Section 2 Motion response
Clasification Society 2024 - Version 9.40
Clasifications Register Rules and Regulations - Rules and Regulations for the Classification of Naval Ships, January 2023 - Volume 1 Ship Structures - Part 5 Environmental Loads - Chapter 3 Local Design Loads - Section 2 Motion response

Section 2 Motion response

Parent topic: Chapter 3 Local Design Loads

2.1 General

2.1.1 The motions of the ship are to be considered in deriving the loads acting on the ship. The formulae given in this section may be utilised or ship motion design values may be derived by direct calculation methods or model testing.

2.2 Ship motions

2.2.1 The ship motion response data given in Table 3.2.1 Ship motions are to be used in the design calculations. Alternatively, the ship motion responses may be derived by direct calculation or equivalent methods.

2.3 Design accelerations

2.3.1 The non-dimensional ship motion acceleration values given in this Section are to be used in the design calculations. The equations given here are applicable to ships with conventional hull forms operating in the displacement mode at their normal ship service speed or cruising speed. It is not normally necessary to consider the ship motion or acceleration values at sprint speeds unless there is a particular requirement to operate at sprint speeds in severe seastates.

2.3.2 The following formulae are given as guidance for the components of acceleration due to ship motions and apply for ships with a length exceeding 50 m and where the speed is such that the ship is operating within the displacement mode based on normal ship service speed. Typically this will apply to most ships with displacement hull forms that are not designed to operate in the planing regime.

Vertical acceleration due to heave, pitch and roll motions

a z =

Transverse acceleration due to sway, yaw and roll motions

a y =

Longitudinal acceleration due to surge motions

a x =

where

A =

and

a x, a y and a z = are the maximum dimensionless accelerations (i.e. relative to the acceleration of gravity) in the respective directions and are considered as acting separately for calculation purposes
a x = measured positive in the forward direction
a y = measured positive in the transverse direction to port.
a z = measured positive in the downwards direction, i.e. adds to g
Note
a x = includes the component due to static weight in the longitudinal direction due to pitching
Note
a y = includes the component due to static weight in the transverse direction due to rolling
Note
a z = does not include the component due to static weight

Note a o, a heave, a pitch, a rollz, a sway, a yaw, a rolly and A are defined in Table 3.2.1 Ship motions

Note
f st = is defined in Table 3.2.1 Ship motions
Note

Note T, L WL, C b and z are defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.1

2.4 Design vertical acceleration for ships in the planing regime

2.4.1 The design vertical acceleration for the derivation of bottom impact pressures for ships operating in the planing regime may be derived using the following Sections.

Table 3.2.1 Ship motions

Motion     Acceleration
Heave   a heave = a o
Pitch   a pitch
Sway   a sway = a o0,78
Yaw   a yaw
Roll Acceleration due to Roll
Vertical direction 		a rollz
Roll Acceleration due to Roll
Transverse direction 		a rolly
    a o
Relative vertical motion   H rm
Symbols
fst = correction factor for long term (10-8) acceleration value to average of the highest 1/100 acceleration values
= 0,8
Cw = a wave head, in metres
= fHs0,0771L WL(Cb + 0,2)0,3 e(-0,0044LWL)
Cw,min =
km =
xm = 0,45 – 0,6Fn but x m is not to be less than 0,2
kr = 2,25 for the determination of pressure loads in Vol 1, Pt 5, Ch 3, 3 Loads on shell envelope
kr = 4,5 for the determination of impact loads in Vol 1, Pt 5, Ch 3, 4 Impact loads on external plating
V is appropriate design speed as follows:
V = Vcr for determination of pressure in Vol 1, Pt 5, Ch 3, 3 Loads on shell envelope, local design loads in Vol 1, Pt 5, Ch 3, 5 Local design loads for decks and bulkheads and Vol 1, Pt 5, Ch 3, 6 Other local loads, and all other loads unless specifically noted
= Vsp for determination of impact loads in Vol 1, Pt 5, Ch 3, 4 Impact loads on external plating
Fn =
K = 1 in general. For particular loading conditions and hull forms, determination of K according to the formula below may be necessary
K = 13 GM / B WL, but ≥ 1,0
GM = metacentric height, in metres

fHS and B WL are defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.1

L CG is defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.4

Note 1. Heave motion is measured positive upwards.

Note 2. Pitch motion is measured positive bow downwards.

Note 3. Sway motion is measured positive to port.

Note 4. Yaw motion is measured positive bow to port.

Note 5. Roll motion is measured positive port side upwards.

2.4.2 The non-dimensional vertical acceleration at the LCG, a op, is defined as the average of the 1/100 highest accelerations and is to be taken as:

a op = 5,66g θB L 1 (H 1 + 0,084) (5 – 0,1θD) F n 2 10-3
where
F n = Froude number based on V sp, where V sp is defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.1, F n is defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.2
g = acceleration due to gravity (9,81 m/sec2)
L 1 = , but is not to be taken as less than 3
H 1 = but not less than 0,2
B c = breadth of hull between the chines or bilge tangential points at the LCG, as appropriate, in metres
H dw = design wave height in metres, see Vol 1, Pt 5, Ch 2, 2.3 Wave environment 2.3.3
θD = deadrise angle at the LCG, in degrees, but is not to be taken as greater than 30o, see Notes 1 and 2 and Figure 3.1.5 Definition of bilge tangential point, B C, B WL and G S
θB = running trim angle in degrees, but is not to be taken as less than 3o.

∆ is defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.1
LCG is defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.4
B WL and L WL are defined in Vol 1, Pt 3, Ch 1, 5.2 Principal particulars

Note 1. For ships with no clearly defined deadrise angle at the LCG, the angle, in degrees, to the horizontal line at the LCG formed by joining the lowest point of the hull or underside of keel and the bilge tangential point is to be taken as the deadrise angle θD, see Figure 3.1.5 Definition of bilge tangential point, B C, B WL and G S

Note 2. For ships with hulls of asymmetric section, where the inner and outer deadrise angles differ, the smaller of the two angles is to be used.

2.4.3 Where the Froude number, F n, is greater than 1,8, the motion response criteria are to be specially considered.

2.4.4 The vertical non dimensional acceleration, a z, at any given distance x along the hull may be taken as:

a z =
where
a z = is the vertical acceleration in terms of g
x wl = distance from aft end of L WL, in metres, to the point at which the vertical acceleration is calculated

LCG is defined in Vol 1, Pt 5, Ch 3, 1.3 Symbols and definitions 1.3.4

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