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Superelevation due to Varying Entrance Channel Cross-Section Formula

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Superelevation is the amount of raise of outer edge with respect to the inner edge of the road surface. In case of railways the amount by which the outer rail is raised is known as superelevation. Check FAQs

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}))

S - Superelevation?a_o - Ocean Tide Amplitude?a_B - Bay Tide Amplitude?D_t - Channel Depth?m - Bank Slope?W - Channel Width corresponding to Mean Water Depth?k - Phase Lag?

Superelevation due to Varying Entrance Channel Cross-Section Example

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Here is how the Superelevation due to Varying Entrance Channel Cross-Section equation looks like with Values.

Here is how the Superelevation due to Varying Entrance Channel Cross-Section equation looks like with Units.

Here is how the Superelevation due to Varying Entrance Channel Cross-Section equation looks like.

2.0029 = 4 \cdot (1 - (\frac{{(\frac{3.7}{4})}^{2}}{4 \cdot (\frac{5.01}{4})}) - (\frac{4}{1.5 \cdot 52}) \cdot (0.5 - (\frac{3.7}{4}) \cdot \cos (185.2) - ((\frac{3}{2}) \cdot {(\frac{3.7}{4})}^{2}) + 4 \cdot {(\frac{5.01}{4})}^{2}))

2.0029m = 4m \cdot (1 - (\frac{{(\frac{3.7}{4m})}^{2}}{4 \cdot (\frac{5.01m}{4m})}) - (\frac{4m}{1.5 \cdot 52m}) \cdot (0.5 - (\frac{3.7}{4m}) \cdot \cos (185.2) - ((\frac{3}{2}) \cdot {(\frac{3.7}{4m})}^{2}) + 4 \cdot {(\frac{5.01m}{4m})}^{2}))

2.0029 = 4 \cdot (1 - (\frac{{(\frac{3.7}{4})}^{2}}{4 \cdot (\frac{5.01}{4})}) - (\frac{4}{1.5 \cdot 52}) \cdot (0.5 - (\frac{3.7}{4}) \cdot \cos (185.2) - ((\frac{3}{2}) \cdot {(\frac{3.7}{4})}^{2}) + 4 \cdot {(\frac{5.01}{4})}^{2}))

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Home » Engineering » Civil » Coastal and Ocean Engineering » Superelevation due to Varying Entrance Channel Cross-Section

Superelevation due to Varying Entrance Channel Cross-Section Solution

Follow our step by step solution on how to calculate Superelevation due to Varying Entrance Channel Cross-Section?

FIRST Step Consider the formula

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}))

Next Step Substitute values of Variables

∴

S = 4m \cdot (1 - (\frac{{(\frac{3.7}{4m})}^{2}}{4 \cdot (\frac{5.01m}{4m})}) - (\frac{4m}{1.5 \cdot 52m}) \cdot (0.5 - (\frac{3.7}{4m}) \cdot \cos (185.2) - ((\frac{3}{2}) \cdot {(\frac{3.7}{4m})}^{2}) + 4 \cdot {(\frac{5.01m}{4m})}^{2}))

Next Step Prepare to Evaluate

∴

S = 4 \cdot (1 - (\frac{{(\frac{3.7}{4})}^{2}}{4 \cdot (\frac{5.01}{4})}) - (\frac{4}{1.5 \cdot 52}) \cdot (0.5 - (\frac{3.7}{4}) \cdot \cos (185.2) - ((\frac{3}{2}) \cdot {(\frac{3.7}{4})}^{2}) + 4 \cdot {(\frac{5.01}{4})}^{2}))

Next Step Evaluate

∴

S = 2.0028877537144m

LAST Step Rounding Answer

∴

S = 2.0029m

Superelevation due to Varying Entrance Channel Cross-Section Formula Elements

Variables

Functions

Superelevation

Superelevation is the amount of raise of outer edge with respect to the inner edge of the road surface. In case of railways the amount by which the outer rail is raised is known as superelevation.

Symbol: S

Measurement: LengthUnit: m

Note: Value can be positive or negative.

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.

Bay Tide Amplitude

Bay Tide Amplitude is the average difference between water levels at high and low tide.

Symbol: a_B

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Channel Depth

Channel Depth is the vertical distance between the water surface and the lowest point of a waterway or conduit.

Symbol: D_t

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Bank Slope

Bank Slope defined as the angle, measured in degrees of deviation from the horizontal, at which earthy or rock material will stand [length-rise/length-run].

Symbol: m

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Channel Width corresponding to Mean Water Depth

Channel Width corresponding to Mean Water Depth is the width of the channel at the water surface level when the water depth is equal to the mean depth of flow.

Symbol: W

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Phase Lag

Phase Lag refers to the local epoch in order to distinguish it from other forms of epochs.

Symbol: k

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

cos

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

Syntax: cos(Angle)

Credits

Created by Mithila Muthamma PA

Coorg Institute of Technology (CIT), Coorg

Mithila Muthamma PA has created this Formula and 2000+ more formulas!

Verified by M Naveen

National Institute of Technology (NIT), Warangal

M Naveen has verified this Formula and 900+ more formulas!

Other formulas in Bay Superelevation category

Go Superelevation

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

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})}}

How to Evaluate Superelevation due to Varying Entrance Channel Cross-Section?

Superelevation due to Varying Entrance Channel Cross-Section evaluator uses 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)) to evaluate the Superelevation, The Superelevation due to Varying Entrance Channel Cross-Section 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. Superelevation is denoted by S symbol.

How to evaluate Superelevation due to Varying Entrance Channel Cross-Section using this online evaluator? To use this online evaluator for Superelevation due to Varying Entrance Channel Cross-Section, enter Ocean Tide Amplitude (a_o), Bay Tide Amplitude (a_B), Channel Depth (D_t), Bank Slope (m), Channel Width corresponding to Mean Water Depth (W) & Phase Lag (k) and hit the calculate button.

FAQs on Superelevation due to Varying Entrance Channel Cross-Section

What is the formula to find Superelevation due to Varying Entrance Channel Cross-Section?

The formula of Superelevation due to Varying Entrance Channel Cross-Section is expressed as 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)). Here is an example- 2.000651 = 4*(1-(((3.7/4)^2)/(4*(5.01/4)))-(4/(1.5*52))*(0.5-(3.7/4)*cos(185.2)-((3/2)*(3.7/4)^2)+4*(5.01/4)^2)).

How to calculate Superelevation due to Varying Entrance Channel Cross-Section?

With Ocean Tide Amplitude (a_o), Bay Tide Amplitude (a_B), Channel Depth (D_t), Bank Slope (m), Channel Width corresponding to Mean Water Depth (W) & Phase Lag (k) we can find Superelevation due to Varying Entrance Channel Cross-Section using the formula - 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)). This formula also uses Cosine (cos) function(s).

Can the Superelevation due to Varying Entrance Channel Cross-Section be negative?

Yes, the Superelevation due to Varying Entrance Channel Cross-Section, measured in Length can be negative.

Which unit is used to measure Superelevation due to Varying Entrance Channel Cross-Section?

Superelevation due to Varying Entrance Channel Cross-Section is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Superelevation due to Varying Entrance Channel Cross-Section can be measured.

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Superelevation due to Varying Entrance Channel Cross-Section Formula

Superelevation due to Varying Entrance Channel Cross-Section Example

Superelevation due to Varying Entrance Channel Cross-Section Solution

Superelevation due to Varying Entrance Channel Cross-Section Formula Elements

Credits

Other formulas in Bay Superelevation category

How to Evaluate Superelevation due to Varying Entrance Channel Cross-Section?

FAQs on Superelevation due to Varying Entrance Channel Cross-Section

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