CRS - Diagrams for design calculations of the stability of ships

Ocean Engng. \'oI. 6, pp. 58 1-592.

Pergamon Press Ltd. 1979. Printed in Great Britain

C'Rs-DIAGRAMS FOR DESIGN CALCULATIONS OF

_THE

STABILITY OF SHIPS

H. E. GULDHAMMER

Department of Ocean Engineering, The Technical University of Denmark, Lyngby, Denmark AbstractThis paper describes the development of a fast diagrammatic method to determine the geometric part of a ship's stability lever, the MS. Additionally, diagrams are given of the contribution to the stability of erections: deck houses and superstructures. The methods are intended for use in the design work.

LIST OF SYMBOLS

Li,,, _{Length for calculation. Length between perpendiculars, but defined here as 0.97 length of waterline.}

For the merchant ship area the definition in the International Convention on Load Lines may be

used.

The stability lever is independent of L, but the definition influences the size of 6 and a.

L- Length atLWL

B Breadth moulded atLWL

D Depth moulded, from BL to lowest point of calculation deck at side

D1 Depth corrected for sheer.D1 = D ± (S + Si.)

D11 _{Depth corrected for sheer and erections.D11 = D1± + D'8}

Definition of L

LD _{Basis correction for deck-houses. D =}

L8Bcz D'H Correction for deckhouses at heel _{.-D'ff =}

h8!8 _{± h}

iD8 Basis correction for superstructures. D8

-aD'8 Correction for superstructures at heel p. _{D'8 = k3fD} EV Total volume of deck-houses considered

h, I, Height and length of poop _{iTo be measured} ;it hin

h,, F,, Height and length of forecastle Jperpendiculars only

kH Correction factor for deck-houses. From Fig. 3

k8 Correction factor for superstructures. From Fig. 4

BL _{Moulded Baseline. Defined in the figures}

PP 1/2 Lpp:O.97 _1WL L wL 581 LWL Calculation WI Definition of BL. Tk.T 0gB CL IWL Midship section K

-582 _{H. E. GULDHAMMER}

T Draft to BL of calculation waterline

T Draft to BL of LWL

T15 Draft for calculating coefficients D, 1.5 LWL Design load waterline

5A Sheer aft lat side S, Sheer forward fat side

Note The term "moulded" will be piain only in the case of steel ships. For wooden ships the

above definitions should all be to outside of planking. y Displacement volume

& Block coefficient

LB-T

&g Block coefficient at T = T (at LWL) ö Block coefficient at T = T15 _DJl.S

'i Waterplane coefficient at T = Tif; a

_-

_{(at LWL)}

U _{"Waterplane" coefficient of calculation deck} (3 Midship section coefficient

= B7'

(3 Midship section coefficient at T = T (Lft'L) (3 Midship section coefficient at T = T15 = D1/l.5

Note The (3 is defined here by means of midship section area, and not by largest secdonal area.

T/B Draft-breadth ratio

D11,8 Depth-breadth ratio j Main parameters in the diagrams

Angle of heel GM Metacentric height BM Metacentric radius GZ Stability lever )

MS Residury stability lever 1GZ = Gi1sin + MS

C33 Residuary stability coefficient

CR3 = i'.'ÍS/BM = C,' ± m [(3, _{-- 0.75) - b (I - (3) (8 - 0.50)]} C'38 Value of C33 for standard conditions. From diagrams Fig.₆

ni _{Correcting factor for deviation of 3 from standard. From diagram Fig. 7} b _{Correcting factor for deviation of b from standard. Printed in calculation fonn.}

INTRODUCTION

STABILITY of ships is as important _{as ever. In spite of recent research involviug modern} theories for ship movements, the f'act remains that classical stability ideas still exist and that the results of any such research has to refer to the classical idea of GM and the stability curve.

In spite of the fact that the calculation _{necessary to determine these parameters will be} no problem today thanks to modern computer techniques, there will _{still be a need for} rapid diagrammatic methods for use in the design stage of a ship. Some of these methods

viJl be mentioned below, one of which will be the main theme of this article. THE "47-METHOD"

In 1947 Professor C. W. Prohaska published a paper, "Residuary Stability". Here the stability lever GZ was proposed divided as follows:

GZ = MS + GM. sin

p

as illustrated in Fig. I.

The advantage of this is that GZ is split into a purely geometric part MS, and a part containing the familiar stability parameter GA'!. The _{stability data of a ship could now be}

1. here Il! so io j.c. bi

I'

Tech: a met.

ii

After only s. Tu metho

-

-.

pres leve kno dete1 seve coe i by 'J

Fio. 1. Definition of the MS.

presented in a very practical way, making possible a direct reading of the size of the stability lever at any angle of heel, if only the displacement and the metacentric height GM were known, see Fig. 2.

However, the major part of the paper from 1947 described an approximate method to determine MS. The method was based on a large number of stability calculations from several shipyards and from different countries. The results were presented as diagrams of a

coefficient on the "residuary stability lever" MS.

The "residuary stability coefficient" CRS is defined as the MS made non-dimensional by division by BM, the metacentric radius, thus:

MS

BM

The only parameters besides the heel p are the draft ratio T/B and the depth ratio D1/B here depth corrected for sheer thus:

D1 = D ±

SA 4-SF

6

In spite of the very simple construction this diagram gave relatively excellent results so long as the ships examined were ordinary merchant ship types having not too fine lines, i.e. block coefficient ought to be larger than say 0.65.

At the Shipbuilding Department (now Department of Ocean Engineering) of the

Technical University of Denmark, responsible for the 47-method, work on development of a method to cover finer shipforms was attempted using systematically varied forms.

The work appeared, however, much more difficult than expected and was suspended. After the introduction of electronic computation, the research was revived to include not only simplified forms but a new systematical series of "real ship forms".

STABILITY DIAGRAMS FOR FINER SHIP FORMS

This work resulted in a new approximate method, the "61-method", or

method", or more precisely the coordinate-method. The method was published in

I

583

o + 1.0 MS [m] 0,5 0 -0.5 -1,0 -1,5 -2,0 -2,5 10° 20' 30° 40° 50° 60° 700 800 P900

FIG.2. _{Stabiflty-diagram for ship's use.}

o Q5 *q5 GM. sin '.p (m] * 1,0 .1,5 +2,0 2,5

Prohaska (1961). The method allows_{a much safer determination of the MS for finer ships} However, this improved accuracy has to be paid for by a substantial enlargement of the work involved.

The 47-method allows the determination of a complete stability curve in only a few minutes. The 61-method will, even if enlarged to last a few hours, still give a relatively fast determination.

STABILITY DIAGRAMS FOR FISHING SHIP _FORMS

Since the investigations described, work _{on stability problçms has continued constantly} in the department. In 1972 results were published from work based on an extension at the 61-method intended to cover the fishing vessel area (Guldhammer et al., 1972).

However, the attraction of the ultra-fast 47-method still persisted and this paper con-tains the results of research on an extension of this method too.

The work was based on results from practical stability calculations, as was the original 47-method, but now based on fishing vessels. Only calculations carried out on electronic computer were employed. The material involved consisted of_{commercial calculations and} the spread in ship size and type was considerable.

The variation included size and type of erections too. The initial work, therefore, largely consisted in "cleaning" the material influencing these erections. The investigations princi-pally involved the development of a method to divide the actual MS-value in two parts, the

one from the hull proper, and the other from the erections. Based_{on these "cleaned"}

stability data a new version of the 47-diagram was constructed, covering the fishing boat area.

THE FINAL VERSION OF THE c3-DIAGRAM

In 1974-75 a revision was made adding a lot of new material. The material now

corn-w h ve 47 re a wi of 13 the by wh Cor eq u also asto reali I Furt H GZrM5#GM.sinço I

L4j!!!!

H k ., ,

--'J N , ___u

'

I -'

kIil

' 584 _{H. E. GULDHAMMER}

4L..-;;

:

C',-diagrams for design calculations of the stability of ships ₅₈₅ prises a total of 8 flush deck vessels, 13 vessels having poop and/or forecastle, and 35 vessels with deck houses. Additionally there are 14 ships with poop/forecastle as well as deck houses.

Naturally, to get the accuracy required, it proved _{necessary to deviate from the original} very simple version. Some dependency ori fineness had to he employed, and the dependency

was on both S and 3.

-This double-dependency has given difficulty_{ever since the first attempts to expand the} 47-method. Here the problem was solved by giving _{a simple set of C$-diagrams} cor-responding to standardized values of S and f3, combined with another set of diagrams giving a correction factor in allowing for the variation with f3. Very fortunately the variation with S could without appreciable error be rated proportional _{to the mforany constant angle} of heel. However, the influence of S has to be diminished with increasing _{f3, being zero at}

f3 = I as will be seen in the formula below.

The standardized values chosen are:

S = 0.50 and f = 0.75,

these being near the average values for the examined material. The_{CRS now is determined} by the equation:

C'RS = C'RS + in {(f3 - 0.75)

- b (I - f3) (S - 0.50)},

where C'RS is the value from Fig. 5, ¡n is the correction coefficient_for

f3 from Fig. 6. The corresponding coefficient for the variation with S is

-

_{in.b.(1 - f3), thus giving the above} equation. The values of b are fixed for every p and are stated on the in-diagrams, but will also be found printed in the calculation form.

THE RANGE OF THE NEW Ç,DIAGRAM

As the new method was developed from results in the fishing boat area, it was quite astonishing to find that in spite of the very big extrapolations required the method still gave realistic results for merchant ships.

In fact, comparison with values froin the 47-diagram _{gave only small differences.}

Further control analysis with forms from Prohaska (1961) disclosed that with only a few 2

o

02 03 04 05

_{VB 06}

Ftc. 3. Correction factor k for deck-houses.

r

586 2 k5 H. E. GULïHAMMEI o 02

Fio. 4. Correction factor k3 for superstructures.

corrections the new diagram would give even better results than the 47-diagram, which has to cover a large area without any dependency on the form coefficients.

The new C-diagram with fineness corrections thus seems to be able to replace ail

other approximative methods including the 47- and 61-methods. CORRECTIONS FOR ERECTIONS

The development of the corrections for erections was to a large degree based on the analysis of calculations for ships with deck houses as these ships formed the largest group. The relatively small number of flush deck vessels were used afterwards as a control.

Analogous with the correction for sheer is the correction for erections applied as an addition to the depth D. The following definition is used:

D11

=

D1 +

± ¿Ds.

Here D11 is the depth to he used as parameter in the C-diagram. D1 is the depth

corrected for sheer (D1

=

D ± (Sf1 + SF)!6).

The D11 and ¿D are corrections for deck-houses and superstructures (poop and

fore-castle), respectively. These corrections are defined as IDH

=

k11. ¿0D11 and D

=

k. ¿ODH, where 0D,1 and 0D are basis-corrections and the k11 and k are factors which are functions of the heel as well as draft, and are presented as diagrams in Figs. 3 and 4.

The basis-correction for deck-houses is

EV

=

. B _.

This definition corresponds to the increase in depth caused by distributing the volume of the deck-house over the whole deck area. The E, is the total volume of the deck-houses etc. considered, and D is the "waterpia!e" coefficient of the calculation deck (upper deck). This D may seem a little inconvenient; it is not generally known beforehand but is very easy to determine on a design, where the upper deck plan is always drawn and the area may be measured. 03 04 05 _T/B 06 (l I th al C t

---HH---I ______ I 7

-60° C I t1 in

e

y y

L

C',-diagrarns for csign calculations of the stability of ships 587 The basis-correction for superstructures is

¡ ¡f

I0D = h,, _-

H-- Here h,, and and Iij and !.- are height and length of the poop and forecastle,

respec-tively. The lengths are measured within the perpendiculars only.

The absence in this case of 0 is purely empirical. No gain in _{accuracy was obtained by} including such a coefficient.

Only poop and forecastle are presented in the above formulation. The material examined did not contain ships with a midship superstructure, but if such a superstructure should be present it must naturally be included. The weighting of such a superstructure relative te a poop forecastle is a little doubtful, however.

It may be surprising that the correction factors _{may exceed 1. But the effect of an}

erection will, at large angles, be greater than of the same volume distributed over the whole deck, thanks to the height of the erection.

REMARKS ON THE CALCULATION

The calculation form Fig. 7 may be used at the calculations. A sample calculation

;

shown (Fig. 8). The resulting MS-curves are shown in Fig. 9. The corresponding computer calculated curves are plotted for comparison.

The block coefficient and midship section coefficient _{to be used in the calculations will} in principle be those at the design load draft TK, andnotat the actual draft.

This may however introduce calculation errors in cases where Dl'TK is substantially different from 1.5 which is the standard value of the method. In such cases the values of 6 and _{at a draft corresponding to DI/T = 1.5 ought to be used, even if only roughly} calculated or estimated values may be obtained.

The definition of the main dimensions will seldom be essential for merchant ships. Troubles and quite unnecessary errors may arise with fishing boat forms however if the designer does not use main dimensions in accordance with the definitions demanded by the method.

Length is not a parameter in the stability calculation directly, but the definition has influence on the size of 6. The depth and draft are moulded dimensions but here too the definition of the base line must be correct in relation _{to the method.}

The symbol list explains the definitions to be used in the method. THE PROBLEM OF FORM-TYPE

The diagrams, the new as well as the old 47- or 61-diagrams are valid for "Normal-form" ships, le. those having neither distinct U- nor V-shaped sections. The problem of how to define this normal form-type is beyond the scope of this article.

However, the form-type will influence the ship's stability and, according to Prohaska (1961), the CRS should be changed by ± 0.04 sin q, plus for U-forms and minus for V-forms. The U- and V-forms should be "moderate" and therefore the correction must be larger if

the abnormality is extreme. The correction is valid for medium-full ship forms (i.e.

0.60 <6 <0.65). For 6

0.50 and S 0.75 the correction must be expected to reduce to almost zero.

588 0,5 0.7 0.5 0,5 0,4 02 03 04 T/ 05 0,2 0,3 04 T'5 0,5 0,8 0,7 0,5 0,4 I-l. E. GULDHAMMER 02 03 04 T/ qs FIG. Sa. 02 03 04 0.5 02 03 04 às 0,2 0,3 Q4 0,5 02 03 04 1/9 05 FIG. Sb. 02 0,8 0,7 0,5 0,5 0,4 0,6 0,5 0,4 02 03 0,4 T/ 05 0,2 03 04 V C4

Fio 5. (a) and (b). C,-diagrams, giving the value C,, for the coefficient at the standard

conditions S = 0.50 and f3 = 0.75. 02 o., .LL

I/Jl

_'6 -'r

45

1p5

r:,.

I I

---15

---:1h--t:o:;

-H

-I I I

,

30

--L

i-1

Is

I1111

- -oA

75

02 ca 0,8 47 0,7 0,5 0,6 CM-0,5 01. 0,4 02 0.3 0,4 0.5 0,3 04 05 02 0.3 06 0.5 C8 0,7 05 45 94 0,8 01/9 0,7 0,8 01v 0,7 C's 0,5 0,4 0,8 0.7 0,5 0,4

005 m b=:o.8

5o

0,7 0,6 0,5 O4 04 _YB 95 93 0/. 0,5

C,,-diagranis for design calculations of the stability of ships

0,7 0,6 0,5 0,4 o 92 03 04 05 0,0 0,7 0,5 0,5 03 04 TÍ 0,5 FIG.6a. 03 04 T/ 95 Fico. 6b.

FIG. 6. (a) and (b) _{en-diagrams, giving the value of the midship section correction coefficiext m.} The values of the fullness correction coefficient b_{are stated in the diagrams too. The coefficients}

m and b to be used by ships differing from standard values 6_{= 0.50 and 3 = 0.75.}

Ò'8 'VB 0,7 0,6 0,5 0,4 02 03 04 _Vs 5 0,2 03 04 _1/s 0.5 589 0,7

L

iì

rbrl.2 'I 52

450

b=,6

r'

'lAI

_I

6°

n"

I 'i

i

i

._I-

_m-I---I I

A

'ir'

b4,O

«1IUU

J1iuI

-b--r,

I

b,OO 03 01. 05 03 O' 0.5 02 02 03 04 05 02 03 03 01. o 0,2 03 04 05 0.5 0,7 0,6 0,5 0,4

590 H. E. GULuHAMMER

FIG. 7. Calculation form.

T r*

i Lpp a Ti Sh9

2 B a

OD

:

m li

3,

lype Erections Date. Sigt

G

ØJSA IX a

rn (i2a

rn _{r&18D,/BaZ)Oa}

.Tç:O/5:

_rn 6 SF a 14 I a _{m 5:} a. D, a D+(SA+ SF)/a.i5 m h9 a m

O I

: m

(1 -x-q5):

8 DI/Tx: 17 h1: _ml p d.gr. T ra T/g .i kH Dçr. Fr;.3 i k5 CaQr. Fig.4 D1VB CR5 Oiagr. Fi.5

b m

Dic;r. Ci.5 CR5 ? Correct _MS rit BM: T1

-- m

-Ui

mi

45________

-

.

---__

_Ululi

60

-

--75

_- -

_4,O

----

_-

-

---g o -

-_-

--

_{lo_}

--___

-

-...

-i

J

It C

t

-c lt .0 o o o o C

t

o Ui o

--t'

for design calculations of the stability of ships

Fic. 8. Sample calculation.

591

r

Lpp _{2Z,am 0,387} $ttip

V

V

ifljB

,7m (1Ofaa ,7oZ

rOit

L - i n - /1 i .'o lype

Cii.'/er ErectionsFoc'/e Deck/to'je

w4ta. Date. Si. 7. 1975

1J

OJSA T a 2 f4' m 0,°//.7

û3Çm 13 'EVa _{Zf2 15) °:/9'LL'T}

_{0,529 2IT"/: 2,3ro m}

a _{0,8/ 14LL}

-

_m -0,072 (22& o Ço () D1 a D.(SA. SF)/5a 15 h0 a

-

_{m '23 1350} 0, fo 3,P/m iSt1 a SQm / [OJ°'/T I,o55

tJj

17h1:

2,fm

0073 _'25-O,75: 4070 (2 3 3 ₉ t degr. T re kH k5 ® Dti/ _CR5 a.®_ .ia5r. b rn iCgr. CR5 Correct- MS 15° ô,2;BM:2Tj9 n, /,ç.co O O o,62 _0,05 .-,o/ -3oo

:___

o,io _c. Q8

-_-

-''

O 21 O O D 19 o 01/ ₅₁₃ 1,2

o 3g - o

-L

o,44'gf

''

O Dog c'Ç6f ' _{li --0 13} -02o

____

--

--

-

V

-

-

V !,3 03g 002 -, _{, 47}

_4/Ç

!

Do/f' DD3 0,Ç. .

-

_{_____} - _¿'o.c

-V

li4111

v c,o.3 03-021 437 119 DO 1,/ _..

_{7o/ °37}

₀₂₂ L

9O0_

----

₁₀

-_--

_:.

-liT.

o MS [m] - 0,5

10

o 15 30 45 60

75.p90°

FIG. 9. Comparison between values of MS from Fig. 8 and computer calculated values. A corresponding influence on the stability exists with variations in the ship waterlines: the extra change in CRS will be about 0.015 sin cp, the plus and minus signs being valid for waterlines hollow or full at the ends respectively. The area of coverage must be expected to be the same as stated above, but only the shape of the design waterline is to be considered.

CONCLUSION

Use of the new C5-diagrams will not be quite so fast as the original 47-diagram due to the dependency on f3 and 6, which is unavoidable. The corrections for erections will naturally also complicate the calculations but this will exist no matter what method is used. These complications vill however be insignificant. This new method really makes it possible to determine the stability curves of all ordinary ship designs very quickly, and with a reasonably high accuracy. The accuracy is in most cases better than necessary in relation to the rather inaccurate determination of the meracentric height.

The principal question of whether the erections should be included in the calculations or not, has not been treated in this paper.

AcknowledgementsThe work presented here represents the collected efforts of several people during

several years.

The work at the Shipbuilding Deptrtment (now Department of Ocean Engineering) for the MSc. thesis of Mr. A. Agustsson and later of Mr. S. G. Ringsted has resulted in the method of allowing for erections, and produced encugh material to allow construction of the new cRdiagran,..

REFERENCES

GULDHAMMER, H. E., AGUSTSSON, A. and RAGNARSON, E. 1972. Fiskefartojers Reststabilitet (in Danish

with English Summary). Tcch. Univ. of Denmark.

PROHASKA, C. W. 1947. Residuary stability. Trans. 1z.stn nay. Arc/i. 89, 342-375.

PROI-IASKA, C. W. 1961.Results of some systematic stability calculations. Trans. Insin Engrs Shipbldrs Scotl.

104, 211-253. n d/ m

s

so dS X k, k h

ME

Abs con to i regt co arb pot con tim det'. of t exa bar, con test for Wa spe

.1

'S 4

i,Computer

Diagram .. -r Compute-r t Diagram -S S- -S

592 H. E. GULDUAMMER _{Ocean Eng,}