Virtual Mass of Vessel given Undamped Natural Period Calculator

✖Undamped Natural Period of a Vessel refers to the inherent oscillation period of a structure, such as a ship or offshore platform, in response to external forces, without considering damping effects.ⓘ Undamped Natural Period of a Vessel [T_n]			+10% -10%
✖Effective Spring Constant refers to the measure of resistance provided by a structure or system to deformation due to external forces, such as waves, currents, or tides.ⓘ Effective Spring Constant [k_tot]			+10% -10%

✖Virtual Mass of the Ship/ Vessel is measured as the summation of mass of the vessel and mass of the vessel due to inertial effects.ⓘ Virtual Mass of Vessel given Undamped Natural Period [m_v]

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Formula

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Virtual Mass of Vessel given Undamped Natural Period

Formula

m v = \frac{{T n}^{2} \cdot k tot}{{(2 \cdot π)}^{2}}

Example

94.8731 kN = \frac{{0.17 h}^{2} \cdot 10.0 N/m}{{(2 \cdot π)}^{2}}

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Virtual Mass of Vessel given Undamped Natural Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2
m_v = (T_n^2*k_tot)/(2*pi)^2
This formula uses 1 Constants, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Virtual Mass of the Ship - (Measured in Newton) - Virtual Mass of the Ship/ Vessel is measured as the summation of mass of the vessel and mass of the vessel due to inertial effects.
Undamped Natural Period of a Vessel - (Measured in Second) - Undamped Natural Period of a Vessel refers to the inherent oscillation period of a structure, such as a ship or offshore platform, in response to external forces, without considering damping effects.
Effective Spring Constant - (Measured in Newton per Meter) - Effective Spring Constant refers to the measure of resistance provided by a structure or system to deformation due to external forces, such as waves, currents, or tides.

STEP 1: Convert Input(s) to Base Unit

Undamped Natural Period of a Vessel: 0.17 Hour --> 612 Second (Check conversion here)
Effective Spring Constant: 10 Newton per Meter --> 10 Newton per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m_v = (T_n^2*k_tot)/(2*pi)^2 --> (612^2*10)/(2*pi)^2

Evaluating ... ...

m_v = 94873.1035153394

STEP 3: Convert Result to Output's Unit

94873.1035153394 Newton -->94.8731035153394 Kilonewton (Check conversion here)

FINAL ANSWER

94.8731035153394 ≈ 94.8731 Kilonewton <-- Virtual Mass of the Ship

(Calculation completed in 00.020 seconds)

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Home » Engineering » Civil » Coastal and Ocean Engineering » Surf Zone Hydrodynamics » Harbor Hydrodynamics » Mooring » Virtual Mass of Vessel given Undamped Natural Period

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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< Mooring Calculators

Effective Spring Constant given Undamped Natural Period

Go Effective Spring Constant = ((2*pi)^2*Virtual Mass of the Ship)/Undamped Natural Period of a Vessel^2

Virtual Mass of Vessel given Undamped Natural Period

Go Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2

Percent Elongation in Mooring Line

Go Percent Elongation in a Mooring Line = 100*(Elongation in the Mooring Line/Length of Mooring Line)

Mass of Vessel due to Inertial Effects of Water entrained with Vessel

Go Mass of Vessel due to Inertial Effects = Virtual Mass of the Ship-Mass of a Vessel

Virtual Mass of Vessel given Undamped Natural Period Formula

Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2
m_v = (T_n^2*k_tot)/(2*pi)^2

What is Mooring in shipping?

Mooring is a procedure to anchor the ship to a fixed or floating element and keep it connected during loading or unloading operations. Safe mooring must withstand several forces, such as wind, the current, the tide and waves.

How to Calculate Virtual Mass of Vessel given Undamped Natural Period?

Virtual Mass of Vessel given Undamped Natural Period calculator uses Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2 to calculate the Virtual Mass of the Ship, The Virtual Mass of Vessel given Undamped Natural Period formula is defined as sum of actual mass or displacement of ship m and added mass ma due to inertial effects of water entrained with ship. This concept related to the dynamic response of vessels or floating structures subjected to wave forces. Virtual Mass of the Ship is denoted by m_v symbol.

How to calculate Virtual Mass of Vessel given Undamped Natural Period using this online calculator? To use this online calculator for Virtual Mass of Vessel given Undamped Natural Period, enter Undamped Natural Period of a Vessel (T_n) & Effective Spring Constant (k_tot) and hit the calculate button. Here is how the Virtual Mass of Vessel given Undamped Natural Period calculation can be explained with given input values -> 0.094873 = (612^2*10)/(2*pi)^2.

FAQ

What is Virtual Mass of Vessel given Undamped Natural Period?

The Virtual Mass of Vessel given Undamped Natural Period formula is defined as sum of actual mass or displacement of ship m and added mass ma due to inertial effects of water entrained with ship. This concept related to the dynamic response of vessels or floating structures subjected to wave forces and is represented as m_v = (T_n^2*k_tot)/(2*pi)^2 or Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2. Undamped Natural Period of a Vessel refers to the inherent oscillation period of a structure, such as a ship or offshore platform, in response to external forces, without considering damping effects & Effective Spring Constant refers to the measure of resistance provided by a structure or system to deformation due to external forces, such as waves, currents, or tides.

How to calculate Virtual Mass of Vessel given Undamped Natural Period?

The Virtual Mass of Vessel given Undamped Natural Period formula is defined as sum of actual mass or displacement of ship m and added mass ma due to inertial effects of water entrained with ship. This concept related to the dynamic response of vessels or floating structures subjected to wave forces is calculated using Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2. To calculate Virtual Mass of Vessel given Undamped Natural Period, you need Undamped Natural Period of a Vessel (T_n) & Effective Spring Constant (k_tot). With our tool, you need to enter the respective value for Undamped Natural Period of a Vessel & Effective Spring Constant and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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