Can't calculate minimum height between stairsteps to set off Slinky walk?

Factual Questions
1

See subject. I ask because at least this guy in 1988 couldn’t [cite]:
In 1946 W.J. Cunningham was midway in his first year as a professor in Yale University’s electrical engineering department when someone gave him a Magi-Koil … [renamed] the Slinky … Forty years ago Cunningham had printed a paper quantifying the actions of his intriguing new toy [in May/June 1987 American Scientist]… [now] he denigrates his earlier self-assurance, now that he is “less sure he really understands all that goes on.” …

In an interview he elaborated on the problems. “The general idea is pretty obvious, but even with all the physical measurements I wanted I couldn’t tell you the minimum height of step to kick it off on a walk down the stairs.” It’s tied up with the damping in the spring, which is hard to measure to begin with. “What’s clear is the larger the damping in the spring, the larger the step height, and I can tell you how long it will take to go down the step. But working from first principles I have not been abe to set up a predictive mathematical model.”

(Personally I think the author of the article, who shares one of my usernames, should have written “deprecates” instead of “denigrates,” or have said it simpler with an extra word or two.)

2

Longuet Higgens did this paper in 53

Here’s a cite for a 2001 paper, which does does reference Cunningham

http://www.researchgate.net/publication/229268651_Energy_threshholds_for_tumbling_springs

3

If there were no energy loss in the system as a whole, then with the right initial conditions you could get a slinky to walk across a flat plane. In reality, for any given real slinky, there is a certain amount of energy loss in each step, and so you need stairs of enough height to replenish that amount of energy. But there are many different mechanisms for energy loss, some of which are themselves difficult to deal with theoretically, so it’s difficult to calculate the total energy loss from first principles. Some energy is lost due to air resistance, some is lost due to interactions of various sorts between the ends of the slinky and the floor, some is lost when the sections of coil collide with each other, some is lost when the metal of the coil flexes, and so on.

4

So…is there a maximum height? Or can you slinky walk off of a cliff?

5

Gotta watch that first step. It’s a doozy.