Superelevation Calculator

✖Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.ⓘ Ocean Tide Amplitude [a_o]			+10% -10%
✖Duration of Inflow is the period over which a stream or river carries a consistent flow of water into a system.ⓘ Duration of Inflow [t]			+10% -10%
✖Tidal Period is the time taken for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.ⓘ Tidal Period [T]			+10% -10%

✖Bay Superelevation means that the average level of the bay is greater than the average elevation of the ocean over a given time period.ⓘ Superelevation [Δ_BS]

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Download Bay Superelevation, Effect of Freshwater Inflow, Multiple Inlets and Wave Current Interaction Formulas PDF PDF Image

Superelevation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period)))
Δ_BS = a_o*(sin(2*pi*t/T)/(1-cos(2*pi*t/T)))
This formula uses 1 Constants, 2 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Bay Superelevation - (Measured in Meter) - Bay Superelevation means that the average level of the bay is greater than the average elevation of the ocean over a given time period.
Ocean Tide Amplitude - (Measured in Meter) - Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.
Duration of Inflow - (Measured in Second) - Duration of Inflow is the period over which a stream or river carries a consistent flow of water into a system.
Tidal Period - (Measured in Second) - Tidal Period is the time taken for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.

STEP 1: Convert Input(s) to Base Unit

Ocean Tide Amplitude: 4 Meter --> 4 Meter No Conversion Required
Duration of Inflow: 1.2 Hour --> 4320 Second (Check conversion here)
Tidal Period: 130 Second --> 130 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Δ_BS = a_o*(sin(2*pi*t/T)/(1-cos(2*pi*t/T))) --> 4*(sin(2*pi*4320/130)/(1-cos(2*pi*4320/130)))

Evaluating ... ...

Δ_BS = 4.51506664035184

STEP 3: Convert Result to Output's Unit

4.51506664035184 Meter --> No Conversion Required

FINAL ANSWER

4.51506664035184 ≈ 4.515067 Meter <-- Bay Superelevation

(Calculation completed in 00.004 seconds)

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Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

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NSS College of Engineering (NSSCE), Palakkad

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< Bay Superelevation Calculators

Superelevation due to Varying Entrance Channel Cross-Section

LaTeX Go Superelevation = Ocean Tide Amplitude*(1-(((Bay Tide Amplitude/Ocean Tide Amplitude)^2)/(4*(Channel Depth/Ocean Tide Amplitude)))-(Ocean Tide Amplitude/(Bank Slope*Channel Width corresponding to Mean Water Depth))*(0.5-(Bay Tide Amplitude/Ocean Tide Amplitude)*cos(Phase Lag)-((3/2)*(Bay Tide Amplitude/Ocean Tide Amplitude)^2)+4*(Channel Depth/Ocean Tide Amplitude)^2))

Tidal Amplitude in Ocean

LaTeX Go Ocean Tide Amplitude = Bay Superelevation/(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period)))

Superelevation

LaTeX Go Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period)))

Depth given Water Surface Slope

LaTeX Go Eckman Constant Depth = (Coefficient of Eckman*Shear Stress at the Water Surface)/(Water Surface Slope*Water Density*[g])

Superelevation Formula

LaTeX Go

Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period)))
Δ_BS = a_o*(sin(2*pi*t/T)/(1-cos(2*pi*t/T)))

What is Bay Superelevation?

A Superelevation of the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams. The effect of long-term (months or years) rises in sea level causing a long-term rise in bay level is not included in this definition of bay superelevation, since both sea and bay are responding simultaneously. The bay may not rise at the same rate as the sea due to possible circulation effects if multiple inlets connect the bay to the ocean.

What is Ocean Dynamics & Ocean Tide?

Ocean dynamics define and describe the motion of water within the oceans. Ocean temperature and motion fields can be separated into three distinct layers: mixed (surface) layer, upper ocean (above the thermocline), and deep ocean. Ocean dynamics have traditionally been investigated by sampling from instruments in situ.
Tides are caused by the gravitational pull of the moon and the sun. Tides are very long-period waves that move through the oceans in response to the forces exerted by the moon and sun. Tides originate in the oceans and progress toward the coastlines where they appear as the regular rise and fall of the sea surface.

How to Calculate Superelevation?

Superelevation calculator uses Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period))) to calculate the Bay Superelevation, The Superelevation formula is defined as the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams. Bay Superelevation is denoted by Δ_BS symbol.

How to calculate Superelevation using this online calculator? To use this online calculator for Superelevation, enter Ocean Tide Amplitude (a_o), Duration of Inflow (t) & Tidal Period (T) and hit the calculate button. Here is how the Superelevation calculation can be explained with given input values -> 4.515067 = 4*(sin(2*pi*4320/130)/(1-cos(2*pi*4320/130))).

FAQ

What is Superelevation?

The Superelevation formula is defined as the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams and is represented as Δ_BS = a_o*(sin(2*pi*t/T)/(1-cos(2*pi*t/T))) or Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period))). Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun, Duration of Inflow is the period over which a stream or river carries a consistent flow of water into a system & Tidal Period is the time taken for a specific site on Earth to rotate from an exact point under moon to same point under moon, also known as “tidal day” and it’s slightly longer than a solar day.

How to calculate Superelevation?

The Superelevation formula is defined as the bay means that the average level of the bay is greater than the average elevation of the ocean over a given time period. An obvious cause of this effect is the introduction of freshwater into the bay from local rivers and streams is calculated using Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period))). To calculate Superelevation, you need Ocean Tide Amplitude (a_o), Duration of Inflow (t) & Tidal Period (T). With our tool, you need to enter the respective value for Ocean Tide Amplitude, Duration of Inflow & Tidal Period 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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