日本財団図書館（電子図書館）　第１８回ＩＳＯ／ＴＣ１８スモールクラフト専門委員会及び同時開催作業委員会ビクトリア会議報告書

添付資料17

SIMPLIFYING THE P_b1/P_b2EQUATIONS

VERSION 1,0 - FOR DISCUSSION BY WG18

NOTE - All formulae are subject to further checking and verification IF approved by WG

PREAMBLE

In Baltimore, WG18 elected to move to a simplified form of load algorithm. This paper describes what is believed to be the simplest possible form for pressure, which still maintains very similar values to that given by the ISO draft, Pre-Baltimore.

TEXT FOR SIMPLIFIED FORM

P_b1 = 0,1 Δ / L_WLB_c (1 + n_cg) k_pr k_L　(1)

Where; n_cg = 0,45 f_w k_β(V/√L_WL)　(2)

f_w = 1,00 (A), 0,95 (B), 0,75 (C), 0,55 (D)

k_β = 0,80 for deep-sea craft (deadrise at midships 18 degrees +), 1 ,0 for other craft
V/√L_WL may not be taken as less than 2,36 and need not be taken greater than 18.

k_pr = pressure reduction factor

PRESSURE REDUCTION FACTOR (kpr)
Component	Low-speed craft V/√L < 3,0	High-speed craft V/√L > 3,0
Plating, where b is the shortest unsupported span	1,14 - 0,0019 b / LWL ^0,4	8,2 L ^0,36 b ^0.6
Secondary stiffeners which support plating (i.e. stringers, deck beams, transverse frames)	0,8 . k_pr (Plating)	0,8 . k_pr (Plating)
Primary frames which support secondary stiffeners (i.e. girders, deep transverse frames, floors)	0,5 . k_pr (Plating)	0,5 . k_pr (Plating)

Limiting values of k_pr

k_pr (max) = 1,0

k_pr (min) = 0,25 when used for flexural strength and stiffness applications, or 0,4 when used in shear strength applications for cored panels

If accepted, the following sections/figures become redundant:

・n_cg equation (2)

・1,39 + 0,2.56 V/√L_WL equation (3)

・Table (3) {new service condition}

・Figure 3 { Measurement of deadrise angle}

・k_ar equation (6)

・Figure (5) - area-reduction factor

・P_b2 equation

THE APPENDICES PROVIDE JUSTIFICATION FOR THE REVISED 'BLUE' TEXT

APPENDIX A

A simplified n_cg = linear function of V/√L_WL

There is a body of evidence that says n_cg Varies as Vⁿ where n is less than 2.

VTT

From Figure 2.3 of the VTT 1997 report, P_base varies as Vⁿ where n averages out at about 1,0.

DnV

The DnV 1993 HSLC rules adopt a design vertical acceleration of;

n_cg = V/√L 3,2/L^0,76 fo

fo = 1 for a yacht (all service area restrictions)

So for a 12m Length yacht, n_cg = 0.48 V/√L

(Note, the formula is unlikely to apply to very small craft)

UNITAS

The UNITAS HSC rules (1995) use a design acceleration of;

n_cg = S V/√L

where S depends on type of service and sea area.

Table C3.3.1

Type of Service

Open sea ¹⁾

Restricted open sea

Moderate environment

Smooth sea

Passenger Ferry Cargo

0,65 CF ²⁾

0,20

0,15

0,09

Supply

CF ²⁾

0,30

0,23

0,14

Pilot

1,33 ・ CF ²⁾

0,40

0,30

Not applicable

Rescue

1,67 ・ CF ²⁾

0,50

Not applicable

Notes:

¹⁾	For this condition, S is defined for each separate case, at the discretion of the Society, depending on the actual service area
²⁾	For passenger, ferry and cargo craft, their seaworthiness in this condition is to be ascertained. In general, S should not be lower than the values given in this Table. where.

The sea areas coincide almost exactly with ISO Design Categories

.3 The sea areas referred in Table C3.3.1 are defined with reference to significant wave blights H_s which are exceeded for an average of not more than 10 percent of the year:

－	Open-sea service:	H_S ≥ 4,0 m;
－	Restricted open sea service:	2,5 m ≤ H_S< 4,0 m;
－	Moderate environment service:	0,5 m < H_S< 2,5 m;
－	Smooth sea service:	H_S≤ 0,5 m.

This means it is easy to find f_w values by dividing the UNITAS factor for a given sea area by the open sea factor for each vessel type. Averaging these out we get,

f_w (D) = 0,44, f_w (C) = 0,71, f_w (B) = 0,94, f_w (A) = 1,0.

These may be compared with the ISO values;

f_w (D) = 0,5, f_w (C) = 0,75, f_w (B) = 0,95, f_w (A) = 1,0.

This is rather encouraging.

Equation (3) of the ISO standard:

n_cg = 1,39 + 0,256 V/√L

This dominates for highest speed-length ratio.

Revised n_cg formula v ISO Eqn (3)

When averaged over the V/√L range 3,0 to 18,0, it is possible to write n_cg = 0,45 V√L Which is in line with DnV (0,48) and UNITAS (0,53 - rescue craft category A).

Reduce by 20% for deep-sea craft.

n_cg = 0,45f_w k_β(V/√L_WL)

V√L_WL Values required to trip new limits in Table 3 (category A).

n_cg = 1,5 means V/√L_WL = 3,3, n_cg = 2.0 means V/√L_WL = 4,4

n_cg = 3,0 means V/√L_WL = 6,7, n_cg = 4,5 means V/√L_WL = 10

n_cg = 6,0 means V/√L_WL = 13,3

So fast recreational sailing yacht will just fail to trip the sail limits of Table 3.

APPENDIX B

Justification for removal of P_b2 equation

Paul Handley has long argued that the Pb1 equation used with ncg = 1,0, gives very similar values to Pb2.

Taking V/√L_WL = 2,36, the revised ncg equation gives 0,45 . 1,0 . 2,36 = 1,062.

This has been checked out for a 'standard' sailing yacht of T_c = L_WL/18 and L_WL/B_WL = 2,3 + L_WL/10, Block coefficient = 0,40. The comparison is very good with the pre-Jour equation and pretty good with the ABS equation.

This is correct for category A.

There will be greater differences for category B (negligible) and C and D. This is because in P_b1, only n_cg varies with f_w, whereas the whole of P_b2 varies with f_w.

Revised Formula for Pb1 v Pb2