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Superelevation Formula

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Bay Superelevation means that the average level of the bay is greater than the average elevation of the ocean over a given time period. Check FAQs

Δ BS = a o \cdot (\frac{\sin (2 \cdot π \cdot \frac{t}{T})}{1 - \cos (2 \cdot π \cdot \frac{t}{T})})

Δ_BS - Bay Superelevation?a_o - Ocean Tide Amplitude?t - Duration of Inflow?T - Tidal Period?π - Archimedes' constant?

Superelevation Example

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Here is how the Superelevation equation looks like with Values.

Here is how the Superelevation equation looks like with Units.

Here is how the Superelevation equation looks like.

4.5151 = 4 \cdot (\frac{\sin (2 \cdot 3.1416 \cdot \frac{1.2}{130})}{1 - \cos (2 \cdot 3.1416 \cdot \frac{1.2}{130})})

4.5151m = 4m \cdot (\frac{\sin (2 \cdot 3.1416 \cdot \frac{1.2h}{130s})}{1 - \cos (2 \cdot 3.1416 \cdot \frac{1.2h}{130s})})

4.5151 = 4 \cdot (\frac{\sin (2 \cdot 3.1416 \cdot \frac{1.2}{130})}{1 - \cos (2 \cdot 3.1416 \cdot \frac{1.2}{130})})

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Superelevation Solution

Follow our step by step solution on how to calculate Superelevation?

FIRST Step Consider the formula

Δ BS = a o \cdot (\frac{\sin (2 \cdot π \cdot \frac{t}{T})}{1 - \cos (2 \cdot π \cdot \frac{t}{T})})

Next Step Substitute values of Variables

∴

Δ BS = 4m \cdot (\frac{\sin (2 \cdot π \cdot \frac{1.2h}{130s})}{1 - \cos (2 \cdot π \cdot \frac{1.2h}{130s})})

Next Step Substitute values of Constants

∴

Δ BS = 4m \cdot (\frac{\sin (2 \cdot 3.1416 \cdot \frac{1.2h}{130s})}{1 - \cos (2 \cdot 3.1416 \cdot \frac{1.2h}{130s})})

Next Step Convert Units

∴

Δ BS = 4m \cdot (\frac{\sin (2 \cdot 3.1416 \cdot \frac{4320s}{130s})}{1 - \cos (2 \cdot 3.1416 \cdot \frac{4320s}{130s})})

Next Step Prepare to Evaluate

∴

Δ BS = 4 \cdot (\frac{\sin (2 \cdot 3.1416 \cdot \frac{4320}{130})}{1 - \cos (2 \cdot 3.1416 \cdot \frac{4320}{130})})

Next Step Evaluate

∴

Δ BS = 4.51506664035184m

LAST Step Rounding Answer

∴

Δ BS = 4.5151m

Superelevation Formula Elements

Variables

Constants

Functions

Bay Superelevation

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

Symbol: Δ_BS

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Bay Superelevation

Ocean Tide Amplitude

Ocean Tide Amplitude is the height difference between high and low tides, reflecting gravitational forces from the moon and sun.

Symbol: a_o

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Ocean Tide Amplitude

Duration of Inflow

Duration of Inflow is the period over which a stream or river carries a consistent flow of water into a system.

Symbol: t

Measurement: TimeUnit: h

Note: Value can be positive or negative.

Formulas to find Duration of Inflow

Tidal Period

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.

Symbol: T

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Tidal Period

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Bay Superelevation category

Go Tidal Amplitude in Ocean

a o = \frac{Δ BS}{\frac{\sin (2 \cdot π \cdot \frac{t}{T})}{1 - \cos (2 \cdot π \cdot \frac{t}{T})}}

Go Superelevation due to Varying Entrance Channel Cross-Section

S = a o \cdot (1 - (\frac{{(\frac{a B}{a o})}^{2}}{4 \cdot (\frac{D t}{a o})}) - (\frac{a o}{m \cdot W}) \cdot (0.5 - (\frac{a B}{a o}) \cdot \cos (k) - ((\frac{3}{2}) \cdot {(\frac{a B}{a o})}^{2}) + 4 \cdot {(\frac{D t}{a o})}^{2}))

Go Depth given Water Surface Slope

h = \frac{Δ \cdot τ}{β \cdot ρ water \cdot [g]}

How to Evaluate Superelevation?

Superelevation evaluator uses Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period))) to evaluate 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 evaluate Superelevation using this online evaluator? To use this online evaluator for Superelevation, enter Ocean Tide Amplitude (a_o), Duration of Inflow (t) & Tidal Period (T) and hit the calculate button.

FAQs on Superelevation

What is the formula to find Superelevation?

The formula of Superelevation is expressed as Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period))). Here is an example- 4.515067 = 4*(sin(2*pi*4320/130)/(1-cos(2*pi*4320/130))).

How to calculate Superelevation?

With Ocean Tide Amplitude (a_o), Duration of Inflow (t) & Tidal Period (T) we can find Superelevation using the formula - Bay Superelevation = Ocean Tide Amplitude*(sin(2*pi*Duration of Inflow/Tidal Period)/(1-cos(2*pi*Duration of Inflow/Tidal Period))). This formula also uses Archimedes' constant and , Sine (sin), Cosine (cos) function(s).

Can the Superelevation be negative?

Yes, the Superelevation, measured in Length can be negative.

Which unit is used to measure Superelevation?

Superelevation is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Superelevation can be measured.

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Superelevation Formula

Superelevation Example

Superelevation Solution

Superelevation Formula Elements

Other formulas in Bay Superelevation category

How to Evaluate Superelevation?

FAQs on Superelevation

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