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Virtual Mass of Vessel given Undamped Natural Period Formula

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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. Check FAQs

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

m_v - Virtual Mass of the Ship?T_n - Undamped Natural Period of a Vessel?k_tot - Effective Spring Constant?π - Archimedes' constant?

Virtual Mass of Vessel given Undamped Natural Period Example

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Here is how the Virtual Mass of Vessel given Undamped Natural Period equation looks like with Values.

Here is how the Virtual Mass of Vessel given Undamped Natural Period equation looks like with Units.

Here is how the Virtual Mass of Vessel given Undamped Natural Period equation looks like.

94.8731 = \frac{{0.17}^{2} \cdot 10}{{(2 \cdot 3.1416)}^{2}}

94.8731kN = \frac{{0.17h}^{2} \cdot 10N/m}{{(2 \cdot 3.1416)}^{2}}

94.8731 = \frac{{0.17}^{2} \cdot 10}{{(2 \cdot 3.1416)}^{2}}

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Virtual Mass of Vessel given Undamped Natural Period Solution

Follow our step by step solution on how to calculate Virtual Mass of Vessel given Undamped Natural Period?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

m v = \frac{{0.17h}^{2} \cdot 10N/m}{{(2 \cdot π)}^{2}}

Next Step Substitute values of Constants

∴

m v = \frac{{0.17h}^{2} \cdot 10N/m}{{(2 \cdot 3.1416)}^{2}}

Next Step Convert Units

∴

m v = \frac{{612s}^{2} \cdot 10N/m}{{(2 \cdot 3.1416)}^{2}}

Next Step Prepare to Evaluate

∴

m v = \frac{612^{2} \cdot 10}{{(2 \cdot 3.1416)}^{2}}

Next Step Evaluate

∴

m v = 94873.1035153394N

Next Step Convert to Output's Unit

∴

m v = 94.8731035153394kN

LAST Step Rounding Answer

∴

m v = 94.8731kN

Virtual Mass of Vessel given Undamped Natural Period Formula Elements

Variables

Constants

Virtual Mass of the Ship

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.

Symbol: m_v

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Virtual Mass of the Ship

Undamped Natural Period of a Vessel

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.

Symbol: T_n

Measurement: TimeUnit: h

Note: Value can be positive or negative.

Formulas to find Undamped Natural Period of a Vessel

Effective Spring Constant

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.

Symbol: k_tot

Measurement: Surface TensionUnit: N/m

Note: Value can be positive or negative.

Formulas to find Effective Spring Constant

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Mooring category

Go Effective Spring Constant given Undamped Natural Period

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

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

m a = m v - m

Go Percent Elongation in Mooring Line

ε m = 100 \cdot (\frac{Δl η'}{ln})

Go Length of Mooring Line given percent Elongation in Mooring Line

ln = \frac{Δl η'}{\frac{ε m}{100}}

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

Virtual Mass of Vessel given Undamped Natural Period evaluator uses Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2 to evaluate 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 evaluate Virtual Mass of Vessel given Undamped Natural Period using this online evaluator? To use this online evaluator 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.

FAQs on Virtual Mass of Vessel given Undamped Natural Period

What is the formula to find Virtual Mass of Vessel given Undamped Natural Period?

The formula of Virtual Mass of Vessel given Undamped Natural Period is expressed as Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2. Here is an example- 0.094873 = (612^2*10)/(2*pi)^2.

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

With Undamped Natural Period of a Vessel (T_n) & Effective Spring Constant (k_tot) we can find Virtual Mass of Vessel given Undamped Natural Period using the formula - Virtual Mass of the Ship = (Undamped Natural Period of a Vessel^2*Effective Spring Constant)/(2*pi)^2. This formula also uses Archimedes' constant .

Can the Virtual Mass of Vessel given Undamped Natural Period be negative?

Yes, the Virtual Mass of Vessel given Undamped Natural Period, measured in Force can be negative.

Which unit is used to measure Virtual Mass of Vessel given Undamped Natural Period?

Virtual Mass of Vessel given Undamped Natural Period is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Virtual Mass of Vessel given Undamped Natural Period can be measured.

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Virtual Mass of Vessel given Undamped Natural Period Formula

Virtual Mass of Vessel given Undamped Natural Period Example

Virtual Mass of Vessel given Undamped Natural Period Solution

Virtual Mass of Vessel given Undamped Natural Period Formula Elements

Other formulas in Mooring category

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

FAQs on Virtual Mass of Vessel given Undamped Natural Period

Variable Name