Mean Zero-upcrossing Period Calculator

✖Zero-th Moment of Wave Spectrum in terms of cyclic frequency.ⓘ Zero-th Moment of Wave Spectrum [m₀]			+10% -10%
✖Moment of Wave Spectrum 2 in terms of cyclic frequency.ⓘ Moment of Wave Spectrum 2 [m₂]			+10% -10%

✖Mean Zero-upcrossing Period is a point where the sign of a mathematical function changes, represented by an intercept of the axis (zero value) in the graph of the function.ⓘ Mean Zero-upcrossing Period [T'_Z]

⎘ Copy

👎

Formula

✖

Mean Zero-upcrossing Period

Formula

`"T'"_{"Z"} = 2*pi*sqrt("m"_{"0"}/"m"_{"2"})`

Example

`"86.44478s"=2*pi*sqrt("265"/"1.4")`

Calculator

LaTeX

Reset

👍

Download Coastal and Ocean Engineering Formula PDF

Mean Zero-upcrossing Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2)
T'_Z = 2*pi*sqrt(m₀/m₂)
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

Mean Zero-upcrossing Period - (Measured in Second) - Mean Zero-upcrossing Period is a point where the sign of a mathematical function changes, represented by an intercept of the axis (zero value) in the graph of the function.
Zero-th Moment of Wave Spectrum - Zero-th Moment of Wave Spectrum in terms of cyclic frequency.
Moment of Wave Spectrum 2 - Moment of Wave Spectrum 2 in terms of cyclic frequency.

STEP 1: Convert Input(s) to Base Unit

Zero-th Moment of Wave Spectrum: 265 --> No Conversion Required
Moment of Wave Spectrum 2: 1.4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T'_Z = 2*pi*sqrt(m₀/m₂) --> 2*pi*sqrt(265/1.4)

Evaluating ... ...

T'_Z = 86.4447828102455

STEP 3: Convert Result to Output's Unit

86.4447828102455 Second --> No Conversion Required

FINAL ANSWER

86.4447828102455 ≈ 86.44478 Second <-- Mean Zero-upcrossing Period

(Calculation completed in 00.020 seconds)

You are here -

Home » Engineering » Civil » Coastal and Ocean Engineering » Water Wave Mechanics » Wave Period Distribution and Wave Spectrum » Mean Zero-upcrossing Period

Credits

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

Chandana P Dev has verified this Calculator and 1700+ more calculators!

< 12 Wave Period Distribution and Wave Spectrum Calculators

Equilibrium Form of PM Spectrum for Fully-Developed Seas

Go Frequency Energy Spectrum = ((0.0081*[g]^2)/((2*pi)^4*Wave Frequency^5))*exp(-0.24*((2*pi*Wind Speed*Wave Frequency)/[g])^-4)

Most Probable Maximum Wave Period

Go Maximum Wave Period = 2*sqrt(1+Spectral Width^2)/1+sqrt(1+(16*Spectral Width^2/pi*Wave Height^2))

Probability Density of Wave Period

Go Probability = 2.7*(Wave Period^3/Mean Wave Period)*exp(-0.675*(Wave Period/Mean Wave Period)^4)

Wave Component Amplitude

Go Wave Amplitude = sqrt(0.5*sqrt(Coefficient of Wave Component Amplitude^2+Coefficient of Wave Component Amplitude^2))

Spectral Bandwidth

Go Spectral Width = sqrt(1-(Moment of Wave Spectrum 2^2/(Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 4)))

Spectral Width

Go Spectral Width = sqrt((Zero-th Moment of Wave Spectrum*Moment of Wave Spectrum 2/Moment of Wave Spectrum 1^2)-1)

Mean Zero-upcrossing Period

Go Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2)

Relative Phase given coefficients

Go Relative Phase = atanh(Coefficient of Wave Component Amplitude/Coefficient of Wave Component Amplitude)

Mean Crest Period

Go Wave Crest Period = 2*pi*(Moment of Wave Spectrum 2/Moment of Wave Spectrum 4)

Mean Wave Period

Go Wave Period = 2*pi*(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 1)

Normal Distribution with Wave Period

Go Wave Period = Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 1

Maximum Wave Period

Go Maximum Wave Period = Coefficient Eckman*Mean Wave Period

Mean Zero-upcrossing Period Formula

Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2)
T'_Z = 2*pi*sqrt(m₀/m₂)

What are the characteristics of progressive waves?

A progressive wave is formed due to continuous vibration of the particles of the medium.
The wave travels with a certain velocity.
There is a flow of energy in the direction of the wave.
No particles in the medium are at rest.
The amplitude of all the particles is the same.

How to Calculate Mean Zero-upcrossing Period?

Mean Zero-upcrossing Period calculator uses Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2) to calculate the Mean Zero-upcrossing Period, The Mean Zero-upcrossing Period is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function. Mean Zero-upcrossing Period is denoted by T'_Z symbol.

How to calculate Mean Zero-upcrossing Period using this online calculator? To use this online calculator for Mean Zero-upcrossing Period, enter Zero-th Moment of Wave Spectrum (m₀) & Moment of Wave Spectrum 2 (m₂) and hit the calculate button. Here is how the Mean Zero-upcrossing Period calculation can be explained with given input values -> 86.44478 = 2*pi*sqrt(265/1.4).

FAQ

What is Mean Zero-upcrossing Period?

The Mean Zero-upcrossing Period is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function and is represented as T'_Z = 2*pi*sqrt(m₀/m₂) or Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2). Zero-th Moment of Wave Spectrum in terms of cyclic frequency & Moment of Wave Spectrum 2 in terms of cyclic frequency.

How to calculate Mean Zero-upcrossing Period?

The Mean Zero-upcrossing Period is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function is calculated using Mean Zero-upcrossing Period = 2*pi*sqrt(Zero-th Moment of Wave Spectrum/Moment of Wave Spectrum 2). To calculate Mean Zero-upcrossing Period, you need Zero-th Moment of Wave Spectrum (m₀) & Moment of Wave Spectrum 2 (m₂). With our tool, you need to enter the respective value for Zero-th Moment of Wave Spectrum & Moment of Wave Spectrum 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search