February 27, 2015

Horse 1847 - Buying A Stairway To Heaven

There's a lady who's sure all that glitters is gold
And she's buying a stairway to heaven.
When she gets there she knows, if the stores are all closed
With a word she can get what she came for.
Ooh, ooh, and she's buying a stairway to heaven.
Ooh, it makes me wonder,
Ooh, it makes me wonder.
- "Stairway to Heaven", Led Zeppelin (1971)

Wonder no more, oh songsmiths from 1971, for where there are numbers to be crunched, I can crunch them.

This problem from the outset appears to be little more than a quantity surveying exercise. The two questions we need to ask are:
1. How big does a stairway need to be before it gets to "heaven"?
2. How much would said stairway cost?

The Greeks had several words for the heavens but the one most useful to us, which suggests a physical place where one could theoretically build to, is "ouranos" or "the starry heavens".
So where do they begin?

There is a great story about how Annie Glenn, the wife of the first American in space John Glenn, went to see their Presbyterian minister to ask if God would protect their husband when he left the earth. Their minister saw no reason why this shouldn't be the case.

Just before the launch of the Friendship 7 capsule that took John Glenn into space, his fellow Mercury Program astronaut Scott Carpenter delivered a most famous sendoff with the words 'Godspeed, John Glenn'.

As John Glenn orbited the earth, he noticed something:

This is Friendship Seven. I’ll try to describe what I’m in here. I am in a big mass of some very small particles, that are brilliantly lit up like they’re luminescent. I never saw anything like it. They round a little; they’re coming by the capsule, and they look like little stars. A whole shower of them coming by.
00 01 15 57
- The Mystery of John Glenn’s Fireflies Returns, Nancy Atkinson, Universe Today, 5th Jan 2001

That shower of little stars turned out to be frost from the condensation which had settled on the spacecraft before takeoff, or another source as Wally Schirra, the astronaut of the sixth Mercury flight on board Sigma 7 said:
"Their source was water released in the heat exchange process that cooled our space suits. Another source was urine. ‘We peed all over the world,’ I’m fond of saying, despite the groans that come from the audience.”

The "starry heavens" (even from the constellation Urion) begin where the atmosphere ends.
The definition accepted by the Fédération Aéronautique Internationale as to where the sky ends and space begins, is called the Kármán line after Hungarian engineer Theodore von Kármán and is set at an aribtrary limit of 100 kilometers.

Knowing this, it's dead simple to cost out our Stairway to Heaven.

A client of ours who is a builder, will build you a standard 1500mm spiral staircase with 12 stairs and a 220mm rise for $480.

220mm x 12 = 2640mm

$480.00 / 2640mm = 18.1818c per mm

10m of stairs would cost $1818.18
100m of stairs would cost $18,181.82
1km of stairs would cost $181,818.18
100km of stairs; which is enough to reach  "the starry heavens" would cost $18,181,818.18

I'm not suprised that "when she gets there she knows, if the stores are all closed
With a word she can get what she came for". Most people can get what they come for if they're willing to flash more than $18 million about the place.

It doesn't make me wonder. I have the power of maths.

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