How to calculate the Area of Segment of Tunnel (Circle)
If length of chord and height of segment are given, the
short-cut 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˚)-(Sinθ/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 Segment has been calculated.
Area = ((73˚44’23.26’’/360˚)-(Sin73˚44’23.26’’/2π)) X78.53981632
=4.0875m²
The above calculation can be verified using Auto-Cad or any
mathematical technique
