Horizontal plane characteristics of two full size personal watercraft

HORIZONTAL PLANE CHARACTERISTICS OF TWO FULL SIZE PERSONAL

WATERCRAFT

Stuart B. Cohen, Marine Hydrodynamics Laboratory, The University of Michigan

ABSTRACT.

Efforts to design water jet craft with mfe stopping characteristics have been hampered by lack of straight ahead and yawed resistance data. The characteristics of a. Kawasáki model 300 stand-up Jet Ski are ëontrasted with a Polaris

model 750 SLT

multi-chiDe person

waiercraft. E)rag and lift were measured in the towng tank with nO jet thrust enabling directional control. To identify other variables that could be useful in design turning circle and stopping field tests of the Polaris craft were

Introduction

Personal watercraft (that is, jet skis) are characten7ed by waler jet propulsion, shallow draft, high speed and extreme maneuverability. In this paper, the term "personal watercrnft" and "jet ski include multi-seat vessels as well as single person, stand-up craft.

Jet skis can perform very small turning circles when the motor is at high power. These vessels can have very high drift angles as they skid in and out of turns. The turning moment is provided primarily by the momentum flux of the jet exit velocity at an angle with the waleitrall

ajecty.

Unlike a boat with a rudder, without the jet operating, there is no mechanism for turning wateivrafL At high vessel speeds; a boat with rudder, keel, Or center board, will provide some turning moment proportional to drill angle. For the personal watercraft there is essentially no turning force at any speed once the water jet is turned off.

This condition can lead to injUry and even

death.

Instinctively, operators reduce throttle and then turn the steering bar to avoid a collision. Rather than coming to an immediate stop, the stopping distance from high speed can exceed 100 ft. In addition, operators may believe that they can continue to steer the vehicle once they release the throttle. In actuality, personal watercraft have no turning

force without the water jets operating and providing

thrust.

The primary focus of this investigation is to identify general design parameters that can be formulated from model tests. Typical design quantities are turning circle diameter and stopping distance as functions of speed. Auxiliary quantities that are easily measured are lift aid

drag at yaw angles, yaw moments, and

location Of

hydrodynamic pressure, all as functions of speed.

Full-scale unpowered tow tank tests were performed on a

made. It was found that most of these quantities follow

linear theory, or are approximately constant as

non-dimensional variables. Measurements of the hydmdynamic forces at midships acting on an unpowered jet ski are the first step to understand vessel control in situations when the engme has been stopped or at very low RPM. These

results can be used to

quantify personal wateicraft

characteristics, and predict stopping disiancs and turning

circle diameters for constant power.

Kawasaki model 300 standup Jet Ski (Cohen 1998h) aid contrasted with a Polaris model 750 SLT (Cohen 1998a) multi-chine three person wateitraft. Additional turning circle and stopping field tests of the Polaris craft were

made.

Results

Kawasaki Hull Tests

To a large degree, the jet ski

total hull drag is

independent oIyaw angle (Figure 1) below planing spl (Fn < 0.8) indicating that hull drift angle has minimal effect on stopping distance. Un-instrumented tests, where the model was simply pushed by hand confirm this at very slow speeds at angles in excess of 45 degrees. At planing speeds there is only a slight increase in drag coefficient

(Figure 2) for increased yaw angle below 8 degrees.

At high speeds. the net side forte coefficient (Figure 3) approaches.zem as the yaw moment remains relatively constant indicating that the resultant hydrodynamic force

(Figure 4) is centered far aft of the center of gravity. At

low speeds, this resultant force is near the center of

gravity as determined by negligible net side force. Polaris Hull Tests.

Like the previous Kawasaki jet ski tests, the total hull drag is independent of yaw angle (Figures 1 and 2) below planing speed indicating that

drift angle has

minimal effect on stopping distance. Only at 20 degrees

yaw angle was there an appreciable increase in resistance.

The yaw moment increases with yaw angle and speed. At very slow speeds (Fn<0.5) and low yaw angles there was no tendency to reduce yaw angle. Tests with video

only,

where the model was simply pushed at

the

At very Slow speeds and yaw angles up to 90 degrees, when the model. was gently pushed at the longitudinal center of gravity the craft moved in the pushed direction with no change m drift angle.

ThC net side force (Figure 3) is proportional to yaw angle and speed. The relative increase in ilet side kite

with - respect to

yaw moment

yields a resultant hydrodynamic force (Figure 4) which is oerde2ed near midshis for all conditions te.sted

Polaris Stopping Tesl&

Fild tests of stopping distance are Shown in Figure 5. The variations, especially at the highest speeds. are diE to the: differences in riding technique from the three drivers For moderate Reynold's numbers (say iO to l0)

drag coefficients for cylinders and for spheres are

approximately constant (see Schlichting (1979) p 17). However, stopping times (Figure 6) as a function of speed are approximately linear, meaning drag is proportional to Vs rather than Vs2. Therefore, the drag acts more like a fiat plate line (see Schlichting (1979) p 663) at planing speeds than a submerged sphere orcylinder.

Polaris Turning Circle Tests

Turning circle tests were done at three nozzle angles and several speeds. In linear theory, R*6/LWL =

N,(Y) I (Y, N6 -Nv Y&) as defined in PNA Vol. ifi

Section 6.4 (pp. 211). The non-dimensional coefficients are normalized by velocity uared, so R*8fV2 is expected to he constant. The turning circle results are graphed as the square root of the turning radius times the nozzle angle versus, vessel speed rather than R*g/V2 for clarity. This verifies a linear relation, expected from linear theory. This choice of variable also shows (see Figure 7) that below 2 knots, the vessel turns around it own center of gravity. Even though the constant. varies slightly with speed, for estimation purposes. based on the slowest planning speed. the value for the Polaris is R*5/Vs2 = 2.39 for speeds above Vs = 3 fps.

The values of Y and N come from the straight line, yawed resistance tests (Figure 1). The values of Y8 and N8 were found to follow the momentum theorem (see Cohen (1994) to within 1%. The values of .Nr and Yr

require horizontal motions of a Planar Motions Mechanism or a rotating arm test. These tests are planned

for the future to see if these values can be predicted

theoretically, but were unavailable for this paper.

Kawasaki Experimental Matrix and Apparatus

The model was tested over a range of speeds .up to 18

feet per, second which is

approximately the planing

threshold. A yaw sweep was conducted to position the model heading directly in line with the tank centerline. The tests included fixed yaw angles of 4, 6, and 8 degrees to pofl from the centerline. The resultant forces were used to determine the location of the net hydrodynamic force relative to midship.

(Y Nr

-All tests w condncted in the MHL towing tank under calm water conditions. The models were ballasted such that the center of gravity coincided with midships. The floating beam dynamometer was used in conjunction with the yacht dynamorneter to provide measurement of drag, Side force, yaw moment and heel moments. The

forces were transmitted to the lOad cells and strain gauges

through a tow point mounting plate at midship 13.5

inches above haseline

The mounting plate allowed for adjusting the yaw

angle in 2 degree increments and the option of fixed or free

movement in heeL The model was free to heave through two precision linear bearings. The weight of the heave staff and the yacht dynamometer were included as pail of the displãcemenl

A Kawasàki model 300 Jet Ski was used for this test program and is identified as U of M Model 1704. The

vessel characteristics as tested are presentedn Table 1.

Table 1. Model 1704

Characteristics

The hull design has a relatively flat bottom, hard chines and vertical sides. The engine, mechanical parts and shrouds were removed to facilitate testing. Trim azi displacement were achieved with the addition of karl ballast. There were no alterations to the wetted surfaces.

Polaris Experimental Matrix and Apparatus

The model was tested in the towing tank at speeds up

to 18 feet per second which, like the Kawasaki. is

approaching the planing threshold. The standard yaw sweep was conducted to establish a.reference position with the model heading directly on the tank centerline. The

tests included fixed yaw angles of 2,4, 10, and 20 degrees to port from the centerline. These measurements e used to calculate the location of the net hydrodynamic

force relative to midship.

All tests conducted in the MHL towing tank were calm. water conditions. The floating beam dynamometer was used in conjunction with side force load cells mounted on the heave staff and at the stern separated by a distance of 50.0 inches. This model was ballasted similarly to the Kawasaki with the center of gravity coinciding with midships. This provided for direct measurement of total

WA

696feet

LWL 6.01 feet

Beam at LWL 1.92 feet Draft (mean) 0.83 feet

Displacement 285 lbs.

LCG midships

dEag and the side forves needed tO calculate yaw moments.

The heave staff assembly, mounted at midship 22.5 inches above baseline, allowed for unrestrained movement in pitch and roll. The model was fme to heave through two precision linear bearings The aft load cell was fixed to a "grass hopper" that held the model in the prescribed yaw pOsiuiofl while allowing free movement in all other axis The weight of the heave staff and the side force kind cell were included as pail of the displacement.

A Polaris model 750 SLT Jet Ski was used for this test program and is identified as U of M Model 1706. The vessel characteristics as tested are presented in Table 2.

Table 2. Model 1706 Characteristics

The hull design (Figure 5) incorporates three distinct chines aft tO achieve a relatively round bottom that softens to form a V" at the Stem The engine, mechanical parts and shrouds were all left intact with only the seat cushion removed to facilitate testing. Trim and displacement representing two passengers (300 Ibs) were achieved with the addition of lead ballast.

For the field tests, only one driver at a time with no rides was aboard. Position was identified Using a GPS device sampling 5 times per. second. Speed and X, Y location was telemetered to shore and recorded by a 486 PC computer. Turning circles were conducted for 1-1(2 turns before changing speed. S1op,ing distances were determined frOm the abrupt fall-off of speed until the craft no longer moved in a straight line, usually at about 2 knots. All runs were video taped. To mark the beginning

of the stopping sequence, the driver raised his arm

OveEhead. Since that also released the hand throttle, it

insured that the throttle was fully and quickly released.

Nomenclature

B= Beafl(ft)

8= NOzzle angle (degrees)

Displacement (non-dimensional)

WA

= Length Over All (It)

LWL = Length of Static Waterline (ft)

N= Moment (non-dimensional)

R= Turning circle Radius (It)

r

= Yaw velocity

Rho= p. Mass density (slugs/ft3)

1= Draft (ft)

V. Vs = Speed (knots. fps) V = Sway velocity

Y Force (non-dimensional)

References

Cohen, S. B.. "Maneuvering Characterization of a Full Size Polaris 750 SLT Jet Ski With and Without a Side Deployed Maneuvering Flap," Marine Hydrodynamics Laboratory Report 376092, March 1998.

Cohen, S. B., "Seakeeping and Maneuvering

Characteristics of a Full Size Kawasaki 300 Jet Ski," Marine HydrOdynamics Laboratory Report 362171-K.

February 1998.

Cohen. S. B., "Model Tests of Stern Flap Concepts to

Provide Bow-up Pitching Moment for Amphibious

Craft". Marine Hydrodynamics Laboratory Report 391387.

February 1994.

Lewis, E. V., Editor, Principles of Naval Architecture, 2nd Edition, Society of Naval Architects and Marine Engineers. NJ. 1989.

Schlichting. H. Doundaty Layer TheOry 7th Edition

McGraw-i-lilt, New York. 1979.

LOA 12030 inches

LWL 107 25 inches

Barn at Lwl 44.25 inches

Draft (mean) 5.55 inches

Displacement 864 lbs

LCG midships

I

0.40 0.30 0.20 0.10 0.10 0.08 * 0.06 0.04 U 0.02 0.00 0.00 0.00 0.00

fr>k

0.50 1.00 Spied Coefficient, Fi = V/(gL)0 1.50

Figure 1. Normalized Drag versus Froude Number

Kawaaki

o

4-degK

o

6-degK

4

X-dcgK

Paris

X

2-degP ifi 4-degP 10.5-deg P 20-degP Kawasai 4-degK

o

6-degK 8.degK Polans X 2-degP W 4-degP 10.5-deg P 20-degP 1.50.. 0.50

100

Speed Coefficient. Fn = V/(gL)03

0

I

-'

- 30 40

Specd, knots

10 20

Figure 6. Polaris Stopping Time as a FUnction of Initial Speed

10 20

30

40

Speed, kts

Figure 5. Polaiis Stoping Distance as a Function of initial Speed

1.50 0 0.50

a

' 0.00

iEdRUUUUU

aiuuiuuuuuui

uuiiiimuui

uiuuumuivauu.

uiaiuiiiiuuu

iuriiuuuu

RUUII

uiiuiiiiaiiiiu

NIU1UIh1!I

-0.50 0.00

- -

1!]

- _ -

N

' iN

I IL

-Speed Coefficient, Fn = V/(gL)°5

Figure 4. LOcation of Resuliant Hydrodynamic FOrce

Kawa'iki

o

4-degK

o

6-degK A S-degK Polaris X 2-degP 4-degP 10.5-deg P 20-degP Kawasald 4.degK

o

6-degK A 8-degK PoLars X 2-degP

B

4-degP 105-deg P 20-degP 0.00 0.50 1.00 1.50 Speed Coefficient, Fn = V/(gL)05

Figure 3. Lift Coefficient versus Froude Number 0.50 0.40 O.30 0.20 0.10 0.00 -o.10 -0.20 0.50 1.00 1.50

40

P30-8

20-110

---'--:

---I--- -- I t 5 I0 15 20 25 Nozzle Angle

0

I23deg

0

lO-deg

0

8-dee

Sped.kts

Figure7. Polaris Turnitig Circle Diarncier as a Fuiictiön of Speed àndNozzlc angle. NOte: Speed ih knots.