hydrodyn.out, 2=GlueCode.out, 3=both files]
"E16.8e2" OutFmt - Output format for numerical results (quoted string) [not checked for validity!]
"A11" OutSFmt - Output format for header strings (quoted string) [not checked for validity!]
---------------------- OUTPUT CHANNELS -----------------------------------------
"Wave1Elev" - Wave elevation at the platform reference point ( 0, 0)
"HydroFxi"
"HydroFyi"
"HydroFzi"
"HydroMxi"
"HydroMyi"
"HydroMzi"
"B1Surge"
"B1Sway"
"B1Heave"
"B1Roll"
"B1Pitch"
"B1Yaw"
"B1TVxi"
"B1TVyi"
"B1TVzi"
"B1RVxi"
"B1RVyi"
"B1RVzi"
"B1TAxi"
"B1TAyi"
"B1TAzi"
"B1RAxi"
"B1RAyi"
"B1RAzi"
"B1WvsFxi"
"B1WvsFyi"
"B1WvsFzi"
"B1WvsMxi"
"B1WvsMyi"
"B1WvsMzi"
"B1HDSFxi"
"B1HDSFyi"
"B1HDSFzi"
"B1HDSMxi"
"B1HDSMyi"
"B1HDSMzi"
"B1RdtFxi"
"B1RdtFyi"
"B1RdtFzi"
"B1RdtMxi"
"B1RdtMyi"
"B1RdtMzi"
END of output channels and end of file. (the word "END" must appear in the first 3 columns of this line)
```

```
HydroDyn Driver file for OC7.
Compatible with HydroDyn v3.00
FALSE Echo - Echo the input file data (flag)
---------------------- ENVIRONMENTAL CONDITIONS -------------------------------
9.80665 Gravity - Gravity (m/s^2)
1025 WtrDens - Water density (kg/m^3)
250 WtrDpth - Water depth (m)
0 MSL2SWL - Offset between still-water level and mean sea level (m) [positive upward]
---------------------- HYDRODYN -----------------------------------------------
"LC1.1_HydroDyn.dat" HDInputFile - Primary HydroDyn input file name (quoted string)
"driver" OutRootName - The name which prefixes all HydroDyn generated files (quoted string)
FALSE Linearize - Flag to enable linearization
110300 NSteps - Number of time steps in the simulations (-)
0.1 TimeInterval - TimeInterval for the simulation (sec)
---------------------- PRP INPUTS (Platform Reference Point) ------------------
0 PRPInputsMod - Model for the PRP (principal reference point) inputs {0: all inputs are zero for every timestep, 1: steadystate inputs, 2: read inputs from a file (InputsFile)} (switch)
"OpenFAST_DisplacementTimeseries.dat" PRPInputsFile - Filename for the PRP HydroDyn input InputsMod = 2 (quoted string)
---------------------- PRP STEADY STATE INPUTS -------------------------------
1.0 2.0 -3.0 0.0 0.0 0.0 uPRPInSteady - PRP Steady-state displacements and rotations at the platform reference point (m, rads)
0.0 0.0 0.0 0.0 0.0 0.0 uDotPRPInSteady - PRP Steady-state translational and rotational velocities at the platform reference point (m/s, rads/s)
0.0 0.0 0.0 0.0 0.0 0.0 uDotDotPRPInSteady - PRP Steady-state translational and rotational accelerations at the platform reference point (m/s^2, rads/s^2)
---------------------- Waves multipoint elevation output ----------------------
FALSE WaveElevSeriesFlag - T/F flag to calculate the wave elevation field (for movies)
5.0 5.0 WaveElevDX WaveElevDY - WaveElevSeries spacing -- WaveElevDX WaveElevDY
3 3 WaveElevNX WaveElevNY - WaveElevSeries points -- WaveElevNX WaveElevNY
END of driver input file
```

The problem is that I think the forces in the x direction are correct and the forces in the y and z directions are incorrect, and the results are as follows.

I used other software to do comparison calculations and found a large gap, as shown below.

I think there is something wrong with my hydrodyn setting. The hydrodynamic coefficient is below.

I would like to know where the problem is and hope to get your help

Best regards,