Report on frictional resistance research

CHÎEF

Leb. y.

Tcchthce

_oscliod

REPORT ON FRICTIONM4 RESISTAIWE RESEARCH

by

Dr. E. V. Telfer

L An examination of available plank data has been made and it has been found that turbulent data can be simply expressed as

1,2

_3ko

(I +

L ) ( ) ) 1/3

200B

VL

in which B is the draught, when the p1nk has freeboard, or the half depth when the plank is fully submerge (as in the Froude

tests).

®

Is the specific resistance x loi.

The above formula satisfactorily interpolates Froudes

var-nished plank tests which are fairly certain to have been made at

a temperature not exceedIng 100 C. which was likely to be the

water temperature at Torquay at the end of April 1872.

Froude's paraffin tests were most probably made during July and August 1872 when the tank water would have a fairly steady temperature of about 180 C0 This higher temperature appears to

be the complete and sufficient explanation of why the paraffin results shoed less resistance than the varnish,

Froudes tests aro thus brought in line with the extrapolator

and by their confirmation of the 3ko value give the minimum tur-bulent friction line without edge effect.

The formula given in (i) allows of a new concept of Froude's

extrapolation from plank to ship. _{Froude ws merely trying to}

extrapolate the resistance of a 19-inch depth plank, to ship

lengths.

In other words he had a strake of platins 19 inches deep,

having two edges, and of ship length. _{He therefore vas} deter-mining not the extrapolated resistance of a smooth ship, but,

granted his extrapoltion was in itself correct, the resistance

of a plated ship having flush butts and strakes _{19 inches wide} (i.e., one edge in 19 square inches of surface per inch run)0

Froude did not, however, make a ccrrect extrapolation0 _He did, nevertheless, use at least one guiding principle0 _He

ac-cepted that the total resistance at constant speed plotted to a base of total length LnUSt always be concave to the base line0

An alternative principle, that beyond 50 feet the resistance curve can be replaced by the tangent at 50 feet was referred to

by Froude as an upper limit0 _{The precise method used by Froude}

does not appear to be on record, only the results of the _method

are, of course, available0

:i

Let us consider these at a ship Reynolds of i0. For 400 feet the Froúde specific resistance Is 1.88, This value is that

obtained from our formula for a plate 400 feet long and 2 feet draught, I.e., by a plate having 4 square feet of wetted surface

per foot run per edge. Thus the actual value of the Froude

spe-cific resistance can be accurately accepted as applying to a

plated ship having strakes 4 feet wide and flush butts and rIvets No wonder the Froude ship frictional coefficients have resisted

attack for nearly 80 years

Actually, the average plate width for a ship 400 feet long

is now about 6 feet, although long after Froude's time 4 feet

would have been about right For 6 feet width the corresponding

Sspecific

the higher figure of Froude 1.88 (or of unity roughnessresistance reduces to 1.766. Thus, the acceptance ofas recom-mended in my

₁₉₄₉

paper) should be a good approximation to the modern plated riveted surface of

ships0

Thus, unity roughness would appear to correspond to a ship

plated with strakes one hundredth of the ship length in width.

A complete analysis has been made of temperature correction to model resistance in the light of the extrapolator for turbulent

and mixed flow. The fact that many tanks use too small a

cor-rection is fairly definite proof of the presence of mixed flow in

their normal routine testing. With stimulated turbulence becoming an agreed tank routine, temperature corrections will need to be

completely overhauled.

Previous (and in ₁₉₃₅ Internationally agreed) corrections do not distinguish between model and ship size. A single term

re-sistance fornula gives the same correction for ship and model,

Sbut

experience clearly suggests a much smaller correction fr

the shIp.

Further, the 1935

correction does not distinguish

between up and down to the standard yet the difference is

con-siderable0

Tables of kinematic viscosity and resistance change have been prepared over a wide temperature range for intervals of _{one tenth}

degree centigrade0

The recent work of Allan, Conn and Emerson, and of those who contributed to the discussion on their papers, particularly

Lindbiand and Dawson,li are attempting to assess diff er-ences in terms of V/L , waterline angle and so on, when clearly mixed-flow conditions first demand consIderation of specific

resistance in terms of Reynolds number. Thus for mixed flow

K

It is

the

value of K we want to knov. For example, the Prandtl

K value for Gebers 1908 tests was 1700. If the R difference

be-tween the unstimulated and the stimulated model at each Reynolds number divided by the Reynolds number be noted, i.e., the K value obtained, the average K value over the whole model speed range is

a much more fundamental factor (and likely to be independent of

size of módel) than is the _{plotting above referred to, The}

ratio of the K values, say to the Prandtl 1700 standard (or _{to some}

other appropriately assessed standard) may be called X , then I

-X

is a measure of the efficiency cf the turbulence stimulation.

The value of K can be shown to equal

_{®T - ®L]x R0 where}

.is

the turbulent specIfic resistance, F the laminar, bot at the critical Reynolds R _{at which turbulence begins. As F}

and ® are calculable once

Re is known it follows that it is R0 which is the vital factor in the K determinatIon. R0

should

therfore be known for every tank by testing a standard smooth plan _{and measuring Rc as has recently been done in Washington by}

Couch. The corresponding K value incidently becomes 2k60. R0 thus obtained is a measure of the tank turbulence and will clearly be governed by the interval between consecutive _{runs. The maximum}

repeatable R0 should be known for every tank.

6. _{Some work has been done on the better understanding}

_{of pnt}

or sand roughness in relation to the extrapolator0

Thus, since a rough plank has a constant specific _resistance and a smooth plank is given by

= a + b ( ) 1/3

VL

we can sy that the rough resistance is given by

a + o (f

) x 1/3

where f

(4)

x (.)

1/3 _{must be a constant, being the transverse}

dimension of the roughness. _{For this to be so, f}

( ) must take

the form (iL_) 1/3 and thus

a 4 _{( vp )} 1/3 _x ( i) ) 1/3 w _VL a + o

L4

)l/3

T 3

V

From which we see that the relative roughness is the ratio

of the roughness to the length. of the surface. Hence the same

roughness on planks of increasing length will have progressively

decreasing specific resistance just as found by W. Froude,

If the constant specific resistance is presumed to continue without transition to the smooth surface specific resistance then

this equality becomes

and hence

VL = b3 . L

e3

which is the Reynolds number at which the rough plank departs

from smooth plank resistance0 This relation may also be written

Vt b3

2)

which thus gives the critical roughness Reynolds number. This relation can be checked against various data, e, f. Perring I.C.S.T.3.

l9k8 p.

108,

from which V. _ say 125, and

therefore b/c 5. Hence as the zero edge Yalue of b is 31..0, the

value of e is

68.

Thus roughness resistance is given by

= a -+

1.2

+

_6834/a

IL

a lower limit of V can be chosen from Perringts data, say 93.

Thenc75and

il

= 1.2 +

These expressions can be checked against the Prandtl-Schlich-ting formula

l03/189 +

1.62 log

L

)2.5

by plotting this to a base of . The values given by Von

The new expression is quite close to the Von Karman data0

These latter differ from the Prandtl-Schlichting by a greater

amount thanthe difference between the new formula and the Von

Karman data0

The data also apparently co firm the retention of the 1.2 term as the limiting value of as _- O.

L

An extremely interesting check on the structure of the

fore-going; i.e0, on the use of the L2 limit and the _3,j roughness

parameter is got by analyzing W0 Froude's rough

Tplank tests0

ifl

this case it is not necessary to know the exact value of

It is sufficient to assume A = unity and to plot the sific re-sistances for the same actual roughness to a base of

34

1 When this is done straight lines can undoubtedly be passed ' through

the spots and through the limit value of 1.2. Separate lines are,

of course, drawn for each of the roughnesses, fine, medium and

coarse used by Freude0 Later it is proposed to show that these separate lines accurately coalesce when the measured roughnesses

of Froude are included in the relative roughness term0

70 The treatment of the roughness problem in the extrapolator

technique is now somewhat clearer0 _{If reference is made to ad} joining diagram (figure (a)) ft is _{seen that for every Reynolds} number there Is a relative roughness which, when saturated, _causes

the specific resistance beyond that point to remain constant. It is thus possible to have a double calibration _{of the extrapolation} diagram base in relative roughness as well as in Reynolds number function.

Now it appears probable from some work by Theodorsen on

roughened rotating cylinders that for lower densities _of rough-ness the point where the resistance begins to increase beyond the

smooth surface value will remain unchanged0 _{Thus depending upon}

density we can draw from the point on the smooth _extrapolator diagram a series of rays between the horizontal ray for complete

roughness and the extrapolator for complete smoothness, Each of

these rays will correspond to a particular density _{of roughness.} This ray arrangement would seem to be independent of the relative

roughness; i.e., the ray would be the same whatever relative roughness were chosen since in the extrapolator _{presentation the} triangle formed by the completely rough and the _{completely smooth}

lines are similar for all Reynolds numbers0 _{This facilitates}

the generalization, for ve can draw a line parallel to the smooth

extrapolator through the orIgin, (figure b), _{then from the origin}

further rays can be drawn corresponding to definite _{densities of}

roughness (which have of course to be experimentally determined),

large near to the base0 _{Thus, to determine the roughness}

addition for known density and roughness in _{any particular ship,}

all that is required is to draw from that _{point on the calibrated} base line correspondlng to the relative _{roughness, a line parallel}

to the particular density ray0

This line should give the pcint roughness _{addition to the ship} resistance; and is seen to imply an increasing _{relative addition}

with increased Reynolds number0 _{There is still the edge}

rough-ness effects to allow for; and these in principle _{can be} repre-sented as rays below the base line corresponding _{to various ratios}

of plate-width to ship length (figure e). _{Thus to combine pnt} and edge roughnesses, ve proceed as before but _{note only the}

inter-section of the line parallel to the pont roughness _{density ray}

on to the zero ordinate0 _{Then from this point join to the point}

on the edge ray below the relative roughness _{abscissae0 This line}

will thus be the total roughness addition0 _{From the construction}

it follows that the sum of the roughnesses may be practically

eonstant This will be the case in the normal riveted _{ship0 In} the ship with welded butts and riveted _{seams and welded frames} the edge roughness may predominate and _{the total roughness will} become less with increasing Reynolds _{number0 With entirely}

welded ships the roughness will, be practically _zero0

One final point may be ent.ioned. _{A statistical analysis of} roughness on actual ships (made available _{by the late G. S. Baker)} shows that as riveted ships increase in _{size their relative} rough-ness rapidly decreases but their roughrough-ness density _definitely

in-creases. _{Similarly the ratio of plate width to ship length}

be-comes smaller the longer the

_ship0

The precise effect of these dfferenees _{may be to equalize}

the total roughness between small, _{and large}

_ships0

_{The smaller}

Reynolds numbers of small shIps _{appears to produce a}

preponder-ating edge

resIstance which generally result in the small ship

always having a larger total roughness _{resistance than the smaller,}

the net effect being probably to _{endorse for riveted ships the}

plausibility of the unity roughness, _{ray concept advanced pre} viously in 19k90

£ RO t) G ADO CCMBN ED N E - oç-LO W D N S T Y

_{I G.}

HIGH PAr'JT RC U G H E SS EDGE

FIG Çct)

PIG()

'-V L 3