Application to Bow Impact Load Estimation

The bow impact load is an essential component for the design ice load model, and hence for the Polar ship design and safe speed methodology. The minimum ice failure load

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The Polar Rules based formula given in Eq. (2.7) can also be used to calculate the bow impact load. However, the flexural failure load (Ff) in this Polar equation is insensitive to the ship velocity. Therefore, the developed velocity dependent flexural failure model is adopted here to investigate the ship velocity effect on the bow impact load.

For the ice crushing load, the Polar Rules based crushing failure model is used. The Polar ice crushing failure model is reasonably good for estimating the ice crushing load and to account for the ship velocity effect [12]. The model is derived based on the energy principle, and incorporated the Popov collision mechanics and pressure-area relationship.

The final ice crushing failure load model in the Polar Rules is presented in Table 5.2.

Details derivation of the model can be found in Daley [50] and Daley and Kendrick [12].

Table 5.2 Ice crushing failure load model in IACS Polar Rules [12, 50]

Ice Crushing Limit Load Model

128 Effective Mass:

𝑀_𝑒 = 𝑀_{𝑠ℎ𝑖𝑝}

𝐶_𝑜 (5.7)

Coefficients:

𝑓𝑥 = 3 + 2𝑒𝑥 (5.8)

𝑓𝑎 = ( tan 𝜃 2⁄ sin 𝛽′ cos²𝛽′)

1+𝑒𝑥

(5.9)

The formula for mass reduction coefficient (Co) can be found in Daley [50]

This section investigates the ship velocity effect on the bow impact load during an ice crushing process or an ice flexural failure process. For this reason, the equation (5.4) is applied for a real ship type (PC 1) to calculate the bow impact load at different ship velocities. The calculated bow impact load is compared with the Polar Rules based bow impact load (Eq. 2.7) for a given ice thickness. Further, the ship velocity effect on the bow impact load is also considered for different ice thicknesses. Finally, the bow impact load is estimated using the Polar Rules specified parameters at different ship displacements (mass). The principal particulars of the ship and ice wedges are listed in Table 5.3.

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Table 5.3 Principal particulars of ship and ice wedges for bow ice load

Parameters Value

Polar Class PC 1

Ship mass, M 10,000 tones

Ship block coefficient, Cb 0.768 Ship water plane coefficient, Cpw 0.7469 Ship mid-ship coefficient, Cm 0.934 Ship waterline angle, α 30⁰ Normal ship frame angle, β' 46⁰

Ice wedge angle, θ 150⁰

Flexural strength of ice, σf 0.58 MPa

For the given ice thickness of 1.5 m, the impact load vs ship velocity curves of different models are plotted in Figure 5.11. These plotted models are the ice crushing model, velocity dependent ice flexural failure model, bow impact load model (Eq. 5.4) and Polar Rules based bow impact load model (Eq. 2.7). The ice crushing model indicates that the impact load increases very quickly with the ship velocity, whereas a gradual change is observed in the flexural failure model. For a particular ice condition, the ice crushing model represents limiting impact load at slow ship velocity. For medium to higher ship velocities, the flexural failure load is lower than the ice crushing load, and hence the flexural failure model dominates the bow impact load for this velocity range. The new bow impact load model in this figure indicates that there is a significant velocity effect in

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the impact load at medium and higher ship velocities. This velocity effect is not included in the Polar Rules model.

Figure 5.11 Ship velocity effect on bow impact load for an ice thickness of 1.5 m

Figure 5.12 is the result of the bow impact load model (Eq. 5.4) for a ship velocity range of 0.1 ms^-1 to 6 ms^-1 at different ice thicknesses. The figure indicates that the crushing failure dominates the resulting impact load for a wide range of ship velocity in the thicker ice. In addition, crushing is also a dominating criterion for the slow velocity interaction with the thinner ice. The figure also indicates that the flexure is the primary failure criterion for the thinner ice at medium to higher ship velocities.

3286.2V^1.3 Ice Flexural Load Bow Impact Load (PC)

Ship Velocity, ms^-1

Bow Impact Load, kN

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Figure 5.12 Ship velocity effect on bow impact load at different ice thicknesses

Now, the bow impact loads for the PC 1 ship at different ship velocities and displacements are estimated using the class dependent parameters such as the ice thickness (7 m) and the flexural strength (1.4 MPa). These bow impact load results are plotted in Figure 5.13 indicating the PC 1 design velocity (5.7 ms^-1). The figure indicates that the crushing is the only failure criterion at lower ship displacements ( 50 kT and 100 kT). For higher ship displacements from 150 kT to 250 kT, both the crushing and flexural failure processes contribute to the bow impact loads.

100 1000 10000 100000

0 1 2 3 4 5 6

h=0.5 m h=1.0 m

h=1.5 m h=2 m

h=3 m h=4 m

h=5 m

Impact Load, kN

Ship Velocity, ms^-1

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Figure 5.13 Ship velocity effect on bow impact load at different ship displacements

The above discussion indicates that the Polar Rules based bow impact load estimation method is reasonable for thicker ice operation, slow velocity interaction or for ships with lower displacement. For thinner ice at medium to higher interaction velocities or the ship with higher displacements, the Polar Rules based method may not be appropriate as their flexural failure model is insensitive to the interaction velocity. Therefore, the developed velocity dependent ice flexural failure model can help to enhance the Polar Rules based design model to account for the velocity effect.

0

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Chapter 6