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Scaling Parameter Formula

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Dimensionless Scaling Parameter is a value used in mathematical or scientific models to scale or normalize variables without units. It is used in the JONSWAP spectrum for fetch-limited seas. Check FAQs

α = 0.076 \cdot {(\frac{[g] \cdot F l}{{V 10}^{2}})}^{- 0.22}

α - Dimensionless Scaling Parameter?F_l - Fetch Length?V₁₀ - Wind Speed at Height of 10 m?[g] - Gravitational acceleration on Earth?

Scaling Parameter Example

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Here is how the Scaling Parameter equation looks like with Values.

Here is how the Scaling Parameter equation looks like with Units.

Here is how the Scaling Parameter equation looks like.

0.1539 = 0.076 \cdot {(\frac{9.8066 \cdot 2}{22^{2}})}^{- 0.22}

0.1539 = 0.076 \cdot {(\frac{9.8066m/s² \cdot 2m}{{22m/s}^{2}})}^{- 0.22}

0.1539 = 0.076 \cdot {(\frac{9.8066 \cdot 2}{22^{2}})}^{- 0.22}

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Scaling Parameter Solution

Follow our step by step solution on how to calculate Scaling Parameter?

FIRST Step Consider the formula

α = 0.076 \cdot {(\frac{[g] \cdot F l}{{V 10}^{2}})}^{- 0.22}

Next Step Substitute values of Variables

∴

α = 0.076 \cdot {(\frac{[g] \cdot 2m}{{22m/s}^{2}})}^{- 0.22}

Next Step Substitute values of Constants

∴

α = 0.076 \cdot {(\frac{9.8066m/s² \cdot 2m}{{22m/s}^{2}})}^{- 0.22}

Next Step Prepare to Evaluate

∴

α = 0.076 \cdot {(\frac{9.8066 \cdot 2}{22^{2}})}^{- 0.22}

Next Step Evaluate

∴

α = 0.153857412415742

LAST Step Rounding Answer

∴

α = 0.1539

Scaling Parameter Formula Elements

Variables

Constants

Dimensionless Scaling Parameter

Dimensionless Scaling Parameter is a value used in mathematical or scientific models to scale or normalize variables without units. It is used in the JONSWAP spectrum for fetch-limited seas.

Symbol: α

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Dimensionless Scaling Parameter

Fetch Length

Fetch Length is the unobstructed distance that wind can travel over water in a constant direction.

Symbol: F_l

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Fetch Length

Wind Speed at Height of 10 m

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.

Symbol: V₁₀

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Wind Speed at Height of 10 m

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Other formulas in Parametric Spectrum Models category

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

E ω = b \cdot {[g]}^{2} \cdot ω^{- 5}

Go JONSWAP Spectrum for Fetch-limited Seas

E f = (\frac{α \cdot {[g]}^{2}}{{(2 \cdot π)}^{4} \cdot f^{5}}) \cdot {(\exp (- 1.25 \cdot {(\frac{f}{f p})}^{- 4}) \cdot γ)}^{\exp (- \frac{{((\frac{f}{f p}) - 1)}^{2}}{2 \cdot σ^{2}})}

Go Frequency at Spectral Peak

f p = 3.5 \cdot {(\frac{{[g]}^{2} \cdot F l}{{V 10}^{3}})}^{- 0.33}

Go Fetch Length given Frequency at Spectral Peak

F l = \frac{({V 10}^{3}) \cdot ({(\frac{f p}{3.5})}^{- (\frac{1}{0.33})})}{{[g]}^{2}}

How to Evaluate Scaling Parameter?

Scaling Parameter evaluator uses Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22 to evaluate the Dimensionless Scaling Parameter, The Scaling Parameter formula is defined as value used in mathematical or scientific models to scale or normalize variables without units. It is used in the JONSWAP spectrum for fetch-limited seas. The larger the scale parameter, the more spread out the distribution. Dimensionless Scaling Parameter is denoted by α symbol.

How to evaluate Scaling Parameter using this online evaluator? To use this online evaluator for Scaling Parameter, enter Fetch Length (F_l) & Wind Speed at Height of 10 m (V₁₀) and hit the calculate button.

FAQs on Scaling Parameter

What is the formula to find Scaling Parameter?

The formula of Scaling Parameter is expressed as Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22. Here is an example- 0.153857 = 0.076*(([g]*2)/22^2)^-0.22.

How to calculate Scaling Parameter?

With Fetch Length (F_l) & Wind Speed at Height of 10 m (V₁₀) we can find Scaling Parameter using the formula - Dimensionless Scaling Parameter = 0.076*(([g]*Fetch Length)/Wind Speed at Height of 10 m^2)^-0.22. This formula also uses Gravitational acceleration on Earth constant(s).

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