KdK (Kinetik der Kontinua) part 1: Introduction

Whips, chains, and their possible relevance to space launch

An early participant in Blue Origin recently sent me this link, which depicts a category of device that when I was there (1999-2006) we referred to as an Aitkenator or, more colloquially, a chain-flinger. This inspired me to dig up some old notes on the topic. I’m going to write them up in a series of posts here and put them up sporadically in coming weeks. For the most part this won’t be about anything that happened at Blue Origin. It’s about a series of scientific papers, the most recent of which was published in 1950.

This all started out as a study of the physics of bullwhips. These are remarkable in that, though they are of prehistoric origin, and extremely simple, they are capable of breaking the sound barrier (as has been well documented at least as far back as 1927, the bang that you hear when someone cracks a whip is actually a sonic boom). On further investigation it became clear that the same physics are at work in the case of chain-flingers such as the one shown in the above linked video. The only difference is that in the case of a whip, one end of the system is free.

During the time I was working on this at Blue Origin I had trouble settling on a name for this field of investigation. I ended up calling it filamentary systems: the physics of long slender flexible things that are moving. I was never really happy with that name. Recently, upon cracking open some of the old papers I found while studying this, I came across the German phrase Kinetik der Kontinua: the physics of continuous media. I like that a lot better and so I’m going to call it by that name, or KdK for short.

Everything that I did was based on these historical papers, which I plan to cover one by one in this series. I don’t claim to have done any original work in this field. I simply went to the library (yes, it was that long ago) and found these papers and translated them.

In this first post, before digging into the actual science, I’m going to address a question that might have already suggested itself to some readers: what possible relevance could bullwhips and moving loops of chain have to the problem of launching things into space? Could you actually build a chain-flinger or a giant bullwhip that was big and fast enough to launch something into orbit?

The answer is absolutely not, for a bunch of reasons. But you don’t have to attain orbital velocity in order to make something that’s actually useful. This is a consequence of the Rocket Equation, which is an exponential. And exponential behavior is notoriously counterintuitive.

Here’s one example that might help to shed some light on it. At one point when I was researching older space launch ideas, I came across a proposal to construct an ocean-going barge somewhere around the earth’s equator and build a space shuttle launch pad on top of it. Because of the earth’s rotation, merely launching from the equator would provide an extra velocity boost of two hundred kilometers per hour compared to launching from Cape Canaveral. In addition, this barge was going to be equipped with an array of jet engines, aimed horizontally, which would be lit up to drive the thing across the surface of the ocean at an additional hundred km/h or so. The space shuttle would then launch vertically from the barge.

From a layperson’s perspective this seems an insane plan. In order to get into orbit the vehicle needs to accelerate to something like 29,000 km/h. How could it possibly be worth all of that trouble and expense to give it an initial velocity boost of a mere 300 km/h?

One way to answer that question is to imagine a space shuttle lifting off from the launch pad at Cape Canaveral and accelerating to the point where it’s going 300 km/h. During that time its engines are burning fuel at a tremendous rate.

This is where the exponential weirdness kicks in: the heavier the rocket gets, the more fuel it takes just to budge it off the launch pad, and the more fuel it takes, the heavier it gets, and so on. If gravity were just a little stronger or rocket engines just a little less powerful, we’d never get into orbit at all—at least, not until we came up with some technology other than chemical rocket engines.

If you could spare that first few seconds’ fuel consumption by giving the vehicle an initial speed boost, then some of the weight saved could instead be used to carry payload. And the cost per kilogram of payload delivered to orbit is exceedingly high. If you pencil it all out, it actually begins to make sense to think in terms of a huge jet-powered launch barge.

Consequently there have been a lot of ideas floated over the decades for schemes to get ordinary rockets moving a little faster and/or launch them from higher altitudes, just to spare some fuel and thereby make those rockets capable of delivering heavier payloads than they could if launched from a standing start at sea level. Of all such ideas we looked at during Blue Origin’s early think-tank era, my favorite was, and still is, the idea of constructing a very tall tower (say, 20 - 25 kilometers). This notion was in no way original, having been systematically investigated by Geoff Landis, who enumerated a whole list of ways in which launching from high altitude would be beneficial.

Having said all of that, huge bullwhips and enormous moving chain loops were a sentimental favorite for a minute just because of their weird beauty and the basically steampunk aesthetic of making a machine so large and powerful. In an alternate timeline where the Victorians decided it would be a good idea to launch things into space, they might have thought in terms of trains rather than rockets, and constructed trains into the sky, making use of physics that had already been worked out by one of the scientists I’m going to talk about in this series.

All of which is basically background to the series of posts I’m going to make here, which is going to focus on the science of KdK and the remarkable collection of scientists who studied the problem between the Victorian era and the aftermath of the Second World War. I’m going to proceed in reverse chronological order, beginning with a paper by Grammel and Zoller completed in 1949 and published in 1950. I’ll post that one immediately and then follow up with others as time permits.

Finally though, I’d just like to stress that, since well before my 2006 departure, Blue Origin has been a level-headed aerospace engineering organization that just makes rockets!