ERDC/CHL TR-20-18 

Shallow Water Seakeeping Tests with 

Columbia Class Submarine for Integration into 

the Environmental Monitoring and Operator 

Guidance System 

Coastal and Hydraulics Laboratory 

Abigail L. Stehno and Jeffrey A. Melby August 2020

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 ERDC/CHL TR-20-18 

August 2020 

Shallow Water Seakeeping Tests with Columbia 

Class Submarine for Integration into the 

Environmental Monitoring and Operator 

Guidance System 

Abigail L. Stehno and Jeffrey A. Melby

Coastal and Hydraulics Laboratory

US Army Engineer Research and Development Center

3909 Halls Ferry Road

Vicksburg, MS 39180-6199

Final report

Approved for public release; distribution is unlimited

Prepared for US Naval Surface Warfare Center 

Carderock Division

West Bethesda, MD 20817-5700

Under MIPR N0002418MP00414
ERDC/CHL TR-20-18 ii

Abstract

The Environmental Monitoring and Operation Guidance System (EMOGS) 

tool was developed in 1989 to provide a real-time risk analysis for 

underkeel clearance for the Ohio class submarine while in transit to the 

Naval Submarine Base at Kings Bay, Georgia. The program computes 

expected submarine response for input water level, depth, speed, wave,

and other input conditions using shallow-water motion transfer functions 

generated by the strip theory tool, Large Amplitude Motion Program 

(LAMP). The integration of the new Columbia class submarine into 

EMOGS required that new transfer functions be developed using LAMP.

The LAMP results are to be validated using measured motions from 

physical model laboratory testing. This report summarizes a laboratory 

study of the Columbia class submarine response in shallow-water waves. 

The study was conducted at the US Army Engineer Research and 

Development Center, Coastal and Hydraulics Laboratory, and was done in 

direct support of the Naval Surface Warfare Center, Carderock Division. 

These seakeeping tests were performed in a shallow basin with a multidirectional wave generator, with measured still water vessel motions and 

measured vessel motion in regular and irregular waves of varying height, 

period, and direction.

DISCLAIMER: The contents of this report are not to be used for advertising, publication, or promotional purposes. 

Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. 

All product names and trademarks cited are the property of their respective owners. The findings of this report are not to 

be construed as an official Department of the Army position unless so designated by other authorized documents.

DESTROY THIS REPORT WHEN NO LONGER NEEDED. DO NOT RETURN IT TO THE ORIGINATOR.
ERDC/CHL TR-20-18 iii

Contents

Abstract.................................................................................................................................... ii

Figures and Tables...................................................................................................................v

Preface...................................................................................................................................viii

1 Introduction ......................................................................................................................1

1.1 Background........................................................................................................1

1.2 Objective.............................................................................................................2

1.3 Approach ............................................................................................................2

2 Experimental Facilities and Equipment........................................................................3

2.1 Directional Spectral Wave Generator (DSWG) .................................................3

2.2 Wave basin.........................................................................................................4

2.2.1 Lane design................................................................................................................. 6

2.2.2 Lane preparation ........................................................................................................ 7

2.3 Data acquisition.................................................................................................9

2.3.1 Senix ultrasonic sensors............................................................................................. 9

2.3.2 Akamina capacitance sensors .................................................................................10

2.4 Submarine model ............................................................................................11

3 Test Procedures..............................................................................................................13

3.1 Gage placements............................................................................................ 13

3.2 Target wave conditions....................................................................................17

3.3 Submarine transit tests.................................................................................. 18

4 Test Results ....................................................................................................................20

4.1 Wave calibration ............................................................................................. 20

4.2 Regular wave tests ..........................................................................................24

4.3 Irregular wave tests ........................................................................................ 25

5 Summary .........................................................................................................................27

References.............................................................................................................................28

Appendix A: Notation............................................................................................................29

Appendix B: Gage Calibration Factors ...............................................................................30

Appendix C: Calibration Results .........................................................................................31

Appendix D: Submarine Testing Results............................................................................45

Unit Conversion Factors.......................................................................................................72
ERDC/CHL TR-20-18 iv

Acronyms and Abbreviations...............................................................................................73

Report Documentation Page
ERDC/CHL TR-20-18 v

Figures and Tables

Figures

Figure 1. Plan view drawing of the shallow-water basin at ERDC with the DSWG at 

the east end (bottom), gate in red at the west end. Blue rectangles on the 

perimeter are wave absorbers, and green rectangles near the DSWG are guide 

vanes. The circles are the roof support poles. Length dimensions are in feet. ....................5

Figure 2. The upright wave absorber panels were placed along the walls of the 

basin, with the least porous panel closest to the wall..............................................................6

Figure 3. The triangular absorbers at the transect lane ends that absorbed waves 

with the remnant waves reflect to the unused portion of the basin.......................................6

Figure 4. Plan view drawing of the transit lane locations in the shallow-water 

basin, depicted by light green rectangles in the basin. Length dimensions are in 

feet...................................................................................................................................................7

Figure 5. Divots filled with concrete and mounds removed.....................................................8

Figure 6. Oblique lane with blue edging, facing east (left) and facing west (right)...............8

Figure 7. Vertical lane with visible patches, facing east. DSWG is in the 

background.....................................................................................................................................9

Figure 8. Gage locations for layout 1 during wave calibration, shown as squares.............14

Figure 9. Gage locations for layout 2 wave calibration, shown as circles............................15

Figure 10. Gage locations during submarine testing, where triangles are Senix 

gages and circles are Akamina gages. .....................................................................................16

Figure 11. Target and measured wave spectra for gage 4 in sea state 3 

calibrations...................................................................................................................................23

Tables

Table 1. DSWG segment specifications (Rexroth 2003). .........................................................3

Table 2. Wave operating requirements at 1 m water depth (Rexroth 2003).........................4

Table 3. Senix sensor specifications (Senix 2015). ................................................................10

Table 4. Akamina wave gage specifications (Akamina 2014)...............................................10

Table 5. Submarine model specifications for shallow water testing (Temple et al. 

2018).............................................................................................................................................11

Table 6. Target regular wave parameters at a 1.927 ft water depth....................................17

Table 7. Irregular wave parameters...........................................................................................18

Table 8. Accuracy metrics for regular wave heights for gage location 9. .............................21

Table 9. Accuracy metrics for regular wave periods for gage location 9..............................21

Table 10. Accuracy metrics for capacitance (C) gages 4, 8, and 13 in sea state 3

calibrations. ..................................................................................................................................23

Table 11. The zero deg wave heights H (inch) for the HS, FS, and BS. ................................24

Table 12. The 5 deg wave heights H (inch) for the BQ, SQ, and BQ-R..................................24
ERDC/CHL TR-20-18 vi

Table 13. The zero deg wave period T (second) for the HS, FS, and BS. .............................25

Table 14. The 5 deg wave period T (second) for the BQ, SQ, and BQ-R...............................25

Table 15. Sea state 3, BQ wave results for the capacitance (C) gages 5, 6, 7, and 

9. ....................................................................................................................................................26

Table 16. Sea state 3, SQ wave results for the capacitance (C) gages 5, 6, 7, and 

9. ....................................................................................................................................................26

Table 17. Sea state 4, BQ wave results for capacitance (C) gages 5, 6, 7, and 9. .............26

Table 18. Sea state 4, SQ wave results for capacitance (C) gages 5, 6, 7, and 9..............26

Table B-1. Gage calibration factors. ..........................................................................................30

Table C-1. Wave heights (inch) for zero deg waves during wave calibration, setup 

1. ....................................................................................................................................................31

Table C-2. Wave height RMSE (inch) for zero deg waves during wave calibration, 

setup 1. .........................................................................................................................................32

Table C-3. Wave height standard deviations (inch) for zero deg waves during wave 

calibration, setup 1......................................................................................................................32

Table C-4. Wave periods (second) for zero deg waves during wave calibration, 

setup 1. .........................................................................................................................................33

Table C-5. Wave period RMSE (second) for zero deg waves during wave 

calibration, setup 1......................................................................................................................33

Table C-6. Wave heights (inch) for 5 deg waves during wave calibration, setup 1. ............34

Table C-7. Wave height RMSE (inch) for 5 deg waves during wave calibration, 

setup 1. .........................................................................................................................................34

Table C-8. Wave height standard deviations (inch) for 5 deg waves during wave 

calibration, setup 1......................................................................................................................35

Table C-9. Wave periods (second) for 5 deg waves during wave calibration, setup 

1. ....................................................................................................................................................35

Table C-10. Wave period RMSE (second) for 5 deg waves during wave calibration, 

setup 1. .........................................................................................................................................36

Table C-11. Wave heights (inch) for zero deg waves during wave calibration, setup 

2, gages 1–10..............................................................................................................................36

Table C-12. Wave heights (inch) for zero deg waves during wave calibration, setup 

2, gages 11–19. ..........................................................................................................................37

Table C-13. Wave height RMSE (inch) for zero deg waves during wave calibration, 

setup 2, gages 1–10...................................................................................................................37

Table C-14. Wave height RMSE (inch) for zero deg waves during wave calibration, 

setup 2, gages 11–19. ...............................................................................................................38

Table C-15. Wave height standard deviations (inch) for zero deg waves during 

wave calibration, setup 2, gages 1–10. ...................................................................................38

Table C-16. Wave height standard deviations (inch) for zero deg waves during 

wave calibration, setup 2, gages 11–19..................................................................................39

Table C-17. Wave periods (second) for zero deg waves during wave calibration, 

setup 2, gages 1–10...................................................................................................................39
ERDC/CHL TR-20-18 vii

Table C-18. Wave periods (second) for zero deg waves during wave calibration, 

setup 2, gages 11–19. ...............................................................................................................40

Table C-19. Wave period RMSE (second) for zero deg waves during wave 

calibration, setup 2, gages 1–10. .............................................................................................40

Table C-20. Wave period RMSE (second) for zero deg waves during wave 

calibration, setup 2, gages 11–19............................................................................................41

Table C-21. Wave heights (inch) for 5 deg waves during wave calibration, setup 2...........41

Table C-22. Wave height RMSE (inch) for 5 deg waves during wave calibration, 

setup 2. .........................................................................................................................................42

Table C-23. Wave height standard deviations (inch) for 5 deg waves during wave 

calibration, setup 2......................................................................................................................42

Table C-24. Wave periods (second) for 5 deg waves during wave calibration, setup 

2. ....................................................................................................................................................43

Table C-25. Wave period RMSE (second) for 5 deg waves during wave calibration, 

setup 2. .........................................................................................................................................43

Table C-26. Sea state 3 irregular wave characteristic statistics............................................44

Table D-1. Wave heights (inch) by heading for wave M1........................................................46

Table D-2. Wave periods (second) by heading for wave M1. .................................................47

Table D-3. Wave heights (inch) by heading for wave M2........................................................48

Table D-4. Wave periods (second) by heading for wave M2. .................................................49

Table D-5. Wave heights (inch) by heading for wave M3........................................................50

Table D-6. Wave periods (second) by heading for wave M3. .................................................51

Table D-7. Wave heights (inch) by heading for wave M4. .......................................................52

Table D-8. Wave periods (second) by heading for wave M4. .................................................53

Table D-9. Wave heights (inch) by heading for wave M5........................................................54

Table D-10. Wave periods (second) by heading for wave M5................................................55

Table D-11. Wave heights (inch) by heading for wave M6......................................................57

Table D-12. Wave periods (second) by heading for wave M6................................................59

Table D-13. Wave heights (inch) by heading for wave M7......................................................61

Table D-14. Wave periods (second) by heading for wave M7. ...............................................63

Table D-15. Wave heights (inch) by heading for wave M8......................................................65

Table D-16. Wave periods (second) by heading for wave M8................................................66

Table D-17. Wave heights (inch) by heading for wave M9. .....................................................68

Table D-18. Wave periods (second) by heading for wave M9................................................69

Table D-19. Irregular wave condition statistics for sea state 3 for SQ..................................71

Table D-20. Irregular wave condition statistics for sea state 4 for SQ..................................71

Table D-21. Irregular wave condition statistics for sea state 3 for BQ..................................71

Table D-22. Irregular wave condition statistics for sea state 4 for BQ..................................71
ERDC/CHL TR-20-18 viii

Preface

The study summarized in this report was conducted at the request of the 

Naval Surface Warfare Center, Carderock Division (NSWCCD), under 

MIPR N0002418MP00414. Mr. Dylan Temple was the primary 

engineering point of contact at NSWCCD, and Mr. Andrew Silver was the 

project lead. The portion of the study reported herein was funded by 

NSWCCD and primarily conducted at the US Army Engineer Research and 

Development Center (ERDC), Coastal and Hydraulics Laboratory (CHL), 

Vicksburg, MS, during the period January 2018–September 2018.

Work was conducted through the Harbors, Entrances, and Structures 

Branch, CHL. Messrs. Raymond R. Reed, Cody M. Bryant, De’Arius 

Christmas, Gregory P. Mitchell, and William C. Gatlin provided technical 

assistance.

Appreciation is expressed to Mr. Glenn B. Myrick for his valuable

contributions to this effort.

The study was performed under the general supervision of Mr. Jim 

Gutshall, Chief, Harbors, Entrances, and Structures Branch, and 

Dr. Jackie Pettway, Chief, Navigation Division. At the time of publication 

of this report, Mr. Jeffrey R. Eckstein was the Deputy Director of CHL, and

Dr. Ty V. Wamsley was the Director.

COL Teresa A Schlosser was the Commander of ERDC, and the Director 

was Dr. David W. Pittman.
ERDC/CHL TR-20-18 1

1 Introduction

This report summarizes a laboratory study of the Columbia class 

submarine response in shallow-water waves. The study was conducted at 

the US Army Engineer Research and Development Center (ERDC), Coastal 

and Hydraulics Laboratory (CHL), and was performed in direct support of 

the Naval Surface Warfare Center, Carderock Division (NSWCCD). Final 

results of the submarine response observations were intended to integrate 

the Columbia class submarine into the Environmental Monitoring and 

Operator Guidance System (EMOGS). These seakeeping tests were 

performed in a shallow basin with a multi-directional wave generator, 

operated by CHL.

1.1 Background

The EMOGS tool was developed in 1989 to provide real-time risk analysis 

for underkeel clearance for the Ohio class submarine while in transit to the 

Naval Submarine Base (NSB) at Kings Bay, Georgia. The controlled dredge 

depth at the entrance channel is 46 ft* mean lower low water. While this 

depth is sufficient for calm sea navigation, vessel motions induced by wave 

conditions create a risk of grounding. Additional dredging was cost 

prohibitive; therefore, the EMOGS tool was created to calculate the risk 

based on the current atmospheric and ocean conditions during transit to 

the NSB. 

The Columbia class submarine has been under development to replace the 

Ohio class submarine, which is nearing the end of its 42-year service life. 

The integration of a vessel into EMOGS requires knowledge of the vessel 

motion in shallow water. Channel depth, roll motion, and vessel design 

components will affect vessel motions under wave forcing. For risk 

assessment, the shallow-water motion transfer functions were generated 

by the strip theory tool, Large Amplitude Motion Program (LAMP). The 

 

* For a full list of the spelled-out forms of the units of measure used in this document, please refer to US 

Government Publishing Office Style Manual, 31st ed. (Washington, DC: US Government Publishing 

Office 2016), 248-52, https://www.govinfo.gov/content/pkg/GPO-STYLEMANUAL-2016/pdf/GPOSTYLEMANUAL-2016.pdf.
ERDC/CHL TR-20-18 2

LAMP results were validated using measured motions from physical 

model testing, accounting for effects due to vessel motion in waves. 

1.2 Objective

ERDC was tasked with facilitating the shallow-water seakeeping study for 

integrating the Columbia class submarine into EMOGS. A shallow-water 

basin was prepared, and wave conditions corresponding to those 

measured near the NSB entrance channel were generated using a 

directional spectral wave generator.

1.3 Approach

Prior to the shallow-water testing described herein, deep-water physical 

model testing was performed at the Maneuvering and Seakeeping Basin at 

NSWCCD. Surface testing for deep-water waves was performed to 

calibrate instruments, measure roll decay, perform sinkage and trim tests, 

and analyze vessel performance under a limited set of regular and 

irregular wave conditions. Shallow-water testing at CHL was conducted in 

a shallow basin with a multi-directional wave generator to investigate the 

seakeeping characteristics of the Columbia class submarine in shallowwater waves and to characterize calm water sinkage, trim decay, and roll 

decay of the surfaced vessel. 

The model was tested at 8 kt and 12 kt prototype speeds at following, head, 

beam, bow quartering, and stern quartering headings, each in nine regular 

wave conditions. Additionally, the model was tested at both speeds at bow 

quartering and stern quartering headings in irregular waves. The irregular 

wave conditions are sea state 3 and sea state 4, which correspond to the 

historical data collected at the wave buoy stationed at the Kings Bay 

Channel. The motion response of the surfaced submarine under regular 

and irregular wave conditions was used by NSWCCD to validate the LAMP 

model for shallow-water wave conditions.
ERDC/CHL TR-20-18 3

2 Experimental Facilities and Equipment

The shallow-water basin at ERDC was graded to a uniform flat bottom and 

included a new directional spectral wave generator that is capable of 

generating multi-directional regular and irregular wave conditions that the 

Columbia class submarine may experience near the seaward entrance of 

the NSB at Kings Bay, Georgia. ERDC facilities allowed NSWCCD to 

accurately measure underkeel clearance of the submarine model for 

EMOGS integration.

2.1 Directional Spectral Wave Generator (DSWG)

The DSWG is a wet-back piston-type segmented wave generator 

consisting of 48 segment wave boards, producing a 76 ft long 

multidirectional wave front. The segment specifications are found in 

Table 1. 

Table 1. DSWG segment specifications (Rexroth 2003). 

Segment height (ft) 4.92

Centerline to centerline distance (ft) 1.62

Amplitude of motion (ft) 1.64

Drive force (normal operation) (lbf) 494.58

Maximum still water level (ft) 3.28

Velocity (normal operation) (fps) 3.28

The operational limits of the DSWG for regular and irregular waves are 

presented in Table 2. Segment movements are computed though GEDAP 

software on a personal computer to generate soliton, regular long crested, 

irregular long crested, and short crested waves, JONSWAP*, TMA†, and 

Pierson-Moskowitz spectra, in perpendicular and oblique directions.

Additionally, the segments may be controlled individually in “manual 

mode” to produce customizable paddle motions. Individual paddle 

accuracy is ±0.5% for amplitude, velocity, and acceleration, and is ±0.1% 

for frequency between 0.2 and 2.0 Hz. Irregular waves produce a ±1% 

deviation of amplitude from the command signal (Rexroth 2003). 

 

* Joint North Sea Wave Project spectrum

† Texel, Marsen, and Arsole Spectrum
ERDC/CHL TR-20-18 4

Table 2. Wave operating requirements at 1 m water depth (Rexroth 2003). 

Regular Wave Operation 

Period Range (s) 0.5 to 5 

Angle of propagation (deg) 0 to 75

Wave height at 1.5 s period (ft) 1.31

Wave height at 2.4 s period (ft) 1.94

Wave height at 3.0 s period (ft) 1.64

Wave height at 5.0 s period (ft) 1.31

Irregular Wave Operation 

Angle of propagation (deg) 0 to 75

Significant wave height at peak period of 3.0 s (ft) 0.98

Significant wave height at peak period of 2.3 s (ft) 1.19

2.2 Wave basin

The shallow water basin is an indoor concrete basin 191 ft long and 149 ft

wide with a maximum depth of 3 ft (Figure 1). Four roof support poles, 

each 8 in. in diameter, are aligned in the north-south direction 94 ft from 

the east wall of the basin and spaced 39 ft apart. The DSWG is located on 

the east end of the basin, and a sealed door is located on the west end of 

the basin. 

The inner perimeter of the basin was lined with upright wave absorbers to 

reduce wave reflections from the sidewalls during testing (Figure 2). 

Additional upright wave absorbers were placed behind the DSWG to 

minimize sloshing effects during operation. The upright wave absorbers

measure 10 ft long, 7 ft wide, and 4 ft high. They are composed of 14 rows 

of perforated vertical expanded metal sheets wired to a frame. The 

porosity of the array decreases from the front to back of the frame. The 

design results in an average wave reflection coefficient of 3.2% and 

maximum wave reflection coefficient of 11.2% (Jamieson and Mogridge 

2000). Smaller, triangular absorbers were placed at the ends of the transit 

lanes to absorb and reflect waves to the unused portion of the basin 

(Figure 3). Guide vanes were placed adjacent to the side of the DSWG to 

prevent waves generated behind the machine from transmitting into the 

testing area. Each guide vane was 9 ft long, 2 ft wide, and 4 ft high.
ERDC/CHL TR-20-18 5

Figure 1. Plan view drawing of the shallow-water basin at ERDC with the DSWG at the 

east end (bottom), gate in red at the west end. Blue rectangles on the perimeter are 

wave absorbers, and green rectangles near the DSWG are guide vanes. The circles 

are the roof support poles. Length dimensions are in feet. 

North
ERDC/CHL TR-20-18 6

Figure 2. The upright wave absorber panels were placed along the walls of the basin, 

with the least porous panel closest to the wall. 

Figure 3. The triangular absorbers at the transect lane ends that absorbed waves 

with the remnant waves reflect to the unused portion of the basin. 

2.2.1 Lane design

The experiment was configured so that individual submarine transits were 

confined to transit lanes (Figure 4). The lane layout for the 2018 EMOGS 

experiment was based on the experiment conducted in 1988 for 

NSWCCD*. Three 8 ft wide lanes were required for the model submarine 

to be exposed to the five relative wave directions used for EMOGS 

calibration. Lanes were delineated by marks on the floor. A 150 ft long 

vertical lane was perpendicular to the wave generator and was offset from 

the centerline of the DSWG by 1 ft to the south. The vertical lane was used 

for head and following seas. A 140 ft horizontal lane was aligned with the 

north-south direction and located 39.8 ft from the face of the DSWG. The 

horizontal lane was used for beam seas. A 205.5 ft oblique lane was 

rotated 40 deg to the north of the vertical lane and was used for quartering 

stern and quartering bow seas.

 

* Outlaw, D. G., D. L. Green, L. A. Barnes, M. J. Briggs, and D. A. Daily. 1988 (unpublished). David Taylor 

Submarine Seakeeping Study. Miscellaneous Paper CERC-88-nn. Vicksburg, MS: Department of the 

Army, Waterways Experiment Station, Corps of Engineers, Coastal Engineering Research Facility. 
ERDC/CHL TR-20-18 7

Figure 4. Plan view drawing of the transit lane locations in the shallow-water basin, 

depicted by light green rectangles in the basin. Length dimensions are in feet. 

2.2.2 Lane preparation

The lane bottoms required a uniform depth within a ±0.01 ft tolerance for 

accurate measurements from the onboard ultrasonic sensors. An initial 

LIDAR scan was taken of the basin floor, which measured a 0.0242 ft 

difference between the highest and lowest points in the basin prior to lane 

preparations. Floor low spots were filled with a sand and concrete mixture, 

and the high spots were ground down to the required tolerance (Figure 5). 

A second LIDAR scan was taken after basin preparations to ensure floor 

variations were within tolerance within the transit lanes. 

North
ERDC/CHL TR-20-18 8

Figure 5. Divots filled with concrete and mounds removed. 

Each lane was painted a safety yellow to create a visual contrast between 

the floor and the submarine during testing. A blue border was added 

alongside the lanes to create a distinct lane edge for the submarine 

operator to view during testing (Figure 6). Additional floor deviations were 

filled with quick-drying epoxy filler (Figure 7). 

Figure 6. Oblique lane with blue edging, facing east (left) and facing west (right). 
ERDC/CHL TR-20-18 9

Figure 7. Vertical lane with visible patches, facing east. DSWG is in the background. 

2.3 Data acquisition

Water surface elevations were measured during wave calibration and 

submarine testing with ultrasonic sensors and capacitance gages. These 

instruments were mounted on tripods, where the ultrasonic sensors were 

13 in. above the still water level (SWL) and the capacitance gages were 

positioned with approximately half of the capacitance wire below the SWL. 

Instrumentation placement within the basin is discussed in Section 3.

A multiplexing box was located on a roof support near the center of the 

basin. Data from the sensors and gages were transmitted to the 

multiplexing box through a double-shielded, twisted-pair cable. Power was 

also supplied from the multiplexing box to the sensors through this cable. 

The data were transferred to the control room over an Ethernet cord to be 

recorded by the data acquisition (DAQ) software, Laboratory Virtual 

Instrumentation Engineering Workbench (LabVIEW).

2.3.1 Senix ultrasonic sensors

Two Senix ToughSonic 14 sensors were placed in the basin during testing. 

These sensors produce ultrasonic pulses and record the time required for 

the sound wave to travel the distance from emitter to the water level and 

return. These high-resolution, noncontact, temperature-compensated 

instruments output voltage loops to a DAQ system for recording. The 

Senix sensors were mounted 13 in. above the water level to allow 
ERDC/CHL TR-20-18 10

measurement of water surface variations up to 12 in. from SWL. Sensor 

specifications from the manufacturer are presented in Table 3.

Table 3. Senix sensor specifications (Senix 2015). 

Accuracy Better than 0.5% of target distance

Resolution 0.0034 in.

Minimum Range 4 in.

Maximum Range 168 in.

Measurement Update Rate Between 20 Hz and 200 Hz

Configuration and calibration of the Senix sensors were done at Carderock 

prior to testing. Results from the calibration are presented in Appendix B. 

The sensors automatically compensate for temperature changes and

therefore do not require recalibration over the course of the testing period. 

The sonar gages sampled at 50 Hz. 

2.3.2 Akamina capacitance sensors

During wave calibration, water level variations were measured with 19 

Akamina Technologies AWP-24-3 gages. These gages measure capacitance 

using digital techniques, which is then converted to an analogue voltage 

(proportional to the level of water variation from SWL), offset adjusted, 

amplified, and filtered to be sent to a DAQ system for recording. The 

Akamina gages were mounted to ensure the calibrated section of the probe 

was submerged to accurately record the full range of water levels under all 

anticipated wave conditions. Gage specifications from the manufacturer 

are presented in Table 4. 

Table 4. Akamina wave gage specifications (Akamina 2014). 

Linearity 0.15% of full scale

Accuracy 0.15% of full scale

Air Temperature Coefficient 0.03% of full scale/°C

Water Temperature Coefficient 0.03% of full scale/°C

Measurement Update Rate 200 Hz

The Akamina gages were configured and calibrated at ERDC prior to wave 

calibration and testing. The configuration procedure in the Akamina 

Technologies AWP-24-3 Wave Height Gage User’s Guide (2014) was 
ERDC/CHL TR-20-18 11

applied. The linear relationship between water depth and gage output 

voltage was determined through calibration. The resultant calibration 

coefficients are presented in Appendix B.

The Akamina Technologies AWP-24-3 wave gages are highly linear 

(0.15%) and highly accurate (0.15%) (Akamina 2014). These gages also 

remain stable through large air and water temperature changes and 

therefore only require the initial calibration prior to water level 

measurements. The capacitance gages sampled at 50 Hz. 

2.4 Submarine model

The model of the Columbia class submarine and hydraulic basin model 

was scaled according to Froude similitude with a geometrically 

undistorted length scale of NL=23.8751 and time and speed scaled 

according to NT = (NL)0.5 = 4.886. The model submarine operated at the 

surface draft of the full-scale Columbia, ballasted to match the center of 

gravity and moments of inertia of the full-scale model. Model length and 

speed specifications are defined in Table 5. Additional specifications are 

defined in Temple et al. (2018). 

Table 5. Submarine model specifications for shallow water testing 

(Temple et al. 2018). 

Parameter Model #5763 (λ: 23.8751) Columbia 

Length overall 23.46 ft 560.05 ft

Diameter 21.78 in. 43.33 ft

Surfaced 

displacement 2976.3 lb (fresh water)

18535 LT 

(saltwater)

Surfaced draft @ FP 18.31 in. 36.42 ft

Surfaced draft @ AP 18.51 in. 36.83 ft

Slow transit speed 2.8 ft/s 8.0 kt

Fast transit speed 4.1 ft/s 12.0 kt

The model was controlled remotely using control surfaces on the X-stern 

for steering and an unclassified propeller for propulsion. The X-stern 

configuration on the model consisted of fixed stabilizers and a trailing 

edge flap to control motions, representative of the full-scale design. The 

propeller operated at known rotations per minute for the respective transit 
ERDC/CHL TR-20-18 12

speeds. The model required approximately 40 ft of spin-up distance to 

obtain full speed and approximately 20 ft to stop by reversing propellers.

Instruments operated by NSWCCD were fitted to the model to measure 

vessel motions and underkeel clearance. These data were transmitted in 

real time to the operator to monitor the motions and safety of the 

submarine during testing. Additionally, the model was fitted with two 

Senix ultrasonic sensors, one mounted on booms forward at the bow and 

one outward to stern port. These sensors were used to measure the 

incident wave, as described in Temple et al. (2018). Underwater sonic 

sensors were used in the shallow-water testing to determine sinkage. All 

onboard probes and sensors were sampled and recorded by NSWCCD 

personnel with their computer equipment and programs and are not 

reported herein. Vessel motion and underkeel clearance data processing 

was completed by NSWCCD and is not discussed further in this report.
ERDC/CHL TR-20-18 13

3 Test Procedures

Wave calibrations were completed prior to the submarine testing to ensure 

the DSWG was producing the expected wave conditions. Wave gages were 

placed into the basin in and around the lanes during wave calibration. 

After wave conditions were calibrated, submarine transit tests occurred. 

Twelve wave gages remained in the basin during the submarine testing, 

allowing a cross-check of the wave conditions with the calibrated wave. 

Measurements of the submarine motions were completed by NSWCCD.

3.1 Gage placements

Three gage layout patterns were used, two during wave calibration and one 

during testing. The two layouts used during wave calibration ensured that 

the desired wave heights were generated within the lanes. Gage locations 

during the wave calibration are shown in Figure 8 and Figure 9, where the 

squares are the locations for the first layout pattern and the circles are the 

locations for the second layout pattern. Multiple layout patterns were used 

to fully capture the wave condition variations in the basin with a limited 

set of gages. The final layout resulted in an array, with the first row parallel 

to the wave machine starting 12 ft away from the face of the DSWG and 

succeeding rows parallel to the wave machine spaced 16 ft from each other. 

In the first layout, the rows perpendicular to the wave machine created by 

the array were spaced 20 ft apart, with the center rows perpendicular to 

the wave machine being aligned with the center of the vertical lane. The 

second layout continued to follow this pattern; however, additional rows 

perpendicular to the wave machine were spaced 10 ft on each side from the 

original array and additional gages were located within the lanes.

A third layout combined gage locations completely outside of the lanes 

from the first two layouts. This arrangement allowed for measured wave 

conditions during submarine testing to be compared to the measured wave 

conditions from the wave calibration. Gage locations during the testing are 

shown in Figure 10, where the circles are Akamina wave gages and the 

triangles are the Senix sensors.
ERDC/CHL TR-20-18 14

Figure 8. Gage locations for layout 1 during wave calibration, shown as squares. 
ERDC/CHL TR-20-18 15

Figure 9. Gage locations for layout 2 wave calibration, shown as circles. 
ERDC/CHL TR-20-18 16

Figure 10. Gage locations during submarine testing, where triangles are Senix gages 

and circles are Akamina gages. 
ERDC/CHL TR-20-18 17

3.2 Target wave conditions

The conditions in the basin for the regular waves are described in Table 6

at model scale. Each wave condition was run at zero deg and 5 deg at a 

1.927 ft water depth, to fulfill the required wave directions that the 

submarine encountered with respect to its heading. These wave conditions 

are similar to those used in Outlaw et al.* and were prescribed by 

NSWCCD (Temple et al. 2018). The values for the target wave conditions 

were scaled using Froude similitude, as discussed in Section 2.4, and 

calibrated to the gages near the transit lanes.

Some wave conditions were modified during testing to reduce the risk of 

submarine grounding. The wave heights were adjusted during testing if 

extreme vessel motions were noticed or expected for certain wave 

frequencies. 

Table 6. Target regular wave parameters 

at a 1.927 ft water depth. 

Wave 

Wave Period 

T (s) 

Wave Height 

H (in.) 

M1 0.963 0.9

M2 1.335 1.5

M3 1.721 2.1

M4 2.402 3.0

M5 2.683 3.0

M6 3.111 3.0

M7 3.543 3.0

M8 3.832 3.0

M9 4.562 3.0

The irregular wave conditions are summarized in Table 7 at model scale 

and a wave angle of 5 deg. The NSWCCD requested sea states 3 and 4. 

The waves were generated with a TMA spectrum with a frequency 

spreading parameter of 3.3, recycling period of 15 min, and cutoff 

 

* Outlaw, D. G., D. L. Green, L. A. Barnes, M. J. Briggs, and D. A. Daily. 1988 (unpublished). David Taylor 

Submarine Seakeeping Study. Miscellaneous Paper CERC-88-nn. Vicksburg, MS: Department of the 

Army, Waterways Experiment Station, Corps of Engineers, Coastal Engineering Research Facility.
ERDC/CHL TR-20-18 18

frequencies of 0.05 and 2.0 Hz. One random number seed was used to 

create the wave spectrum for the wave calibration. During calibration, 

1 min increments were run to ensure fully formed waves were present 

throughout the testing area. During testing, the wave spectrum was run 

for approximately 2 to 2.5 min increments to ensure fully formed waves 

were present throughout the testing area prior to submarine transit. The 

increments were concatenated to form the full spectrum to analyze the 

wave spectral parameters.

Table 7. Irregular wave parameters. 

Wave Peak Wave Period 

Tp (sec)

Significant Wave Height 

(Hm0) (in.)

SS3 1.840 1.38

SS4 1.517 3.324

3.3 Submarine transit tests

The submarine was remotely controlled by a model driver positioned on 

top of the DSWG. The model driver was responsible for diving the model 

and monitoring it during runs. The data were collected in real time to 

monitor vessel motions, which were used to make decisions for any onthe-fly adjustments to the test plan, such as modifying the wave height. 

Three to four submarine handlers were positioned in the basin to ensure 

safe operation. A punt operator was located at the start of the transit 

lane to align the model against the alignment poles, set the model up for 

its zero reading, and position the model in the center of the lane and at 

the correct heading prior to initiating a transit. The additional handlers 

were located at the end of transit lane to catch the model as it stopped. 

These handlers controlled the submarine before and after testing, and 

re-positioned the submarine at the beginning of the transit lane after 

each test. A wave generator operator was located in a control room to 

start and stop wave generation and modify wave conditions based on the 

submarine operator’s decisions.

Within each of the transit lanes, the submarine operational area was 

limited by the spin-up and stopping distances for the fast and slow transit 

speeds of 12 and 8 kt, full scale. Although the layout of the lanes was 

designed to produce maximum wave encounters during submarine transit, 

the operational zone was limited. Multiple iterations of each test were 

performed to increase wave encounters.
ERDC/CHL TR-20-18 19

The submarine transit start times depended on the influence of the waves 

in the transit lane. Operation began once the wave front was in the transit 

lane for regular waves; however, care was taken that there were minimal 

wave re-reflections in the basin and that the model did not outrun the 

wave field. For the irregular waves, the strategy was to run the full 

spectrum in short segments to limit the effect of wave re-reflections from 

basin walls. In this case, the submarine transit started after the slowest 

wave had reached the west wall, approximately 1 min after the generator 

started producing waves. The full 15 min wave spectrum was run in 

increments of approximately 2 to 2.5 min, where each increment started at 

the end of the previous increment. Transit time for the submarine lasted

approximately 1 min and began once the basin was fully saturated with the 

irregular wave. Once the entire signal had been generated, a new one was 

created using a different random number seed. The increments were 

concatenated to ensure each seed produced the desired wave conditions. 
ERDC/CHL TR-20-18 20

4 Test Results

The wave conditions during the calibration and testing phases were 

measured, and an error analysis was completed. The calibration of the 

zero deg waves were compared with the measurements for the head seas 

(HS), following seas (FS), and beam seas (BS). The testing for these 

headings required either a zero deg wave or a 90 deg wave, which was 

accomplished using waves generated with no obliquity but with different 

submarine orientations in the vertical and horizontal tracks. The 45 deg 

heading was accomplished with a combination of 5 deg wave generation 

obliquity and 40 deg lane angle. The calibration of the 5 deg waves was 

compared with the measurements for the bow quartering seas (BQ), stern 

quartering seas (SQ), and the bow quartering sea repeats using M6 and M7 

(BQ-R). Testing procedures are detailed in Temple et al. (2018).

During calibration and testing, some of the gages were placed outside of 

the influence of the generator (to define the wave falloff in the shadow 

areas), and some were affected by reflections from the roof support poles 

or from the walls at a 5 deg wave generation obliquity. Additionally, some 

of the gages were impacted by the submarine wake. Because of these 

factors, wave analysis focused only on gages where these laboratory effects 

were minimized. The results from gage location 9, from calibration setup 1 

and during testing, is presented herein for the regular waves because its 

location was within the influence of the generator to measure fully formed 

waves and was not heavily impacted by the submarine wake. The results 

from gage locations 4, 8, and 13, from calibration setup 2, is presented for 

the irregular wave calibrations and gage locations 5, 6, 7, and 9, from the 

testing setup, is presented for the irregular transit test waves. These gages 

were selected to define the irregular wave characteristics because their 

locations were within the influence of the generator at a 5 deg wave 

generation obliquity.

4.1 Wave calibration

Wave calibrations were performed prior to submarine testing to ensure that 

the target wave conditions were being achieved in the basin, specifically in 

the transit lanes. The complete set of calibration results is found in 

Appendix C.
ERDC/CHL TR-20-18 21

During wave calibrations, it was noticed that the Akamina capacitance 

gages were not measuring the crest of the regular waves, resulting in a 

flattened top. The wave heights measured from the Akamina gages were 

compared to those measured from the Senix gages. The difference between 

the wave heights measured was within the resolution and accuracy 

tolerances of the two gages; therefore, the errors from the Akamina 

measurements were determined to be insignificant.

The M1-M9 regular waves were generated in the zero and 5 deg directions. 

Two sets of gage arrangements were used to determine the wave field. For 

each gage, wave height (H) and wave period (T) were determined using a 

zero-crossing method. The root-mean-square-error (RMSE) (HRMSE and 

TRMSE), and standard deviation (Hstdev) were used as metrics for 

measurement accuracy for each wave condition, where the target 

conditions from Table 6 were the predicted value for comparison. 

During wave calibration, each gage was analyzed; however, some gages 

were either outside the wave influence or affected by reflected waves. 

Calibration metrics for gage location 9 is presented due to its location in 

the influence of waves, shown in Table 8 and Table 9. 

Table 8. Accuracy metrics for regular wave heights for gage location 9. 

M1 M2 M3 M4 M5 M6 M7 M8 M9 

0 ̊ H (in.) 0.86 1.37 2.19 3.63 2.86 3.36 3.44 3.28 2.56

Hstdev (in.) 0.04 0.15 0.12 0.65 0.22 0.36 0.53 0.29 0.46

HRMSE (in.) 0.02 0.07 0.09 0.14 0.17 0.08 0.28 0.04 0.14

5 ̊ H (in.) 0.85 1.69 2.44 3.26 3.22 2.80 2.81 2.91 2.93

Hstdev (in.) 0.06 0.21 0.35 0.27 0.24 0.20 0.22 0.10 0.13

HRMSE (in.) 0.03 0.08 0.03 0.08 0.08 0.05 0.11 0.06 0.12

Table 9. Accuracy metrics for regular wave periods for gage location 9. 

M1 M2 M3 M4 M5 M6 M7 M8 M9 

0 ̊ T (s) 0.96 1.34 1.72 2.40 2.68 3.11 3.53 3.83 4.57

TRMSE (s) 0.03 0.02 0.02 0.03 0.03 0.02 0.10 0.03 0.05

5 ̊ T (s) 0.96 1.34 1.72 2.40 2.68 3.12 3.55 3.84 4.56

TRMSE (s) 0.01 0.01 0.02 0.04 0.03 0.03 0.04 0.03 0.06
ERDC/CHL TR-20-18 22

The calibration of the wave heights and periods showed that the DSWG 

was accurately producing the target regular wave conditions. There was 

some deviation from the anticipated wave heights in the zero deg wave 

from M4 to M9, but this remained acceptable. The deviation in wave 

periods were insignificant. The low RMSE and standard deviations in both 

the zero and 5 deg wave directions provided confidence that the generator 

was performing consistently.

The remainder of the gages were analyzed for deviations in both wave 

height and period. Any deviations from the target regular waves were 

insignificant or explainable. Significant deviations were due to gage 

placement outside of the DSWG influence. It was determined that the 

target regular waves were being produced in the transit lanes and the 

regular waves were accepted for submarine testing.

The 15 irregular wave calibrations were performed in 1 min increments 

and were concatenated together to characterize the wave energy density 

spectrum. The sea state 4 waves were planned to be run at a zero deg 

heading and were calibrated as such; however, during submarine transit 

testing, it was decided that sea state 4 waves would provide more valuable 

results at a quartering heading. This wave condition was not calibrated 

prior to the submarine testing but was verified during testing.

The second gage layout was used for calibration of irregular waves. 

Because this gage layout focused on wave characteristics within the lanes, 

rather than throughout the basin, there were limited gage locations during 

calibration that overlapped with locations during submarine transit 

testing. Therefore, gages 4, 8, and 13 were analyzed to characterize the 

wave spectrum for quartering sea headings during calibration.

A spectral analysis was completed for each gage using concatenated 1 min 

signals. The results of the spectral analysis were compared to the TMA 

wave spectrum. Target and measured wave spectra for gage 4 are shown in 

Figure 11. Here the measured energy in the basin was less than the target 

TMA energy due to the concatenation. 

The statistical analysis for gages 4, 8, and 13 are presented in Table 10. The 

remaining irregular wave calibration results are found in Appendix C. The 

energy-based significant wave heights were computed using Hm0=4(m0)0.5.

The irregular wave period Tp was computed from the peak frequency as Tp
ERDC/CHL TR-20-18 23

= 1/fp. The standard deviation was computed for the energy-based 

significant wave height, and the RMSE, with respect to predicted values, 

were computed for the peak wave period. 

Figure 11. Target and measured wave spectra for gage 4 in sea state 3 calibrations. 

Table 10. Accuracy metrics for capacitance 

(C) gages 4, 8, and 13 in sea state 3 

calibrations. 

Sensor C4 C8 C13 Average 

Hm0 (in.) 0.95 1.04 0.91 0.97

H1/3 (in.) 1.14 1.11 1.13 1.13

Hm0stdev (in.) 0.02 0.02 0.02 0.02

Tp (s) 1.86 1.86 1.86 1.86

TpRMSE (s) 0.02 0.02 0.02 0.02

The energy-based wave heights (Hm0) for sea state 3 were lower than the 

target wave conditions. Uncertainty in the Hm0 statistic was primarily due 

dispersion and rereflection of the relatively small number of total waves 

per increment (approximately 30) that influenced the testing area. Thus, 

the zero upcrossing method was also used to determine the significant 

wave heights (H1/3) for comparison (Table 10). The H1/3 statistic was a 

more reliable measure of the irregular wave heights for this study. 

However, related studies required Hm0 to be defined for comparison. 
ERDC/CHL TR-20-18 24

The zero crossing significant wave heights were similar to the energybased significant wave heights. Although the measured Hm0 values were 

lower than the target Hm0, these wave heights were deemed acceptable in 

order to reduce the risk of the submarine hitting the bottom of the basin. 

The Hm0 values were not spatially uniform; however, the H1/3 were. The 

Hm0 was not reliable so the differences between gages do not necessarily 

indicate that the waves were spatially non-uniform. The energy-based 

significant wave height standard deviations for sea state 3 were low, 

providing confidence in the repeatability of the wave conditions. The peak 

wave periods were consistent during calibration and had little error.

4.2 Regular wave tests

The wave heights and periods from gage 9 are presented in Table 11

through Table 14. Multiple runs were completed for each heading and 

wave condition, so the values presented are averaged over these runs. The 

full set of results is in Appendix D.

During the submarine testing, the vessel motions resulted in a small 

underkeel clearance due to the influence of waves. To limit the submarine 

motions, the wave height was reduced, denoted in red in Table 11 and 

Table 12. The wave periods were not adjusted during testing.

Table 11. The zero deg wave heights H (inch) for the HS, FS, and BS. 

M1 M2 M3 M4 M5 M6 M7 M8 M9 

HS 0.96 1.29 2.22 3.72 1.26 1.41 1.23 1.95 1.23

FS 0.96 1.49 2.47 3.61 2.94 3.29 3.36 3.26 2.64

BS 0.92 1.49 2.30 2.15 1.43 1.53 3.38 3.37 2.68

Table 12. The 5 deg wave heights H (inch) for the BQ, SQ, and BQ-R. 

M1 M2 M3 M4 M5 M6 M7 M8 M9 

BQ 0.82 1.71 2.28 2.81 2.39 2.14 2.32 2.48 3.55

SQ 0.83 1.67 2.24 2.29 2.16 2.14 2.36 2.44 2.93

BQ-R 2.12 2.34
ERDC/CHL TR-20-18 25

Table 13. The zero deg wave period T (second) for the HS, FS, and BS. 

M1 M2 M3 M4 M5 M6 M7 M8 M9 

Cal 0.96 1.34 1.72 2.40 2.68 3.11 3.53 3.83 4.57

HS 0.97 1.33 1.70 2.33 2.69 2.91 3.30 3.51 3.92

FS 0.96 1.34 1.72 2.39 2.67 3.12 3.54 3.81 4.54

BS 0.96 1.33 1.72 2.38 2.70 3.13 3.54 3.80 4.31

Table 14. The 5 deg wave period T (second) for the BQ, SQ, and BQ-R. 

M1 M2 M3 M4 M5 M6 M7 M8 M9 

Cal 0.96 1.34 1.72 2.40 2.68 3.12 3.55 3.84 4.56

BQ 0.96 1.33 1.72 2.40 2.67 3.11 3.54 3.83 4.54

SQ 0.96 1.33 1.72 2.40 2.68 3.11 3.54 3.84 4.55’

BQ-R 3.11 3.54

4.3 Irregular wave tests

The irregular waves were analyzed using an energy-based spectral 

analysis. Each heading and sea state required multiple iterations of transit 

to ensure the submarine encountered enough waves. The BQ waves 

required 14 iterations for sea state 3 and 15 iterations for sea state 4. The 

SQ waves required 18 iterations for sea state 3 and 19 iterations for sea 

state 4. The measured water surface oscillations from these increments 

were concatenated to create the input for the spectral analysis. From the 

spectral analysis, the wave characteristics were computed. 

The results from gage locations 5, 6, 7, and 9 are presented for irregular 

waves because their locations were within the influence of the 5 deg wave 

direction. Additionally, the results from these gages were averaged and 

presented in the last column of each table. The results for influenced gages 

are found in Appendix D.

The measured significant wave heights for sea state 3 waves were similar 

to those measured during the wave calibration (Table 15 and Table 16). All 

tests were run in short bursts to minimize re-reflection impacts, but some 

were still present during irregular wave tests. The spectral peak wave 

periods were accurate during the irregular wave testing.
ERDC/CHL TR-20-18 26

Table 15. Sea state 3, BQ wave results for the capacitance (C) gages 5, 6, 7, and 9. 

C5 C6 C7 C9 Average 

Hm0 (in.) 0.82 0.81 1.07 1.15 0.97

Tp (s) 1.78 1.78 1.78 1.78 1.78

Table 16. Sea state 3, SQ wave results for the capacitance (C) gages 5, 6, 7, and 9. 

C5 C6 C7 C9 Average 

Hm0 (in.) 0.54 0.53 0.87 0.91 0.71

Tp (s) 1.78 1.78 1.86 1.86 1.78

The wave condition analysis and statistics for sea state 4 are presented in 

Table 17 and Table 18. Because a calibration of the 5 deg, sea state 4 wave 

condition was not completed prior to testing, the statistics were analyzed 

during the transit testing. The wave conditions were consistent throughout 

the tests; however, Hm0 values were smaller than the target TMA wave 

height. Therefore, the H1/3 was used as a validation. Although the energy in 

the basin was lower than the target condition, the wave conditions were 

deemed acceptable in order to reduce the possibility of the submarine 

impacting the floor. 

Table 17. Sea state 4, BQ wave results for capacitance (C) gages 5, 6, 7, and 9. 

C5 C6 C7 C9 Average 

Hm0 (in.) 1.09 1.08 1.88 1.83 1.52

H1/3 (in.) 1.56 1.57 1.52 1.60 1.56

Hm0stdev (in.) 0.02 0.02 0.06 0.06 0.04

Tp (s) 1.46 1.46 1.52 1.52 1.52

TpRMSE (s) 0.05 0.05 0.00 0.00 0.00

Table 18. Sea state 4, SQ wave results for capacitance (C) gages 5, 6, 7, and 9. 

C5 C6 C7 C9 Average 

Hm0 (in.) 1.34 1.34 2.07 2.10 1.71

H1/3 (in.) 1.59 1.59 1.56 1.62 1.59

Hm0stdev (in.) 0.04 0.04 0.07 0.08 0.06

Tp (s) 1.46 1.46 1.46 1.46 1.46

TpRMSE (s) 0.05 0.05 0.05 0.05 0.05
ERDC/CHL TR-20-18 27

5 Summary 

The experimental results described in this report are focused on the wave 

and water level conditions measured during submarine transits. The 

submarine transits were parallel and perpendicular to the plane of the 

wave generator and oblique creating following, head, beam, BQ, and SQ

headings relative to the waves. The model was tested at 8 kt and 12 kt 

prototype speeds for nine regular wave sea states at varying frequencies. 

Tests were conducted in regular and irregular waves of varying height and 

period. Waves were calibrated within the transit lanes and throughout the 

constant-depth basin and then measured near the transit lanes and at 

other locations in the basin during transits. Those measurements are 

described relative to the target wave conditions in the main report and 

then listed in detail in appendices.
ERDC/CHL TR-20-18 28

References

Akamina Technologies. 2014. AWP-24-3 Wave Height Gauge User’s Guide. Akamina 

Technologies Inc. Ottawa, ON. https://masde.net/images/PDFS/AWP-24-3-usersguide.pdf

Brougham, Captain William J. 2014. “Ohio Replacement Program System Description.” 

Sea, Air, and Space Symposium, April 8, 2014. 

Jamieson, W., and G. Mogridge. 2000. Model Tests of Upright Wave Absorbers for the 

ERDC Shallow Water Multidirectional Wave Basin. Technical Report HYDCTR-092. National Research Council Canada, NRC Canadian Hydraulics Centre.

Ottawa, ON. 

O’Rourke, R. 2018. Navy Columbia (SSBN-826) Class Ballistic Missile Submarine 

Program: Background and Issues for Congress. Congressional Research Service.

Rexroth Hydraudyne B. V. 2003. System Description, Segmented Wave Generator. 

Rexroth Bosch Group, Netherlands.

https://www.boschrexroth.com/en/xc/industries/machinery-applications-andengineering/hydrodynamic-research/products-and-solutions/wave-generator/index

Senix Corporation. 2015. ToughSonic 14 Level & Distance Sensor. Senix Distance 

Measurement. Hinesburg, VT. https://senix.com/wpcontent/uploads/2019/09/toughsonic-14-30mm-data-sheet.pdf

Temple, D., A. Percival, A. Punzi, K. Silva, and R. Thomas. 2018. Deep and Shallow 

Water Seakeeping Tests for Integration of Columbia into Environmental 

Monitoring and Operator Guidance System. Naval Surface Warfare Center, 

Carderock Division. West Bethesda, MD. 
ERDC/CHL TR-20-18 29

Appendix A: Notation

H Wave height

Herr Wave height error

Hm0 Energy-based significant wave height

Hm0err Significant wave height error

Hm0RMSE Significant wave height root mean square error

Hm0stdev Significant wave height standard deviation

HRMSE Wave height root mean square error

Hstdev Wave height standard deviation

H1/3 Explicit significant wave height

T Period

Terr Period error

Tp Peak wave period

Tperr Peak wave period error

TpRMSE Peak wave period root mean square error

Tpstdev Peak wave period standard deviation

TRMSE Period root mean square error

Tstdev Period standard deviation
ERDC/CHL TR-20-18 30

Appendix B: Gage Calibration Factors

Table B-1 presents gage calibration factors.

Table B-1. Gage calibration factors. 

Physical Gage Column Slope cm/V Intercept Bias RMSE (cm) 

Akamina 5 1 5.882 -22.8 -0.001 0.07

Akamina 21 2 5.797 -26.28 -0.021 0.13

Akamina 11 3 5.929 -28.23 0.000 0.05

Akamina 3 4 5.953 -27.23 0.000 0.11

Akamina 4 5 5.943 -27.27 0.000 0.05

Akamina 12 6 5.892 -22.82 0.000 0.04

Akamina 10 7 5.896 -22.7 0.000 0.05

Akamina 16 8 5.909 -22.94 0.000 0.09

Akamina 15 9 5.91 -22.86 0.000 0.05

Senix 1 10 -3.01542 0.012345

Akamina 22 11 5.834 -25.85 0.000 0.10

Senix 2 19 -3.01542 0.012345
ERDC/CHL TR-20-18 31

Appendix C: Calibration Results

The wave characteristics and statistics measured during the wave 

calibration are presented in the tables below (Tables C-1 through C-26). 

M# refers to the wave conditions, and C# refers to the wave gage. Gages 

measuring outside of the wave influence are not presented. The gage 

locations for each of the setups is presented in Section 3.1. 

C.1 Regular waves

C.1.1 Setup 1

The gage locations for setup 1 are presented in Figure 8.

Table C-1. Wave heights (inch) for zero deg waves during wave calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.924 0.892 0.859 0.860 0.873 0.861 1.042 0.828 0.778 0.820

M2 1.409 1.340 1.513 1.352 1.519 1.367 1.658 1.626 1.272 1.579

M3 1.991 2.151 1.982 2.346 1.873 2.189 1.653 2.327 2.235 2.264

M4 2.687 2.513 2.824 3.606 3.005 3.632 2.970 2.797 2.006 2.845

M5 3.355 3.162 3.412 2.755 2.217 2.861 2.960 3.343 2.632 3.156

M6 3.248 3.180 3.365 3.522 2.088 3.356 3.712 3.193 3.100 3.265

M7 3.045 2.417 3.279 3.699 2.426 3.441 4.042 2.676 3.533 2.767

M8 3.256 2.160 3.189 3.374 2.564 3.285 3.626 2.147 3.794 2.613

M9 3.410 1.826 3.379 2.571 3.093 2.563 3.626 2.252 3.846 2.286
ERDC/CHL TR-20-18 32

Table C-2. Wave height RMSE (inch) for zero deg waves during wave calibration, 

setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.029 0.026 0.049 0.043 0.054 0.044 0.156 0.091 0.129 0.091

M2 0.100 0.171 0.022 0.165 0.071 0.151 0.164 0.132 0.237 0.096

M3 0.114 0.087 0.124 0.257 0.230 0.124 0.457 0.236 0.139 0.192

M4 0.326 0.508 0.191 0.617 0.087 0.647 0.111 0.256 1.003 0.213

M5 0.371 0.188 0.473 0.304 0.790 0.215 0.103 0.357 0.413 0.210

M6 0.263 0.240 0.391 0.529 0.921 0.364 0.730 0.214 0.279 0.285

M7 0.091 0.587 0.377 0.704 0.583 0.530 1.048 0.336 0.592 0.290

M8 0.259 0.858 0.283 0.390 0.440 0.287 0.640 0.863 0.814 0.395

M9 0.426 1.178 0.459 0.433 0.107 0.456 1.165 0.750 0.852 0.722

Table C-3. Wave height standard deviations (inch) for zero deg waves during wave 

calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.017 0.025 0.028 0.017 0.048 0.022 0.066 0.056 0.041 0.043

M2 0.042 0.058 0.018 0.075 0.068 0.073 0.043 0.039 0.066 0.055

M3 0.036 0.072 0.039 0.077 0.036 0.087 0.096 0.066 0.034 0.102

M4 0.092 0.147 0.077 0.118 0.089 0.142 0.109 0.159 0.140 0.150

M5 0.110 0.099 0.209 0.186 0.111 0.169 0.097 0.103 0.195 0.140

M6 0.090 0.162 0.145 0.087 0.136 0.077 0.167 0.094 0.269 0.106

M7 0.082 0.071 0.225 0.090 0.101 0.278 0.122 0.089 0.237 0.179

M8 0.038 0.160 0.175 0.117 0.063 0.039 0.141 0.133 0.191 0.086

M9 0.121 0.097 0.266 0.064 0.054 0.136 1.028 0.054 0.113 0.108
ERDC/CHL TR-20-18 33

Table C-4. Wave periods (second) for zero deg waves during wave calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.962 0.963 0.963 0.963 0.962 0.963 0.963 0.961 0.962 0.963

M2 1.335 1.334 1.334 1.336 1.336 1.338 1.337 1.336 1.338 1.334

M3 1.721 1.721 1.721 1.721 1.721 1.721 1.717 1.720 1.721 1.720

M4 2.399 2.404 2.400 2.400 2.396 2.401 2.408 2.400 2.398 2.398

M5 2.679 2.682 2.670 2.681 2.678 2.680 2.679 2.685 2.682 2.678

M6 3.113 3.106 3.114 3.109 3.114 3.112 3.110 3.110 3.109 3.111

M7 3.549 3.551 3.521 3.543 3.532 3.526 3.543 3.540 3.528 3.538

M8 3.836 3.842 3.838 3.819 3.836 3.832 3.818 3.844 3.831 3.836

M9 4.559 4.573 4.562 4.567 4.551 4.571 4.112 4.571 4.559 4.559

Table C-5. Wave period RMSE (second) for zero deg waves during wave calibration, 

setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.021 0.026 0.031 0.024 0.021 0.026 0.067 0.028 0.023 0.027

M2 0.022 0.028 0.018 0.023 0.028 0.022 0.050 0.020 0.019 0.016

M3 0.028 0.024 0.025 0.019 0.020 0.024 0.054 0.022 0.021 0.015

M4 0.025 0.031 0.037 0.033 0.046 0.033 0.062 0.036 0.031 0.032

M5 0.032 0.028 0.070 0.032 0.046 0.027 0.092 0.045 0.054 0.033

M6 0.032 0.027 0.032 0.028 0.029 0.024 0.048 0.024 0.037 0.028

M7 0.048 0.037 0.141 0.047 0.055 0.104 0.048 0.049 0.086 0.040

M8 0.043 0.030 0.058 0.052 0.022 0.031 0.047 0.016 0.045 0.035

M9 0.059 0.071 0.040 0.039 0.059 0.049 1.219 0.047 0.037 0.063
ERDC/CHL TR-20-18 34

Table C-6. Wave heights (inch) for 5 deg waves during wave calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.931 0.832 1.026 0.979 0.820 0.849 0.801 1.054 1.013 1.097

M2 1.533 1.464 1.423 1.296 1.403 1.694 1.262 1.396 1.553 1.606

M3 1.972 1.924 1.929 1.792 2.133 2.445 2.027 2.191 1.884 2.151

M4 2.783 2.779 3.116 3.315 2.618 3.261 2.884 3.207 2.525 2.831

M5 2.780 2.697 3.048 2.985 2.409 3.224 2.846 3.537 2.930 2.521

M6 3.052 2.953 3.763 3.558 2.350 2.803 3.316 3.330 2.833 2.819

M7 3.138 2.442 3.371 3.877 2.580 2.815 3.682 2.409 3.345 2.809

M8 3.536 2.333 2.933 3.141 2.709 2.915 3.466 2.635 3.700 2.658

M9 3.357 1.881 3.043 2.597 2.870 2.933 3.678 2.393 3.814 1.979

Table C-7. Wave height RMSE (inch) for 5 deg waves during wave calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.043 0.072 0.128 0.084 0.084 0.058 0.118 0.168 0.122 0.200

M2 0.054 0.048 0.111 0.206 0.100 0.211 0.243 0.126 0.058 0.110

M3 0.133 0.199 0.191 0.348 0.054 0.346 0.126 0.125 0.234 0.126

M4 0.225 0.226 0.143 0.329 0.446 0.272 0.197 0.237 0.479 0.229

M5 0.225 0.311 0.210 0.190 0.609 0.236 0.225 0.555 0.297 0.510

M6 0.105 0.146 0.798 0.568 0.654 0.204 0.379 0.337 0.191 0.228

M7 0.188 0.574 0.431 0.899 0.433 0.215 0.691 0.602 0.356 0.308

M8 0.539 0.668 0.131 0.168 0.314 0.101 0.481 0.374 0.750 0.354

M9 0.372 1.122 0.204 0.416 0.148 0.132 0.709 0.621 0.819 1.026

 
ERDC/CHL TR-20-18 35

Table C-8. Wave height standard deviations (inch) for 5 deg waves during wave 

calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.030 0.024 0.023 0.027 0.026 0.027 0.066 0.070 0.048 0.036

M2 0.043 0.032 0.078 0.031 0.022 0.084 0.050 0.072 0.024 0.031

M3 0.035 0.088 0.083 0.165 0.044 0.031 0.105 0.088 0.091 0.114

M4 0.058 0.047 0.086 0.093 0.232 0.080 0.160 0.113 0.068 0.159

M5 0.051 0.074 0.203 0.194 0.150 0.078 0.169 0.144 0.296 0.180

M6 0.095 0.143 0.241 0.106 0.079 0.055 0.216 0.070 0.097 0.143

M7 0.131 0.136 0.197 0.207 0.112 0.114 0.108 0.120 0.090 0.251

M8 0.065 0.046 0.117 0.096 0.120 0.057 0.124 0.088 0.281 0.095

M9 0.110 0.087 0.209 0.109 0.074 0.120 0.174 0.135 0.087 0.113

Table C-9. Wave periods (second) for 5 deg waves during wave calibration, setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.963 0.963 0.962 0.963 0.964 0.962 0.963 0.962 0.963 0.962

M2 1.336 1.334 1.336 1.335 1.334 1.335 1.334 1.334 1.334 1.335

M3 1.720 1.720 1.717 1.722 1.721 1.722 1.720 1.718 1.719 1.719

M4 2.401 2.402 2.399 2.402 2.401 2.403 2.406 2.400 2.397 2.398

M5 2.681 2.683 2.682 2.683 2.679 2.678 2.676 2.684 2.685 2.682

M6 3.111 3.107 3.112 3.109 3.109 3.117 3.114 3.110 3.113 3.106

M7 3.546 3.551 3.524 3.528 3.545 3.546 3.539 3.541 3.541 3.544

M8 3.838 3.832 3.830 3.829 3.840 3.836 3.827 3.838 3.835 3.845

M9 4.561 4.557 4.555 4.553 4.564 4.558 4.567 4.563 4.567 4.566
ERDC/CHL TR-20-18 36

Table C-10. Wave period RMSE (second) for 5 deg waves during wave calibration, 

setup 1. 

C2 C3 C4 C7 C8 C9 C10 C13 C14 C15 

M1 0.014 0.019 0.020 0.027 0.021 0.013 0.034 0.017 0.008 0.020

M2 0.012 0.026 0.016 0.024 0.020 0.012 0.037 0.016 0.020 0.018

M3 0.024 0.024 0.043 0.018 0.044 0.021 0.052 0.024 0.022 0.032

M4 0.038 0.026 0.034 0.025 0.024 0.039 0.071 0.031 0.036 0.023

M5 0.033 0.031 0.024 0.025 0.041 0.035 0.047 0.035 0.034 0.032

M6 0.035 0.041 0.021 0.033 0.030 0.032 0.060 0.024 0.031 0.039

M7 0.060 0.045 0.118 0.071 0.055 0.037 0.074 0.045 0.042 0.046

M8 0.026 0.040 0.046 0.033 0.028 0.032 0.045 0.039 0.025 0.043

M9 0.045 0.055 0.034 0.051 0.062 0.056 0.091 0.040 0.034 0.035

C.1.2 Setup 2

The gage locations for setup 2 are presented in Figure 9.

Table C-11. Wave heights (inch) for zero deg waves during wave calibration, setup 2, 

gages 1–10. 

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 

M1 0.987 1.006 0.689 1.006 0.707 0.814 0.857 0.869 0.359 1.062

M2 1.540 1.174 1.349 1.365 0.936 1.424 1.458 1.509 1.123 1.690

M3 2.724 2.249 1.794 2.363 1.310 2.470 2.124 1.912 1.611 1.692

M4 3.626 3.855 3.377 3.090 1.943 2.885 2.621 2.976 2.368 3.068

M5 3.724 3.936 3.291 2.651 2.123 2.791 3.130 2.221 2.869 3.075

M6 3.653 3.952 3.807 3.073 1.474 2.558 3.183 2.111 2.989 3.621

M7 3.431 3.467 3.306 2.873 1.437 3.387 3.103 2.488 3.338 3.998

M8 2.718 3.974 3.966 3.908 2.349 3.212 3.080 2.654 3.149 3.657

M9 3.686 3.753 3.763 3.674 2.281 3.402 2.965 3.075 2.669 3.984

 
ERDC/CHL TR-20-18 37

Table C-12. Wave heights (inch) for zero deg waves during wave calibration, setup 2, 

gages 11–19. 

C11 C12 C13 C14 C15 C16 C17 C18 C19 

M1 0.509 0.732 0.830 0.777 0.792 0.802 0.966 0.859 1.007

M2 1.018 1.245 1.346 1.327 1.362 1.181 1.326 1.470 1.437

M3 1.474 1.841 1.975 2.197 1.862 1.756 2.261 1.779 2.465

M4 2.329 2.269 3.442 2.050 3.419 2.223 3.854 2.372 3.096

M5 2.092 1.972 2.931 2.637 3.119 1.977 3.214 2.115 2.713

M6 1.840 1.860 3.192 3.197 3.117 1.932 3.314 2.344 2.639

M7 1.106 2.226 3.115 3.552 2.997 2.329 3.727 2.311 2.194

M8 2.030 2.461 3.297 4.013 3.069 2.675 3.132 2.626 2.384

M9 1.975 1.845 3.155 3.855 3.002 1.975 3.802 2.785 1.610

Table C-13. Wave height RMSE (inch) for zero deg waves during wave calibration, 

setup 2, gages 1–10. 

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 

M1 0.120 0.108 0.215 0.108 0.195 0.087 0.050 0.035 0.548 0.167

M2 0.105 0.334 0.169 0.137 0.565 0.115 0.055 0.037 0.383 0.212

M3 0.639 0.197 0.337 0.270 0.791 0.406 0.095 0.194 0.503 0.416

M4 0.648 0.881 0.382 0.130 1.066 0.134 0.386 0.099 0.645 0.120

M5 0.748 0.952 0.337 0.464 0.884 0.226 0.155 0.783 0.228 0.092

M6 0.675 0.973 0.821 0.147 1.527 0.468 0.189 0.897 0.157 0.622

M7 0.486 0.472 0.422 0.201 1.565 0.414 0.179 0.517 0.400 1.002

M8 0.317 1.023 1.105 1.024 0.776 0.270 0.133 0.368 0.268 0.664

M9 0.837 0.761 0.782 0.708 0.813 0.453 0.167 0.106 0.377 0.988

 
ERDC/CHL TR-20-18 38

Table C-14. Wave height RMSE (inch) for zero deg waves during wave calibration, 

setup 2, gages 11–19. 

C11 C12 C13 C14 C15 C16 C17 C18 C19 

M1 0.391 0.168 0.071 0.135 0.109 0.108 0.075 0.058 0.113

M2 0.488 0.256 0.159 0.178 0.141 0.320 0.177 0.077 0.091

M3 0.650 0.263 0.133 0.109 0.253 0.351 0.247 0.452 0.392

M4 0.707 0.735 0.465 0.956 0.438 0.780 0.898 0.631 0.123

M5 0.915 1.037 0.165 0.415 0.216 1.027 0.366 0.893 0.301

M6 1.174 1.143 0.228 0.340 0.206 1.068 0.329 0.679 0.382

M7 1.907 0.796 0.130 0.559 0.110 0.711 0.787 0.699 0.941

M8 1.078 0.595 0.337 1.061 0.162 0.461 0.308 0.416 0.667

M9 1.043 1.160 0.262 0.863 0.163 1.043 0.809 0.308 1.698

Table C-15. Wave height standard deviations (inch) for zero deg waves during wave 

calibration, setup 2, gages 1–10. 

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 

M1 0.088 0.023 0.036 0.023 0.025 0.011 0.026 0.016 0.090 0.040

M2 0.100 0.074 0.078 0.022 0.023 0.085 0.036 0.036 0.065 0.075

M3 0.142 0.117 0.144 0.063 0.034 0.172 0.092 0.046 0.122 0.084

M4 0.172 0.218 0.065 0.096 0.140 0.071 0.074 0.098 0.133 0.102

M5 0.192 0.176 0.176 0.315 0.107 0.089 0.086 0.077 0.194 0.054

M6 0.178 0.210 0.158 0.131 0.048 0.159 0.049 0.126 0.162 0.045

M7 0.218 0.070 0.302 0.161 0.071 0.150 0.153 0.081 0.223 0.093

M8 0.151 0.326 0.533 0.493 0.442 0.176 0.110 0.132 0.232 0.105

M9 0.412 0.119 0.178 0.229 0.399 0.221 0.169 0.078 0.190 0.088

 
ERDC/CHL TR-20-18 39

Table C-16. Wave height standard deviations (inch) for zero deg waves during wave 

calibration, setup 2, gages 11–19. 

C11 C12 C13 C14 C15 C16 C17 C18 C19 

M1 0.010 0.010 0.012 0.058 0.014 0.044 0.036 0.042 0.035

M2 0.082 0.026 0.038 0.040 0.027 0.035 0.029 0.072 0.067

M3 0.179 0.044 0.046 0.051 0.089 0.069 0.192 0.325 0.147

M4 0.229 0.070 0.149 0.107 0.133 0.076 0.219 0.065 0.078

M5 0.113 0.134 0.155 0.206 0.186 0.086 0.308 0.120 0.094

M6 0.188 0.086 0.126 0.287 0.176 0.045 0.098 0.182 0.127

M7 0.236 0.195 0.062 0.094 0.114 0.245 0.314 0.120 0.491

M8 0.490 0.262 0.166 0.331 0.154 0.341 0.256 0.191 0.269

M9 0.202 0.104 0.197 0.123 0.172 0.203 0.116 0.234 0.987

Table C-17. Wave periods (second) for zero deg waves during wave calibration, setup 

2, gages 1–10. 

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 

M1 0.955 0.962 0.961 0.962 0.960 0.963 0.963 0.963 0.963 0.967

M2 1.329 1.331 1.333 1.337 1.337 1.336 1.335 1.335 1.335 1.332

M3 1.721 1.715 1.720 1.722 1.720 1.720 1.716 1.722 1.722 1.720

M4 2.401 2.405 2.396 2.399 2.396 2.402 2.405 2.399 2.408 2.399

M5 2.685 2.683 2.682 2.682 2.680 2.683 2.681 2.678 2.679 2.679

M6 3.121 3.105 3.111 3.107 3.106 3.112 3.111 3.113 3.111 3.107

M7 3.526 3.554 3.542 3.543 3.576 3.542 3.547 3.538 3.542 3.544

M8 3.847 3.825 3.808 3.835 3.818 3.827 3.833 3.840 3.840 3.835

M9 4.526 4.563 4.560 4.571 4.540 4.569 4.569 4.552 4.566 4.569

 
ERDC/CHL TR-20-18 40

Table C-18. Wave periods (second) for zero deg waves during wave calibration, setup 

2, gages 11–19. 

C11 C12 C13 C14 C15 C16 C17 C18 C19 

M1 0.962 0.963 0.964 0.963 0.963 0.964 0.962 0.962 0.963

M2 1.334 1.337 1.333 1.336 1.335 1.335 1.332 1.334 1.339

M3 1.722 1.718 1.719 1.722 1.719 1.713 1.722 1.714 1.720

M4 2.396 2.399 2.400 2.399 2.400 2.398 2.386 2.407 2.397

M5 2.692 2.669 2.683 2.666 2.676 2.691 2.677 2.698 2.686

M6 3.103 3.109 3.113 3.105 3.111 3.121 3.111 3.112 3.106

M7 3.481 3.547 3.537 3.543 3.540 3.547 3.540 3.550 3.287

M8 3.845 3.814 3.819 3.832 3.841 3.836 3.791 3.823 3.841

M9 4.578 4.571 4.573 4.560 4.569 4.567 4.560 4.583 2.956

Table C-19. Wave period RMSE (second) for zero deg waves during wave calibration, 

setup 2, gages 1–10. 

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 

M1 0.021 0.022 0.030 0.021 0.038 0.020 0.021 0.029 0.020 0.068

M2 0.019 0.022 0.018 0.033 0.029 0.014 0.028 0.026 0.023 0.061

M3 0.018 0.047 0.030 0.020 0.035 0.017 0.039 0.021 0.022 0.042

M4 0.030 0.034 0.029 0.024 0.041 0.026 0.031 0.032 0.040 0.046

M5 0.030 0.043 0.025 0.036 0.035 0.030 0.030 0.036 0.036 0.061

M6 0.021 0.030 0.031 0.029 0.043 0.050 0.020 0.026 0.030 0.062

M7 0.056 0.037 0.046 0.038 0.081 0.043 0.034 0.041 0.040 0.044

M8 0.057 0.038 0.108 0.031 0.051 0.038 0.040 0.022 0.049 0.058

M9 0.103 0.030 0.033 0.036 0.115 0.045 0.054 0.079 0.062 0.054

 
ERDC/CHL TR-20-18 41

Table C-20. Wave period RMSE (second) for zero deg waves during wave calibration, 

setup 2, gages 11–19. 

C11 C12 C13 C14 C15 C16 C17 C18 C19 

M1 0.027 0.020 0.030 0.014 0.013 0.017 0.009 0.050 0.051

M2 0.028 0.028 0.030 0.018 0.020 0.026 0.042 0.067 0.027

M3 0.037 0.029 0.031 0.022 0.026 0.051 0.019 0.040 0.075

M4 0.065 0.031 0.028 0.029 0.026 0.027 0.056 0.052 0.072

M5 0.037 0.088 0.033 0.104 0.045 0.026 0.035 0.076 0.060

M6 0.062 0.033 0.025 0.049 0.019 0.031 0.028 0.108 0.061

M7 0.250 0.059 0.040 0.040 0.041 0.038 0.057 0.060 0.769

M8 0.042 0.098 0.068 0.023 0.019 0.048 0.139 0.092 0.071

M9 0.072 0.067 0.042 0.041 0.039 0.076 0.023 0.135 2.012

Table C-21. Wave heights (inch) for 5 deg waves during wave calibration, setup 2. 

C3 C4 C6 C7 C8 C9 C12 C13 C14 C15 C18 

M1 0.892 0.774 1.174 0.953 0.851 0.344 0.859 0.915 0.857 0.951 0.698

M2 1.409 1.817 1.736 1.284 1.400 1.271 1.499 1.642 1.531 1.274 1.104

M3 2.168 2.183 2.160 2.048 2.189 1.537 2.040 1.946 1.850 2.337 1.309

M4 3.006 3.620 2.768 2.741 2.637 2.753 2.441 2.702 2.503 3.409 1.932

M5 2.835 2.865 2.628 2.684 2.449 2.799 2.587 2.415 2.927 3.398 1.925

M6 3.275 2.892 1.721 2.640 2.418 3.199 2.304 2.996 2.864 3.327 1.561

M7 3.179 2.359 2.323 2.757 2.595 3.969 2.420 3.554 3.343 3.007 1.134

M8 3.869 3.018 2.354 3.052 2.803 3.575 2.335 3.682 3.880 2.703 1.916

M9 3.313 2.955 2.967 3.149 2.879 2.605 2.123 3.520 3.814 2.533 2.130

 
ERDC/CHL TR-20-18 42

Table C-22. Wave height RMSE (inch) for 5 deg waves during wave calibration, 

setup 2. 

C3 C4 C6 C7 C8 C9 C12 C13 C14 C15 C18 

M1 0.021 0.137 0.275 0.054 0.055 0.556 0.042 0.054 0.054 0.067 0.203

M2 0.098 0.318 0.237 0.220 0.103 0.239 0.042 0.143 0.048 0.230 0.398

M3 0.088 0.097 0.083 0.145 0.103 0.567 0.077 0.171 0.254 0.248 0.815

M4 0.057 0.630 0.263 0.263 0.394 0.264 0.563 0.319 0.498 0.424 1.074

M5 0.190 0.238 0.377 0.325 0.574 0.230 0.419 0.595 0.255 0.420 1.083

M6 0.351 0.198 1.286 0.363 0.589 0.228 0.706 0.093 0.176 0.332 1.484

M7 0.312 0.656 0.701 0.261 0.422 1.029 0.619 0.556 0.352 0.138 1.904

M8 0.937 0.337 0.661 0.162 0.272 0.610 0.689 0.704 0.949 0.356 1.099

M9 0.343 0.194 0.435 0.186 0.147 0.424 0.881 0.525 0.817 0.492 0.886

Table C-23. Wave height standard deviations (inch) for 5 deg waves during wave 

calibration, setup 2. 

C3 C4 C6 C7 C8 C9 C12 C13 C14 C15 C18 

M1 0.020 0.053 0.016 0.010 0.023 0.016 0.008 0.051 0.034 0.042 0.023

M2 0.038 0.026 0.025 0.043 0.026 0.065 0.042 0.019 0.037 0.043 0.038

M3 0.056 0.051 0.060 0.140 0.052 0.068 0.047 0.076 0.046 0.068 0.204

M4 0.058 0.119 0.129 0.045 0.157 0.096 0.065 0.116 0.036 0.111 0.124

M5 0.099 0.199 0.066 0.081 0.168 0.116 0.072 0.113 0.252 0.141 0.140

M6 0.226 0.172 0.135 0.049 0.090 0.117 0.121 0.096 0.117 0.062 0.369

M7 0.268 0.146 0.182 0.099 0.121 0.361 0.223 0.046 0.079 0.144 0.384

M8 0.369 0.353 0.147 0.168 0.195 0.211 0.186 0.180 0.371 0.205 0.191

M9 0.148 0.201 0.458 0.117 0.089 0.161 0.088 0.080 0.074 0.165 0.183

 
ERDC/CHL TR-20-18 43

Table C-24. Wave periods (second) for 5 deg waves during wave calibration, setup 2. 

C3 C4 C6 C7 C8 C9 C12 C13 C14 C15 C18 

M1 0.961 0.962 0.963 0.964 0.962 0.962 0.963 0.961 0.963 0.960 0.963

M2 1.338 1.334 1.336 1.336 1.335 1.335 1.335 1.336 1.335 1.334 1.336

M3 1.721 1.720 1.722 1.705 1.720 1.724 1.718 1.721 1.722 1.723 1.724

M4 2.397 2.396 2.403 2.403 2.403 2.407 2.403 2.404 2.400 2.400 2.409

M5 2.678 2.681 2.682 2.681 2.680 2.685 2.685 2.685 2.683 2.684 2.687

M6 3.112 3.077 3.117 3.115 3.110 3.110 3.106 3.108 3.109 3.112 2.892

M7 3.548 3.549 3.531 3.542 3.528 3.546 3.541 3.533 3.542 3.540 3.117

M8 3.838 3.840 3.825 3.842 3.840 3.838 3.832 3.835 3.835 3.842 3.828

M9 4.561 4.565 4.558 4.552 4.560 4.566 4.564 4.565 4.563 4.576 4.550

Table C-25. Wave period RMSE (second) for 5 deg waves during wave calibration, 

setup 2. 

C3 C4 C6 C7 C8 C9 C12 C13 C14 C15 C18 

M1 0.012 0.012 0.021 0.016 0.021 0.010 0.015 0.023 0.008 0.022 0.041

M2 0.017 0.018 0.028 0.021 0.030 0.029 0.017 0.020 0.026 0.016 0.045

M3 0.028 0.014 0.030 0.062 0.027 0.018 0.027 0.021 0.017 0.023 0.039

M4 0.026 0.034 0.030 0.033 0.030 0.033 0.033 0.030 0.032 0.025 0.046

M5 0.036 0.034 0.029 0.041 0.035 0.037 0.046 0.036 0.033 0.026 0.067

M6 0.033 0.120 0.076 0.020 0.024 0.029 0.030 0.042 0.044 0.028 0.636

M7 0.039 0.027 0.049 0.051 0.071 0.036 0.040 0.045 0.043 0.037 0.943

M8 0.026 0.039 0.046 0.045 0.018 0.030 0.047 0.030 0.019 0.030 0.072

M9 0.033 0.040 0.054 0.024 0.063 0.047 0.050 0.031 0.052 0.058 0.203

 
ERDC/CHL TR-20-18 44

C.2 Irregular waves

Irregular wave calibrations were only measured using setup 2. During 

testing, it was determined beneficial to test both sea state 3 and sea state 4 

in quartering seas; therefore, no results for zero deg are presented. The 

gage locations are presented in Figure 13.

Table C-26. Sea state 3 irregular wave characteristic statistics. 

C3 C4 C6 C7 C8 C9 C12 C13 C14 C15 C18 

Hm0 (in.) 1.08 0.95 0.53 0.95 1.04 0.92 0.85 0.91 0.76 1.25 0.30

Hm0stdev (in.) 0.02 0.02 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.03 0.00

Hm0RMSE (in.) 0.30 0.43 0.85 0.43 0.34 0.46 0.54 0.48 0.62 0.14 1.09

Tp (s) 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.86 1.78

TpRMSE (s) 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.06
ERDC/CHL TR-20-18 45

Appendix D: Submarine Testing Results

The tables presented in this appendix are arranged by heading then wave 

condition (Tables D-1 through D-22).. For each wave condition, the wave 

heights and wave period are presented for each run. The results presented 

are for the gages that are influenced by the waves during the runs. The run 

numbers are presented as “R#” in the left column of each table. The gages 

are designated as either “C#” or “S#”, where C gages are Akamina 

capacitance gages and S gages are Senix sonar gages. The gage locations 

for the submarine testing are presented in Figure 10. The average value for 

each regular wave condition is presented in the last row for each heading.
ERDC/CHL TR-20-18 46

D.1 Wave M1

Table D-1. Wave heights (inch) by heading for wave M1. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R2 1.0 1.2 1.2 0.4 0.4 0.9 1.0 0.4 0.4

R3 1.0 1.0 1.4 0.5 0.5 0.9 0.9 0.5 0.6

R4 1.0 1.0 1.2 0.4 0.4 0.8 1.0 0.3 0.4

R5 0.8 1.5 1.3 0.5 0.5 0.8 0.9 0.3 0.3

Av 1.0 1.2 1.3 0.5 0.5 0.9 1.0 0.4 0.4

Head R1 1.1 0.9 1.0 0.6 0.6 0.7 0.9

R2 0.8 1.4 1.3 0.3 0.4 0.9 1.0

Av 0.9 1.1 1.2 0.4 0.5 0.8 1.0

Beam R1 0.6 0.9 0.7 0.7 0.7 0.9 0.9 0.2 0.3

R2 0.8 0.9 0.9 0.5 0.5 0.9 0.9 0.2 0.3

R3 1.0 0.8 1.1 0.6 0.5 0.9 0.9 0.4 0.5

R4 0.9 0.9 1.0 0.4 0.4 0.8 0.9 0.3 0.3

R5 0.9 1.1 0.9 0.5 0.5 0.9 0.9 0.4 0.3

R6 0.7 1.3 1.1 0.5 0.5 0.9 1.0 0.2 0.3

Av 0.8 1.0 0.9 0.5 0.5 0.9 0.9 0.3 0.3

SQ R1 0.8 0.5 0.5 0.8 0.8 0.3

R2 0.7 0.6 0.5 0.9 0.9 0.3

Av 0.8 0.5 0.5 0.9 0.8 0.3

BQ R1 0.8 0.4 0.4 0.9 0.8

R2 0.7 0.4 0.4 0.9 0.8

Av 0.8 0.4 0.4 0.9 0.8

 
ERDC/CHL TR-20-18 47

Table D-2. Wave periods (second) by heading for wave M1. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.7

R3 0.9 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9

R4 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.8

R5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 0.7

Av 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.8 0.8

Head R1 0.9 1.0 1.0 1.0 1.0 0.9 1.0

R2 0.9 1.0 1.0 0.8 0.9 1.0 1.0

Av 0.9 1.0 1.0 0.9 0.9 1.0 1.0

Beam R1 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 0.7

R2 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.6 0.6

R3 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.9

R4 1.0 0.9 1.0 1.0 1.0 1.0 1.0 0.7 0.7

R5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.9 0.8

R6 0.9 0.9 1.0 1.0 1.0 1.0 1.0 0.6 0.7

Av 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.7 0.7

SQ R1 1.0 1.0 1.0 1.0 1.0 0.7

R2 1.0 1.0 1.0 1.0 1.0 0.8

Av 1.0 1.0 1.0 1.0 1.0 0.7

BQ R1 1.0 1.0 1.0 1.0 1.0

R2 1.0 1.0 1.0 1.0 1.0

Av 1.0 1.0 1.0 1.0 1.0
ERDC/CHL TR-20-18 48

D.2 Wave M2

Table D-3. Wave heights (inch) by heading for wave M2. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 1.5 1.5 1.8 1.3 1.3 1.5 1.3 0.5 0.7

R2 1.5 1.8 1.6 1.2 1.2 1.5 1.6 0.5 0.6

R3 1.5 1.8 1.6 1.1 1.1 1.6 1.5 0.6 0.6

R4 1.4 1.7 1.7 1.1 1.1 1.6 1.4 0.5 0.6

R5 1.2 1.6 1.5 0.8 0.7 1.5 1.4 0.4 0.6

R6 1.1 1.7 1.8 1.1 0.8 1.5 1.5 0.6 0.5

R7 1.3 1.9 1.7 0.8 0.8 1.6 1.7 0.6 0.6

Av 1.4 1.7 1.7 1.1 1.0 1.5 1.5 0.5 0.6

Head R1 1.7 1.5 1.6 1.3 1.3 1.5 1.3

R2 1.3 1.6 1.8 1.4 1.4 1.4 1.3

Av 1.5 1.5 1.7 1.3 1.3 1.5 1.3

Beam R1 1.6 1.4 1.6 0.9 0.9 1.5 1.4 0.5 0.4

R2 1.3 1.5 1.7 1.1 1.1 1.5 1.4 0.4 0.4

R3 1.6 1.4 1.6 1.2 1.2 1.5 1.6 0.6 0.5

R4 1.6 1.4 1.6 1.2 1.2 1.5 1.5 0.6 0.5

R5 1.7 1.5 1.5 1.1 1.1 1.5 1.5 0.6 0.4

R6 1.3 1.5 1.3 1.2 1.2 1.5 1.5 0.4 0.5

Av 1.5 1.5 1.5 1.1 1.1 1.5 1.5 0.5 0.5

SQ R1 1.7 1.1 1.0 1.4 1.7 0.6

R2 1.4 1.2 1.1 1.4 1.6 0.4

R3 1.6 1.1 1.1 1.4 1.7 0.6

Av 1.6 1.1 1.1 1.4 1.7 0.5

BQ R1 1.8 1.2 1.2 1.4 1.7

R2 1.5 1.2 1.1 1.4 1.7

Av 1.7 1.2 1.2 1.4 1.7

 
ERDC/CHL TR-20-18 49

Table D-4. Wave periods (second) by heading for wave M2. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.0 1.1

R2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 0.9 1.0

R3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.1 1.1

R4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.0 1.1

R5 1.3 1.3 1.3 1.3 1.3 1.3 1.3 0.9 1.1

R6 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.0 0.8

R7 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.1

Av 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.0 1.1

Head R1 1.3 1.3 1.3 1.3 1.3 1.3 1.3

R2 1.3 1.3 1.3 1.3 1.3 1.3 1.3

Av 1.3 1.3 1.3 1.3 1.3 1.3 1.3

Beam R1 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.0

R2 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.0 0.9

R3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.1

R4 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.1 1.0

R5 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.2 1.0

R6 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.0 1.1

Av 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.1 1.0

SQ R1 1.3 1.3 1.3 1.3 1.3 1.3

R2 1.3 1.3 1.3 1.3 1.3 0.9

R3 1.3 1.3 1.3 1.3 1.3 1.1

Av 1.3 1.3 1.3 1.3 1.3 1.1

BQ R1 1.3 1.3 1.3 1.3 1.3

R2 1.3 1.3 1.3 1.3 1.3

Av 1.3 1.3 1.3 1.3 1.3
ERDC/CHL TR-20-18 50

D.3 Wave M3

Table D-5. Wave heights (inch) by heading for wave M3. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 2.4 2.6 1.9 1.7 1.7 2.0 2.5 0.8 0.9

R2 2.2 2.6 1.6 1.6 1.6 1.9 2.4 0.8 0.5

R3 2.2 2.5 1.8 1.8 1.7 1.9 2.5 0.7 0.7

R4 2.2 2.4 1.8 1.7 1.7 2.0 2.5 0.6 0.8

Av 2.2 2.5 1.8 1.7 1.7 1.9 2.5 0.7 0.7

Head R1 2.6 2.5 1.8 2.2 2.2 2.0 2.3

R2 2.6 2.5 1.9 2.0 1.9 1.8 2.2

Av 2.6 2.5 1.8 2.1 2.0 1.9 2.2

Beam R1 2.3 2.4 2.0 2.2 2.2 1.9 2.3 0.8 0.9

R2 2.3 2.4 2.1 2.2 2.2 1.9 2.3 0.8 0.8

R3 2.5 2.5 1.9 2.2 2.2 1.9 2.3 0.7 0.8

Av 2.4 2.4 2.0 2.2 2.2 1.9 2.3 0.8 0.8

SQ R1 2.6 2.0 2.0 1.9 2.3 0.8

R2 2.5 2.3 2.0 2.0 2.1 0.7

R3 2.3 1.7 1.8 2.0 2.1 0.9

R4 2.4 2.1 2.0 2.0 2.2 0.9

R5 2.4 1.8 2.0 2.0 2.3 0.8

R6 2.3 1.9 1.9 1.9 2.4 0.9

R7 2.3 2.0 2.0 2.0 2.2 0.8

Av 2.4 2.0 1.9 2.0 2.2 0.8

BQ R1 2.6 2.3 2.3 1.8 2.3

R2 2.4 2.3 2.3 1.8 2.3

Av 2.5 2.3 2.3 1.8 2.3

 
ERDC/CHL TR-20-18 51

Table D-6. Wave periods (second) by heading for wave M3. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.4 1.5

R2 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.4 1.0

R3 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.3 1.3

R4 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.2 1.4

Av 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.3 1.3

Head R1 1.7 1.7 1.7 1.7 1.7 1.7 1.7

R2 1.7 1.7 1.6 1.7 1.7 1.7 1.7

Av 1.7 1.7 1.7 1.7 1.7 1.7 1.7

Beam R1 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.5 1.5

R2 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.5 1.4

R3 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.1 1.3

Av 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.4 1.4

SQ R1 1.7 1.7 1.7 1.7 1.7 1.4

R2 1.7 1.7 1.7 1.7 1.7 1.4

R3 1.7 1.7 1.7 1.7 1.7 1.6

R4 1.7 1.7 1.7 1.7 1.7 1.7

R5 1.7 1.7 1.7 1.7 1.7 1.3

R6 1.7 1.7 1.7 1.7 1.7 1.5

R7 1.7 1.7 1.7 1.7 1.7 1.3

Av 1.7 1.7 1.7 1.7 1.7 1.5

BQ R1 1.7 1.7 1.7 1.7 1.7

R2 1.7 1.7 1.7 1.7 1.7

Av 1.7 1.7 1.7 1.7 1.7
ERDC/CHL TR-20-18 52

D.4 Wave M4

Table D-7. Wave heights (inch) by heading for wave M4. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R2 3.2 2.8 2.8 1.5 1.5 2.8 3.6 1.2 1.0

R3 3.2 2.9 2.9 1.4 1.4 2.8 3.6 1.3 0.9

R4 3.2 2.9 2.9 1.3 1.3 2.8 3.6 1.1 1.0

R5 2.7 2.8 2.6 1.4 1.3 2.9 3.6 1.0 0.9

R6 3.3 2.8 2.5 1.2 1.3 2.9 3.6 1.1 0.8

Av 3.1 2.8 2.8 1.4 1.4 2.9 3.6 1.2 1.0

Head R1 3.3 3.3 2.9 1.4 1.4 2.7 3.8

R2 3.1 3.2 2.6 1.3 1.3 2.3 3.6

Av 3.2 3.3 2.7 1.4 1.4 2.5 3.7

Beam R1 1.5 1.5 1.3 0.7 0.7 1.4 1.8 0.6 0.5

R2 1.4 1.5 1.4 0.7 0.7 1.4 1.8 0.4 0.4

R3 1.5 1.6 1.4 0.7 0.7 1.4 1.8 0.5 0.4

R4 3.1 2.9 2.8 1.3 1.3 3.0 3.6 1.2 1.2

R5 1.5 1.6 1.3 0.7 0.7 1.3 1.7 0.4 0.5

Av 1.8 1.8 1.6 0.8 0.8 1.7 2.1 0.6 0.6

SQ R2 2.1 1.0 1.0 2.2 2.3 0.9

R3 2.0 0.9 0.9 2.2 2.3 0.9

R4 2.1 1.0 1.0 2.1 2.3 0.7

R5 2.0 0.9 0.9 2.1 2.2 0.7

R6 2.0 1.0 0.9 2.2 2.3 0.6

R7 1.9 0.9 0.9 2.2 2.3 0.7

R8 1.9 1.0 0.9 2.2 2.3 0.6

Av 2.0 1.0 0.9 2.2 2.3 0.7

BQ R2 2.3 1.1 1.1 2.7 2.8

R3 2.5 1.2 1.2 2.7 2.9 0.8

R4 2.5 1.2 1.2 2.7 2.8 0.7

R5 2.4 1.2 1.2 2.7 2.7 0.8

R6 2.4 1.1 1.1 2.7 2.8 0.8

R7 2.5 1.3 1.3 2.7 2.8 0.7

R8 2.3 1.1 1.1 2.7 2.8 0.8

Av 2.4 1.2 1.2 2.7 2.8 0.8
ERDC/CHL TR-20-18 53

Table D-8. Wave periods (second) by heading for wave M4. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R2 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.3 2.0

R3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.8

R4 2.4 2.4 2.4 2.4 2.3 2.4 2.4 2.0 2.0

R5 2.2 2.4 2.4 2.3 2.3 2.4 2.4 2.0 2.0

R6 2.4 2.4 2.4 2.2 2.3 2.4 2.4 2.0 1.7

Av 2.3 2.4 2.4 2.3 2.4 2.4 2.4 2.1 1.9

Head R1 2.4 2.4 2.4 2.4 2.4 2.4 2.4

R2 2.4 2.4 2.4 2.3 2.4 2.3 2.3

Av 2.4 2.4 2.4 2.4 2.4 2.3 2.3

Beam R1 2.4 2.4 2.4 2.4 2.3 2.4 2.4 2.3 1.6

R2 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.4 1.5

R3 2.4 2.4 2.4 2.4 2.4 2.4 2.4 1.5 1.4

R4 2.4 2.4 2.4 2.4 2.4 2.4 2.4 2.2 2.2

R5 2.4 2.4 2.4 2.3 2.3 2.4 2.4 1.4 1.5

Av 2.4 2.4 2.4 2.3 2.3 2.4 2.4 1.8 1.6

SQ R2 2.4 2.4 2.4 2.4 2.4 1.9

R3 2.4 2.2 2.2 2.4 2.4 1.9

R4 2.4 2.4 2.4 2.4 2.4 1.6

R5 2.4 2.4 2.4 2.4 2.4 1.8

R6 2.4 2.4 2.4 2.4 2.4 1.7

R7 2.4 2.1 2.1 2.4 2.4 1.8

R8 2.4 2.2 2.1 2.4 2.4 1.5

Av 2.4 2.3 2.3 2.4 2.4 1.8

BQ R2 2.4 2.4 2.4 2.4 2.4

R3 2.4 2.4 2.3 2.4 2.4 1.9

R4 2.4 2.4 2.4 2.4 2.4 1.6

R5 2.4 2.4 2.4 2.4 2.4 2.0

R6 2.4 2.4 2.4 2.4 2.4 1.7

R7 2.4 2.4 2.4 2.4 2.4 1.6

R8 2.4 2.4 2.4 2.4 2.4 1.9

Av 2.4 2.4 2.4 2.4 2.4 1.8
ERDC/CHL TR-20-18 54

D.5 Wave M5

Table D-9. Wave heights (inch) by heading for wave M5. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.1 2.8 2.1 1.8 1.8 3.5 2.9 1.0 1.0

R2 2.9 2.8 2.1 1.8 1.8 3.5 2.9 0.9 0.9

R3 3.0 2.6 1.8 1.7 1.7 3.6 3.1 0.8 0.8

R4 3.0 2.6 2.3 1.7 1.7 3.6 3.0 0.8 1.1

R5 3.0 2.6 2.1 1.7 1.7 3.4 3.0 0.8 1.1

R6 2.8 2.6 1.9 1.8 1.8 3.4 2.9 0.7 0.9

R7 3.1 2.6 2.0 1.8 1.8 3.5 2.9 0.8 0.9

R8 2.9 2.7 2.4 1.8 1.8 3.6 2.9 0.8 1.0

R9 2.7 2.8 2.4 1.8 1.8 3.6 2.9 0.9 1.1

Av 2.9 2.7 2.1 1.8 1.8 3.5 2.9 0.8 1.0

Head R1 1.6 1.5 1.3 1.0 1.0 1.5 1.3

R2 1.6 1.4 1.4 1.0 1.0 1.7 1.4

R3 1.3 1.2 1.1 0.8 0.8 1.5 1.1 0.3 0.3

R4 1.1 1.2 1.0 0.9 0.9 1.4 1.1 0.3 0.3

R5 1.3 1.2 1.0 0.8 0.9 1.4 1.1 0.4 0.3

R6 1.2 1.2 1.0 0.8 0.8 1.2 1.2 0.3 0.3

R7 1.6 1.6 1.3 1.0 0.9 1.7 1.4 0.6 0.3

R8 1.5 1.6 1.3 1.0 0.9 1.6 1.4 0.5 0.3

Av 1.4 1.4 1.2 0.9 0.9 1.5 1.3 0.4 0.3

Beam R1 1.4 1.3 1.1 1.0 1.0 1.6 1.4 0.4 0.4

R2 1.3 1.3 1.2 1.0 1.0 1.6 1.4 0.4 0.4

R3 1.3 1.3 1.2 0.9 0.9 1.6 1.4 0.4 0.4

R4 1.3 1.3 1.2 1.0 0.9 1.6 1.5 0.4 0.3

R5 1.3 1.3 1.2 0.9 0.9 1.6 1.4 0.4 0.4

Av 1.3 1.3 1.1 1.0 0.9 1.6 1.4 0.4 0.4

SQ R1 1.9 0.9 0.9 2.1 2.2 0.5

R2 1.9 1.0 1.0 2.1 2.1 0.6

R3 1.9 1.0 1.0 2.1 2.2 0.4

Av 1.9 1.0 1.0 2.1 2.2 0.5
ERDC/CHL TR-20-18 55

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

BQ R2 2.1 1.2 1.2 2.4 2.4

R3 2.0 1.1 1.1 2.4 2.4

R4 2.1 1.1 1.1 2.4 2.4

R5 2.2 1.2 1.2 2.4 2.4 0.6

R6 2.2 1.2 1.2 2.4 2.4 0.7

R7 2.0 1.3 1.3 2.4 2.4 0.6

R8 2.1 1.2 1.2 2.4 2.4 0.7

R9 2.1 1.2 1.2 2.4 2.4 0.8

R10 2.1 1.2 1.2 2.5 2.4 0.7

Av 2.1 1.2 1.2 2.4 2.4 0.7

Table D-10. Wave periods (second) by heading for wave M5. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 2.7 2.7 2.5 2.7 2.7 2.7 2.7 2.3 2.2

R2 2.7 2.7 2.5 2.7 2.7 2.7 2.7 2.1 1.9

R3 2.7 2.7 2.3 2.7 2.7 2.7 2.7 1.9 1.9

R4 2.7 2.7 2.7 2.7 2.8 2.7 2.7 1.9 2.3

R5 2.7 2.7 2.3 2.8 2.8 2.7 2.7 1.9 2.3

R6 2.6 2.7 2.3 2.7 2.7 2.7 2.7 1.7 2.2

R7 2.7 2.6 2.7 2.7 2.7 2.7 2.5 1.8 1.9

R8 2.7 2.7 2.7 2.7 2.7 2.7 2.7 1.8 2.2

R9 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.1 2.3

Av 2.7 2.7 2.5 2.7 2.7 2.7 2.7 1.9 2.2

Head R1 2.0 2.7 2.7 2.7 2.8 2.7 2.7

R2 2.5 2.7 2.7 2.7 2.7 2.6 2.7

R3 2.7 2.7 2.8 2.7 2.7 2.7 2.7 1.6 1.8

R4 2.6 2.7 2.7 2.7 2.7 2.7 2.7 1.4 1.4

R5 2.7 2.7 2.7 2.7 2.7 2.7 2.7 1.8 1.4

R6 2.7 2.7 2.8 2.7 2.7 2.7 2.7 1.7 1.4

R7 2.7 2.7 2.7 2.7 2.7 2.7 2.6 2.4 1.2

R8 2.2 2.7 2.7 2.7 2.6 2.7 2.7 2.0 1.2

Av 2.5 2.7 2.7 2.7 2.7 2.7 2.7 1.8 1.4
ERDC/CHL TR-20-18 56

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Beam R1 2.7 2.7 2.7 2.7 2.6 2.7 2.7 1.9 1.8

R2 2.7 2.7 2.7 2.7 2.7 2.7 2.7 1.6 1.9

R3 2.7 2.7 2.7 2.7 2.7 2.7 2.7 2.2 1.6

R4 2.7 2.7 2.7 2.8 2.8 2.7 2.7 1.7 1.3

R5 2.7 2.8 2.7 2.8 2.8 2.7 2.7 2.1 1.7

Av 2.7 2.7 2.7 2.7 2.7 2.7 2.7 1.9 1.6

SQ R1 2.7 2.5 2.5 2.7 2.7 1.8

R2 2.7 2.7 2.7 2.7 2.7 2.1

R3 2.7 2.5 2.5 2.7 2.7 1.2

Av 2.7 2.6 2.6 2.7 2.7 1.7

BQ R2 2.7 2.7 2.7 2.7 2.7

R3 2.7 2.7 2.7 2.7 2.7

R4 2.7 2.7 2.7 2.7 2.7

R5 2.7 2.7 2.7 2.7 2.7 1.9

R6 2.7 2.7 2.7 2.7 2.7 2.2

R7 2.7 2.7 2.7 2.7 2.7 2.0

R8 2.7 2.7 2.7 2.7 2.7 2.2

R9 2.7 2.7 2.7 2.7 2.7 2.4

R10 2.7 2.7 2.7 2.7 2.7 2.3

Av 2.7 2.7 2.7 2.7 2.7 2.2
ERDC/CHL TR-20-18 57

D.6 Wave M6

Table D-11. Wave heights (inch) by heading for wave M6. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.1 2.5 1.7 2.8 2.8 3.3 3.3 0.7 0.7

R2 3.0 2.4 1.7 2.8 2.8 3.3 3.3 0.7 0.7

R3 3.0 2.5 1.7 2.8 2.8 3.3 3.3 0.7 0.7

R4 3.1 2.5 1.7 2.7 2.8 3.3 3.1 0.9 0.7

R5 3.1 2.5 1.9 2.8 2.8 3.3 3.3 0.8 0.5

R6 3.1 2.2 2.0 2.9 2.8 3.4 3.3 0.7 1.0

R7 2.7 2.4 2.1 2.7 2.8 3.3 3.3 0.8 0.7

R8 2.8 2.7 1.7 2.7 2.7 3.4 3.4 0.6 0.7

R9 2.9 2.6 1.9 2.8 2.7 3.3 3.4 0.6 0.8

Av 3.0 2.5 1.8 2.8 2.8 3.3 3.3 0.7 0.7

Head R1 1.4 1.3 1.1 1.2 1.2 1.4 1.4

R2 1.4 1.1 1.0 1.3 1.3 1.4 1.5

R3 1.5 1.2 0.9 1.2 1.2 1.6 1.5

R4 1.2 1.3 0.7 1.4 1.3 1.5 1.5 0.3 0.3

R5 1.3 1.2 0.8 1.2 1.2 1.5 1.4 0.2 0.3

R6 1.3 1.2 0.8 1.3 1.3 1.5 1.6 0.3 0.3

R7 1.2 1.3 0.6 1.1 1.1 1.5 1.4 0.4 0.3

R8 1.3 1.2 0.8 1.3 1.1 1.3 1.2 0.3 0.3

R9 1.2 1.3 0.8 1.2 1.2 1.2 1.2 0.3 0.3

Av 1.3 1.2 0.8 1.2 1.2 1.4 1.4 0.3 0.3

Beam R1 1.2 1.2 0.9 1.3 1.3 1.5 1.5 0.3 0.3

R2 1.2 1.1 0.9 1.3 1.3 1.5 1.6 0.3 0.3

R3 1.2 1.2 0.9 1.3 1.3 1.5 1.6 0.3 0.3

R4 1.3 1.2 0.9 1.2 1.3 1.5 1.5 0.3 0.2

R5 1.2 1.2 0.9 1.3 1.3 1.5 1.5 0.3 0.2

R6 1.2 1.2 1.0 1.2 1.2 1.5 1.5 0.3 0.2

R7 1.2 1.1 1.0 1.3 1.3 1.5 1.5 0.3 0.2

R8 1.2 1.2 0.9 1.3 1.3 1.5 1.5 0.3 0.2

Av 1.2 1.2 0.9 1.3 1.3 1.5 1.5 0.3 0.3
ERDC/CHL TR-20-18 58

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

SQ R1 1.7 2.1 2.1 2.8 2.1 0.7

R2 1.8 2.1 2.1 2.8 2.2 0.5

R3 1.9 2.1 2.1 2.8 2.1 0.7

R4 1.8 2.1 2.1 2.8 2.1 0.7

Av 1.8 2.1 2.1 2.8 2.1 0.6

BQ R1 2.1 2.0 2.0 2.8 2.1

R2 2.0 2.0 2.0 2.8 2.1

R3 1.9 2.1 2.1 2.8 2.1

Av 2.0 2.1 2.0 2.8 2.1

BQ Repeats R1 1.9 2.2 2.1 2.8 2.1 0.7

R2 1.9 2.1 2.1 2.7 2.1 0.5

R3 1.8 2.1 2.1 2.8 2.1 0.6

R4 1.9 2.2 2.1 2.8 2.1 0.5

R5 2.0 2.1 2.1 2.7 2.1 0.7

R6 1.9 2.1 2.1 2.7 2.1 0.6

R7 1.9 2.1 2.1 2.7 2.1 0.6

R8 1.8 2.1 2.0 2.7 2.1 0.6

R9 1.9 2.1 2.1 2.7 2.1 0.6

R10 1.9 2.1 2.1 2.7 2.2 0.6

R11 2.1 2.1 2.1 2.7 2.2 0.6

R12 2.0 2.1 2.1 2.7 2.1 0.7

R13 2.0 2.1 2.1 2.8 2.1 0.5

R14 2.0 2.1 2.0 2.8 2.2 0.4

R15 1.9 2.1 2.0 2.8 2.1 0.7

R16 1.8 2.0 2.0 2.7 2.1 0.7

R17 1.9 2.1 2.0 2.7 2.1 0.6

R18 1.9 2.1 2.0 2.8 2.1 0.8

R19 1.9 2.1 2.1 2.8 2.1 0.5

R20 1.9 2.0 2.0 2.7 2.1 0.6

Av 1.9 2.1 2.1 2.7 2.1 0.6
ERDC/CHL TR-20-18 59

Table D-12. Wave periods (second) by heading for wave M6. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 2.1 2.1

R2 3.1 3.1 3.1 3.1 3.1 3.1 3.1 2.1 2.0

R3 3.1 3.1 3.1 3.1 3.1 3.1 3.1 2.1 2.0

R4 3.1 3.1 2.7 3.0 3.1 3.1 3.1 2.3 1.7

R5 3.1 3.1 3.2 3.1 3.1 3.1 3.1 2.2 1.5

R6 3.1 2.4 3.1 3.1 3.1 3.1 3.1 1.8 2.7

R7 2.7 2.7 3.1 3.1 3.1 3.1 3.1 2.3 1.9

R8 3.1 3.1 2.8 3.1 3.1 3.1 3.1 1.8 2.1

R9 3.1 3.1 3.0 3.1 3.1 3.1 3.1 1.7 2.4

Av 3.1 3.0 3.0 3.1 3.1 3.1 3.1 2.0 2.0

Head R1 2.3 3.1 3.1 3.1 3.1 3.1 3.1

R2 2.3 2.6 3.1 3.1 3.1 3.1 3.1

R3 2.5 3.1 2.7 3.1 3.1 3.1 3.1

R4 3.1 3.1 3.0 3.1 3.1 3.1 3.1 1.8 1.6

R5 3.0 3.1 3.1 3.1 3.1 3.1 2.9 1.3 1.6

R6 3.1 3.1 3.1 3.1 3.1 3.1 3.1 1.6 1.6

R7 2.8 3.1 1.9 2.9 2.8 3.1 2.8 2.0 1.5

R8 3.0 3.1 2.5 3.1 2.9 3.1 2.3 1.4 1.6

R9 2.3 3.1 2.3 3.1 3.1 3.1 2.5 1.9 1.5

Av 2.7 3.0 2.8 3.1 3.1 3.1 2.9 1.7 1.6

Beam R1 3.1 3.1 3.1 3.1 3.1 3.1 3.1 2.1 1.7

R2 3.1 2.9 3.1 3.1 3.1 3.1 3.1 1.7 1.8

R3 3.1 3.2 3.1 3.1 3.1 3.1 3.1 1.6 1.8

R4 3.1 3.1 3.1 3.1 3.1 3.1 3.1 1.6 1.5

R5 3.0 3.1 3.1 3.1 3.1 3.1 3.1 1.8 1.4

R6 3.1 3.2 3.1 3.1 3.1 3.1 3.1 2.1 1.5

R7 3.2 3.1 3.1 3.1 3.1 3.1 3.1 1.6 1.5

R8 3.1 3.1 3.1 3.1 3.1 3.1 3.1 1.8 1.3

Av 3.1 3.1 3.1 3.1 3.1 3.1 3.1 1.8 1.6

SQ R1 3.1 3.1 3.1 3.1 3.1 2.3
ERDC/CHL TR-20-18 60

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R2 3.1 3.1 3.1 3.1 3.1 1.5

R3 3.1 3.1 3.1 3.1 3.1 2.2

R4 3.1 3.1 3.1 3.1 3.1 2.3

Av 3.1 3.1 3.1 3.1 3.1 2.1

BQ R1 3.1 3.1 3.1 3.1 3.1

R2 3.1 3.1 3.1 3.1 3.1

R3 3.1 3.1 3.1 3.1 3.1

Av 3.1 3.1 3.1 3.1 3.1

BQ Repeats R1 3.1 3.1 3.1 3.1 3.1 2.4

R2 3.1 3.1 3.1 3.1 3.1 1.8

R3 3.1 3.1 3.1 3.1 3.1 2.2

R4 3.1 3.1 3.1 3.1 3.1 1.8

R5 3.1 3.1 3.1 3.1 3.1 2.4

R6 3.1 3.1 3.1 3.1 3.1 2.2

R7 3.1 3.1 3.1 3.1 3.1 2.0

R8 3.1 3.1 3.1 3.1 3.1 2.2

R9 3.1 3.1 3.1 3.1 3.1 2.0

R10 3.1 3.1 3.1 3.1 3.1 2.2

R11 3.1 3.1 3.1 3.1 3.1 2.1

R12 3.1 3.1 3.1 3.1 3.1 2.4

R13 3.1 3.1 3.1 3.1 3.1 1.9

R14 3.1 3.1 3.1 3.1 3.1 1.6

R15 3.1 3.1 3.1 3.1 3.1 2.4

R16 3.1 3.1 3.1 3.1 3.1 2.7

R17 3.1 3.1 3.1 3.1 3.1 2.3

R18 3.1 3.1 3.1 3.1 3.1 3.1

R19 3.1 3.1 3.1 3.1 3.1 1.9

R20 3.1 3.1 3.1 3.1 3.1 2.1

Av 3.1 3.1 3.1 3.1 3.1 2.2
ERDC/CHL TR-20-18 61

D.7 Wave M7

Table D-13. Wave heights (inch) by heading for wave M7. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.1 2.4 2.6 1.7 1.7 3.4 3.4 0.7 0.6

R2 3.1 2.3 2.6 1.7 1.7 3.4 3.4 0.7 0.6

R3 3.3 2.2 2.3 1.4 1.4 3.3 3.4 0.9 0.4

R4 3.1 2.2 2.2 1.4 1.5 3.4 3.3 0.7 0.6

R5 3.3 2.3 2.3 1.7 1.7 3.3 3.4 0.8 0.8

R6 3.1 2.1 2.6 1.7 1.7 3.3 3.3 0.6 0.6

R7 3.1 2.3 2.5 1.7 1.6 3.3 3.3 0.8 0.6

Av 3.2 2.2 2.4 1.6 1.6 3.4 3.4 0.8 0.6

Head R1 1.4 0.8 0.9 0.7 0.7 1.2 1.3

R2 1.3 0.7 1.0 0.7 0.6 1.2 1.0

R3 1.5 0.7 0.9 0.6 0.6 1.3 1.3

R4 1.0 0.7 0.8 0.6 0.6 1.3 1.3 0.2 0.1

R5 1.1 0.7 0.8 0.6 0.6 1.3 1.3 0.2 0.1

R6 1.2 0.7 0.9 0.6 0.6 1.3 1.4 0.2 0.1

R7 0.9 0.7 0.8 0.6 0.6 1.0 1.2 0.2 0.1

R8 1.1 0.7 0.9 0.5 0.6 1.2 1.1 0.1 0.1

R9 1.0 0.8 0.7 0.5 0.5 0.9 1.1 0.2 0.1

Av 1.2 0.7 0.9 0.6 0.6 1.2 1.2 0.2 0.1

Beam R1 2.9 2.3 2.3 1.3 1.4 3.4 3.4 1.0 0.5

R2 3.0 2.3 2.3 1.6 1.6 3.3 3.3 0.8 0.5

R3 2.9 2.3 2.2 1.5 1.4 3.4 3.3 0.7 0.7

R4 3.0 2.1 2.3 1.6 1.6 3.4 3.6 0.8 0.7

R5 2.9 2.3 2.3 1.7 1.6 3.3 3.4 0.8 0.6

R6 3.0 2.1 2.2 1.6 1.6 3.3 3.3 0.6 0.6

Av 3.0 2.2 2.3 1.5 1.6 3.3 3.4 0.8 0.6

SQ R1 2.5 1.6 1.6 2.8 2.3 0.4

R2 2.6 1.6 1.4 2.8 2.3 0.4

R3 2.5 1.7 1.6 2.8 2.3 0.3

R4 2.4 1.6 1.6 2.8 2.4 0.5
ERDC/CHL TR-20-18 62

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R5 2.5 1.6 1.6 2.8 2.4 0.4

R6 2.4 1.6 1.6 2.9 2.4 0.6

Av 2.5 1.6 1.6 2.8 2.4 0.4

BQ R1 2.5 1.7 1.7 2.8 2.3

R2 2.6 1.6 1.6 2.8 2.3

R3 2.4 1.6 1.6 2.8 2.3

R4 2.5 1.7 1.6 2.8 2.3

Av 2.5 1.7 1.6 2.8 2.3

BQ Repeat R1 2.6 1.6 1.6 2.8 2.3 0.4

R2 2.5 1.7 1.7 2.8 2.3 0.5

R3 2.5 1.6 1.5 2.8 2.4 0.5

R4 2.5 1.5 1.5 2.8 2.3 0.4

R5 2.4 1.5 1.5 2.7 2.4 0.5

R6 2.5 1.6 1.5 2.8 2.3 0.4

R7 2.3 1.5 1.5 2.8 2.4 0.6

R8 2.5 1.6 1.6 2.8 2.4 0.5

R9 2.5 1.6 1.6 2.8 2.3 0.5

R10 2.5 1.6 1.6 2.8 2.3 0.4

R11 2.5 1.6 1.6 2.8 2.3 0.4

R12 2.5 1.6 1.6 2.8 2.4 0.5

R13 2.6 1.6 1.6 2.8 2.4 0.4

R14 2.6 1.6 1.6 2.8 2.4 0.4

R15 2.6 1.6 1.6 2.8 2.3 0.4

R16 2.6 1.6 1.6 2.8 2.4 0.4

R17 2.5 1.6 1.6 2.7 2.3 0.5

R18 2.5 1.6 1.6 2.8 2.3 0.4

R19 2.4 1.6 1.6 2.7 2.3 0.4

R20 2.4 1.5 1.5 2.7 2.3 0.5

Av 2.5 1.6 1.6 2.8 2.3 0.5
ERDC/CHL TR-20-18 63

Table D-14. Wave periods (second) by heading for wave M7. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.5 3.5 3.6 3.5 3.5 3.5 3.5 2.4 2.6

R2 3.5 3.5 3.5 3.5 3.5 3.6 3.5 2.3 2.2

R3 3.5 3.5 2.9 2.8 2.8 3.5 3.5 3.1 1.7

R4 3.5 3.5 2.9 2.6 3.0 3.5 3.5 2.3 2.2

R5 3.5 3.5 3.0 3.5 3.5 3.5 3.5 2.7 3.0

R6 3.5 3.5 3.5 3.4 3.5 3.6 3.5 2.0 2.3

R7 3.5 3.5 3.5 3.5 3.5 3.6 3.5 2.7 2.7

Av 3.5 3.5 3.3 3.3 3.3 3.5 3.5 2.5 2.4

Head R1 3.5 3.6 2.3 3.6 3.6 3.6 3.5

R2 2.8 2.8 2.9 3.5 3.5 3.5 2.7

R3 3.6 3.1 3.5 3.1 3.1 3.6 3.6

R4 3.2 3.1 3.0 3.6 3.5 3.6 3.5 1.4 1.0

R5 3.6 3.6 3.5 3.3 3.5 3.6 3.6 1.7 1.4

R6 3.5 3.5 3.0 3.4 3.4 3.6 3.6 1.9 1.3

R7 2.5 2.7 2.8 3.0 3.2 2.9 3.3 1.3 0.9

R8 2.7 3.4 3.5 3.4 3.5 3.5 2.9 1.0 1.0

R9 2.5 2.7 2.6 2.6 2.6 2.6 3.1 1.3 0.8

Av 3.1 3.2 3.0 3.3 3.3 3.4 3.3 1.4 1.1

Beam R1 3.6 3.5 3.5 2.6 3.0 3.6 3.5 3.6 2.4

R2 3.6 3.5 3.5 3.5 3.5 3.6 3.5 2.8 2.3

R3 3.6 3.6 3.5 3.0 3.0 3.5 3.6 2.3 2.8

R4 3.6 3.6 3.5 3.5 3.5 3.6 3.5 2.7 2.5

R5 3.5 3.6 3.6 3.5 3.5 3.5 3.5 2.8 2.5

R6 3.5 3.2 3.5 3.4 3.4 3.5 3.5 2.1 2.3

Av 3.6 3.5 3.5 3.3 3.3 3.5 3.5 2.7 2.5

SQ R1 3.5 3.5 3.6 3.5 3.5 1.6

R2 3.5 3.1 2.9 3.5 3.5 1.5

R3 3.5 3.5 3.5 3.5 3.5 1.3

R4 3.5 3.5 3.5 3.5 3.5 2.0

R5 3.5 3.5 3.5 3.5 3.5 1.7
ERDC/CHL TR-20-18 64

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R6 3.5 3.5 3.5 3.6 3.6 2.6

Av 3.5 3.4 3.4 3.5 3.5 1.8

BQ R1 3.5 3.5 3.5 3.5 3.5

R2 3.5 3.5 3.5 3.5 3.5

R3 3.5 3.5 3.5 3.5 3.5

R4 3.5 3.5 3.5 3.6 3.5

Av 3.5 3.5 3.5 3.5 3.5

BQ Repeat R1 3.5 3.5 3.5 3.5 3.5 1.7

R2 3.5 3.5 3.5 3.5 3.5 2.3

R3 3.5 3.5 3.5 3.5 3.5 2.5

R4 3.5 3.5 3.5 3.5 3.5 1.6

R5 3.5 3.5 3.5 3.5 3.5 2.1

R6 3.5 3.5 3.5 3.5 3.5 1.9

R7 3.5 3.5 3.5 3.5 3.5 2.8

R8 3.5 3.5 3.5 3.5 3.5 2.7

R9 3.5 3.5 3.5 3.5 3.5 2.3

R10 3.5 3.5 3.5 3.5 3.5 2.1

R11 3.5 3.5 3.5 3.5 3.5 1.9

R12 3.5 3.5 3.5 3.5 3.5 2.6

R13 3.5 3.5 3.5 3.5 3.5 1.9

R14 3.5 3.5 3.5 3.5 3.5 1.8

R15 3.5 3.5 3.5 3.5 3.5 2.2

R16 3.5 3.5 3.5 3.5 3.5 2.2

R17 3.6 3.5 3.5 3.5 3.5 2.6

R18 3.5 3.5 3.5 3.5 3.6 2.1

R19 3.5 3.4 3.5 3.5 3.5 1.8

R20 3.5 3.5 3.3 3.5 3.5 2.5

Av 3.5 3.5 3.5 3.5 3.5 2.2
ERDC/CHL TR-20-18 65

D.8 Wave M8

Table D-15. Wave heights (inch) by heading for wave M8. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.8 2.2 2.4 0.9 0.9 3.2 3.2 1.1 0.6

R2 3.7 2.0 2.4 1.1 0.9 3.3 3.1 1.0 0.6

R3 3.5 2.1 2.5 0.9 0.9 3.2 3.3 0.9 0.5

R4 3.5 2.1 1.9 1.0 1.2 3.4 3.2 0.6 0.8

R5 3.4 2.0 2.5 1.0 1.0 3.3 3.2 1.0 0.7

R6 3.5 2.1 2.1 1.2 1.1 3.3 3.3 0.7 0.7

R7 3.5 1.8 2.4 1.1 1.1 3.4 3.3 0.7 0.6

R8 3.3 2.1 2.2 1.0 1.1 3.3 3.2 0.6 0.7

R9 3.2 2.1 2.3 1.1 1.1 3.3 3.5 0.6 0.5

R10 3.1 2.3 2.6 0.7 0.9 3.2 3.2 0.9 1.0

R11 3.5 2.0 2.4 0.9 0.9 3.2 3.3 0.5 0.7

Av 3.5 2.1 2.3 1.0 1.0 3.3 3.3 0.8 0.7

Head R1 1.6 0.7 0.6 0.4 0.4 0.9 0.9 0.0 0.0

R2 1.7 0.6 0.8 0.3 0.3 0.9 0.9 0.0 0.0

R3 1.7 0.8 0.7 0.4 0.3 1.2 1.1 0.0 0.0

R4 1.5 0.8 0.7 0.4 0.3 1.2 1.1 0.0 0.0

R5 3.4 1.9 1.9 1.0 1.0 3.1 3.0 0.9 0.8

R6 4.0 2.3 2.7 0.6 0.8 2.9 3.0 1.0 0.9

R7 4.0 2.5 2.2 0.8 0.9 3.3 3.7 0.9 1.0

Av 2.5 1.4 1.4 0.6 0.6 1.9 2.0 0.4 0.4

Beam R1 3.4 2.1 2.2 1.3 1.3 3.2 3.3 0.8 0.8

R2 3.4 2.2 2.1 1.0 1.0 3.3 3.4 0.6 0.7

R3 3.6 2.1 2.2 1.0 1.1 3.3 3.4 0.8 0.6

R4 3.1 2.2 2.1 1.0 1.1 3.3 3.2 0.8 0.6

R5 3.2 2.2 2.3 1.1 1.3 3.3 3.4 0.8 0.5

R6 3.3 2.3 2.3 1.3 1.3 3.3 3.4 0.9 0.8

R7 3.4 2.3 2.3 1.1 1.1 3.3 3.4 0.8 0.6

R8 3.3 2.3 2.2 1.1 1.1 3.3 3.5 0.6 0.6

Av 3.3 2.2 2.2 1.1 1.2 3.3 3.4 0.8 0.7
ERDC/CHL TR-20-18 66

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

SQ R1 2.7 0.6 0.7 2.5 2.4 0.5

R2 2.7 0.5 0.6 2.5 2.4 0.5

R3 2.7 0.8 0.8 2.5 2.4 0.6

R4 2.6 0.6 0.6 2.5 2.4 0.4

R5 2.7 0.6 0.7 2.5 2.4 0.6

R6 2.6 0.6 0.6 2.5 2.4 0.6

R7 2.4 0.6 0.6 2.5 2.5 0.4

R8 2.7 0.7 0.7 2.5 2.6 0.5

R9 2.7 0.7 0.7 2.5 2.5 0.4

R10 2.7 0.8 0.7 2.5 2.5 0.5

Av 2.6 0.7 0.7 2.5 2.4 0.5

BQ R1 2.4 0.7 0.8 2.5 2.5

R2 2.4 0.7 0.9 2.5 2.5

R3 2.5 0.5 0.6 2.5 2.5

R5 2.5 0.6 0.7 2.5 2.5

Av 2.4 0.6 0.7 2.5 2.5

Table D-16. Wave periods (second) by heading for wave M8. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.8 3.8 3.8 2.4 2.4 3.8 3.8 3.0 2.2

R2 3.8 3.8 3.8 3.0 2.5 3.8 3.8 2.7 2.1

R3 3.8 3.8 3.8 2.4 2.4 3.8 3.8 2.5 1.7

R4 3.8 3.9 2.8 2.3 3.1 3.8 3.8 1.9 2.8

R5 3.8 3.8 3.8 2.7 2.7 3.8 3.8 2.9 2.6

R6 3.8 3.8 2.8 3.3 3.1 3.8 3.8 2.1 2.6

R7 3.8 3.3 3.8 2.9 2.8 3.8 3.8 2.4 2.1

R8 3.8 3.8 3.8 2.8 2.9 3.8 3.8 2.0 2.4

R9 3.8 3.8 3.8 3.1 3.1 3.8 3.8 2.3 1.6

R10 3.3 3.9 3.9 1.7 2.3 3.7 3.7 2.8 2.9

R11 3.8 3.8 3.8 2.5 2.5 3.8 3.8 1.6 2.4

Av 3.8 3.8 3.6 2.6 2.7 3.8 3.8 2.4 2.3

Head R1 3.9 3.7 2.5 3.2 3.8 3.2 3.2 0.1 0.1
ERDC/CHL TR-20-18 67

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R2 3.8 3.1 2.4 2.2 2.5 3.4 2.7 0.1 0.1

R3 3.9 3.4 2.9 3.0 2.4 3.9 3.6 0.1 0.1

R4 3.3 3.4 2.9 2.9 2.6 3.8 3.7 0.1 0.1

R5 3.9 3.5 3.3 2.9 2.9 3.8 3.9 3.3 2.7

R6 3.8 3.8 3.8 1.9 2.4 3.6 3.5 2.9 2.8

R7 3.8 3.8 3.3 2.4 2.9 3.8 3.8 2.7 3.3

Av 3.8 3.5 3.0 2.6 2.8 3.6 3.5 1.3 1.3

Beam R1 3.8 3.8 3.8 3.9 3.9 3.8 3.8 2.5 2.9

R2 3.8 3.8 3.8 2.9 2.9 3.8 3.8 2.0 2.3

R3 3.8 3.8 3.8 2.8 3.0 3.8 3.8 2.8 2.3

R4 3.8 3.8 3.8 2.8 3.3 3.9 3.8 2.9 2.4

R5 3.8 3.8 3.8 3.1 3.8 3.9 3.8 2.6 1.8

R6 3.8 3.8 3.8 3.8 3.8 3.8 3.8 3.1 3.0

R7 3.8 3.8 3.8 2.9 3.1 3.8 3.8 2.7 2.2

R8 3.8 3.8 3.8 3.2 3.1 3.8 3.8 2.1 2.1

Av 3.8 3.8 3.8 3.2 3.4 3.8 3.8 2.6 2.4

SQ R1 3.8 2.0 2.1 3.8 3.8 2.0 2.8

R2 3.8 1.6 1.8 3.8 3.9 1.8

R3 3.8 2.1 2.2 3.8 3.8 2.3

R4 3.8 1.8 1.8 3.8 3.8 2.0

R5 3.8 1.7 1.9 3.8 3.8 2.4

R6 3.8 1.6 1.7 3.8 3.8 2.4

R7 3.8 2.1 2.2 3.8 3.8 2.2

R8 3.8 2.1 2.2 3.8 3.9 2.2

R9 3.8 2.1 2.1 3.8 3.8 1.9

R10 3.8 2.2 1.8 3.8 3.8 2.0

Av 3.8 1.9 2.0 3.8 3.8 2.1

BQ R1 3.8 2.4 2.8 3.8 3.8

R2 3.8 2.4 3.0 3.8 3.8

R3 3.8 1.6 1.9 3.8 3.8

R5 3.8 1.7 2.2 3.8 3.8

Av 3.8 2.0 2.5 3.8 3.8
ERDC/CHL TR-20-18 68

D.9 Wave M9

Table D-17. Wave heights (inch) by heading for wave M9. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.2 2.1 3.0 1.1 1.1 3.5 2.6 0.5 0.4

R2 3.2 1.8 2.7 1.3 1.3 3.6 2.6 0.8 0.5

R3 3.3 2.2 2.6 1.2 1.0 3.5 2.6 0.7 0.5

R4 3.0 2.3 2.6 1.4 1.2 3.6 2.6 0.5 0.7

R5 3.0 2.1 2.5 1.5 1.2 3.6 2.7 0.6 0.6

R6 3.0 1.9 2.1 1.4 1.4 3.5 2.6 0.6 0.5

R7 3.6 2.2 2.7 1.4 1.2 3.7 2.7 0.5 0.5

R8 2.7 1.6 2.1 1.4 1.4 3.4 2.7 0.6 0.6

R9 3.5 2.0 2.9 1.4 1.4 3.4 2.7 0.4 0.4

Av 3.2 2.0 2.6 1.3 1.3 3.5 2.6 0.6 0.5

Head R1 0.7 0.5 0.9 0.4 0.5 0.9 0.8 0.0 0.0

R2 1.2 0.4 0.8 0.3 0.4 0.8 0.9 0.0 0.0

R3 1.1 0.6 0.9 0.3 0.2 0.9 0.7 0.0 0.0

R4 1.5 0.6 0.8 0.3 0.3 1.0 0.8 0.0 0.0

R5 1.4 0.6 0.9 0.2 0.3 1.0 0.8 0.0 0.0

R6 3.1 2.2 2.5 1.2 1.2 3.0 2.1 0.7 0.5

R7 3.5 2.7 2.9 1.4 1.4 2.9 2.5 0.6 0.6

Av 1.8 1.1 1.4 0.6 0.6 1.5 1.2 0.2 0.2

Beam R1 3.3 2.3 2.7 1.4 1.4 3.5 2.6 0.7 0.7

R2 3.3 1.8 2.7 1.4 1.3 3.4 2.7 0.4 0.6

R3 3.3 2.4 2.7 1.4 1.4 3.5 2.6 0.5 0.7

R4 2.5 1.9 2.7 1.4 1.4 3.5 2.2 0.7 0.6

R5 2.9 1.7 2.7 1.5 1.5 3.4 2.9 0.5 0.7

R6 3.5 1.5 2.6 1.5 1.4 3.6 2.9 0.6 0.4

R7 3.4 1.6 2.7 1.4 1.4 3.4 2.9 0.4 0.5

R8 3.0 2.1 2.7 1.4 1.4 3.4 2.4 0.4 0.5

Av 3.1 1.9 2.7 1.4 1.4 3.5 2.7 0.5 0.6

SQ R1 3.7 1.6 1.6 3.1 2.9 0.5

R2 3.8 1.6 1.6 3.1 3.0 0.4
ERDC/CHL TR-20-18 69

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R3 3.7 1.6 1.6 3.0 3.0 0.3

R4 3.9 1.6 1.4 3.0 3.0 0.6

R5 3.8 1.3 1.3 3.1 3.0 0.5

R6 3.6 1.2 1.2 3.1 2.9 0.4

R7 3.7 1.6 1.6 3.2 2.9 0.6

R8 3.6 1.2 1.1 3.0 2.9 0.4

R9 3.8 1.3 1.4 3.1 2.9 0.4

R10 3.6 1.5 1.5 3.2 2.9 0.4

R11 3.6 1.6 1.4 3.2 2.8 0.3

R12 3.5 1.6 1.5 3.1 2.8 0.3

R13 3.8 1.5 1.7 3.2 3.0 0.4

R14 3.7 1.4 1.5 3.2 3.0 0.4

R15 3.7 1.5 1.4 3.2 2.9 0.5

Av 3.7 1.5 1.5 3.1 2.9 0.4

BQ R1 3.0 1.3 1.3 2.7 2.4

R2 3.0 1.2 1.2 2.7 2.4

R3 3.0 1.2 1.2 2.6 2.4

R4 3.1 1.3 1.2 2.7 2.4

R5 3.0 1.3 1.3 2.6 2.4

R6 3.1 1.3 1.3 2.7 2.4

Av 3.0 1.3 1.2 2.7 2.4

Table D-18. Wave periods (second) by heading for wave M9. 

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

Following R1 3.9 3.9 4.5 4.0 4.0 4.6 4.6 1.8 1.7

R2 3.9 3.4 3.9 4.7 4.7 4.6 4.5 2.8 1.8

R3 3.9 4.5 3.9 4.1 3.6 4.5 4.5 2.4 2.1

R4 3.6 4.5 3.4 4.4 4.3 4.6 4.5 1.9 2.8

R5 3.6 4.2 3.8 4.6 3.8 4.6 4.6 2.0 2.0

R6 3.6 3.8 2.9 4.7 4.5 4.6 4.5 2.2 1.9

R7 4.5 4.6 3.9 4.6 3.8 4.5 4.6 1.6 2.1
ERDC/CHL TR-20-18 70

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R8 3.2 3.0 3.2 4.8 4.6 4.5 4.6 2.3 2.6

R9 4.5 3.8 4.5 4.6 4.7 4.5 4.5 1.5 1.9

Av 3.9 4.0 3.8 4.5 4.2 4.6 4.5 2.1 2.1

Head R1 1.8 2.3 3.1 3.6 4.5 3.6 3.9 0.1 0.1

R2 3.4 1.7 3.1 2.3 2.8 3.4 3.9 0.1 0.1

R3 3.8 3.0 3.0 1.7 1.8 3.6 2.9 0.1 0.1

R4 4.6 3.3 3.9 2.7 2.5 4.5 4.4 0.1 0.1

R5 4.5 3.3 4.5 2.5 2.9 4.5 3.9 0.1 0.1

R6 4.3 3.6 3.6 4.2 4.3 4.3 3.9 2.3 2.0

R7 4.5 4.6 4.6 4.6 4.6 4.3 4.5 2.2 2.3

Av 3.8 3.1 3.7 3.1 3.3 4.0 3.9 0.7 0.7

Beam R1 4.6 4.6 4.6 4.6 4.6 4.5 4.6 2.6 2.8

R2 4.5 3.6 4.6 4.7 4.7 4.5 4.6 1.4 2.4

R3 4.5 4.6 4.6 4.7 4.7 4.5 4.5 2.1 2.6

R4 3.1 3.4 4.6 4.6 4.7 4.5 3.4 2.3 2.5

R5 3.7 2.7 4.6 4.6 4.6 4.5 4.5 2.1 2.8

R6 4.6 2.3 4.6 4.6 4.5 4.6 4.5 2.1 1.4

R7 4.6 2.7 4.6 4.5 4.5 4.4 4.6 1.4 2.3

R8 3.8 3.7 4.6 4.4 4.6 4.5 3.8 1.2 2.0

Av 4.2 3.4 4.6 4.6 4.6 4.5 4.3 1.9 2.4

SQ R1 4.6 4.6 4.6 4.6 4.5 2.1

R2 4.6 4.7 4.7 4.6 4.6 1.5

R3 4.6 4.6 4.7 4.5 4.5 1.3

R4 4.5 4.6 4.5 4.6 4.5 2.5

R5 4.5 3.7 3.7 4.5 4.6 2.0

R6 4.5 3.1 3.1 4.5 4.6 1.5

R7 4.6 4.6 4.6 4.6 4.6 2.4

R8 4.6 3.6 3.6 4.5 4.5 1.7

R9 4.5 3.7 4.2 4.6 4.5 1.4

R10 4.6 4.5 4.5 4.6 4.6 1.4

R11 4.6 4.7 4.0 4.6 4.6 1.4

R12 4.6 4.6 4.3 4.5 4.6 1.3
ERDC/CHL TR-20-18 71

Heading Run C1 C2 C4 C5 C6 C7 C9 S1 S2 

R13 4.6 3.9 4.7 4.6 4.5 1.5

R14 4.6 4.0 4.5 4.6 4.6 1.7

R15 4.5 4.1 4.1 4.6 4.5 1.6

Av 4.6 4.2 4.3 4.5 4.6 1.7

BQ R1 4.5 4.7 4.7 4.5 4.5

R2 4.5 4.5 4.7 4.6 4.5

R3 4.6 4.6 4.6 4.6 4.6

R4 4.6 4.7 4.1 4.6 4.5

R5 4.5 4.7 4.7 4.6 4.5

R6 4.6 4.7 4.7 4.6 4.6

Av 4.6 4.6 4.6 4.6 4.5

D.10 Irregular seas – SQ

Table D-19. Irregular wave condition statistics for sea state 3 for SQ. 

C4 C5 C6 C7 C9 S1 Average 

Hm0 (in.) 0.57 0.54 0.53 0.87 0.91 0.44 0.64

Tp (s) 1.86 1.78 1.78 1.86 1.86 1.78 1.82

Table D-20. Irregular wave condition statistics for sea state 4 for SQ. 

C4 C5 C6 C7 C9 S1 Average 

Hm0 (in.) 1.08 1.34 1.34 2.07 2.10 1.44 1.56

Tp (s) 1.52 1.46 1.46 1.46 1.46 1.46 1.47

D.11 Irregular seas – BQ

Table D-21. Irregular wave condition statistics for sea state 3 for BQ. 

C4 C5 C6 C7 C9 S1 Average 

Hm0 (in.) 0.83 0.82 0.81 1.07 1.15 0.62 0.88

Tp (s) 1.86 1.78 1.78 1.78 1.78 1.78 1.79

Table D-22. Irregular wave condition statistics for sea state 4 for BQ. 

C4 C5 C6 C7 C9 S1 Average 

Hm0 (in.) 1.19 1.09 1.08 1.88 1.83 1.71 1.46

Tp (s) 1.64 1.46 1.46 1.52 1.52 1.52 1.52
ERDC/CHL TR-20-18 72

Unit Conversion Factors

A sponsor requirement for this study was the use of English Customary 

units of measurement. Most measurements and calculations were done in 

International System (SI) units and then converted to English Customary. 

The following table can be used to convert back to SI units.

Multiply By To Obtain 

feet 0.3048 meters

cubic feet 0.02831685 cubic meters

pounds (force) 4.448222 Newtons

square feet 0.09290304 square meters

knots 1.6878099 feet per second

knots 0.5144444 meters per second
ERDC/CHL TR-20-18 73

Acronyms and Abbreviations

BQ bow quartering seas

BQ-R bow quartering sea repeats

BS beam seas 

CHL Coastal and Hydraulics Laboratory

DAQ data acquisition 

DSWG Directional Spectral Wave Generator 

EMOGS Environmental Monitoring and Operator Guidance System

ERDC US Army Engineer Research and Development Center

FS following seas 

HES Harbors, Entrances, and Structures

HS head seas 

LabVIEW Laboratory Virtual Instrumentation Engineering Workbench

LAMP Large Amplitude Motion Program 

LIDAR Light Detection and Ranging

MASK Maneuvering and Seakeeping Basin 

NSB Naval Submarine Base 

NSWCCD Naval Surface Warfare Center, Carderock Division 

RMSE root-mean-square-error 

SI International System

SQ stern quartering 

TMA Texel, Marsen, and Arsole Spectrum
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PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE 

August 2020

2. REPORT TYPE

Final Report

3. DATES COVERED (From - To)

4. TITLE AND SUBTITLE

Shallow Water Seakeeping Tests with Columbia Class Submarine for Integration into the 

Environmental Monitoring and Operator Guidance System

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Abigail L. Stehno and Jeffrey A. Melby

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

Coastal and Hydraulics Laboratory

US Army Engineer Research and Development Center

3909 Halls Ferry Road

Vicksburg, MS 39180-6199

8. PERFORMING

ORGANIZATION REPORT

NUMBER

ERDC/CHL TR-20-18

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

US Naval Surface Warfare Center 

Carderock Division

West Bethesda, MD 20817-5700

10. SPONSOR/MONITOR'S ACRONYM(S)

NSWCCD

11. SPONSOR/MONITOR'S

REPORT NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution is unlimited.

13. SUPPLEMENTARY NOTES

MIPR N0002418MP00414

14. ABSTRACT

The Environmental Monitoring and Operation Guidance System (EMOGS) tool was developed in 1989 to provide a real-time risk 

analysis for underkeel clearance for the Ohio class submarine while in transit to the Naval Submarine Base at Kings Bay, Georgia. The 

program computes expected submarine response for input water level, depth, speed, wave, and other input conditions using shallowwater motion transfer functions generated by the strip theory tool, Large Amplitude Motion Program (LAMP). The integration of the new 

Columbia class submarine into EMOGS required that new transfer functions be developed using LAMP. The LAMP results are to be 

validated using measured motions from physical model laboratory testing. This report summarizes a laboratory study of the Columbia 

class submarine response in shallow-water waves. The study was conducted at the US Army Engineer Research and Development 

Center, Coastal and Hydraulics Laboratory, and was done in direct support of the Naval Surface Warfare Center, Carderock Division. 

These seakeeping tests were performed in a shallow basin with a multi-directional wave generator, with measured still water vessel 

motions and measured vessel motion in regular and irregular waves of varying height, period, and direction.

15. SUBJECT TERMS 

Columbia Class (Submarines), Hydrodynamics, Kings Bay (Ga.), Navigation, Water waves

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF 

ABSTRACT

SAR

18. NUMBER 

OF 

PAGES

84

19a. NAME OF RESPONSIBLE PERSON

a. REPORT Abigail L. Stehno

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified 19b. TELEPHONE NUMBER (Include area code)

601-634-2062

Standard Form 298 (Rev. 8/98)

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