I’m always up for a bit of a challenge so after digging around on the internet for awhile and reading some documents provided by some of my mentors here is what I have for classical columns:
1.) The diminution ratio seems to be 5/6 for most columns that are 15ft of less. I will label this ratio as “m”.
2.) There is a height to diameter ratio however I think I should leave it up to the user to specify whatever diameter they chose for any particular height however I could suggest the classical (recommended) diameter for a given height.
3.) If we let the base diameter be “d” then the entasis radial difference “E” is given by:
E = d(1-m)/2.
4.) Let h = height of the shaft. The entasis (or diminution) begins at a height of 1/3h. The entasis is not a linear reduction in diameter but rather follows a curved profile with the radius of curvature tangent to the lower cylindrical portion of the shaft.
5.) The radius of the entasis curvature is given by r = 2h^2/9E + E/2.
6.) The angle of the sweep of the arc is given by theta = asin(2h/3r)
The above derivation and observations should then give me enough information to be able to properly draw the shaft of any classical column. The base and capital however are a whole nother story.
