Undamped Natural Period of Vessel Solution

STEP 0: Pre-Calculation Summary
Formula Used
Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant))
Tn = 2*pi*(sqrt(mv/ktot))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Undamped Natural Period of a Vessel - (Measured in Second) - Undamped Natural Period of a Vessel [time] depends on the virtual mass of the ship.
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.
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
Virtual Mass of the Ship: 100 Kilonewton --> 100000 Newton (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
Tn = 2*pi*(sqrt(mv/ktot)) --> 2*pi*(sqrt(100000/10))
Evaluating ... ...
Tn = 628.318530717959
STEP 3: Convert Result to Output's Unit
628.318530717959 Second -->0.174532925199433 Hour (Check conversion here)
FINAL ANSWER
0.174532925199433 0.174533 Hour <-- Undamped Natural Period of a Vessel
(Calculation completed in 00.004 seconds)

Credits

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Coorg Institute of Technology (CIT), Coorg
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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

Undamped Natural Period of Vessel Formula

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

What is Froude law?

Froude's Law, defines that the speed attainable by a creature or a ship is proportional to the square root of its scale. Froude number (Fr), in hydrology and fluid mechanics, dimensionless quantity used to indicate the influence of gravity on fluid motion.

How to Calculate Undamped Natural Period of Vessel?

Undamped Natural Period of Vessel calculator uses Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)) to calculate the Undamped Natural Period of a Vessel, Undamped Natural Period of Vessel is defined for undamped natural period whereas motion of ship in surge is assumed to be independent of other directions of motion. Damping is assumed to be small for low-frequency motions of ship in surge. Undamped Natural Period of a Vessel is denoted by Tn symbol.

How to calculate Undamped Natural Period of Vessel using this online calculator? To use this online calculator for Undamped Natural Period of Vessel, enter Virtual Mass of the Ship (mv) & Effective Spring Constant (ktot) and hit the calculate button. Here is how the Undamped Natural Period of Vessel calculation can be explained with given input values -> 4.8E-5 = 2*pi*(sqrt(100000/10)).

FAQ

What is Undamped Natural Period of Vessel?
Undamped Natural Period of Vessel is defined for undamped natural period whereas motion of ship in surge is assumed to be independent of other directions of motion. Damping is assumed to be small for low-frequency motions of ship in surge and is represented as Tn = 2*pi*(sqrt(mv/ktot)) or Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)). 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 & 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 Undamped Natural Period of Vessel?
Undamped Natural Period of Vessel is defined for undamped natural period whereas motion of ship in surge is assumed to be independent of other directions of motion. Damping is assumed to be small for low-frequency motions of ship in surge is calculated using Undamped Natural Period of a Vessel = 2*pi*(sqrt(Virtual Mass of the Ship/Effective Spring Constant)). To calculate Undamped Natural Period of Vessel, you need Virtual Mass of the Ship (mv) & Effective Spring Constant (ktot). With our tool, you need to enter the respective value for Virtual Mass of the Ship & 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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