Isosceles Triangle Method Calculator

✖Number of Crossing - Crossing or ‘frog’ is a device that provides two flangeways through which the wheels of the flanges may move when two rails intersect each other at an angle.ⓘ Isosceles Triangle Method [N]

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Formula

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Isosceles Triangle Method

Formula

`"N" = (1/2)*cosec("α"_{"Crossing"}/2)`

Example

`"14.32685"=(1/2)*cosec("4°"/2)`

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Isosceles Triangle Method Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Crossing = (1/2)*cosec(Angle of Crossing/2)
N = (1/2)*cosec(α_Crossing/2)
This formula uses 2 Functions, 2 Variables

Functions Used

sec - Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine., sec(Angle)
cosec - The cosecant function is a trigonometric function that is the reciprocal of the sine function., cosec(Angle)

Variables Used

Number of Crossing - Number of Crossing - Crossing or ‘frog’ is a device that provides two flangeways through which the wheels of the flanges may move when two rails intersect each other at an angle.
Angle of Crossing - (Measured in Radian) - Angle of Crossing is the angle that the gauge faces make with each other.

STEP 1: Convert Input(s) to Base Unit

Angle of Crossing: 4 Degree --> 0.0698131700797601 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (1/2)*cosec(α_Crossing/2) --> (1/2)*cosec(0.0698131700797601/2)

Evaluating ... ...

N = 14.3268541739246

STEP 3: Convert Result to Output's Unit

14.3268541739246 --> No Conversion Required

FINAL ANSWER

14.3268541739246 ≈ 14.32685 <-- Number of Crossing

(Calculation completed in 00.004 seconds)

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Credits

Created by Smriti Singh

MIT Academy of engineering, Pune (MITAOE), Alandi, Pune

Smriti Singh has created this Calculator and 25+ more calculators!

Verified by Rachana B V

The National Institute of Engineering (NIE), Mysuru

Rachana B V has verified this Calculator and 50+ more calculators!

< 10+ Points and Crossings Calculators

Switch-Lead SL

Go Switch Lead = sqrt(2*Radius of Outer Curve of Turnout*Heel Divergence)

Curve Lead (C.L )

Go Curve Lead = sqrt(2*Radius of Outer Curve of Turnout*Gauge Length)

Switch Angle

Go Switch Angle = asin(Heel Divergence/Length of Tongue Rail)

Theoretical Length of Tongue Rail

Go Length of Tongue Rail = Heel Divergence/sin(Switch Angle)

Number of Crossing (N)

Go Number of Crossing = Spread at Leg of Crossing/Length of Crossing from TNC

Isosceles Triangle Method

Go Number of Crossing = (1/2)*cosec(Angle of Crossing/2)

Centre Line Method

Go Number of Crossing = (1/2)*(cot(Angle of Crossing/2))

Curve Lead (C.L ) if given N

Go Curve Lead = 2*Gauge Length*Number of Crossing

Right Angle or Cole's Method

Go Number of Crossing = cot(Angle of Crossing)

Curve Lead

Go Curve Lead = Switch Lead+Crossing Lead

Isosceles Triangle Method Formula

Number of Crossing = (1/2)*cosec(Angle of Crossing/2)
N = (1/2)*cosec(α_Crossing/2)

Isosceles triangle method

This method is important for layout of tramways
Since the angle of crossing is very small, so the difference in the values of ‘N* by different methods is also small.

How to Calculate Isosceles Triangle Method?

Isosceles Triangle Method calculator uses Number of Crossing = (1/2)*cosec(Angle of Crossing/2) to calculate the Number of Crossing, The Isosceles Triangle Method formula is used to calculate number of crossings , using angle of crossing as input. Number of Crossing is denoted by N symbol.

How to calculate Isosceles Triangle Method using this online calculator? To use this online calculator for Isosceles Triangle Method, enter Angle of Crossing (α_Crossing) and hit the calculate button. Here is how the Isosceles Triangle Method calculation can be explained with given input values -> 14.32685 = (1/2)*cosec(0.0698131700797601/2).

FAQ

What is Isosceles Triangle Method?

The Isosceles Triangle Method formula is used to calculate number of crossings , using angle of crossing as input and is represented as N = (1/2)*cosec(α_Crossing/2) or Number of Crossing = (1/2)*cosec(Angle of Crossing/2). Angle of Crossing is the angle that the gauge faces make with each other.

How to calculate Isosceles Triangle Method?

The Isosceles Triangle Method formula is used to calculate number of crossings , using angle of crossing as input is calculated using Number of Crossing = (1/2)*cosec(Angle of Crossing/2). To calculate Isosceles Triangle Method, you need Angle of Crossing (α_Crossing). With our tool, you need to enter the respective value for Angle of Crossing and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Crossing?

In this formula, Number of Crossing uses Angle of Crossing. We can use 3 other way(s) to calculate the same, which is/are as follows -

Number of Crossing = Spread at Leg of Crossing/Length of Crossing from TNC
Number of Crossing = cot(Angle of Crossing)
Number of Crossing = (1/2)*(cot(Angle of Crossing/2))

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