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Simplified Launching
Calculations
BY
A. SILVERLEAF,
B.SC.PUBLISHED BY TEE INSTITUTION ELMEANK CRESCENT
GLASGOW 1952
Simplified Launching
Calculations
BY
A. SILVERLEAF, B.SC.
The responsibility for the statements and
opinions expressed in papers and discussions rests with the individual authors: the Institu.
tion as a body merely places them on record.
Reprinted from the
Transactions of the institution of Engineers
and Shipbuilders in Scotland
Paper No. 115-I
SIMPLIFIED LAUNCHING CALCULATIONS
By A. SILVERLEAF,* B.Sc.
Associate Member of the Institution
12th February, 1952
SYNOPSIS
The paper is divided into three sections : the first describes a
method by which launching curves for any ship and any launch
conditions can be rapidly derived with an accuracy approaching that obtained from a normal detailed calculation. Diagrams of buoyancy and moment coefficients, and a standard calculation form, are given. The second section presents a brief analysis of the effects on stern lift conditions of variations in launching factors. The final section
of the paper is concerned with launch stability. A direct method
of calculating stability during launching is outlined, and a diagram of stability coefficients given. A typical calculation illustrates the
method.
STANDARD LAUNCHING CURVES
The calculation and plotting of curves showing vertical forces and moments in terms of travel down launching ways are part of the routine work of most ship design offices. Although it is
generally recognized that these calculations give only an
approxi-mation to the true conditions during an actual launch, they are often lengthy and laborious to perform. Any simple and short
way of deriving these curves which does not introduce any
additional inaccuracies due to the method of calculation should
thus be of practical value.
There are two stages in the calculation of standard launching
18 SiMPLIFIED LAUNCEING CALCULATIONS
curves. The first is entirely geometric, and consists of
deter-mining the position of the ship at any given point in its travel down the launching ways up to the pivoting point, or point of stern lift. This depends solely on the initial relative positions of
ship, ways, and water level, and the proffle of the ways. The
second stage involves the hydrostatic and weight characteristics
of the ship. The buoyancy corresponding to the previously determined positions, and its moments about convenient trans-verse axes, have to be evaluated and balanced against the cor-responding force and moments due to the launch weight of the
ship. These two independent, though related, stages of the
alcu1ation are discussed separately.
Launch Geoinetr. It is not uncommon for the position, or attitude, of a ship at different points of its travel to be determined
from small-scale profile drawings of ship and launch ways. The
ship proffle is moved over the launch ways proffle, on which the
anticipated water level is also marked, and t.he ship draughts at
the required travels are read directly from the interception
points of water level and ship profile. Clearly this method is awkward and liable to error through distortion of the drawings, scale errors, arid the like. The tabular numerical method pro-posed by Hillhouse and Riddlesworth' is far quicker, simpler, and more accurate. In this, the position of the ship after any
given travel is defined in terms of the draught at the afterniost and
lowest point of the keel (usually at the AP.), and of the trim.
It is obtained by combining the effects of "fall," or change in
position due to the movement of the launch cradle down the
ways, and of "round-down," or change in trim of the ship due
to increase in keel declivity caused by camber of the ways. The
cambered ways are taken as parabolic arcs, thus enabling fall
and round-down to be readily calculated. As given by Hilthouse, this tabular calculation, though far more direct and accurate than
the "pictorial" method, must be carried out afresh for every
ship and each anticipated launching condition. However, by presenting the results of an analysis of the same nature in
non-dimensional form, it is possible to derive a chart which can
serve for any ship under any set of launching conditions.
In Fig. 1, which represents diagrammatically the attitude of a ship before and during launching, let
SIMPLIFIED LAUNCHING CALCULATIONS 319 l=Length of standing ways, ft.
L =Displacement length of ship, ft.
E=Initial distance from K1 to after end of standing ways
(A.E.W.), ft.c=Camber of standing ways, ft. H=Depth of water at A.E.W., ft.
h=Initial height of K1 above top of standing ways, ft, s=Travel of K1 beyond A.E.W., ft.
T=Total travel from initial position =s+E, ft.
(A) INITIAL POSITION
A W
(B) BEFaR: 5TERN LIFT POINT
V
I
f s
A
Fig. 1.Launch posüions.
L
L
5+E
w= Declivity of chord of standing ways.
/c=Initial declivity of keel.
d==iDraught at K1 after total travel T, ft. ,
t=Trim by stern of ship in length L after total travel T, ft. K1 is on the keel line at the A.P., which, for twin-screw ships is taken to be at the after end of the L.W.L. As is usual, cam-bered standing ways may be taken as parabolic arcs with suffi-cient accuracy for all practical purposes. Then it can be readily
320 SIMPLIFIED LAUNCHING CALCULATIONS
dÁIL ==(Hh)/L+ (8/L) [w+ (4c/l)(1 +Il)] (1) t/L=k+(8c/l)[(s+E)/l1 . . (2)
Equations (1) and (2) completely define the position of a
ship during every part of its launch for which the standing and sliding ways remain fully in contact, in other words, up to the point of stern lift. The only portion of this part of the launch that is of practical interest is when K1 has moved beyond the A.E.W., and for this $ is positive. It should be noted that .r
has been used in equations (1) and (2) in preference to the more
commonly used total travel T, partly because of its greater,
conveniehce for computation and plotting, and partly because
its use gives a direct indication of the "overhang" of the ship
over the A.E.W. at any time, which is of especial use in relation to the problem of tipping moments.
Fig. 2 gives a graphical, non-dimensional solution of equations
(1) and (2) covering all likely values of the variables involved, and from it the position and attitude of any ship launched from any likely set of ways can rapidly be determined throughout its travel up to the point of stern lift. In this diagram, declivities are given in the more usual form of in. per ft., rather than in the
true gradient form required by equations (1) and (2). The
accuracy given by this diagram equals that from a Hilihouse tabular calculation, since it is equivalent to such a calculation,
and exceeds that generally obtained by the pictorial method.
The diagram enables the effects of changes in any of the launch
conditions to be rapidly assessed, and (lirect inspection will often
indicate the broad effect of certain changes without any need for further computation.
It may be noted that in much published launch data at least one essential item of launch geometry is omitted. Frequently
this is the height of the keel above the standing ways, and it
is possible that it is sometimes not appreciated that this has the same significance as the depth of water at the afterend of ways. Buoyancy and Moment Coefficients. After the attitude of the
ship at a given travel has been determined either in terms of
draught forward and aft or draught aft and trim, the next step in a standard launching calculation is to evaluate the
corres-ponding buoyancy and its moment about some convenient
S
Sn ri
.,I 11UW ri
ii
WlaVA' r
IrAii.iRr,
UiAVAUW4'
I WAI1VA VV
V
iii
"-S-.
I
OIAGRAP
li,
W4U H\
TRIM,,,
S - TAVrL OI A' PYÖND AtW
rl)
,
I
AW (Fr)A A 11
li
(n)j
rp
m1i11vA
j
1LairAvA,i
AÌi! IIii
4v-ArArÀrAr.
ÍÍ41ß
VV
SSS!V4V1FNRI/
APlilIW
fig. 2.I,a U Ile!,, ,I ulf ¡f du diii,rini. 0 03 04 d 05SIMPLIFIED LAUICIIING CALCULATIONS 321
sectional areas, often ploted directly on the scale ship profile, from which the buoyancy and its momeit are calculated in the normal fashion, a separate calculation being required for each attitude Hillhouse suggested that sets of cross curves should first be plotted from such calculations for a series of selected appropriate and convenient values of draught aft and trim. From these cross curves the buoyancy and its moment corresponding to any draught and trim within the range considered can be read
off directly. Such a plot undoubtedly saves time and labour
when numerous ship attitudes are to be considered.
In an attempt to eliminate the need to carry out buoyancy
ca].culations for every ship individually, buoyancy and moment calculations have been made for a number of forms covering a wide range of hull parameters, including block coefficient and position of L.C.B. For each form, the displacement and position of centre of buoyancy were determined for a range of draughts
aft and trim covering all likely launch attitudes, and it was
found that simple coefficients could be derived which applied
equally well to all the single-screw, or to all the twin-screw forms
examined A buoyancy cöefficierit gives the ratio of the dis-placement corresponding to a given draught aft and trim to the
load displacement, while a further coefficient ß gives the distance
of the L.C.B. of this partial displacement from the AP, as a
fraction of the ship length. It may seem surprising that such coefficients could apply with any accuracy to ships of varying
form and fullness, but it should be remembered that their use
is restricted to the extreme conditions of draught and trim met with during launching. These coefficients are given in Fig. 3, and from them, using the ship attitudes given by Fig. 2, standard launching curves for any given set of conditions can be rapidly computed with sufficient accuracy for most practical purposes.
In these static force and moment calculations it is usual to
ignore the launch cradle, assuming that its weight and buoyancy
are almost equal and that its centres of buoyancy and weight
have the same longitudinal position.
The formulae involved in the calculation of standard launching
curves may be summarized as follows:
Let
V=Buoyancy at draught dA at K1, and trim t in length L, tons. =L.C.B. of buoyancy V forward of A.P., ft.
SINGLE ± LOG FRQMAPA,,j& SCREW FORMS L SHIP LEÑGTH B.0 0-4
PNRUU
-U AVA
= I1Er A ORAGH7 d.-322 SIMPLIFIED LALTNCHI (.\LCULATIONS
O-4 I S 06 0-7 0-5 09 l-0 I I 2 I-3 '4
(a)
Fig. 3.Buoyoncy and L.C.B. coefficients.
dLoad draught. 5 .45 35 -30 25 20 15 8 .7 6 .5 .4 .3 2
0
TWIN SCREW
LOB R051 AFT END LW.L. P7 5 ¼
FORMS l L SAIP LOI-JOlI-I 051 LW.L.
.-
0.3-V4f4W
V)P4 (4 fA F
PLAC1CMEÑT A7A00R64Td.p-SIMPLIFIED LAUNCNG CALCULATIONS
33
C-4 05 0-6 C OB 09 0 I: 1.4
(b)
dA=Draughi at A.P. after travel T. t=Trim in length L after travel T. 30 45 40 -30 -25 20 15 08 0-7 0-6 0-5 0-4 03 -z
324 SIMPLIFIED LAUNCHING CALCULATIONS
J =Displacement at load draught d, tons.
O = Overhang forward of ship beyond fore poppet, ft.
W=Launch weight of ship, tons.
g=L.C.G. of weight from raid-length (+forward,aft), ft.
Similar expressions with non-dimensional coefficients can be derived for moments against tipping and for way end pressures, hut these are too involved to justify general use. In any parti.
ciilar instance it is simpler to proceed from the buoyancy and
weight moments about the A.E.W. already found, when the
net moment against tipping (MT, say) is given directly by the difference between them. We then have:
Load on ways==R=WV (7) Centre of pressure of load from A.E.W.==r =M/(WV) (S)
The way end pressure is generally only of interest when the after
end of the sliding ways has moved beyond the A.E.W., and for this the overlap between standing and sliding ways is given by
Overlap= .=lT.
. . (9)Taking the load distribution on this overlap to be linear, the way end pressure is then given by:
Pressure at A.E .W. =p =(2RÌa A) (2-3r/ A) for r> A!3 (lOa)
=2R/3ar for r-<A/3 (lOb)
=0 for r> 2A, (10e)
where a =total width of sliding ways.
Typical Calculatio'n,s. In order to ifiustrate the application of the proposed simplified method, launching curves have been derived for the Queeï Mary using only the outline launch data
Then
cV/Z1, ß=/L, f=O/L,
=g/L,and we have:
Buoyancy moment about fore poppet =JL (1f--ß) (3)
Weight moment about fore poppet =WL(05fp)
(4)Buoyancy moment about A.E.W.
=zL (s/Lß)
(5) Weight moment about A.E.W.=WL(s/L O5-9) (6)
given by McNeil2 and the load displacement given by Pigott.3
The complete calculation is given in Table I, and Fig. 4 shows the
curves so obtained and also those given by McNeil, which were obtained from a normal detail calculation. It will be seen that
the agreement is reasonably close, particularly over the critical
range up to the stern lift point.
M" (moNo) 10x10' O
N
N
OrSIMTLIFIED LAIJNCfflNG CALCULATIONS 325
EF
'Ol,,.
-'('--ASCO
LAUNCHINO FACTORS
Perhaps the most useful feature of non-dimensional diagrams
such as Figs. 2 and 3 is that they facilitate the rapid study of
the effect of variations in basic launch factors. Further, they
can be used to construct other non-dimensional charts which
illustrate the effect of such variations in a direct and striking
manner. Two such diagrams are given here. The first illustrates
the conditions which exist at the stern lift point. Stern lift occurs when the nioments of buoyancy and launch weight about
the fore poppet pivoting point are equal, and then, from (3)
and (4),
[(1f)ß](W/)/(OE5fp)
. . (11)ElOPT OF SHIP MOMENT OF WEIGHT ABOLrr FOEE POPPET
- 4000C 50000
w
(TONS)
-!Q000
A - BUOYANCY (DETAIL METHOD)
B - BUOYANCY (SIMPLIFIED METhOD)
05x10" C - MOMENT OF BIJOYANCY ABOUT FORE POPPET (DETAn.. METHOD)
D -
...
(SIMPUFIED MtTHOE - MOMENT OF BUOYANCY ABOUT AFTER END OF WAYD (DETAIL METHOD)
F - . - (SIMPLIFIED METHOD)
800 700 (TRAVEL. FT.) bO 500 0
i
Total travel, ft.
2
Travel of A.P. beyond A.E.W., ft.
3 Travel ratio 4 Travel ratio 5 a
Draught ratio (Fig. 2)
6
Trim ratio (Fig. 2)
TABLE 1LAWICHING CURVES FOR Q.S.S. Queii Mari,'
L=l,004 ft. WL 1=9425 ft. E=32 ft. c=l5 ft. w= fr in. per ft. k= in. per ft. H=lI5 ft. h=493 ft. E/l= 0032 c/t=0. 00150 (BIh)/L = 000656 400 00 600 368 468 588 0391 0497 0602 Ø367 0466 0566 00269 00328 00388 00484 00497 005l1 700 800 668 788 0709 0815 0665 0765 0'0449 00511 00525 0'0539 w a L= 1,004 ft. WL d=385 ft. ,=74,440 tons
p launch=3584 eu.ft. per ton
L/d= 26.1 latmch= 72,700 tons Overhang, O=935 ft. f=O/L=0.093 1f=O'093 E
70 Draught ratio
(l,/(i 0702 0856 1012 1171 i332 M E Trim ratio 1263 l297 1332 1368 F406Buoyancy coefficient (Fig. 3)
ix 0.100 0180 0295 0435 0595 10 Buoyancy, tons V = 7,300 13,100 21,500 31,600 43,300 IL O
L.C.B. coefficient about A.P. (Fig. 3)
fi O300 0330 0352 0367 0376 Ib
L.C.B. coefficient about fore poppet
O607 0577 0ö55 0540 0531 Ui
-Moment coefficient about fore poppet
a[( lf)ß]
00607 01047 0l637 02350 03160 14Buoyancy moment about fore poppet, ft. tons
Lix[( 1f)ß] 4,440,004) 7,650,000 11,960,000 17,170,000 23,100,000 15 0
L.C.B. coefficient about A.E.W.
sILfi
0067 0136 0214 0298 038916t N ornent coefficient about A.E.W.
a(s/Lfi) 00067 0.0245 001331 01297 02315
li
Buoyancy moment about A.E.W., ft. tons
¿La(s/Lß) 490,000 1,790,000 4,610,000 9,470,000 16,930,000 18 19 20 W=35,500 tons W/i=0488 çj=l74 ft.. aft p=q/L=-00l73 a=105ft.. x2=2lft.
L.C.G. coefficient about fore poppet Moment coefficient about fore poppet Weight moment about fore poppet, ft. tong
(W/)(05f---ç) WL (Oö.f--ip)
O424 0207
15,130,000
constant constant constant
21
L.C.G. coefficient about A.E.W.
.5/L-0.5p
0166
0017
0083 Oi82 0282 22Moment coefficient about A.E.W.
(Wf)(8/LOE5--p) 0081
00083
0040 0089 0138 23Weight moment about A.E.W. ft. tons
WL(s/L-05---p) 5,920,000 610,000
2,960,000
6.480,000
10,040,000
24
Net moment against tipping, ft. tons
MT= 17--23 6,410,000 2,400,000 1,650,000 2,990,000 5,090,000 25 , 26
Load on ways, tons Centre of pressure from A.E.W., ft.
r=MJR 28,200 228 22,400 117 1,000 118 3,900
-27 .. Overlap, ft. 542 442 342 28Pressure at A,E.W., tons per sq. in.
p
3.7
6.0
SIMPLIFIED LAUNCnING CALCULATIONS 32T To each pair of draught and trim ratios there correspond values
of buoyancy and L.C.B. coefficients c and /9. Thus, for a fixed
overhang ratio f, a diagram can be constructed relating the
moment coefficients given in (11) which indicates the conditiQns
occurring at the stern lift point.. Fig. S is such a diagram drawn
for single-screw forms and an overhang ratio of 01, and a similar
diagram can be readily constructed for any other overhang ratio. From Fig. 5 it is possible to determine directly for any
combin-ation of launch weight and L.C.G. position all the possible sets of
draught and trim ratios at stern lift.. By plotting on this diagram
the draught and trim ratios corresponding to a given set of launching conditions, the particular attitude at stern lift for
any weight and L.C.G. position can be found, and also the travel at which it occurs. A series of such 'travel plots' showing the, effect of varying launch conditions is shown on Fig. 5, and will be discussed later.
A second diagram gives the locl on the ways corresponding
to any ship attitude. We have
R=WV
. (7)and V=
giving
R/W=1/(Wf)
. (12)and
V/W=/(W!)
. . . (13)Thus, for any given draught and trim ratios, the buoyancy and
load on the ways corresponding to any launch weight can be
directly determined. Fig. 6 is a graphical plot of these relations (12) and (13), and applies to all single-screw forms throughout the launch range. Up to t.he stern lift point the load on the ways. is distributed, either linearly o in some other manner, along the whole of the overlap between standing and sliding ways, and is responsible for the way end pressure previously discussed. At
and beyond the stern lift point the load is concentrated at the fore poppet pivoting point. Knowing the ship attitude at the stern lift point, say from Fig. 5, then Fig. 6 gives the corres ponding fore poppet load, which affects not only structural
stresses in this region but also the effective stability lever, a.s. will be shown later.
To illustrate the use of these diagrams, and to study in outline the general effect of variations in certain launch parameters, a
i.'
10 09 08 07 0G 05 Oir --OlA AFig. 5.Stern lift attitudes. (Single-screw forms.) Overhand ratio 01.
¿Load draught. WLaunch weight
¿AD raught at A.P. after travel T. sLoad displacement.
tTrim in length L.
Ei- ':
lILI
III-_11iiI1I
'ilk
L
IlliliLlii
-Il-iIiii;'I_I1I
1
NLIk-4iiiiir
U
1111111
flUlill
i IN
i
IN
.05 0111120 'IklIk
301111
MONIE NT COEFUNU.
d=Load draught.
dADraught at A.P. after travel T.
t= Trim in length L after travel T.
SIMPLIFIED LAUNCflTNG CALCULATIONS 329
W=Launch weight.
V=Buoyancy after travel T. R = Load on ways after travel T.
¿X = Load displacement.
N
ui;
'u-'J'_
o.ç o__
0604
e 0 1404
08330 SIMPLIFIED LAUNCHING CALCULATIONS
basic launch condition was chosen after an examination of a
considerable amount of launch data, including much unpub-lished information, and it was found that for the great majority of ship launches there is surprisingly little variation in essential launch factors, the greatest variation being in tide height ratio. The range of values, and those chosen for the basic launch con-dition, are as follows:
Ratio
Ship length to length of standing ways Extension aft to length of standing ways Overhang forward to length of ship Camber to length of standing ways Keel declivity (in. per ft.)
Ways declivity (in. per ft.)
Tide height
Basic
Symbol Rango value
L/l 08 to 11 1.0 E/i 005 to 030 01 OIL O05to015 04 c/i O to 00025 0 k
ltof
Wtof
(Hh)/L 0005 to O02 001
From the basic condition a series of conditions was then derived
in which the camber, declivities of keel and ways, and tide height
were varied in turn. For each condition the draughts and trims for travel ratios (Tu, T/L) from 03 to 08 or beyond were found for a ship with length/draught ratio (L/d) of 20. The 'travel plots' for these conditions are shown in Fig. 5, and stern lift attitudes for three representative launch weight and L.C.G.
values at each condition were noted. From Fig. 6 the corres-ponding values of buoyancy and fore poppet pivoting load were
then found.
The results aro summarized in Table II, and even from this brief analysis it is possible to recognize certain general effects that can be stated in the following form:
VAlUATIoN STERN Lrr CoNDITIoNs
Travel Draught aft Buoyancy Fore poppet load
Increasing
camber Reduced Increased Almost unchanged Almost unchanged Increasing
declivity Reduced Increased Erratic decrease Err4tic increase
Increasing tide
height Reduced Unchanged Unchanged Unchanged
Increasing launch
weight Increased Increased Increased Increased, but less
than weight
in-crease Movement of
SIMPLIFIED LAITNCHING CALCULATIONS 331 This analysis can be readily extended to cover any other point of interest, such as the moment against tipping or the pressure at A.E.W., though any change in launch conditions that makes
the stern lift occur earlier will generally increase the anti-tipping
moment and reduce the maximum way end pressure.
A further useful application of Figs. S and 6 is the examination of the conditions between the points of stern lift and free fitation.
TABLE II
VARIATIONS fl LAUNCH CONDITIONS
For all conditions L/i==1-0, E/i=0-1,f=O/L=0.I, L/d=20
Throughout this part of the launch the buoyancy and weight
moments about the fore poppet must balance, and thus the suc-cessive attitudes of the ship can be found from Fig. 5 by noting
the different draught ratios corresponding to the fore poppet
moment coefficient for the appropriate weight and L.C.G. ratios.
These draught ratios lie on the vertical 'key' line drawn down-wards from the travel plot through decreasing trim ratio values. In this way the path of the lowest point of the keel can be traced
No. Launching factors Ship condition Stern lift conditions
c/i k w
(Hh)/L W/
L.C.G./L T/L dA/d t/cl VÌW R/W (in. per ft.) I 0 4 9 0-01 0-5 0 0-81 94 1-04 0.74 0.26 0-3 0 0-63 076 l-04 0.70 0-30 O-3 01 0-70 0-83 l-04 0-94 0-06 II 0-001 4 0-01 0-5 O 0-77 0-99 1-16 0-77 0-23 0-3 0 0-61 0.79 1.14 0-70 0-30 0-3 0.1A 0-67 0-87 1-15 0-90 0-10 III 0-002 9 9 0-01 0-5 0 OE73 F03 1-27 0-74 0-26 0-3 0 0-59 0-83 122 0-71 0-29 0-3 Ø.1A 0-65 091 124 0-90 0l0 TV () 4 0-01 0.5 0 0-90 0-87 0-83 0-81 0-19 03 0 0-68 0-68 0-83 0-73 0-27 V 0 9 4 0-01 O-3 05 0.1A, O 0-76 076 O-76 F02 0-83 F25 1-00 074 0 026 0-3 0 061 0-84 125 070 0-30 0-3 0.1A 0-67 091 i-25 0-90 0-10 VI O 9 0t5
O-
0-94 F04 0-77 0-23 0-3 0 0-83 0-76 1-04 0-75 0-25 0-3 0.1A-
0-83 1-04 0-97 0-03332 SÌMPLIv[ED LAUNCHING CALCULATIONS
up to the final free flotation condition. By markiri.g the
suc-cessive pairs of draught and trim values on Fig. 6 the corres-ponding values of the fore poppet load can be found. These
will decrease steadily from a maximum at stern lift to zero at
free flotation.
LAUNCH STABILITY
It is well known that the transverse stability of a ship is
reduced during launching, but attempts to estimate the magni-tude and significance of the effect are seldom made, and few, if any, calculations relating to launch stabffity have been
pub-lished. Although the problem is generally ignored, it is not
with-out practical importance, and in some instances, particularly in launches from a single way, may be critical.
The reduction in transverso stability is due to the upward
reaction of the load on the ways, which has the effect of raising the virtual position of the ship centre of gravity, equivalent to a
reduction in transverse metacentric height. It is important only for that part of the launch between the points of stern lift and final free flotation, and in most instances the critical position is at the actual point of stern lift. Then the upward thrust from the ways concentrated at the fore poppet has its greatest value relative to the buoyancy, and the available hydrostatic stability is likely to be at a mirdmuiu. The effect is precisely the same
as that on the transverse stability of a ship being dry-docked
with an initial trim relative to the keel blocks, where the maxi-mum reduction usually occurs just as the ship is about to touch down completely on the blocks. The initial stabifity when the ship is floating freely after launching is not a reliable guide to the effective stability at the stern lift point. As is shown in the following paragraphs, it depends to a considerable extent on the
launch conditions.
Calculation Methods. Fig. 7 represents diagrammatically the forces acting at any point at or after stoni lift.
Let V be the buoyancy of the immersed huH, acting through B,
the centre of buoyancy,
W be the launch weight of the ship, acting through G, the centre of gravity,
SIMPLIFIHD LAUNCHING CALCULATIONS 333
w
A E.W.
Alp SHIP AFTER STERN LIFT POINT.
Fig. 7.-Launch stability.
R
w
TRANSVERSE FORCES.
where G is the virtual position of the centre of gravity, taking
into account the effect. of R, and the moment levers are
pro-jections on a vertical plane.
Equations (3) and (4) give
G1M=GM(R/W)FM (16)
which relates the nominal and effective metaceutric heights at any point of the launch.
From Fig. 7, for a travel T giving a. draught aft dA and trim
tin ship length L; we have,
GM=KMKG---t(OE5+pß) (17)
FM=KM+FKt(1---f--ß)
. (18)R be the reaction of the load on the ways, acting through F, the pivoting point,
M be the metacentre corresponding to V.
Then, resolving forces vertically,
W=V+R.
(14)Now, for a small angle of heel, O, the net restoring moment is given by
334 SIMPLIFIED LAUNCHING CALCULATIONS where
KM=KB+BM=Metacentre above keel line for buoyancy V
cor-responding to dA and t
KG=Launch weight e.g. above keel line
g= pL =Launch weight e.g. from mid-length (+forward,
aft)
=ßL=L.C.B. of buoyancy V forward of A.P.
FK=Height of keel above standing ways at
pivot-ing point.
O==fL=Overhang forward of ship beyond pivoting
point.
From equations (16), (17) and (18) the virtual or effective
metacentric height can be evaluated at any point for which the sliding ways pivot about the standing ways. It is generally true that the minimum effective G.M. occurs at the point of stern lift, when the upward reaction R is greater than at any subsequent
point, and in practice it is only necessary to determine the stability for this condition. The amount by which the nominal G M. is reduced wifi clearly depend on the launch conditions, and may
be severe if the load on the ways at stern lift point is large in
relation to the launch weight.
In order to facilitate the calculation of this virtual meta-centric height during launching, values of KB and BM were
determined for a number of hull forms for a range of draughts
aft and trims covering all likely launch attitudes, particularly
those corresponding to points of stern Lift. From the results
expressed in non-dimensional form, Fig. 8 was derived, which enables KÌVI to be estimated as
K:M=-rd+B2id . . (19)
where B and d are the L.W.L. maximum beam and the load
draught respectively, and y and are stability coefficients
depend-ing on the ship attitude. In this estimate, and in the expressions (17) and (18), the slight effect on KB, KG and FK of the ship trim
has been neglected. These distances should be taken perpen-dicular to the keel line, not to the waterline as has been done,
but since the keel trim rarely exceeds 5° the error so introduced is
of little importance.
The procedure to be followed to find the effective metacentric height at stern lift in any given case may be summarized thus:
030 025 0.10 005 KB K B = CENTRE OC BUOYANCY
KEEL LINE AT AND
ABOVE C/d
d. LOAD DRAUGtT
pr
u1-ii
BMMETACENTRE ABOVE CENTRE OF
BUOYANCY AT aA/a AND /d
-B = ,MAXII1UM BEAM AT L.W.L.
U. LOAD DRAUGkT.
i.0
SIMPLIFIED LA1JNC}UNG CALCULATIONS 335
06 07 0 03 IO LA» II i;? 3
Fig. 8.Stability coefficients. dA=Draught at A.P. after travel 1'.
t=Trim in length L after travel T.
06 05 04 0-3 0-2 0-t 020 g OIS
336 SIMPLIFIED LAUNCHING CALCULATIONS
1Known dataLaunch geometryi, E, c, w, k, H, h, f, FK
Ship form
L, B, d, ¿Ship weight
W, L.C.G., KG.2From Fig. 2 (launch attitudes) determine draught and trim
ratios (dA/d, t/d) for various travels.
3Mark these on Fig. 5 (stern lift attitudes) and, for given W
and L.C.G. note draught and trim ratios at stern lift point. From Fig. 3 (buoyancy and L.C.B. coefficients) note cor-responding value of ß and from Fig. 6 (load on ways) value
of R/W.
4From Fig. 8 (stability coefficients) note corresponding values of y and and, for given B and d, calculate KM=KB+BM
from equation (19).
5With data now available, calculate GM from equation (17),
FM from equation (18), and finally G1M from equation (16). Typical Calculations. To illustrate the proposed method of
esti-mating the virtual stability at stern lift, a number of calculations
have been made for a typical single-screw ship form for several of
the launch conditions previousy examined and given in Table II. The complete calculations are given in Table III, and in addition to illustrating the method of calculation, the results broadly in-dicate the influence of some changes in launching conditions.
For instance, it is generally true that increases in camber or declivities tend to reduce the virtual G.M. at stern lift, while
reduction in launch weight or movement of the L.C.G. aft in.. creases the virtual G.M.
Comparison with the inetacentric height in the free flotation condition following launching is of interest. For the vessel
considered in Table Ill, the probable "free flotation" G.M. for
W/ O5 is about 3 ft., and for W/ O3 about 8 ft. Clearly the reduction during launching can be substantial.
Acknowledgment. The assistance of colleagues who carried
out many computations and drew diagrams is gratefully
ack-nowledged. In particular, the substantial contribution made
by Mr. P. H. Tanner, especially in the early stages of the work,
towards developing the methods given here was essential to
5 6 7 8 9
10
li
12 13 14 15 16 17 18 19.'
20
i
TABLE ITTTYPICAL LAUNORING STABILITY CALCULATIONS
L=400 ft. B=55 ft. d=20 ft. B2/d=1513
=- tons
W= tons
L.C.G. from (l;I=g=_ ft..Launch weight ratio
W/L 0.5 05 05 03 03 03
Launch weight L.C.G. from (I)
p=g/L O o o O 0
01
Launch weight L.C.G. from A;P.
O.S+p 05 0.5 05 05 05 04
Launch weight KG above keel, ft.
-25 25 25 25 25 251, E, f, c, k, w, H, h, as for corresponding condition in Table II with FK= 1 ft.
Condition as in Table II I
Ill
IV I III I Draught ratio dA/d 094 103 0'87 076 0'83 083 Trim ratio 1O4 127 083 104 122 104 Trim, ft. t 208 25'4 166 0'8 24'4 208L.C.B. coefficient from A.P. (Fig. 3)
ß 038 035 0'41 0'34 032 0'355 L.C.B. coefficient from KG
(05+p)ß
012 015 009 0'16 018 O'145 Trim correction to KG, ft. P=t[(05+q)ß] 25 38 15 33 4.4 30L.C.B. coefficient from fore poppet
(1f)ß
052 0.55 049 0'56 058 0545Trim correction to fore poppet, ft.
Q=t[(1--f)--ß] 108 140 81 1i6 142 113 KB coefficient (Fig. 8) 0305 0325 0290 0'225 0'245 0255 KB, ft. yd 61 65 58 45 4.9 51 BM coefficient (Fig. 8) OE172 0174 0i66 O242 0'231 0'212 BM, ft. &B2/d 260 263 251 366 350 321 KM, ft. KB±BM 321 328 309 4F! 39,9 372 GM, ft.
KMKGP
4(l 4.0 44 128 10'5 92 FM, ft. KM+FKQ 223 19'S 238 30'S 26'7 269Fore poppet load coefficient (Fig. 6)
RIW 023 026 019 025 0'29 0O3 Reduction in GM, ft. (R/W)FM 52 51 4.5 7.7 7'7 08 Effective GM, ft. GiM = GM(R/W)FM-0.6
11
01
5.1 28 84338 SIMPLT1TED LAUNCHING CALCULATIONS
was begun when the writer was with William Denny & Bros. Ltd., and the facilities which were available there are acknow-ledged with thanks.
The paper is published by permission of the Director, National
Physical Laboratory.
BIBLI0GRarHY
"On Launching," by P. A. Hilihouse and W. H. Riddlesworth.
Trans. Inst. Naval Arch., 1917, vol. 59, p. 172.
"Launch of the Quadruple-screw Turbine Steamer Queen Mary," by
J. M. McNeilL ibid, 1935, voI. 77, p. 1.
"Some Special Features of the S.S. Queen Mary," by S. J. Pigott.
ibid, 1937, vol. 79, p. 18.
" Proposed New Basis for the Design of Single-Screw Merchant Ship Forms and Standard Series Lines," by F. H. Todd and
F. X. Forest. Trans. Soc. Naval Arch. & Mar. Eng., 1951,
vol. 59.
Disca.ssion,
Mr. A. R. MITCHELL, M.B.E., M.C. (Member of Council): Before a vessel is laid down, the shipyard manager generally wishes to know the minimum depth of water at the after end of the standing ways in which the vessel can be safely launched, so that be can determine the length, declivity and, if necessary
the camber of the standing ways.
With this informationavailable he can then fix the building declivity and the position
of the vessel in relation to the water edge. For a rapid estimate of draughts at any travel down the ways, assuming a figure for declivity and camber, Fig. 2 is invaluable and from the results obtained applied to Fig. 3 the approximate travel at which the stern begins to lift can be found. By trial and error the most suitable conditions can be quickly ascertained.
The writer has checked calculated draughts on Fig. 2 for a most unusual form and found the chart to be correct for the
draught aft and only slightly out forward, the error being about I in. If the chart is used solely for the purpose of determining the draughts without transferring the results directly to Fig. 3
for the estimation of buoyancy and moment of buoyancy, its only weakness appears to lie in the fact. that no matter how
SIMPLIFIED LAUNCHING CALCULATIONS 339 the ratio of the length of the ship to unity. Does the Author agree?
Comparing the launch conditions on p. 330 with the usual
practice in the writer's yard, it appears that the vessels con-sidered were much larger than is the usual run of merchant
vessels built there. Owing to the great variation of types of sterns and cut-ups, some vessels can be built much closer to
the water edge than others and this naturally affects the length
of the standing ways. The ratio of camber to length of standing
ways used by the writer's firm is approximately 0003, the keel
declivity * in. and the average declivity of chord of standing
ways about in. This large declivity is found to be necessary to offset the low initial pressure on the ways, frequently under
i ton per sq. ft., due to the very light weight of the vessels built as well as the greater ratio of camber used to get the
vessels past the critical period from the point at which the stern begins to lift until the vessel is fully waterborne. No difficulty is experienced in obtaining sufficient water at the A.E.W., bit
it is interesting to note that the basic value of the tide height is equivalent to the height of the keel at the after end above the standing ways plus one-hundredth of the length of the
vessel. This figure agrees very well with customary practice in
destroyers, the lengths of which are now approaching 400 ft.,
but bears no relationship to the figures for small craft of shallow
draught up to 250 ft. in length.
In most small yards it is not usual to carry out launching calculations unless the vessel is of a type not normally built,
and even then it is generally considered sufficient to determine
the load on the fore poppet and the value of the anti-tipping moment. The graphical methods of determining stern lift
conditions and load on ways given in Figs. 5 and 6 respectively should prove extremely useful when this additional information
is required.
The writer congratulates the Author on his ingenious
pre-sentation of this subject.
Mr. E. W. COTTON, M.B.E. (Member of Council): The idea of standardized curves for ship calculations is by no means new, and
a paper* entitled "The Standardization of Stability Curves"
was presented by Sir Wilfrid Ayre in January, 1916. Standard *Trans. N.E.C. Inst. Eng. & Shipbldrs., 1915-1916 voI. 32 p. 164.
340 SIM1'LIFIED LAUNCE1NU CALCULATIONS
diagrams are also used at the present time to obtain the curves of floodable length.
Several important particulars are accurately required for
con-sideration before the launch of a vessel takes place, namely,
pressure per sq. ft. on the ways; starting force down the ways; maximum draught aft during travel down ways; total draught
and dip forward when vessel drops off way ends; minimum
moment against tipping; maximum pressure on fore poppets; and total travel of vessel after leaving ways. Without wishing
in any way to depreciate the academic qualities and mental
agility of the Author, or the great amount of work which he and his colleagues have obviously put into compiling this paper, the
question arises as to whether the shipbuilder is prepared to accept
a launching diagram composed of particulars prepared from standardized curves and coefficients which may or may not
exactly fit the particular hull form under conideration, for such a vital operation as that of moving a vessel from her building
berth into the water. The writer is inclined to doubt if the
majority of shipbuilders would accept such a proposition.
Fig. 3 depicts buoyancy and L.C.B. coefficients based upon a
standard series of ship forms covering a wide range of hull para-meters. These are said to represent the ratio of displacement,
block coefficient and L.C.B., etc., corresponding to a given
draught aft and trim to the load displacement. It is surprising
to find that two sets of curves are necessary, one for single-screw
ships and another for twin-screw, as normally there is no radical difference in the underwater form between them, unless fully plated bossings versus bare shafts are allowed for, which is not
stated in the paper.
In addition, if one considers the relatively small volume of
displacement at the launch draught as compared with that at
the full load draught, does it not seem that a change in say the rise of floor or in underwater shape of midship section would
seriously upset the accuracy of the curves in Fig. 3
On p. 330 the Author states that increasing the camber of the ways, leaves the buoyancy for stern lift, and fore poppet load "almost unchanged." The writer would join issue with him here, because increasing the camber of the ways has always been a
method in the past of increasing the moment of buoyancy against tipping.
SIMPTJIED LAUNCHING CALCULATIONS 341 The final section of the paper deals with the transverse stab-ility of the ship during launching. Is the Author making too much of this point, and is this part of -the paper redundant Is it not a fact that in any launch if, at the moment the stern
lifted, either the port or starboard bow poppet were to collapse, the vessel would fall over sideways. The bow poppets must be sufficiently strong to withstand the whole of the lifting pressure brought to bear on them throughout the.length of travel. What is more important is the transverse stabifity of the vessel when
wholly water-borne, as witness the disaster in 1883 to the Daphne which when launched, and with some 200 men on board, capsized through lack of stability, with the consequent loss of many lives.
Prof. A. M. R0BB, D.Sc. (Member of Council): The writer is much impressed by the ingenuity and patience that have been
exercised in the making of this paper. Fig. 2, in particular,
appeals to him on the ground of both neatness and usefulness. It is, however, possible to criticize Fig. 3 on a ground indicated
by Mr. Cotton. If it is possible to derive curves of buoyancy and location of centre of buoyancy in standard form it is surely irrational to present different curves for single- and twin-screw
ships. According to the paper the draughts for the twin-screw ships are measured at the after end of the load waterline. The position of measurement for the single-screw ships is not given. But the minor differences between the curves for single- and
twin-screw ships suggest that for the single-screw ships the draughts are measured at the rudder post.
If that be so it
would appear to be rational to adopt one position of measure-ment for draught and present one set of curves for both single.
and twin-screw ships. This suggestion is based on the
assump-tion that displacement of shaft bossing is excluded from the
reckoning; the curves in Fig. 3 suggest that the displacement of bossing has been excluded. It is possible also to criticize the
statement, made on p. 318 of the paper, that even when a
tabular method is adopted a fresh calculation must be made
for each anticipated condition. In fact, from one basic calcu-lation, whether tabular or pictorial, it is easily possible to trace,
with reasonable accuracy, the effects of all likely variations.
Incidentally, when presenting the paper the Author described as archaic the pictorial method of calculationdetermiriing
dis-342 SIMPLiFIED LAUNCHING CALCULATIONS
placements and positions of centres of buoyancy by sliding a
representation of a profile down a representation of standing
ways. He may be surprised to learnas
the writer was--thatin a thoroughly reputable Clyde shipyard the archaic method
is still adopted, and the tabular calculation viewed with
dis-favour. It is possible also to agree in some measure with the
criticism of the investigation of stabifity voiced by Mr. Cotton. If a ship is supported Jy fore poppets in the common maimer
is there any need for concern about stabffitysubjectonly to one qualification? A year or two ago there appeared a photo-graph of a large ship heeled to a considerable angle when about
to leave the ways; it was obvious that the starboard poppet
had collapsed. Is it possible that a concern with stabffity should
be associated with the possibffity of an exaggerated load on one or other poppet
The foregoing criticisms are, however, of minor significance
and the writer congratulates the Author on a first-class piece of work.
Mr. W. P. WALKER (Member): The Author is to be
con-gratulated on producing a compact paper which will undoubtedly
have a wide appeal among naval architects, and will equally
undoubtedly provoke considerable discussion. This is natural in
any paper which offers a novel and labour saving method of reducing calculations hitherto regarded as unavoidably detailed
and tedious by the introduction of empiricalcoefficients.
it is suggested that the acid test of any such method is twofold,
namely: wifi it give results that are useful for comparative
analyses and will it also give results sufficiently accurate for
quantitative prediction? To the writer it seems that the answer to test one is probably yes, but that the answer to test two may be no.
One can have nothing but admiration for Fig. 2. This is most
ingenious and does enable the effect of changing any variable to be assessed by inspection. Fig. 3, however, is a little more
difficult to accept despite the Author's claim that it evolved from
a consideration of many forms covering a wide range of
para-meters, including block coefficient. Consider two simple forms,
one a box-shaped vessel with constant rectangular section and the other with a constant triangular section, and assume that
SIMPLIFIED LAUNCRING CALCULATIONS 343
these two float at a trim such that the trimmed waterline passes through the load waterline at the aft perpendicular and through
the base line at the forward perpendicular. Then the ratio of
the trimmed buoyancy to the load buoyancy in exampleone is
0'5, while in the second example it is 033.
At the same time the L.C.B. of example one is 033 of the length
from the A.P., while in example two it is 025. These differences could not be deduced from the curves in Fig. 3. It would seem,
therefore, that some parameter taking account of fineness of
form is essential particularly at the lighter draughts aft and the heavy trims. This is borne out by inspection of a comparison
between a launching calculation done in detail for a 500-ft. single-screw cargo liner of normal proportions with the calcula-tion by the Author's method. Here the displacements given by
the formula are very much in excess of those calculated in detail
for the lighter draughts aft, are still 10 per cent, in excess at the point of stern lift, and only comeinto line when the draught aft is practically equal to the designed load draught. This excess of
displacement, as calculated, leads to large discrepancies against
tipping, and finally leads to the conclusion that whereas the
formula requires some 3 ft. 9 in. of water over the way ends to prevent tipping the detailed method would point to 5 ft. 6 in. This is directly traceable to the initial error involved iii using Fig. 3 to assess displacement.
An identical calculation for a twin-screw cross-channel steamer of fine block coefficiency shows a similar discrepancy of a smaller
order, though it is still principally the displacement from the
formula that is the culprit, the calculated L.C.B. being acceptable.
The section of the paper dealing with launch stability is novel and the writer contents himself withone query. It is felt that
the force due to the upward thrust of the ways on the fore poppet should be assumed to be applied to the hull, in the area of actual contact of fore poppet and hull, that is, at some point considerably
above the point F as located in Fig. 7. This would lead to a
re-duction in FM in Table III which in turn would result in an
increase in the effective G.M. If there still existed a tendency to heel transversely during the launch the moment so calculated would be resisted by the righting arm produced by the fore poppet
load acting at half the spread between the poppets where they contact the hull.
344 SIMPLIFIED LAUNCHING CALCULATIONS
These suggestions are offered for the Author's consideration
in the belief that with very little adjustment this paper could
form a very useful addition to the naval architect's equipment for launch calculations.
Mi. J. BROWN, B.Sc. (Member of Council): The essential
feature of the paper is Fig. 3 containing the buoyancy and
moment coefficients. The preceding diagram in Fig. .2 is merely
a graphical presentation of equations (1) and (2) and many
will prefer to carry out the derivation ofthe position and attitude
of the ship in any particular instance by tabular numerical
evaluation of the terms of the equations usingHillhouse's or any equivalent procedure. Several typical examples tested out by the use of Fig. 2 suggest that inaccuracies might arise in tracing the successive steps through the diagram, although this danger
could be mitigated by a larger scale presentation for normal
drawing office use.
Fig. 3 is a different proposition, containing as it does a
general-ized method of obtaining buoyancy and L.C.B. for appropriate positions of the ship. It is rather surprising that it has been found possible to reduce the wide variety of ship forms to two plots, one for single-screw and one for twin-screw forms, and each practitioner will doubtless wish to test the charts against his own records before accepting the plot as presented, and
perhaps to replot to suit the types of vessels he normally
en-counters. The Author's own comparison with results of detailed
calculation for Qizeen Mary is only moderately good and
al-though he does not include them in the comparative curves
the values of way end pressures which he presents in Table I show quite large differences from the values obtained in the
original calculation.
The extension of the procedure to the production of Figs. 5 and 6 is an interesting exercise in thenon-dimensional method,
but as stated later in the paper,
there is surprisingly littlevariation in essential launch factors. Where such variation is of critical importance, exact calculation would be preferable to results dependent on the approximate curves of Fig. 3.
On p. 332 it is stated that theproblem of reduced stability
during launching is generally ignored. That this is true may be due to the normally ample values of the free flotation G.M. in the
SIMPLIFTED LAUNCI[ING CALCULATIONS 345 launching condition. It may be questioned whether occasions
aris frequently of the nature used by the Author in his illus-tration, in which the free flotation G.M. in one cônclition is as
low as 3 ft., leading to negative values during launching. Again,
although reference is made to launches from a single way, the
general British practice is to launch from double ways, the usual spread of which will give a two-point support with a
corresponding resistance to the transverse upsetting rnoment, if such should arise.
The Author is to be congratulated on the ingenuity displayed in devising the non-dimensional procedure, but it wifi require
some extended experience of it in practice before it can be
accepted as a substitute for the tabular calculations in cqrrent
use.
Mr. D. G. M. WATSON, B.Sc. (Associate Member): The writer
tried the method on a single-screw vessel of 470 ft. The keel declivity was in., and the declivity of chord of ways about 060 in. The graphs in Fig. 2 gave (as, of course, they must) complete agreement with the calculated figures for draught aft and trim. If, however, there is to be a gain in speed over the
ilulihouse method a larger scale for the graph is desirable.
The agreement in buoyancy and moment of buoyancy as
obtained from Fig. 3 and by the Hhihouse calculation method
were satisfactory. The percentage error for the buoyancy was about 3 percent. and for the moments about 15 per cent. The
writer cannot see any advantage in extending the coefficient method to the calculation of the weight and weight moment
curves as there is less arithmetical work in drawing these curves by
the conventional method.
The real value of the paper lies in the graphs of Fig. 3, which save a considerable amount of work in drawing Bonjean curves and calculating displacements and moments. It is felt that these curves may be used with confidence for single-screw ships of
normal form, but the writr is rather dubious about those for
twin-screw ships where bossing would be a large factor. The paper does not state whether a mean bossing is assumed in these
curves or not. Possibly it would be best to draw these curves for a bare hull, that is, excluding bossing, and calculate bossing displacement and moments separately. If this were done then
346 SIMPLIFIED LAUNCHING CALCULATIONS
the curves for single-screw and twin-screw vessels might be
combined in one diagram.
Generally in launch calculations there are two critical factors which it is desired to investigate. These are the load on the fore poppet and the minimum water at the A.E.W. to avoid tipping. In one shipyard a standard fore poppet is in use which was designed to take a load of 1,000 tons. With the declivities in use this corresponded to a launch weight of about 5,000 tons. This fore poppet has now been fitted to about a dozen diforent ships, of varying form and dimensions, by adjusting its position from the fore perpendicular and the distance between the ways. For ships whose launch weight is less than 5,000 tons a
calcula-tion of the fore poppet load is not required as the standard poppet
will be more than adequate.
From the records of many launch calculations it is known that
the minimum water to prevent tipping is about 3 ft. As between
6 and 8 ft. is usually obtained at the writer's yard they really
do not need to worry greatly about this. From these considera-tions one should be able to eliminate the necessity of making
launch calculations. However, they have also been endeavouring
to reduce the amount of wood used in make-up. To do this the
pressure at the A.E.W. is studied and related to that portion
of the ship which is passing the A.E.W. at the given time. Then the make-up which is fitted at each point is made sufficient to take the pressure that will occur at that point as it passes over the A.E.W. By this means it has been possible, with safety, to reduce the make-up considerably.
In the section of the paper on launch stability the Author
introduces a new calculation. His figures for the effective G.M. during launching are striking when compared with the as-launched values. It would be interesting to know whether any of the
instances of capsizing at launch could be attributed to this cause,
or whether they were due to a lack of stability in the ship which persisted into the as-launched condition.
Mr. J. S. SaD, B.Sc. (Student): As pointed out by a previous
contributor, in Fig. 7 the load from the fore poppet would appear to be acting at the base of the fore poppet whereas it should act in the region of contact between poppet and hull,
SIMPLIFIED LAUNCHING CALCULATIONS 347
The stability çoefficients shown in Fig. 8 are independent of
block coefficient, and a fact so surprising is worth investigation.
In testing the accuracy of the derived KM it will be sufficient
to check BM values only, since KB is normally by far the smaller component. Spots on the chart were checked by normal calculat-ion for three ships, keeping the ratio of trim to load draught
con-stant at 1 and varying the ratio of draught aft to load draught. For block coefficient of 0'5i5 the error in BM varied from 10
per cent. at dA/d=O'8 to 7 per cent. at dA/d=l2 per cent.
For block coefficient of 0'6l the error varied from 3 per cent.
at dA/dr=O'8 to 14'7 per cent, at dA/d=l'2 per cent. For
block coefficient of O'74 the error varied from 2 7 per cent. at dAJd=OE8 to 135 at dA/d=F2 per cent.
The main point about the results was that there was one distinct curve for each ship, although the two higher values
of block coefficient gave curves very close to each other. In
fairness to the Author it must be said that the greater errors
occur at values of dA/d not normally encountered but, never-theless, within the range of the given chart.
In conclusion, the speed with which the calculation can be
performed using the simplified method makes it a valuable
guide as to whether a full investigation of stabifity is required for any particular launch, and the Author is to be congratulated on a most interesting and useful paper.
Mr. I. C. BRIDGE, RSe. (Member) In the first part of his
most interesting paper the Author succeeds in reducing the pro-blem of predicting launching behaviour to such a simple and straightforward process that one is inevitably surprised that the normal calculation methods have persisted for so long. The
derivation and preparation of the line chart in Fig. 2 has called for considerable ingenuity and a great deal of work and within the limits of working accuracy it is, of course, exact.
Unfortunately the same cannot be said to hold good for
Fig. 3, which is an approximation. From severa i comparisons
with calculated results it appears that while the L.C.B.
co-efficient ß accurately defines the position of the centre of
buoyancy, the buoyancy coefficient gives results varying by
about ± 10 per cent. from the actual values. This same
348 SIMPLIFIED LAUNCRING CALCULATIONS
Queen Mary. In other words, the shape of the curve of
im-mersed areas is correctly interpreted but not the actual area.
It is suggested that a fullness coefficient or parameter would
have to be inìcluded to achieve the necessary degree of
ac-curacy.
As it stands, the method is very valuable for preliminary
discussions on layout of berth, launch position, etc., as indicated
in the second part of the paper. A detailed checkon the final
figures would, however, still be necessary; particularly if the anti-tipping moment was at all critical.
With regard to stability during the launch, the Author has made the assumption that the way reaction can be treated as
a single force on the centre line and gives a method for estimating
the resulting G.M. With twin poppets, instability can only arise if one poppet partially collapses, in which event an up-setting moment results from an unbalanced force applied to the
ship at the top of the intact poppet. Heel is then inevitable
but, provided that the hydrostatic stability at that moment is positive, equilibrium should be re-established at a small
angle.
Fig. 8 is based on the standard approximation to KM as the sum of functions of draught and beam/draught but again both functions should vary with fullness, in particular the vertical prismatic coefficient of the immersed form.
In conclusion, it
is hoped that the Author will consider
modifying Fig. 3 to include a fullness parameter and thus very considerably increase the value of the paper.
Prof. A. AUsTIN, R.C.N.C.: This paper is of considerable
in-terest in providing a clear analysis of the effect of various factors
on a launch and it will probably be of practical use to those
responsible for the launch calculations of a number of similar
ships. The choice of the Queen Mary as an example is perhaps
unfortunate since the cost of such a vessel justifies detailed
calculations while there must be some doubt as to the applica-bility of the method in such an instance.
There is one point whic}ì the writer would question and that is the use of the approximate stability calculation. The method proposed is to approximate to the position of the C.B. and to
SIMPLIFIED LAUNCHING CALCULATIONS 349
it would appear that the ordinary hydrostatic curves can provide the answer quite as easily and accurately.
Mr. P. II. TANNER: The simplified launching calculation
method put forward in the paper was developed as a result of a query by the late Mr. E. W. Russell as to the stabifity during launching of a ship about which he was unhappy on this point. It became evident that, in order to be able to arrive at a reason-able estimate of stability during launching without undue work,
a set of standard curves for this quantity was essential; from there it was only a short step to the development of a set of
standard coefficients from which all the static launching curves could be derived.
The work of trying to arrive at such a set of coefficients was delegated to the writer by the Author, while he busied himself
with the development of diagrams leading to Fig. 2, which is the
best part of the paper. At the time of the Author's departure south, a considerable part of the writer's job had been done, and
he was beginning to discern some traces of the wood between the trees. It is presumed that it is largely to this work of the writer's
that the Author refers in his acknowledgments.
Early on in the writer's work along these lines, he plotted a
set of displacement coefficients, which differed only by a constant
from the Author's a coefficients in Fig. 3, for 4 ships of varying
block coefficient. He found it impossible to reconcile these coefficients into a coherent set of curves, and the main part of his work was therefore directed towards trying to obtain a reasonable
diagram in which the effect of block coefficient was taken into account. The writer is somewhat disappointed that the. Author should have gone back to the earlier and most inadequate plot, in which no account was taken of fullness. He has tried out
these a coefficients on two ships for which he had data readily available and found the displacements to be in error by amounts ranging from 5 per cent. at the deeper draughts to 80 per cent.
at the lower dA/d values. Had he known that this was the standard
of accuracy expected of his curves, the writer could have saved
himself a great deal of what now appears to have been
un-necessary labour.
For the ß coefficients, the writer has nothing but admiration. He himself was completely bogged down trying to arrive at a
350 SIMPLIFIED LAUNCmNG CALCULATIONS
satisfactory plot for the centre of buoyancy, and he must confess
to a considerable degree of mortification at the closeness with which these simple coefficients apply to the forms on which he
has tried them.
Turning to the section dealing with launch stability, a point
arises in Fig. 7 to which the writer believes attention has already been called. The force R in this diagram should be shown acting
on the ship in the region of contact between the fore poppet and
the hull, and not at the point F as shown. The writer can absOlve
the Author of all blame in this connection. At the time of the preliminary submission of the paper, the Author was away on holiday, and the writer was entrusted with the preparation and dispatch of the sample diagrams that accompanied it. One of
these diagrams was the forerunner of Fig. 7, and it bears the
same error, which must have been copied unnoticed onto the final
version. The writer apologizes most humbly to the Author for having led him astray here. As far as the rest of this section is concerned, the writer is inclined to think that the coefficients
suffer from the same trouble as the values. He has not had the opportunity, however, to check them.
To conclude, the Author must be congratulated on a very
interesting paper. It is a pity, however, that its utffity should have been so badly marred by the inadequacy of his displace. ment coefficients, which has the effect of rendering the method useless for estimating the margin against tipping, and the way end pressures, while the results obtained for the stern lift
con-dition should be treated with care.
Mr. A KILUN; The Author is to be congratulated on an
extremely concise paper, and especially on Fig. 2, which should save a great deal of tedious arithmetic. The writer, however, disagrees with his statement that block coefficient hasP little or no effect on the values of in Fig. 5. As stated by him, these values apply to the ship in extreme conditions of draught and
trim, but that, it is felt, hardly justifies the complete iieglect
of C as a vital factor in the estimation of buoyancy. After all, any difference in 0B is usually obtained by adding or removing displacement towards the ends and low down, thus giving an
exaggerated effect in the area of launch buoyancy.
SIMPLIFIED LAUNCHING CALCtJLATIONS 351 of launch calcu1aions for ships whose C varied from 0-65 to o-75. In the extreme cases, the corrections required to the buoy ancy obtained from the Author's oc values, ranged from abzut
15 per cent. for the 0-65 form to+5 per cent, for the O-75
form. tTnfortunately, the writer had not sufficient data to do more than this, but from what he did have it appeared that there may be a possibility of obtaining a straight or nearly straight
line graph of percentage correction on a base of block coefficient for varying values of dA /d. Naturally, the corrections decrease
as the dA/cl value increases to a point where the immersed volume more nearly corresponds to a working displacement for the ship.
It is hoped that someone with more launch data than the writer
will be able to develop this idea further.
Mr. J.-E. J&NssoN, S.M.: The Author is to be congratulated
on his new and ingenious approach to the launching calculations.
The launching attitude diagram wifi certainly save much time when using cambered ways and the "standard series " diagrams
for buoyancy, L.C.B. and stability coefficients will in most
instances make it possible to avoid time-consuming work. The calculation carried through for the Queen Mary gives sorne
indication of the accuracy of the method proposed. The relative accuracy seems to be around 10 per cent, for buoyancies and
moments, but when a difference is considered as for the moment
against tipping the accuracy is only about 40 per cent. The Queen Mary is, of course, not at all representative of the average
merchant ship, and the accuracy of the method applied to more normal ships may therefore be better. It would be interesting if the Author could give some information on the accuracy of the method using Fig. 3, and of the stability using Fig. 8.
In Fig. 3 separate diagrams are shown for single-screw and
twin-screw forms. These indicate that the fullness of the ship
is of great importance. it is, therefore, surprising that the block
coefficient is not considered. Could accuracy be gained if the block coefficient were entered as a separate correction or if tbe
present classification of ship forms were replaced by one diagram
considering, in. addition to the present parameters, the block
coefficient or the block coefficient and the L.C.B. at road draught'?
The writer has carried out some investigations in connection
352 SIMÌ'L[F[ED LAUNCHING CALCULATIONS
the Author. He would add, however, that n increasing block
coefficient has the same general effect as an increasing declivity
of the ways.
Defining the virtual position M', of the metacentre instead of
a virtual position of the centre of gravity may visualize the stability at the pivoting point or later. By making additions to Fig. 7a (drawiiig a parallel to the water line through F), as shown in Fig. , equation (15) can be written thus:
M0=V. F1M sin eW.F'G sin O M0/W sin O=V. F1M/WF'G
Conditions of equilibrium give V/W=F'F/F1F
M0/W sin O=F1M. F'F/F1FF'G
==F'M'F'G'=M'G
and M9=W. M'G sin O.
w Fig. 9.
If the centre of gravity, G, is below the straight line from the metacentre, M, to the fore poppet, F, there is positive stability in the case of a single way or crushed double ways. Because of
dynamic considerations it is probably safe to allow the centre of
gravity to be somewhat above the line for a short moment.
A disadvantage of this method compared with the method given in the paper is that it makes comparison with the free floating
condition more difficult.
The calculation method of Fig. 8 can, of course, be applied
even in the case of "the virtual metacentre."
All the methods proposed by the Author apply, as launching
calculations in general, to an infinitely slow launch. Actually the conditions are not statical but dynamical. It is generally believed
that pivoting starts later than calculated, (lue to inertia effects,
but observations are on record where wave formations have caused s
