Measurements of components of resistance on a tanker model

A Station of the

Ministry of Technology

December 1967

NATIONAL PHYSICAL

LABORATORY

SHIP DIVISION

MEASUREMENTS OF COMPONENTS OF RESISTANCE ON A TANKER MODEL

by

B.N. Steele

,

_be

_{note inside cover}

Crown Copyright Reserved

Extracts from this report may be reproduced

provided the source is acknowledged.

Approved on behalf of Director, NPL by

Mr. J. A. H. Paffett, Superintendent of Ship Division

Measurements of the Components of Resistance on a Tanker Model

by

B.N. Steele

Summary

This report gives details of measurements of local shear stress, pressure,

wave pattern, and total resistance on a model of a raked bow

tanker.

The shear

stress and pressure measurements have been integrated, over the hull

surface to

give the frictional and pressure components of resistance.

Combination of these

measurements suggests that the method of measurement of skin friction and the

hypothesis upon which it is based are sound.

The pressure form effect has been

deduced and is seen to be large compared with that of a streamlined body.

1.

Introduction

For economic reasons there is a tendency for the size and fullness

of

modern tankers to increase, and because of draft lrntaions in some ports

and

docks, increase in displacement is often obtained by an increase in

beam.

These

increases pose many interesting hydrodynrnc problems, and it may be

dangerous

to extrapolate extsting data to take account of them.

They include such factors

as flow separation and bilge vortex formation giving rise to

low hull and

propeller efficiencies and often to severe vibration.

At present the designer

has insufficient information upon which to predict the likelihood of

their

occurrence.

To remedy this deficiency, the resistance research programme

at I'PL

is biased towards a greater understanding of the components of resistance

of full

form vessels.

As a first stage, the basic resistance components on a range of

hull s are being measured to derive -the effects of variations in form on them, aM

to determine those components that are worthy of further consideration, with a

view to their reduction.

The resistance of a hull to motion may be considered in two basic ways.

Firstly, it may be equated to the total enerr dissipation, which may be split

broadly into viscous and wavemaking parts.

The viscous part may be determined by

measuring the enerr in the wake and this is usuni ly known as the wake traverse

resistance.

The wavemaking part, as its name implies, is the enerr expended

in

the formation of waves and nay be determined by measurement of the wave pattern

behind the hull.

Analyses of wake traverse and wave pattern measurements to

obtain the viscous and wavenaking components of resistance entail the acceptance

of certain assumptions which the experience quoted in reference

1

indicates are

vlid. Alternatively, the total resistance nay be equated to the suDnation of

the fore and aft oomponents of force acting upon each element of hull surface.

These forces may be resolved into tangential and normal components both of which

may, in principio, be measured.

The integral of the fore

aM

aft components of

the tangential forces is referred to as the frictional resistance, whilst the

corresponding integral of the normal forces is known as the pressure resistance.

These, to the authors knowledge, have not previously been measured simultaneously,

and although the determination of the pressure resistance is independent of any

assumptions, the method by which the frictional resistance has 'been measured in

these experiments and in those given in reference 2, is not.

The measurements

detMl ed in this report are concerned primarily with force measurement, although

a few measurements of the wave pattern resistance are included.

-2--When making an eerimental study of the type described here, it is necessary to ensure that the experiment techniques used are sound, and that the assumptions upon which they are based aro well founded. The method. used to detemine the

shear stress is knovn as the Preston tube technique and falls into this category. The most convincing method of validating this technique is to determine whether the integrated friction and pressure measurements sum correctly to the measured total resistance. Such a siinuation will not only confirm the calibration, but will provide strong evidence to support the underlying assumptions upon which the technique is based and this is considered to be an important part of the investi-gation. The basic objectives were, therefore, to measure the magnitude of the various resistance components on a particular tanker model, to ascertain that the methods of measurement determined these components correctly, and. implicit in the latter, to study the effects of pressure gradient on the law of the waJI on which the technique is based.

\'Then conducting the investigation, existing data was used as far as possible, since a large number of measurements of skin friction and pressure distribution over tanker models have recently been made at NFL. Measurements of trim, wave profiles and wave pattern resistance were also requlrod. and these were made on the tanker model for which the other data had already been obtained.

2. Nomenclature

L = Length of model

y

= Distance from the hnll surface

z = Vertical ordinate

x

= Horizontal ordinate

d. External diameter of the Preston tube

V = Speed of model

u = Velocity at distante y from the hn]1 surface

D =

Total resistance of the model

in line of motion

F = Total fore and aft frictional resistance

M Total pressure resistance parallel to the keel

D' =

F+ (M-we)

Total wave pattern resistance

S = Total wetted surface area of model

O = Trinangle

W

Weiit of model

V = Kinematic viscosity

¶ = Local shear stress

o

¡7-U =

I_2

fD

po = Local nomal pressure

p = Preston tube pressure

h = Pressure above even keel static pressure

'r C ° f

1u2

2P C po p _pV2 F = I 3fV2S M - we Cl = p _-pV2S Rw C w ..pV2s D C = T jpV2S Cl

Cl+CI

T p f

C = Pressure fom effect CT - (9

+ c)

C. Velocity forn effect = C. - 2 Dimensional Cf

2 - Dimensionsi C used. is Hughes value = 0.066 (log10R - 2.03)_2

3. Methods of Measurement and their limitations

.3

The litations aro nainly associated vith the validity of the j:ieasurenent techniques used and. the experimental limits of accuracy of the measurements.

(a) Friction distribution measurements: Those measurements wore mad.e using the PDeston tube techrique() which depends for its acceptance on the hypothesis that close to a sur1ace in a finid stream there is a region in which the 1ow is

dependent only upon the shear stress, the kinenatic viscosity of the nedii, and. a representative lonth. This is implicit in the relationship

u

-- = f

-which is known as the "law of the wnl

i t?

and is supported by the findings of

Ludweig and TiJDrLn1P

This relationship was used by Preston who obtained a

universal calibration for pitot tubes placed close to the surface, this

ciibration being of the form;

¶d2

(

log10

_2__

à + B log10

p-p)d2

4pu2

- pv2

the constants A

and

B-

being determined, by experiment.

Preston performed

experiments on tubes of various diameter in a 2 in.

diameter pipe, end obtained.

values for A

and.. B

of

2,60L

and 0.875 respectively.

Subsequent investigators have questioned these experiments for two main

reasons.

Fïrstly, they have argued that the boundary layer in a pipe flow differs

significantly from that on a flat surface and therefore

the constants determined

from pipe flow experiments apply only to flow in a pipe.

Secondly, they have

expressed. doubts regarding the law of the wnii in pressure gradients, and suggest

that under these conditions the law of the wall is not

correctiy represented by

equation 1.

Either of the above points, if substantiated, would render the

Preston tube suitable only for qualitative measurements on a

ships hull. A

calibration on a flat plate could. be obtained, and this has

been attempted by

several investigators, some having obtained ci-îbrations

fairly close to Presto&s

(5,6,7).

Other ecperimenters (8,9,10) have studied the effects of pressure

gradients on Preston tubos, but have reached conflicting conclusions, some stating

that it has no effect, and others that its effect is quite large.

To prove that the Preston tube calibration is independent of pressure

gradient it would. be necessary to measure the local

friction by the Preston tube

technique in various pros sure gradients and to

ascertain that the friction and

the local pressure resolved correctly to the resultant force at each point.

The

resultant force is not amenable to accurato measurement

and may only be deduced

from local friction and pressure neasureraents

However if the local friction

and pressure measurements can be shown to sum to the

total resistance, over a

surface on which the pressure gradients aro severe, such as on a ship model, it

would suggest that the Preston tube calibration

is not seriously in error.

The measureents of skin friction were made in the NPL

No. 2 circulating

water channel(h1),

preceded by flow observation experiments to determine

the

angles at which the Preston tubes should be

set.

The manner

in

which the Preston

tube technique was adapted. for uso on a ship model is

described, fully in

reference 2, and consists essentialy of inserting

the stubs of -the tubes in

static pressure tappings set in the hull and using

the same transmission lines

to transmit the Preston tube and static pressures

in turn.

Since making the

measurements on the liner forms described.

in

this reference, the experiment

procedure has been modified, and improved to some

extent, and. the repeatability

-5

hen resolving

the components

parallel

to the keel, as is the usunl practice

with

pressure measurements,

the

normal pressures over the bottom and. along the

parallel

middle-body arc

not required.

This

is no-b the case with

friction

measurements, where it is necessary to

measure the shear

stress over

the

whole

hiilJ

surface.

(b)

Pressure

measurements;

These do not

suffer

fron doubts regarding the

validity

of the

method

of measurement, and. providing the pressure over the

hiffl

can be accurately

measured., the pressure resistance is in principle simple to

compute,

Accurate measurement of the pressure

distribution is fafrly difficult

because of the very

small pressures

involved, and. -this applies equally -to the Preston tube measurements. To compute the pressure resistance, it is necessary

to measure -the sinkage and. trim

of

the

model, in addition to

the pressure, to a

high order of acouracy.

If -the

forces

are resolved parallel to

-the keel,

it nay be shown

that:-Dcos 0+WsinOFM.

If O is smnll, cas O - I and. sin 6 -' O and hence:- D

#

We = F + ivI.

The resistance of the model in the line of notion

is therefore given by the

expression

D = F + (LI -

Je)

...

(3)

Because the weight of the model is large relative to the drag the weight component WO becomes a significant factor. For example, at service speed. an error of 0.10 ins, in the measurement of trim for this model can lead. to a

change in VIO of 2

of D.

To mir-inise the possibility of discrepancies duc to

errors in

trim,

it was measured at a number of speeds

and.

a smooth curve drawn

through the roints; any runs giving

unfili' points were repeated.

when resolving

the friction component an accurate measurement of -the trim is not very important

since it is fairly small

and. appears only as a cosine tern.

From equation 2, it can be seen that the static pressure as well as the

Preston tube pressure is required. to determine the local shear stress. Consequently the pressure distribution of the whole model was obtained as a by-product of the friction measurements. Since the pressure forces M wore resolved. parallel to the keel, only the measurements in the forward arid after bodies were required. to determine -the pressure resistance of the model.

The Preston

tube

and. static pressures were measured. on a

multi-tube nanometer

mounted on

the

circulating water channel instrument platform

appromately

six

feet above the water surface.

The manometer was sloped to an an.&e

of 30° to the

horizontal in order to magnify the

readings.

(e) Wave pattern measurements: The wave pattern resistance was measured using

the Eggers cut technique(12). The elevations of waves produced by this 10 ft tanker model were quite small, and. the main difficulty was to measure them

sufficiently accurately. s a check on the measurements each experiment was repeated, and. it was found that the wavenaking resistance usually repeated. to wi-thin better than 1% of the total resistance.

To check the wave pattern measurements, snflar experiments were performed. on a 20 ft model of the form used. in this investigation.

-6

The wave pattern measurements were made in the NFL No. 2 tank where the wave eleva.ons were measured. by pointers placed. ¿ ins, apart across half of the width of the tank and. attached. to the towing carriage.

(a.) 7ave profile measurements: Wave profile measurements were required to

define the linits of integration of the friction and pressure measurements. The experiments were conducted in No. 2 tank. The model was run at the

required speed. ana. pins inserted in the wax hnll at the air-water interface, This procedure was inconvenient around the cruiser stern due to the dffficulr of

observing the wave profile, and. a new measurement technique, which was found to be very successful, was therefore devised.. It comprised. spraying the hnll in way of the water surface with a PVC aerosol spray; the PVC did not. run dovm below the water surface, and a very clearly defined wave profile was obtained. Careful choice of spray colours enabled experiments at three to four speeds to be run before it was necessary to lift the model from the water to measure the profiles and remove the PVC. Sprays other than PVC have been found to give a less clearly defined profile.

¿. The Model

The model was nade of paraffin wax, was 10 ft long, and is shown in Pig. 1.

The block coefficient was 0.80, -the beam to draft ratio 2.50, and the length to bean ratio

7.36.

Pressure tappings were inserted. at approximately 110 points on the hull, and comprised brass tubos 0.2 ins. diameter and. .3 ins, in length, the

pressure orifices having a diameter of 0.062 ins. The tubes were made a tight fit into the hull and. the ends were filed to be flush with the surface, care being taken to ensure that the wax did. not move relative to them when the model was immersed in water. At soue locations, particularly near the ends of the model, it was not possible to use these units and the pressure tappings were then made from hypodermic tubing which was let into the wax hull, care being taken to ensure that the internal diameter of the static tapping was such that a tight fit of the stub of the Preston tube could. be obtained.

5.

Results of Friction Distribution Measurements

The local sldn friction measurement using the Preston be techn!quo gives the shear stress w0. To put this in a non-dimensional form this shear stress i .ìvied by the velocity head j-pV2, arid, hence Cf = ,

where V is the

free strean velocity measured. ahead of the mod.el. The free stream velocity has been taken rather than the local velocity at the edge of the boundary layer due -to the difficulty of measuring the boundary layer thickness and. velocity

distribution.

These local stresses and coefficients may be resolved into fore and aft components, allowing for.waterline and body section angles and flow direction, giving op and CfF. Integration of either of the above over the hull surface wl] lead to the total frictional resistance of the hull, hence

s s f-' ¶ d.s or pV3 j Cf ds j °F& o o

7

Consequently the mean skin friction coefficient for the hull is given by

F 01 ₌

f

The friction distribution over the model is given in Figs, 2 to 5 at Freude

numbers of

0e179, O19)+, 02O9 and. O022L- respectively0

These results were

published in a preliminary form in reference 13 which gives a comparison between

local friction measurements made on this model and those made on a similar

model having a bulbous bow0

The effect of the bulbous bow was found. to differ

from that on the liner forms reported in reference 2, and the integrated values

of skin friction on the bulbous and non-bulbous tanker forms viere almost

identical0

Measurements were made at waterlines representing 75% (A), so% (B)

and 2

(c) of load draft, at an outboard buttock (n), an inboard buttock (E)

and along the centreline of keel ()

The position of these waterlines and.

buttocks are shown in the body plan in Fig0 10 The effects of speed are

relatively small, except at waterline A where an increase in speed causes an

increase in the amplitude of the

Cf

undulations along the length, these

undulations being 1800 out cf phase with the wave profile0

Since the local

Cf

values are calculated with respect to the free stream velocity, they are

directly proportional to the local shear stress,

The local velocities will be

heavily influenced by the wave orbital velocities near the free surface and

hence these undulations in Cf will be greater in this region0

Measurements

ahead. of station 9* were prone to scatter which could be attributable to

misalignment of the Preston tubes or to the presence of lnminar flow0

The

Preston

ubcs were extremely difficult to align at the forward end due to the

large rate of change of flow direction particularly at the lower waterlines in

this regton0

Measurements along the buttocks at the forward end also suffer

from this 9fficulty0

Laminar flow at station 7--is rather unliholy, sino

at--this

position the Reynolds number o1 culated with respect to the distance from the

bow, and. the froc stream velocity, is 6 X

Also the turbulence level of the

water in the circulating water channel is such that one would expect transition

from laminar to turbulent flow at a lower Reynolds number than in a towing tank.

Along the waterlines

A, B

and

C,

the curves of

Cf

are in general tenns

m-fl ar, showing a high Cf

near the bow, gradually falling to near Hughes! line

at nmdships and then decreasing rapidly aft of station 2. Near the after end,

at some waterlines,

C

tends to fnll to zero, indicating that the flow is

separating.

The position of separation determined in this manner agrees fairly

well with that determined from flow visualisation experiments using wool tufts,

suggesting that the doubts regarding the validity of the Preston tube technique

in adverse pressure gradients are perhaps unnecessary, although more evidence

would be necessary to confirm this suggestion, and this is discussed later.

Over the bottom of the model,

Cf

is fairly uniform, except forward of

station 7- where it rises a little0

Aft of station 7 it agrees closely with

the Hughes two dimensional friction formulation for a 10

ft

long flat plate.

Perhaps the roost interesting feature of these distribution measurements is

the very large variation in Cf

over the length of the model.

In this respect,

it is interesting to see that this two dimensional flat plate formulation so

closely equates to the mean value over the hnfl

-8--Graphical integrations of the results have been made and.

C

for the hull

determined,

at each speed. These are given in Fig.

6 end Table 1, and are

seen

to lie close to

the

Hughes

line. Clearly to define bettor the curve of C it

would have been desirable to

have

run

the experiments

at closer

intervals

of speed.

The results of these graphical integrations tond. to contrad.ict

the findings

of Lauto(1, Hogbofl(15) and

TOwnsifl(16)

who deduced. the frictional resistance to bo considerably in excess of that given by two

dimensional

friction

formulations.

However, subsequent similar

experiments

by

Tows±fl(17) and. by

Shearer and

ross(18)

give

far

lower friction values which in some instances

are

close to the Hughes two dimensional f ermulation and. hence in reasonable

agreement

with the measurements detailed herein.

Clearly insufficient information is at

present available to allow any definite conclusions to 'be

drawn, and in view of

the large discrepancies in the findings of various

experimenters, moro

experiments and. analyses of the type given in this report are

roqiired.

6.

Results of Pressure Distribution Heasu,reuents

The pressure distribution at Froucle numbers of 0.179, 0.19)+, 0.209 and 0.22L4 is given in Figs. 7 to 10 respectively, and. the trin and. mean sinkage in

Fig. 11.

ou these data, the pressure resistance of

the

hifi in

line

of motion

-

we)

has

been determined at each of the four speeds, and is plotted in

coefficient

forti

in

Fig. 6 and

tabiiotcd in Table 1. Pig. 1, shows the

distribution of pressure at seivice speed where pressures are plotted at

water-lines at

, 25%,

50%, 75%, 87.5% of load draft, together with

the wave profile.

Measurements of pressure were made at the 25%, 50% and. 75% waterlines,

at

two

buttocks and. along the keel at the positions

shown,

and the velues for the

and 87.5% waterlines were obtained by cross plotting the measured data.

This

interpolation was particularly neoessaxr at the lower waterline to

define better

the lower ending of the curve of f hdz.

Measurements of pressure were

not nade above the

load waterline, and the

curves

of

_f

hdz were assumed to be linear between this point and. 'the free surface. A study of other similar measurements sugrests that this assumption is not too

unreasonable.

The procedure by which the pressure resistance has been

obtained has

net been

described in detail, since this has been well documented by (12 15 and 18)

other auhors

7.

Results of

iave pattern Measurements

Measurements of the wave pattern resistance of the hull were made at Freude

numbers

of 0.179, 0.192 and 0.209. The results of the measurements on the 20 ft

C

models are given

in reference 19, the values of - for both models are shown CT

in Fig. 12. A

skin friction correction was made

to the total resistance measurements on the 20 ft model in order to make this comparison f

It

CT

may be seen that

the wave resistance as a percentage of the

total resistance is

s'rniiar

on both models, the results for the 20 ft model being up 'to approximately 1% above those for the 10 ft model. This suggests that despite the low amplitude

f the waves behind

the

smaller model, the experiments were sufficiently accurate

to measure the wave pattern

resistance to within reasonable limits.

The

9

C with speed and the pressure form effect

would

therefore probably become less

a higher speeds. At Proude

numbers

below 0.179, the wave pattern resistae is obviously sn11

and

the pressure resistance would be olnost entirely due to pressure form effects.

As would be expected the wave pattern resistance increases with speed, and at the lowest speed represents and, at the

highest speed

10% of the totnl resistance.

Results

of Thve profile measurements

Measurements of the wave profile were made

at Froude numbers of 0.179, 0.191,

0.209 and 0.221 and aro

shown in Pia. 13 It should be noted. that at the Fn of 0.221+ the form was considerably overdrivon.

Considerable difficulty was experienced in

obtaining measurements right at

the after end,

and. the

importance

of

measurements in

this

regirn

is

evident when

studying

Fig.

1.

Precise definition of

the

wave profile between station

and

the centre line is essential

if

the pressure resistance

is to be

computed

accurately.

Comparison of Components

Fig. 6 shows the results of measurements of friction, pressure, wave pattern and to-bel resistance in coefficient form plotted against Froude number. The summation of the friction and pressure components is seen to lie very alose to the total measured resistance coefficient at nfl speeds. The accuracy of the

individual measurements is probably not as good as this and clearly the integration has smoothed out some of the sn11 discrepancies.

Since the suriation of the components is so reasonable, it tends to confirm Preston's calibration, and to indicate that the Preston tube technique is suitable

for the quantitative measurement

of

skin

friction. In addition, and perhaps even

more imortan-t,

it

suggests

that the

law of the

wall expressed by

the relationship

u

Uy

= f

--

j

holds in non-uniform pressure gradients. This fact is of

considerable importance not only in

hydrodynamics

but in all fiold of fluid flow,

since, due to the large variations

in pressure gradient around the hull, the test of the relationship is fairly rigorous.

The curve of C for the model is seen to cross the Hughes two dinensional

friction formulation for a 10 ft

long

flat

plate. Llthough there is a fnirly wide

variation of skin friction along the length of the model, the relatively high

friction in

the fore body tends

to offset the

low friction in the after body.

It

is

u3eful

to comparo the frictional resistance of a hiifi with that of a flat plate. The difference in these two quantities is refered. to as the velocity form effect.

The difference between the total pressure resistance and the wavemaking component of pressure resistance is known as the pressure form effect. This difference is equivalent to the pressure resistance of the

vessel

if immersed at

10

-The pressure f orn effects as shown by (C/CT) in Table I

and. by the

difference between the curves of

CT and.

(c!

+

in Fig. 6 are very large,

r-iounting to approdnately 3y, of the total.

The wave resistance given by the

Eggers cut moasurereents is vary snafl and at service speed is 3 to ¿

of the

total resistance, or 1O of the pressure resistance.

Since the wavereaking effect of a pressure disturbance reduces exponentially

with depth, this suggests that the greater part of the pressure resistance is at

waterlines too low to result in surface waves.

This is shown in Fig. 14. where

the readinmi pressure effect appears at about half draft,

Further evidence for

this is given in reference 20.

Considering the ireplications of this for a bulbous bow nodal, it is obvious

that a bulb below hnlf draft will have little influence on the vïave resistance,

which is in any case snail, and the effect of the bulb nust be on the large

residual pressure resistance.

In addition, noasurenents on liner forms described.

in reference 2 suggest that a bulbous bow nay slightly reduce the frictional

conponent of resistance, although expernents on tanker models given in

reference 13, do not support this suggestion on these slower, fuller, forres.

Clearly investigations of ways of reducing the resistance of very full ships

are likely to be most usefully concentrated in attempts to reduce this very

large residual pressure resistance. It is interesting, for example, to compare

the results obtained on this model with the Royal Aeronautical Society Data

Sheets for the pressure resistance of streenlined bodies of revolution.

At

corresponding beem to length ratio and.ReyncE.Bnunber, the form effect would only

be approdnately 1

of the total resistance, and therefore the fifll form ship

having high angles of entrance and run has a pressure resistance 2CF higher.

The low pressure recovery at the stern can lead. to flow separation causing poor

inflow to the propeller and. also vibration.

Iviethods increasing the pressure

recovery tern and. consequently of preventing flow separation are at present

receiving very active attention.

10.

Conclusions

The measured. friction and. pressure components sum to the measured

total resistance.

The results of this investigation suggest that the law of the wail

holds in nonuniform pressure gradients.

The calibration of the Preston tubo obtained. by Preston is

confirmed.

4..

The frictional resistance of this nodal is shown to be close to

Hughes lino.

On this model the frictional component of resistance amounts to

64Z and the pressure component to 3

of the total resistance at

service speed.

The wave pattern resistance accounts for only j7 of the total

resistance at service speed, and implies that the pressure form

effect is 35, of the total resistance.

The basic objectives of the investigation have therefore been achieved

although more s nilar exporitients and analyses are required to confirm these

findings.

Reference s

Jahrbuch der STG-,

1933,

32, p. 202.

15. Hogben, N. "Ship Hull Pressure Measurements"

Prans

INA,

Vol. 99,

1957.

Î.

G-acld, G.E.

aid "An Appraisal of the

Ship

Resistance Problem in Light Hogben, N, of Measurement of

the

Iave Pattern. Ship Division

Rep.

36.

2. Steele, B.N. and "Experimental Determination of the Distribution of Pearce, G-.B.

Skin Friction on

a

model of a high

speed.

linertt.

Trans. RINA June 1967.

3. Preston, J.H. "The Determination of

Turbulent

Skin Friction by means of Pitot tubes". J.Roy..Lero.Soc., Vol.

58, 1951.

2.

Luthieig, H. ana "Investigations of the VJall Shearing Stress in

T i i rann,

'j.

Turbulent

Boundary

Layers". Trans. HACA TM No. 1285,

1950.

5.

Dutton, R.A,

"The Accuracy of Measurement

of Turbulent Skin Friction

by Means of Surface Pitot Tubes

and the Distribution of

Skin Friction on a Flat Plate".

RC Tech. Rep. R

and M

3058.

6.

Head., M.R. and.

"The Preston Tube as a Means of Measuring

Skin Friction".

Rechenberg, I.

Journal of Fluid Mechanics, Vol. 12, Part

1, 1962.

7.

Hsu, E.Y.

"The Measurement of Local Turbulent

Skin Friction by

Means of Surface Pitot tubes".

DT

Rep. 957,

Lug. 1955.

8. Patel, V.C. "Calibration of the Preston tube and Hnitation of its use in

Pressure

Gradients"

Journal

of Fluid Meshanics Vol. 23, Part 1, 1965.

9.

Bidwell, J.M. "The Application of the Van Karnan Momentum Theoruro

to

Turbulent Boundary Layers". HACA Tech. Note 2571, 1951.

10. Perriss, D.H. "Preston Tube Measurements in Turbulent Boundary Layers

and Fully Developed Pipe Flow". NPL Aero Report 1122 1965.

Il.

Steele, B.N. ana "Design and Construction of

the 1'PL

Circulating Uater Turner, R.T. Channel". Proceedings of NPL Symposium, May 1967.

12. Eggers, K.

"Uber die Emittung des Weflenwiderstandes

eines

Schiffsuodells durch Analyse Seiner

ellensystems

Schiffstechnick Bd.

9, 1963.

13. Stoel, B.N.

"Comparison of the Friction

Distribution on Models

of

a Tanker having Bulbous

and Raked Bows".

Ship

Division

TM 185.

12

-16.

Tovmsin,

R.L. "Frictional and. Pressure Resistance of a Victory Model". Trans. N.E.C. Inst. Vol.

78, 1961-62.

17.

Townsin,

R.L. "The Frictional and Pressure Resistance of Two Lucy fshton eosiras", Trans. RINA, Jan.

1967.

18. Shearer,

J.R.

and "The Experimental Determination of the Components of Cross,

J1,J.

Ship Resistance for a Mathematical Model". Trans.

RINf Vol. 107, 1965.

19.

Shearer, J.R. and. "Comparison of ;Tave Pattern Resistance on Bulbous and. Steele, B.N. Non Bulbous Forms. Ship Division Th

_159.

20. Landweber, L. and. "Study of Eors' method. for the Determination of Tzou, K.T.S. %Iavemaking Resistance". lIER Report No. 103.

13 -TABLE I RESISTANCE C0P0NEIiTS Speed (ft/see) v/1Î Fn F

(lbs)

M (lbs) WO (lbs) (ii - ;ro) (lbs) D' = F + (M - WO)(lbs) D (lbs) F C' =

M -

WO

C' = P Dt - G' + C' = C' pVZS f D T D

C,

pV2S ± ow + ow

C'

= Pressure

Forti

PF _Effect G. =

Velocity Fam

F Effect Cl -C Ci

5

0T 3.20

0.60

3.47

0.65

3.74.

0.70

4.01

0.75

0.179

0.192 0.209 0.224 0.681 0.799 0.880 1.062 1.356 1.600 2.108 2.212 0.987 1.151 1,282 1.64.6 0.369 0.229 0.626 0.766 1.050 1.228 1.506 1.828 1.030 1.250 1.530 1.830 0.0034.1 0.0034.0 0.00320 0.0034.0 0.001825 0.00191 0.00230 0.00226 0.005255 0.00531 0.00550 0.00586 0.00515 0.00532 0.00562 0.00587 0.000100 0.000129 0.00034.8 0.00351 0.00355 0.00355 0.00399 0.001 66

0.00177

0.00207 0.00188 -0.00007 -0.00001 -0.00018 +0.00008 0,322 0.331 0.368 0.320 -0.013 -0.002 -0.033 +0.014.

LIII

-f

L

i 4

Ibll

1V NIL

IllÌiPIi'

5 -7,6,5 E D PRESSURE

DISTRIBUTION

OVER MODEL

AT F

= 0224

10004 so9' (s) 25°4 (C)

% LOAD C DA FT 0006 O004 -O.00 -O

0006

o004 -o-002 o 0004

-HuI-iEs LINE FOR 10 -. PLANK o

RAKED Bow Cç °/o LOAD DRAFT 0 006 O-004

a-o

U)

- 0.002

o 0-00E

0.004

0-002 I I I I I I I O 0 1 2 3 4 5 6 7 B IO AP STATIOÑS FP

FRICTION

DISTRIBUTION ON MODEL - F

O-179

0004

o 0-002

I.-J

o FIG. 2

%LOAD C DRAFT N w 000B

0006

0004

000 2 O

0006

0004

0.002 O

0004

O002 o A.P

HUGHES UNE FOR IO . PLANK

RAKED BOW

T I I

t I t I

STATIONS

FRICTION

DISTRIBUTION ON MODEL - F-

O 't94

-

DRAFT

0006

- 0004

- 0002

-

-

o O I 2 3 4 s 6 7 8 9 10 Cf % LOAD o

- 0004

- 0006

- IL

-0004

*$ -j u w

- 0'002

EP o FIG.3.

0006

-

0004-(n r

₀₀₀₂

-w u o t-3 tO o o -

_{- 0004}

O004

0002

-I F f F F

HUGHES LiNE FOR PLANK

RAKED OW

o&----o--

-0002

F F i I i F I i O 0 1 2 3 4 5 6 7 B 9 10 AP. STATIONS FP.

FRICTION

DISTRIBUTION ON MODEL - F

= 0209

o - Cf o

-0006

DRAFT

- 0004

- 0002

- 0002

O o

- 0006

0004

tO

o

(n

o

o t-

I-J

tO -FIG. 4. % LOAD DRAFT cc

0002

-O

0006

-

0004-(n ('3

%L0AD _c DRAF1

0006

0004

Ln N ₀₀₀₂ o

0006

0004

0.00e o O004 o

HUHE UNE FOR I0

PLANK RAKED BOW 0-006 0-004 0.o0 o 0-004

0002

o L I i i I i I I O 0 1 2 3 4 5 6 7 8 9 10 A.P STATIONS FP

FRICTION DISTRIBUTION ON MODEL - F

O-224

% LOAD DRAFT FIG. 5. O-006

o-004

w 00O'2 w

,- 0003

u

3

u

-. .0..

u

u

0002

0001

0.18

o

i

060

HuGHES LINE

û

w

w

û-U)

u,

t-,

>

w

U)

O65

I

o

w

¿3w

-j

wo

>LL

0.20

_Cf

c + c

ìi

O7O

CF

COMPARISON

OF RESISTANCE COMPONENTS

O-22

O-75

V/

t

Q-o

t

03

02

01 o

-0I

-02

-0-3

03

02

0 o

-0-I

-02

-03

o

-0-I

-02

Q-0-3 O-2 o o

-0

U)

-0-z

-03

-0'4

O

-0.

-o-2 -O-3 FIG. 7. Q 4 o -J t o o

I-J

- PRESSU SHOWN BY MAÑOME1E PESSUEFEREÑC

TziT

PRESSURE ELATIV - T ¶0 WATER SUACE o

REMOTE FROM MOOEL

L_____

110101V

i

0 o 2 3 5 6 9 Io STATIOÑS FR.

N

03

02

01 o

-01

(ti

-02

-0'3

o

-03

FIG. 8. --Q i i

a

i r i

r

-rr-PRESSURE RELATIVE TO WA-rER SURFACE

REMOTE POM MODEL

- r -r- i r i i PRESSURE DIFFERENCE DUE TO 1ThM

/

_Q

r o A

i

IBY

o

-PRESSURE Si-1OWN MANOMETER

-z Q o o Q

-o o Q o G e o O o o o o ' ¿ o o e I o I Q _o O I I i o i i - I-L u o o O- G-O

u

-J f

03

02

01

0J

n-O--Iti I-L û: O cb t) û O -J o 2 4 5 6 7 s 9 lo AP STAT IONS FP

PRESSURE DISTRIBUTION - F1

= 0.194

0-1 o

-o.

-03

-0.4

o

-01

_o

O

-02

I-J

-03

o

o-u

03

02

0'l

o

-o,'

- 02

-03

0.3

02

01 o o

-o.'

- 02

-03

FIG. 9 N D O--It" t-L O O O -j o f o A PRESSURE REAflVE TD WATER SURFACE

REMOTE FROM MODEL.

PRESSURE SHOWN 8't' MANOMETER

L________

vo

4°j_

PRESSURE DIFFEREÑCE DUE TO TRIM

LU11W1

- e o e o

!PPIP.

o 2 3 4 S 6 7 8 9 to AP STATIONS FP PRESSURE

DISTRIBUTION -

= O '209

o.'

0

-0t

-O2

o

-03

ti

<r

_IN a û JI o

o

03 I

02

0l

o 'il N - 02

-03

03

0.2 01 o - O3 o

-01

-°.

-O3 Q û-

o-o

1' o

-o.

-O3

o FIG. 10. u o I-

I.-J

-0.

-oUa

-03

T

r

i r i r r ì i

rr-ì

I ¡ T A PRESSURE RELATIVE TO WATER SURFACE

REMOTE FROM MODEL

PRESSURE SkOWN o BY MANOMETER

V rWLW

PREsSuRE EUFFERENCE UE TO TRiM.

ììì

U

o * e -o e o

ÌIIo

io

o o 2 3 4 5 6 7 B 9 10 AP STATIONS FP

PRESSURE DISTRIBUTION - F

= 0224

03

02

t

CURVES OF TRIM AND SNKAGE

0-15

FIG. 12.

COMPARISON OF WAVE PATTERN RESISTANCE MEASUREMENTS

ON lOft. AND

20f1. MODELS

018

02

022

o

10

o

o

l0

o

10

w

>

<

o

-10

2O

t'0

WAVE PROFILES

FIG. 13

= O179

Fn

O194

A LWL LWL F

0209

F= O224

LWL

-J

o

2 3

4

5 G 7 B 9

% 0F LOAD

DRAFT

I00

7S

50

25

PRESSURE REStSTAÑCE

(tb PER

I 0 DEPTH)

VARtATION OF PRESSURE RESISTANCE WITH DRAFT