Virtual Mass of Vessel given Undamped Natural Period Calculator

✖Undamped Natural Period of a Vessel [time] depends on the virtual mass of the ship.ⓘ Undamped Natural Period of a Vessel [T_n]			+10% -10%
✖Effective Spring Constant [force/length] A mooring system is composed of many lines, but only those in tension contribute to the stiffness or effective spring constant.ⓘ 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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Virtual Mass of Vessel given Undamped Natural Period

Formula

`"m"_{"v"} = ("T"_{"n"}^2*"k"_{"tot"})/(2*pi)^2`

Example

`"94.8731kN"=(("0.17h")^2*"10N/m")/(2*pi)^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 [time] depends on the virtual mass of the ship.
Effective Spring Constant - (Measured in Newton per Meter) - Effective Spring Constant [force/length] A mooring system is composed of many lines, but only those in tension contribute to the stiffness or effective spring constant.

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 00.004 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

Mithila Muthamma PA has created this Calculator and 2000+ more calculators!

Verified by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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< 12 Mooring Calculators

Undamped Natural Period of Vessel

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

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

Individual Stiffness of Mooring Line

Go Individual Stiffness of a Mooring Line = Axial Tension or Load on a Mooring Line/Elongation in the Mooring Line

Elongation in Mooring Line given Individual Stiffness of Mooring Line

Go Mooring Line Elongation = Axial Tension or Load on a Mooring Line/Individual Stiffness of a Mooring Line

Axial Tension or Load given Individual Stiffness of Mooring Line

Go Axial Tension or Load on a Mooring Line = Mooring Line Elongation*Individual Stiffness of a Mooring Line

Elongation in Mooring Line given Percent Elongation in Mooring Line

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

Length of Mooring Line given percent Elongation in Mooring Line

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

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

Mass of Vessel given Virtual Mass of Vessel

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

Virtual Mass of Vessel

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

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, Virtual Mass of Vessel given undamped natural period 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. 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?

Virtual Mass of Vessel given undamped natural period 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 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 [time] depends on the virtual mass of the ship & Effective Spring Constant [force/length] A mooring system is composed of many lines, but only those in tension contribute to the stiffness or effective spring constant.

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

Virtual Mass of Vessel given undamped natural period 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 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.

How many ways are there to calculate Virtual Mass of the Ship?

In this formula, Virtual Mass of the Ship uses Undamped Natural Period of a Vessel & Effective Spring Constant. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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