A Comparison of Two Methods for Determining Wave Heights from a Discus Buoy with a Strapped-Down Accelerometer

L. C. Bender III, N. L. Guinasso Jr., & J. N. WalpertGeochemical & Environmental Research Group

Texas A&M UniversityCollege Station, TX 77845 USA

S. D. HowdenUniversity of Southern Mississippi

Stennis Space Center, MS USA

Motivation

How does one get wave heights and directions from a heave/pitch/roll buoy equipped with an accelerometer and a tilt sensor?

Why should the buoy heel make a difference in the wave height calculations made from a heave/pitch/roll buoy?

MethodologyInstrumentation

Crossbow 3D accelerometer => ax, ay & azHoneywell HMR compass => heading, pitch & rollAll the raw data was saved on board.

Platforms3-m discus buoy2.25-m discus buoy

HurricanesKatrina – August 29, 2005Ike – September 12, 2008

TestOWIF at NDBC

Summary of Conclusions•Wave heights from a strapped-down 1D accelerometer can be overestimated during storm events

•if the buoy is small: 3m discus •if the buoy is heeled: >6o

•if the buoy is in shallow water: <100m

•A strapped-down 3D accelerometer can give comparable wave heights to an internally gimbaled accelerometer if the orientation of the strapped-down accelerometer is properly accounted for.

•Using a heave/pitch/roll buoy with a strapped-down 1D accelerometer to report on individual, large wave events in shallow water is not for the faint of heart.

What does an accelerometer measure?•Acceleration?•Force!•=> A Gravity Offset•Orientation is important•“Contamination” of g into three axes•Buoy heel becomes an issue for a strapped-down1D accelerometer.

•Two buoys and two hurricanes•One test•A theoretical model

Confirmation

INSTRUMENTATION

• Crossbow IMU400/440 accelerometer3-axis linear accelerationPitch, roll & yaw rate

• Honeywell HMR 3300 compassHeading, pitch and roll

Instrument Well

Crossbow Accelerometer

30' 95oW 30' 94oW 30' 93oW 30' 92oW 30'

27oN

30'

28oN

30'

29oN

30'

30oN

Buoy N Buoy V

Buoy FBuoy B

Buoy RHouston

1100

1700

2300

0500

2130

PLATFORMSHurricane Katrina

Hurricane Ike

Remove the Gravity Offset

I. Strapped-down 1D accelerometer only.Assume the tilt is small.Subtract 1g from the measurements,Instead of subtracting the component of gravity.

II. Strapped-down 3D accelerometer with pitch, roll & heading.Mathematically gimbal to get earth-referenced vertical acceleration.orz-axis only => 1D

26 27 28 29 30 31 010123456789

1011

August 2005

Sig

nific

ant W

ave

Hei

ght,

m

1DGimbaled

0 6 120

3

6

9

12

Hsig, m

Hsi

g, m

0 5 10 150

5

10

15

Peak Period, s

Pea

k P

erio

d, s

3 7 113

5

7

9

11

Mean Period, s

Mea

n P

erio

d, s

09 10 11 12 13 14 15 16 170123456789

10

September 2008

Sig

nific

ant W

ave

Hei

ght,

m

1DGimbaled

0 5 100

2.5

5

7.5

10

Hsig, m

Hsi

g, m

4 11 184

7.5

11

14.5

18

Peak Period, s

Pea

k P

erio

d, s

2 6 102

4

6

8

10

Mean Period, s

Mea

n P

erio

d, s

Hurricane Katrina

3m discus19m depth

Hurricane Ike

2.25m discus89m depth

Horizontal axes – 1DVertical axes – Mathematically

Gimbaled

Horizontal axes – 1DVertical axes – Mathematically

Gimbaled

0 5 10 15 20 25 30 350

2

4

6

8

10

12

14

16

18

Buo

y H

eel,

deg.

Wind Speed ms-1

0 5 10 15 20 250

2

4

6

8

10

12

14

16

18

Buo

y H

eel,

deg.

Wind Speed ms-1

Hurricane Katrina

Hurricane Ike

3m discus

2.25m discus

0 2 4 6 8 10 12 14 160

20

40

60

Buoy Heel, deg.

Hei

ght O

vere

stim

atio

n, %

0 5 10 15 20 25 300

20

40

60

Wind Speed ms-1

Hei

ght O

vere

stim

atio

n, %

Hurricane Katrina Hurricane Ike

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

Buoy Heel, deg.

Hei

ght O

vere

stim

atio

n, %

0 5 10 15 20 250

10

20

30

40

Wind Speed ms-1

Hei

ght O

vere

stim

atio

n, %

1m arm => HS = 2.83 m

A series of 38 runsPeriods: 6, 9, 12, 15, 18, 21 sTilts: 0, 8, 24 deg.Heel: 0, 20 deg.

Hippy 40SchaevitzInclinometer

Microstrain 3DM-GX1

Crossbow 400CC IMU

0 5 10 15 20 25 30 35 40 45-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

Time, s

Ver

tical

Acc

eler

atio

n, m

s-2

Hippy 40

Z-axis Crossbow

Mathematically GimbaledCrossbow

Hippy 40

15s period, 8o tilt, 20o heel

HS = 7.36m

HS = 2.75m

HS = 2.75m

HS = 2.72m

Summary of Conclusions•Be a discriminating user of buoy wave heights.

•Shallow water, smaller diameter buoys with a strapped-down 1D accelerometer can be significantly affected if the buoy is heeled.

•Deep water discus buoys with large diameter hulls and strapped-down 1D accelerometers are largely unaffected if the buoy is heeled.

•A strapped-down 3D accelerometer with pitch, roll and heading data can give comparable wave heights to an internally gimbaled accelerometer.

•Using a heave/pitch/roll buoy with a strapped-down 1D accelerometer to measure individual, large wave events in shallow water can lead to overestimated wave heights.

Questions?