Sunday, June 21, 2015

Roman Arch – Area and Volume Derivation

It’s good to be back. 


This is your basic Roman Arch, with the top part having an elliptical shape, which sits on two pillars.



Dimensions:
S = length of the track
H = height of the pillars
D = depth of the arch, usually small
W = gap between the pillars
R = gap between the bottom of the curve to the point where the arch curves

Surface Area:

A = Total Surface Area
AT = Area of the Elliptical ring (top)
A0 = Outer Elliptical Area
AI = Inner Elliptical Area
AP = Pillars Area (2 pillars)


Area of the Elliptical Ring (top)
AT = AO – AI
AT = π*(S + W/2)*(S + R) – π * W/2 * R
AT = π*((S + W/2)*(S + R) – W/2 * R)
AT = π*(S^2 + R*S + S*W/2)

Area of the Pillars (there are two of them):
AP = 2*H*S

Total Surface Area:
A = AT + AP
A = π*(S^2 + R*S + S*W/2) + 2*H*S
Volume of the Roman Arch:
V = D * A
V = D * (π*(S^2 + R*S + S*W/2) + 2*H*S)

Eddie


This blog is property of Edward Shore.

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