OK, let’s say I have some cord which weighs 1 gram per cm. And let’s say it has a breaking strain of 100kg.
If I were to start unreeling a length down the side of a fictitiously tall building, would it eventually break under its own weight?
And would that length be approximately 1,000m as the numbers might suggest, or are there other factors at work here?
Thanks
M
Yes, it will eventually break under its own weight, and it should break right up at the top since that’s the part holding the greatest total weight.
If you let it out slowly you should come pretty close to the expected length where weight=breaking strength (1km in your example). If the rope is bouncing around, twisting, being run over a sharp bend other such things it may break sooner.
That’s the main factor that’s prevented us from building a ‘space elevator’ so far. We just don’t have any cable with a high enough tensile strength and low enough mass to not break from it’s own weight. There are lots of science fiction books on this concept – see David Gerrold for some recent ones.
I’ve heard that spider web silk would meet this requirement, if only we knew how to mass-produce spiderwebs, and if the tensile strength/mass ratio stayed constant when ramped up to a multi-ton cable.
Is that so? I thought there was nothing even close to being strong enough for space elevator on Earth (other than still-to-be-invented versions of nanotubes). Anyone with the numbers for this?
[extreme, fussy, nitpick]“Strain” is the amount by which the material deforms in response to a load. “Stress” is the magnitude of the load. “Unit stress” is the magnitude of the load/unit of cross section area.[/extreme, fussy, nitpick]
Wikipedia article (Spider silk - Wikipedia) claims that spider silk is about as strong as good steel (this matches what I heard way back in my “Strength of materials” class back in college) however it’s considerably lighter.
Overall it’s as good as modern synthetic fibers like Kevlar, which as I recall is a long way off from being strong enough to support a few hundred (thousand?) miles of its own weight.
I’ll nitpick the nitpick.
“Strain” is the elongation divided by the original length, as explained here.
“Stress” is a force per unit area.
In principle, you could construct a self-supporting cable of any length, from any material. The trick is to taper the cable. At the top end, where it needs to support a lot of weight, you make it very wide, and at the bottom, where it doesn’t need to support it much, you make it narrower to save weight. The catch for something like a space elevator is that, for ordinary materials like steel or spiderweb, you’d need an impractically large taper ratio, such that the “top” of the cable (actually the middle, for a space elevator) would have to be thousands or millions of times thicker than the ends. Even for a hypothetical nanocable, you’d still need a taper, but there is a more plausible 5 to 1 or so.