Graphs for predicting the resistance of large stepless planing hulls at high speeds

HYDROMECHANICS

0

AERODYNAMICS

0

STRUGTUR4L MECHANICS

0

APPLIED MATHEMA11CS

April 1959

by

Eugene Po Clement

and

Jaies D0 Pope, LTJG

USN

GRAPHS FOR PdF0DICT .LNG THE ISI3TNGE

OF LARGE STEPLES PLANING tJLLS

AT HIGH SPES

HID MEGrIAN lOS LAORAT OR!

RESEARCH AND DEVELOPMENT REPORT

V.

uITe

Technische Hogeschool

Deift

Apr

1959

GRAPHS FOR PREDICTING TH RESISTANCE

OF LJGE STEPLESS PLANING HULLS

AT HIGH SEES

by

Eugene P. Clement and James D. Pope, LTJG,

USN

Report 1318

NOTATION

Aspect ratio, b/

b Beam of planing surface, ft'

Cf. Skin-friction ôoefficient

Lift coefficient based on principal wetted area,

t/pSV2; also, GequalsC*Q

Lifting line term in expression for Cross-flow term in expression for

Froude huznber based on volume of water displaced at rest,

V

in any consistent units V/ t/gV 1/3

Acceleration due to 'gravity, 32.16 ft/sec2

L Lift of planing surface, lb

Mean wetted length (distance from aftend of planing surface to the mean of the heavy spray line), ft

Center-of-pressure location (measured forward of trailing

CP _{edge), ft}

1cp Nonimensional center-of-pressure location

R Resistance of planing surface, lb

Re Reynolds number, V1,

S Principal wetted

iea

(bounded by trailing edge, chines,

and heavy spray line), sq ft

S5 Area wetted by spray, sq ft V Horizontal velocity, ft/sec

vm Mean water velocity over pressure area

Angle of deadri.se, radians unless otherwise 'stated

Trim (angle between planing bottom and horizontal),

radians unless otherwise stated.

Kinematic viScosity, sq ft/sec Gross weight, lb

Effective increase in friction area length-beam ratio due to spray contribution to drag

Graphs are preseflted for pedicing the resistance of

steples planing hulls at highspeeds. These grphs were developed from semiempiical equations derived by the

National Aeronautics. and Space Administration for the pure

planing lift and center-of-pressure on flat and V-bottom

planing surfaces. The development of the graphs is ex-plained, and an example is presented to show the process of estimating the resistance of a typical large planing boat. A comparison of the resistanôe cuzves determined from model tests with the values of high-speed resistance obtained from these graphs shows good agreement.

INTRODIJGT ION

A recent report by the National Aeronautics and Space Administration1 (formerly the National Advisory Committee fOr Aeronautics), presents semi-empirical equations for the pure planing lift and center of pressure on

flat an V-bottom planing surfaces. This reference shows that there is good agreement between the equations and data from extensive tests of prismatic planing surfaces0 Solutions to these equations for the range of values of aspect ratio, trim angle, and deadrise angle applicable to stepless planing boats were calculated at the David Taylor Model Basin by electronic digital computer. The solutions are given in graphical form in

the present report. Equations for resistance were also developed. These

are presented, together with solutions in graphical form. Auxiliary graphs are also presented to facilitate the process of predicting the performance

of stepless planing boats. A sample perQorrnance prediction is made, and

the results are compared with the resuIts Of a model test.

DEVELOPMENT OF GRAP!S

The equations presented in Reference 1, for flat and V-bottom planing surfaces having straight sections, are as follows:

Lift

Lifting line

= O.57rA1 cos2T

ABSTRACT

1Raferences are listed on page 6.

term Cross-flow term CL

ship

Center of pressure

-c

=

0.875

°LL + 0.50

C

(2)

'rn _0L3

Solutions to Equations (1)

and

(2) are presented in graphical form in Figures 1 and 2, respectively.

The resistance of a prismatic planing bottom can be expressed as:

R.

= L tan T+/cVm 230f+P V

5$ CoS

$

Cf

where Vrn is the mean water velocity over the pressure area,

S5 is the area wetted by spray, and

B is the angle between the outer spray edge and the keel and is measured in a projected plane which is parallel to the keel and normal

to the usual hull

centerline.

As in Reference 2, for simplification, let

53 cos

₀

iiXb2

Reference 2 gives both a mathematical expression and a

graph

of

An expanded version of the graph, including additional trim angles,

is presented in Figure

3.

Eliminating S3cos8 and S by means of Equation

(4)

and the

relation-C

=

L

-

2

the expression for resistance becomes

R L tan

T+

L Cf 2

A

.cb2

Cf

cos

The term b2 can be eliminated as follows:

birn

5=

cos1g

and

lIn=-A

Then

s_

bb/A =

b2

- cós,

From Equations (3) and (10)

so that

From Reference

_3,

1m=

A

Re-'

_-

Vim 1IAcos'

:ii- Vcc.v2

2

or, in a slightly different form,

)-Vr2Lc0516m

-(13) (14) (15) (16)

v

V _V cos'T cos, (17)

Curves of Ft//i were calculated for a displacement of 100,000 pounds

for the same range of values of A, T , and,8 previously assumed for calculating lift coefficient and center of pressure0 The curves of R/ are given in Figure 4. It is interesting to note that it was not neces-sary to specify the speed for the purpose of calculating R/I , because

for the assumed condition of constant values forA, A,T, and

_A

both

resistance and R/4 are independent of speed in the planing condition. Substituting for S from Equation (5), the equation for b2 becomes

b2..L

Aoos,9

(10)

21.3

Next, substituting this value for

b2

in Equation (6), the following

expression is obtained: 2

R =Ltan

+ L

+ L

L... (11) Then R/L =

= tanT +

Cf

[2

₊

] (12)

C1C is given by Equation (1), Cf is given as a function of Reynolds

numberThy the 1947 &TTC friction formulation, and Reynolds number is

In Figure 5 are curves of ]./b against aspect ratio with trim

angle as parameter. These curves re presented to facilitate the

pro-ces of predicting the performance of stepless planing boats. Values

of l/b were calculated from the available values of 1p/1m and aspecrtio mehs of the relationship

.

lCp

_;

-m

b

11m

Resistance., trim angle, and wetted surface in the planing condi-.

tion can be determined readily from the graphs which have been

present-ed. The graphs can be used to determine the performance of a projected

design for a stepless planing boat, and also to show the effects on

performance of changing the major planing parameters; i.e.., the effects of 'changing load, beam, center of gravity location, or deadrise.

The following example' shows the process of estimating theperforin-ance of a typical planing boat. The dimensions assumed are as follows:

Displacement: 100,000 pounds,

xjmuni beam over chines: 15.9 feet,

Average deadrise angle fr fter half of length: 10 degrees, Distance of g.for!ard..of..transnl; ?7,9 feet0

The iiumbered columns below indicate the sequence of the calcula-.-tion process;

First, a number of trim angles are assumed and entered in Column 1, Next, the ratio 1/b is determined. This is:

=

27,9/15.9

= 1.76

Then the values of the aspect ratio A for the different trim angles

are read from Figure 5 and. entered in Column 2, Next, 'values of R/ are

read from Figure 4, and entered in Column 3. Then, multiplying the values of H/ by the boat displacement (100,000 pounds) will give the

T

(2) (3) R/ . () . G b'/A (6) 100,000 (7) V, fps (8) V,Knots (9) Fn

iO

.486 .319 .0078 520 . 24,630 151 93.0 8.12 105 .481 . .208 ,01l9 525 . l6,00Q . 126 74.6. . 6.55 2.0 .476. .164 .0161 530 11,720 108 64.0

560

2.5 .472 .142 .0205 535 9,120 95.5 56.6 4.94 3 0 .467 .131 .0252 541 7,340 85 7 50.8 4043 3.5 .463 .1265 .0298 545 ,i60 7805 4605 4.06 4.0 .459 .1255 .0348 550 5,220 72.2 42.8 3.74

boat resistance in pounds0

(These

values have not been entered above,)

The resistance is now known, and the remainingcalculations _{are for the} purpose of determining the corresponding values of speed. The speed is

determined by solving for V in the expression C

_./*,Osv2,

with

*Passi.üüéd equa1 to 1.

Then V2

s

is read from Figure 1 and enteed in Column _{4. Next, S is}

calculated from the relatiohip S _{= 'b/A and entered in Column 5. The}

quantity lOO,OOO/3C

_{is then computed and entered in Column 6. The}

square root of Column 6 gives the velocity in feet per second (Column 7). Speed in knots has been entered in Column 8, and the dimensionless _speed coefficient _Fn in Column

_9.

The dimensions of the boat selected for the above example were, the

same (as regards gross weight, beain,.and LOG location) as the dimension

of a design for which the resistance had been deteraned from tests _{of a}

geometrically similar model (TI Model 4667Reference 4), However, the deadrise assumed above was 10 degrees9 while the doadrise of the planing

bottom of Model 4667 was 12* degrees. Accordingly, the above calculation process was repeated for a deadrise angle of 15 degrees, and the results averaged to give a predicted resistance curve (except for the air-drag)

'for a boat having a deadrise angle of 12* degrees,

Values for the air drag of a planing boat model were obtained by repeating a test of a representative planing boat model behind a wind screen which eliminated any air drag on'the model. The difference, at

each test speed, between the total. drag value without and with the wind

screen, gave the amount of the air drag on the model. In the planing range the air drag was found. to be equal to 5 percent of the hydro...

dynamic drag. .

In Figure 6 the resistance values obtained as described above

(and increased by 5 percent to include an allowance for air drag) are compared with the resistance values as predicted from a test of

Model 4667 (This is the middle comparison of the three shown.) Two

other comparisons, arrived at in the same manner, which represent the approximate extremes of loading for planing boats, are also shown in

Figure 6. It can be seen that, in general,' there is close agreement

between the predicted and experimental values of resistance, Evidently,

then, by means of the graphs in this report, it is possible in a short

time to make quite accurate predictions of thE high- speed planing -resistance of stepless planing boats.

REFERENcES

1 Shuford, C L , Jr , "A Theoretical and Lxperimental Study of

Planing Surfaces Including Effectsof Cross Section and Plan Form,'1 National Aeronautics and Space Adminitration Repoit

1355 (1958).

Savitsky, D. and Ross, E.W., "Turbience Stimulation in the

Boundary Layer of Planing Surfaces. Part II, Preliminary Experimental Investigation," Report

444,

Experimental TowirgTank Stevens Institute

of. Technology (Aug' 1952).

Chambliss, D.B. and Boyd, G.M., Jr., "The Planing Character-istics of Two V-Shaped Prismatic Surfaces Having Angles of Deadrise of 20 Degrees.and 40 Deree," NACA TN 2876 (Jan

1953).

Clement, E.P,, "Deeioprnent arid Model Tests of an Efficient

Planing HuJl Design," David Taylor Model Basin Repoit

13]4 (Apr 1959).

.04 .03 .02 .01

I

A

A

ArrdrA

/

"pp

0 1 2 .3 4 r

(deg.)

Figure ]. - Lift Coeffi3ient versus Trim AngIe with Aspect

Ratio as ?araraeter

A

.60

58 .55 .52 50 .48 .46 .44 .42 .40 .38 .36 .34 .32 .30 .25 .20

.02

.01

WA

/

25

20

0 2 4

(deg.)

Figure 1 (Continued)

.04

.03

CLS

60

58 55

52

50

48 46

44

42

40

38

36

34

32

30

01

/

/

41

'"'p

$=.Ioo

.25

.20

0 1 2 3 4 r

(cleg.)

Figure 1 (Continued)

.04

.03

0LS

.02

A-.60

.58

.55

.52

.50

.48

.45

.42

.40

.38

.36

.34

32

.30

.04

.03

CLS

.02

.0].

A

"Pr

vvrr

AMII

_______I

_a

/

V

3=I5°

/

/

0

1 2

w (deg.)

Figure 1 (Concluded)

3

A-.50

.55

.50

.48

.45

.42

.40

.38

.36

.34

.32

.30

4

.25

.20

.87

.86

.85

.84

.83

.82

1CP/lm

.81

.80

79

.78

.77

.76

.75

0

inn

k

_N

A.

.55

.25

.20

3 4 1 2

r (deg.)

Figure 2 - Center of Pressure versus Trim Angle with Aspect Ratio as Parameter

.44

.42

.40

.38

.36

.34

.32

.30

.87

.86

.85

.84

.83

.80

.79

.78

.77

.76

/3

50

A-6

.5

.55

.40

38

36

34

.32

30

25

20

1 2 3 4

r (deg.)

Figure 2 (Continued)

.75

t(deg.)

Figure .2 (Continued)

.25

.20

.87

.86

.85

.84

.83

.82

1c.p/lm

.81

.80

.79

.8

.77

.76

.60

.55

.50

.46

.44

.40

.38

.36

.34

.32

.30

.87

.86

.85

.84

.83

.82

lcp/lm

.81

.80

.79

.78

.77

.76

.75

0

N

/3

=15°

1 2 T

(deg.)

Figure 2 (Concluded)

3

.60

.55

.50

.46

.44

.40

.38

.36

.34

.32

.30

.25

.20

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.

U

I

I-.

0.rI

H ) cI4

o

U) 0 (-I

E °

C)

.,

cI

00

. a) C)

0

a:, '0 S S r1

0

_Ic

0

0

.3 .3 .3 .2 .2 R/8 .2 .2 .2 .1 .1 .1 .1 40 C 6 4 32 0 6 4 £

UM

U.

0

0

A

.2O-.25 .30 .35, .40: .50 .60 (deg.)

Figure 4 - Res±stanee versus Trim Angle with Aspect

Ratio as Parameter

C.

.3

.36 .3 .32 .3 .2 .26 RI £ .2 .2 .2 .1

ii'

'U

UL1iih

.UUa

/3

5

0

.20 .25. .30 35 .40 50 60 1 2 3 c (deg.)

Figure 4 (Continued)

4 .1 .1 .1 .3. .40 .38

.4 .3 .3 .3 .3

S..

iIiLik

IIIiIL_

/3=100

A-.20 .25 .30 .35 .40 - .50 .3 .2 R/a .2 .1 .1 .1 2 3

Figure 4 (Continued)

4 .2 .2 .2

.4 .40 .38 36 .3 .3 .3 28 R/8 .26 .2 .2 .2

/3=15°

c (deg.)

Figure 4 (Concluded)

.1 .16 .1 A-.20 .25 .30 .35 .40 .50 .60 -.1 ₁ 2 3 4

3.0 2.5

10/b

2.0 1.5 .30 .35 40 .45 50 56 .60 A (A8pect Ratio)

3.0 2.5 S 2.0 1.5

Figure 5 (Gontinued)

.60 .50 .30 .35 .40 .45 A (Aspect Ratio)

.3.0 2.5

10/b

2 .0 1.5

'5

a30 .30 .36 .40 45 A (Aspect Ratio). Figure 5 (Continued)

3.0 2.5 2.0 1.5

p=..Io

I .30 .35 .40 .45 .50 .55 .60 A (Aspect Ratio)

Figure 5 (Conàiüdèd)

0.4 0.3

+0.2

0.

F, =

Figure 6 - Comparison of Predicted and Experimental Values

of High-Speed Planing Resistance

2 0

H H I

I I o 0 0

Predicted Experimental (Model 4667.Rer.4)

-0

/

/

LC0-5%L art cent101d art A/v'P-6 LCG-5%L centrold

LCG1O%L art centroid

2

4

6

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