Scaling Parameter Calculator

✖Fetch Length is the unobstructed distance that wind can travel over water in a constant direction.ⓘ Fetch Length [F_l]			+10% -10%
✖Wind Speed at Height of 10 m refers to the average speed of the wind measured at a height of 10 meters above ground level.ⓘ Wind Speed at Height of 10 m [V₁₀]			+10% -10%

✖Dimensionless Scaling Parameter is used in the JONSWAP spectrum for fetch-limited seas.ⓘ Scaling Parameter [α]

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Formula

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Scaling Parameter

Formula

`"α" = 0.076*(("[g]"*"F"_{"l"})/"V"_{"10"}^2)^-0.22`

Example

`"0.153857"=0.076*(("[g]"*"2m")/("22m/s")^2)^-0.22`

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Scaling Parameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22
α = 0.076*(([g]*F_l)/V₁₀^2)^-0.22
This formula uses 1 Constants, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Dimensionless Scaling Parameter - Dimensionless Scaling Parameter is used in the JONSWAP spectrum for fetch-limited seas.
Fetch Length - (Measured in Meter) - Fetch Length is the unobstructed distance that wind can travel over water in a constant direction.
Wind Speed at Height of 10 m - (Measured in Meter per Second) - Wind Speed at Height of 10 m refers to the average speed of the wind measured at a height of 10 meters above ground level.

STEP 1: Convert Input(s) to Base Unit

Fetch Length: 2 Meter --> 2 Meter No Conversion Required
Wind Speed at Height of 10 m: 22 Meter per Second --> 22 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α = 0.076*(([g]*F_l)/V₁₀^2)^-0.22 --> 0.076*(([g]*2)/22^2)^-0.22

Evaluating ... ...

α = 0.153857412415742

STEP 3: Convert Result to Output's Unit

0.153857412415742 --> No Conversion Required

FINAL ANSWER

0.153857412415742 ≈ 0.153857 <-- Dimensionless Scaling Parameter

(Calculation completed in 00.004 seconds)

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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 M Naveen

National Institute of Technology (NIT), Warangal

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< 19 Parametric Spectrum Models Calculators

JONSWAP Spectrum for Fetch-limited Seas

Go Frequency Energy Spectrum = ((Dimensionless Scaling Parameter*[g]^2)/((2*pi)^4*Wave Frequency^5))*(exp(-1.25*(Wave Frequency/Frequency at Spectral Peak)^-4)*Peak Enhancement Factor)^exp(-((Wave Frequency/Frequency at Spectral Peak)-1)^2/(2*Standard Deviation^2))

Frequency of Spectral Peak

Go Frequency at Spectral Peak = ([g]*18.8*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.33)/(2*pi*Wind Speed at Height of 10 m)

Frequency of Spectral Peak Given Wind Speed

Go Frequency at Spectral Peak = ([g]*(Controlling Parameter for the Angular Distribution/11.5)^(-1/2.5))/(2*pi*Wind Speed at Height of 10 m)

Wind Speed given Maximum Controlling Parameter for Angular Distribution

Go Wind Speed at Height of 10 m = [g]*(Controlling Parameter for the Angular Distribution/11.5)^(-1/2.5)/(2*pi*Frequency at Spectral Peak)

Maximum Controlling Parameter for Angular Distribution

Go Controlling Parameter for the Angular Distribution = 11.5*((2*pi*Frequency at Spectral Peak*Wind Speed at Height of 10 m)/[g])^-2.5

Wind Speed at Elevation 10m above Sea Surface given Scaling Parameter

Go Wind Speed at Height of 10 m = ((Fetch Length*[g])/(Dimensionless Scaling Parameter/0.076)^(-1/0.22))^0.5

Fetch Length given Scaling Parameter

Go Fetch Length = (Wind Speed at Height of 10 m^2*((Dimensionless Scaling Parameter/0.076)^-(1/0.22)))/[g]

Scaling Parameter

Go Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22

Dimensionless Time

Go Dimensionless Time = ([g]*Time for Dimensionless Parameter Calculation)/Friction Velocity

Significant Wave Height given Significant Wave Height of Lower and Higher frequency Components

Go Significant Wave Height = sqrt(Significant Wave Height 1^2+Significant Wave Height 2^2)

Significant Wave Height of Higher Frequency Component

Go Significant Wave Height 2 = sqrt(Significant Wave Height^2-Significant Wave Height 1^2)

Significant Wave Height of Lower Frequency Component

Go Significant Wave Height 1 = sqrt(Significant Wave Height^2-Significant Wave Height 2^2)

Fetch Length given Frequency at Spectral Peak

Go Fetch Length = ((Wind Speed at Height of 10 m^3)*((Frequency at Spectral Peak/3.5)^-(1/0.33)))/[g]^2

Frequency at Spectral Peak

Go Frequency at Spectral Peak = 3.5*(([g]^2*Fetch Length)/Wind Speed at Height of 10 m^3)^-0.33

Shape Factor for Higher Frequency Component

Go Shape Factor for Higher Frequency Component = 1.82*exp(-0.027*Significant Wave Height)

Wind Speed at Elevation 10m above Sea Surface given Frequency at Spectral Peak

Go Wind Speed = ((Fetch Length*[g]^2)/(Frequency at Spectral Peak/3.5)^-(1/0.33))^(1/3)

Phillip's Equilibrium Range of Spectrum for Fully Developed Sea in Deep Water

Go Phillip's Equilibrium Range of Spectrum = Constant B*[g]^2*Wave Angular Frequency^-5

Weighing Factor for Angular Frequency greater than One

Go Weighing Factor for Angular Frequency = 1-0.5*(2-Coast Wave Angular Frequency)^2

Weighing Factor for Angular Frequency Lesser than or Equal to One

Go Weighing Factor = 0.5*Wave Angular Frequency^2

Scaling Parameter Formula

Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22
α = 0.076*(([g]*F_l)/V₁₀^2)^-0.22

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 Scaling Parameter?

Scaling Parameter calculator uses Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22 to calculate the Dimensionless Scaling Parameter, The Scaling Parameter is defined as a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution. Dimensionless Scaling Parameter is denoted by α symbol.

How to calculate Scaling Parameter using this online calculator? To use this online calculator for Scaling Parameter, enter Fetch Length (F_l) & Wind Speed at Height of 10 m (V₁₀) and hit the calculate button. Here is how the Scaling Parameter calculation can be explained with given input values -> 0.153857 = 0.076*(([g]*2)/22^2)^-0.22.

FAQ

What is Scaling Parameter?

The Scaling Parameter is defined as a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution and is represented as α = 0.076*(([g]*F_l)/V₁₀^2)^-0.22 or Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22. Fetch Length is the unobstructed distance that wind can travel over water in a constant direction & Wind Speed at Height of 10 m refers to the average speed of the wind measured at a height of 10 meters above ground level.

How to calculate Scaling Parameter?

The Scaling Parameter is defined as a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more spread out the distribution is calculated using Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22. To calculate Scaling Parameter, you need Fetch Length (F_l) & Wind Speed at Height of 10 m (V₁₀). With our tool, you need to enter the respective value for Fetch Length & Wind Speed at Height of 10 m 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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