Tests of impact acceleration on a flow bow plate for a high speed craft

TESTS OF IMPACT ACCELERATION ON A FLAT BOW PLATE

FOR A HIGH SPEED CRAFT

Stuart B. Cohen

Marine Hydrodynamics Laboratory, University of Michigan

ABSTRACT:

Model tests of vertical impact acceleration of a plaflmg boat bow flap at zero speed in calm water showed

significant differences between a zero-angle and

12-degree angle of entry. The resUlts differed from pressure measw-ements of impact found in the literature since the plates were flat and had no deadrise. However, the force proportionality with heigh that is with V2, is confinned. The structures can be represented by a single degree of freedom, with no consideration for trapped air, or water

spray jets. Results indicate that the water provides a

suction force,, and preliminary theoretical calculations give a similar indicaiion.

Introduction

Effectiveness of instrumentation on a full size

planing vessel was limited by vertical

acceleration

considtions. The crafi had a two part,

flat bow plane, neither part with any deadrise. The lower plate (closest to the forward perpendicular) was completely horizontal, and the upper plate was fixed such that on plane it met the waves at a 12-degree trim angle to the horizontal. The

plate was attached to the craft with heavy mounting

beams. Since the bow plane was nearly square, the aspect ratio was nearly unity and two-dimension fluid theory was considered suspect. Model tests of vertical impact on a flat plate were requested with 12 degree trim angle and with zero angle to be used to determine if a simplified structural model was appropriate. Vertical acceleration was measUted. All tests were done at zero speed in calm water.

These tests were basically an investigation of the structural response. It provided a re-verification of some aspects of similar tests done measuring impact pressures.

However, the forces on the plate are the result of

integrated pressure, and the responses at the instrumentation position were not expected to be as severe as the pressure tests in the literature.. In addition, it was not always clear that the pressure tests would give similar information needed for the flat plates fortwo reasons: the plates have a natural frequency that might be important in either the fUll-scale or the model tests, and the pressure measurements were Universally done on a model that had some curvature, slope or deadrise.

Typical theOrmical calculations are based on circular or nearly circular cylinders (Arai 1995), (Troesch, 1986), (Greenberg, 1967) and only show a single peak

the edges were considered important. Strain, as well as

pressure, was measured for "V" bottom and wedges

(Chuang, 1970) and some vibratory motion was noted but not analyzed. Bluff bodies in still water and in waves (Gerlach, 1967, 1968, 1970) were mostly concerned with the corresponding difference

in peak pressures. Air

entrapment was considered a very important dynamic consideration (Sellars, 1971) for ship models. Measured values of forte for a highly curved body are available (Troesch, 1988) and responses oncwved pne1s are given in (Hagiwara, 1975). One of the few accelerumeter tCsts on flat panels, however with deadrie, is from ((buang,

1969). Modeling

The instrumentation comprised mounting an accelerometer at the center of gravity of the test fixture. The characteristics of the fixture are shown in Table 1. The box was guided vertically along two 3/4-inch steel vertical pipes. In the case of the zero-degree angle entry into the water, the tube guides on the box hardly touched the vertical pipes and had virtually no effect. For the 12-degree impacts, the guide tubes restrained the box from pitching as the leading edge first touched the water. The large weight of the box, coupled with the low friction of the guide tubes over the vertical pipes, insured that the velocity of the box was minimi1ly affected by the pitch moment

Table 1. Characteristics of Model 1691

Length inch 3581 Width inch 21.88 Aspect RatiO n-d 1.637 Weight lbs 44.70 Sample Rate sps 15000 (i)a(b0X) HZ 410

oa(plate)

Hz 650

The transducer

used ivas _a piezo-eleclic accelerometer from PCB, Inc.,

capable of more than

l000g meaSurements. It does not measure static

acceleration and therefore was calibrated dynamically. Upward acceleration was considered positive. The box was constructed of reinforced plywood, and sheathed, with 1/4-inch aluminum plate, the ballasted with lead to the required weight.

Figure Ia. Usual model of base

excitation where the

accelerometer mass determines natural frequency.

Because of the full-scale vessel construction, it is

not immediately clear

what mathematical model

of

excitation or structure sbould be

used to analyze the

response. These tests were to determine which of two base excitation models seemed most appropdate. The usual way is to assume that the accelerometer has a small mass, which is spring coupled to the larger vessel mass as

in Figure la. However, if the

aluminum bow plate is viewed as a secondary structure, withthe heavy support beams taking the priniary loads, then it can vibrate on its own and the springcoupling of the accelerometer can be neglected as shown in Figure lb.

Accelerometer

Sensor

Figure lb. AlternaUve model of base excitation where the late mass determines natural frequency..

Results

Like the pressure tests, the acceleration curves are linearly related to initial height. A non-dimensional vertical acceleration coefficient can

be defined as C =

mal(O.5 p V2 A). For constant acceleration, V2 = 2g * h. So if C, is invanant withmodel. size, the results will be directly proportional to V2 and linearly proportional to drop height. In Figure 2 the noimalized acceleration, y,

for drop hcighi from 2 to

6 fCet shows the expected

similarity when normalized by drop height, h.

-100 -200 a C rj b23/2 bh2S/2

.I1II1I.

If

200 150 100 50 bb2'(/4 bh26/6 10 15 20 25 Time (msec)

Figure 2. Impact

Acceleration of Zero-Degree Plate

Normalized By Drop Height, for 2 to'6 foot heights. The initial impulse lasted about 7 milliseconds and like the'pressurC tests, rises exponentially Taking the. average values of Figure2, the equation y = 0.090Exp(t) fits the exponential nsê data

well, where t is time in

milliseconds.

0 10 20

time (Insec)

Figure 3. Exponential and harmonic functions fitted to average of 2-ft to 6-ft measured data' for zero angle.

200

100

Unlike the pressure tests, the response is a single degree Of motiOn harmonic under exponential decay. The remiiifling time history of Figure 3 is well described by the equation y =1170 sin(l.41t) * Exp (-0.2301). This

indicates that the model represented in Figure lb is

appropriate. The response due to the natural frequency of the acelerometer can be identified in peaks and troughs of the larger drop height data in Figure 4. This outcome represents the dynarnc model in Figurela and is seen as slight secondary effects due to the plate vibration at a natural frequency of over 600 Hz.

-I

Time (msec)

Figure 4. Measured values for zero angle and 7-ft 10 10-ft drop heights.

The results for the 12-degree angled box has

several differences with both the pressure measurements

and 0-degree tests.

Most notably, it contains two frequencies and the peak values are less than one-quarter.

The initial rise is exponential but not very visible in

Figure 5.

-- Timc(mscc)

Figure. 5,. The normalized acceleration of the box at 12-degrees emIly angle.

The average of the 6-ft to 10-ft data can be

decomposed into an exponential rise and a Single degree of freedom harmonic. An equation that fits the initial rise is y' = 0.005 Exp(5t) where I is in milliseconds, and is plotted in Figure 6 along with the calculated harmonic.

.75 50 25 U

:o

25 -50 -75 0

hit a!

.Calc

hvrig

10 15 20

Time (msec)

Figure 6. Avage 12-degree angle data decomposed into initial exponential rise.

50 -50 0

Total

Sne

Cosine

Expon mtial

10

.15

20

Time (msec)

Figure 7. Components of the 12-degree angle impact

acceleration response.

The response can be broken into two lngonometrc functions. Given A=80 and o = 0.970 the equation that governs the decay is y*= [-A Sin(oj 1) + AJ2 Cos(2 oj t)] * Exp (-3.0 t). Note that the damped

frequency ad its

first harmonic are involved. The

I . -- sbh2O/7 sbh27/8 .

..

sbh22/9

It

,_..

sbh2919 sbb25/1O 0 5 10 j5 21 sba36(6ft) sba3l(lft) sba4o(Sft) _____:

-

sba3t(9ft)

-0 25 S.-U -25 2 I . 5 2 -2

the instant of the slightest initial measured values. The use

of the sine function is an

artifact of the curve fitting

process to get the

cont phasing since

matching the phasing of the measured values was done approximately by eye.

An Unresolved Problem

thuhisecönds during and after the I iial water contact, there is a very strong negativeacceleratiorL This implies that the water provides a suction force. Evidence of a single j,eak pressUre, abubble

of air orwateriet at the

interface seems to be missing in

these tests. A quick

check of the exciting force was

desired. Since the accelerometer has its own mass as in Figure la, and the plate seems to act as asingle degree of freedom, there is an unpublishedcalculation by (Troescb, 1995) that uses the theOreticál impulse response function to determine the exciting force from the response record. It is done in a step-wise fashion where the acceleration response value at time t is found from theprevious measurement corrected by the previous response divided by the convolution of the impulse response. up to that time.

Using the 10-ft data, the excitation determined

this way is shown in Figure 8. It does not show the

exponential rise of the pressure data in the literature or the response in Figure 3, but rather an enlarged impulse that

goes negative before

returning positive. This is an additional reason to believe that there may be a suction force. However, due. to the unpublished nature of the computer program, this conclusion is not yet resolved.

20000

10000

10

-10000

-20000

0 2

3.

Time (ins)

Figure 8. Calculated excitation force based on 1fl, 0-angle impact test data.

5

Nomenclature

a = Acceleration,

ftlsec2 A = Area opposed toflow, ft2 C= Acceleration Coefficient, non-dim

g = Gravitational

acceleration, fl/sec2

h = Drop height, ft

= Mass, slugs

I = Time, milliseconds

V = Velocity, fl/sec

Natural frequency in air, Hz = Damped frequencyinwater, Hz

y = Normalized

acceleration, g/foot

Bibliography

Arai, M., et al., "A Computing Method for the Analysis of Water Impact of AEbiraiy Shaped Bodies (2nd Report)",

1. Soc. Nay. Arch of Japan,VoL 177, June 1995.

Chuang S..L., "Impact Pressure Distributions On wedge -Shaped Hull Bottoms of High-Speed Craft", Naval Ship Research and Development Center Report 2953, AuguSt

1969.

Chuang, S.-L., "Investigation

of Impact of Rigid and

Elastic Bodies with Watef', Naval Ship Research and Development Center Report.3248, Februaly 1970. Gerlach, C. R.., "bvesligationof Water Impact of Blunt Rigid Bodies-Real Fluid Effects", Technical Report No. SouthweSt Research Institute Project 02-2036, December 1967.

Gerlach, C. R., "Investiga on of Water Impact of Blunt Rigid Bodies - Size Scale Effects", Technical Report No. Southwest Research Institute Project 02-2036, November 1968.

Gerlach, C. R., "Investigation of WaterImpact of Blunt Bodies", Final Report Project 02-2036, Southwest Research Institute, December l970

Greenberg M. D., "Prediction ofShip S11Immmg Loads: On the Water Impact of'a Circular Cylinder: Numedcal Results", Therm Advanced Research, Inc., TAR-TR Nb.

6705, Ithaca, NY, December 1967.

Hagiwara, K., Yuhara, 1., "Fundamental Study of Wave

Impact Loads on Ship

Bow", Chapter 6, ava1

çjtecture. and Ocean Engineering,

talen from L

Society of N.A. of Japan Vol. 135 June 1974, VoL 136 Dec. 1974, VoL 137 June 1975.

Hágiwara, K., Yuhara, T., "Fundamental Study of Wave Impact Loads on Ship Bow (2ndReport) - Effect of the

Scale of the Model on Maximum impact Pressure and Equivalent Static Pressure", Naval Architecture and

Ocean.Engn. VoL l5 Chap 9, Soc. Nay. Arch.

Japan,1977.

Sellars, F. H., "Slamming Impact Pressure", MPR Associates, Inc., Washington, DC, Fitial Riort MPR -282, June 1971.

Troesch, A.. W., Kang, C.-G.,. "Bow Impact Loads

Inchithng the Effects of Flare Pail I

,

U S Maritime

Administration Report MA-RD-760-870 13, U S

Department of Transportation, December 1986.

Troesch, A. W., Kang, C.-G., "Evaluation of. Impact Loads Associated with Flare S1ammmg", Spring

MeetingfSTAR.Symsum / 3rd IMsDc, Paper S9, held in Pittsburgh PA, Society of Naval Architects and Manne Engiieers, June 8-10, 1988.

Troeth, A. W., "Impact Tests", unpublished ilianuscript from personal communication, November, 1995 with unpublished computer pmgram, CONVOLVE, November