Once the constants c and v are known, the entire shell can be generated from the knowledge of one cross-section: each point (x,y,z) generates the curve F(t) = e^(vt)(x cos(ct) + y sin(ct), -x sin(ct) + y cos(ct), z), and these curves together generate the entire surface of the shell.
In generating the models for this column, I have assumed that the section is an ellipse in the (x,z)-plane, of the form (h + a cos s, 0, k + b sin s), for s between 0 and 2 Pi. (For more general cross-sections see Randolf Schultz's Shelly page.) The Maple instruction that generates the mathematical models is plot3d([exp(v*t)*(h+a*cos(s))*cos(t),-exp(v*t)*(h+a*cos(s))*sin(t), exp(v*t)*(k+b*sin(s))],s=0..2*Pi,t=-10..-1,grid=[30,50],scaling=constrained); The constants v,c,a,b,h,k were chosen by eye, without careful measurements, to give the best match to the available images. Their effect on the shape of the shells is shown in the examples below and in the Flat-coil examples (k=0).