How to calculate the area of a segment of a tunnel (circle)
If the length of the chord and height of the segment are given, the
shortcut calculation has been developed, called the CBS Factor. The calculation
has been shown below. …..
Area of Segment of Tunnel/Circle = ((Angle of Sector θ/360) - (Sin θ/2π)) X CBS FACTOR
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Where,
CBS FACTOR = 78.53981632
θ = 2X (cos-1 (1-h/r))
where h = height of segment
r = radius of circle
θ=Angle of sector
r=(c²/8h)+(h/2)
where c = length of chord
h=height of segment.
From the above formula,
we can calculate the area of a segment of a circle instantly with simple multiplication.
For example….
For 6 mtrs. Chord length
and 1 mtr. height of segment, the area of the segment has been calculated.
Area = ((73˚44’23.26’’/360˚)-(Sin73˚44’23.26’’/2π)) X78.53981632
=4.0875 m²
The above calculation can be verified using AutoCAD or any
mathematical technique
