Giovanni,
Whoops! You are correct, of course...meant to say KILOmeters...slight difference.
As to what it has to do with heat input in a weld, I suspect this formula is derived from some basic law of thermodynamics that deals with heat transfer, and is related to E=MC^2, Energy (E) equals mass (M) times the speed of light (C), squared.
If this is not complicated enough for you, take a look at a paper entitled "An upwind numerical solution of nonlinear advection-diffusion problems with a moving heat source" at http://link.springer.de/link/service/journals/00231/bibs/8034004/80340287.htm.
The abstract says, "In the present work, two-dimensional temperature variations and a position of a weldpool within a workpiece during keyhole plasma arc welding are determined. The model allows to include temperature dependent thermal properties, variable welding speed, different keyhole radii and a nonlinear boundary condition of the third kind on the upper and the lower surfaces of the workpiece."
As a writer/software developer, taking up welding as a hobby, I ran across this BBS by accident, and I am amazed at the richness of the subject. I have never realized how important welding is to our civilization, or how much science is involved. I'm glad you guys are on top of this...I just hope to learn to run a nice looking bead on two pieces of mild steel with a gas torch, and maybe later learn MIG and TIG!
John Phillips