Empirically Determined Functions of Beach Slope Parameter B Calculator

Formula Used:

\[ B = \frac{1.56}{1 + e^{-19.5 \cdot \tan(\beta)}} \]

Functions of Beach Slope B:

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1. What is the Empirically Determined Functions of Beach Slope Parameter B?

The Empirically Determined Functions of Beach Slope Parameter B is an empirically derived parameter that establishes correlations between the slope angle and wave dynamics, sediment transport, and coastal erosion rates in coastal engineering studies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ B = \frac{1.56}{1 + e^{-19.5 \cdot \tan(\beta)}} \]

Where:

\( B \) — Functions of Beach Slope B (dimensionless)
\( e \) — Napier's constant (approximately 2.71828)
\( \tan \) — Tangent trigonometric function
\( \beta \) — Slope of Beach of Surf Zone Waves (radians)

Explanation: This formula uses an exponential function with a tangent component to model the relationship between beach slope and the empirically determined parameter B.

3. Importance of Beach Slope Parameter Calculation

Details: Accurate calculation of the beach slope parameter B is crucial for coastal engineering studies, beach erosion prediction, sediment transport modeling, and coastal management planning.

4. Using the Calculator

Tips: Enter the slope of the beach in radians. The slope should be a positive value representing the angle of the beach in the surf zone.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range of values for parameter B?
A: Parameter B typically ranges between 0 and 1.56, approaching 1.56 as the beach slope increases.

Q2: Why is the tangent function used in this formula?
A: The tangent function is used to convert the slope angle into a ratio that can be used in the exponential relationship, capturing the nonlinear behavior of beach dynamics.

Q3: Can I use degrees instead of radians?
A: The formula requires the slope input in radians. If you have degrees, convert them to radians first (radians = degrees × π/180).

Q4: What are the practical applications of this parameter?
A: This parameter is used in coastal engineering for predicting wave breaking characteristics, sediment transport rates, and beach profile evolution.

Q5: Is this formula applicable to all beach types?
A: While empirically derived, the formula may have limitations for extremely steep or very flat beaches, and site-specific calibration may be necessary for optimal results.