Pyramid Skyscraper To Orbit?

[Jadzia]

Skyscrapers are pretty high but they can only go so high before they become unstable and susceptible to the high winds and also there's the whole problem with lift shafts and pumping water around etc.

Now a pyramid building would be completely stable and would never topple over and with it designed like it is plenty of lift shaft could be fitted in to allow travelling to all levels.

For a pyramid building to be stable it has to be at a certain angle.
What angle would it be stable at? 45 degrees would be most stable I suppose but surely it could rise at a steeper angle and still remain stable?

The shallower the angle, the more stable. 45 degrees isn't a special angle for engineering.

Now for my ultimate question: If we were to build a pyramid so the tip of the Pyramid reached orbit (orbit being in this case the location where the Earths atmosphere borders the Vacuum of space which is 75 miles I think??) how steep could we have the pyramid and how much land area would it need to take up in order to have a pyramid at that angle and at that height?

If we look at this purely from a physics point of view, the relevant factors are compressive stresses on the structure, and whether or not it is likely to topple.

For granite, a typically strong construction material, the compressive strength is about 200 x 10^6 N/m^2

It has a density of 2650 kg/m^3

For a pillar, the compressive stress on the base computes as

= density * gravity (9.8) * height

So a perfect granite pillar erected on the surface of the earth could theoretically support it's own weight upto a height of around 7700 m high, or 7.7 kilometers. Any higher than this and the base would certainly deform.

In a pyramid you're using a greater base, so it can support more weight.

The volume of a pyramid is = Area of the base * Height * 1/3

The compressive stress on the base would therefore be:

= density * volume * gravity / base area
= density * gravity * (base area * height * 1/3) / base area
= density * gravity * height / 3

200 x 10^6 = 2650 * 9.8 * Height / 3

So you could build a granite pyramid no more than 3 times higher than a granite pillar, which is a pyramid no higher than 23km. Notice that the slope angle does not affect the compressive stress on the base at all.


So the answer is no it can't be done with today's construction materials. Diamond maybe. This calculation also has tentative implications for the maximum possible heights of mountain ranges, which are nature's own pyramids.

Incidentally, the difference between the highest (Everest) and lowest (Mariana's Trench) on Earth is about 20km, which sits nicely within the 23km bounds, and may or may not be relevant.

 

[Trekker4747]

You know, the hour-long elevator ride to the top of this thing would SUCK!

 

[Australis]

Dude, it's called in-elevator entertainment.

"Tall and tan and young and lovely,
The gir from Ipanema goes walking..."

 

[Trekker4747]

Dude, it's called in-elevator entertainment.

"Tall and tan and young and lovely,
The gir from Ipanema goes walking..."

Nothing says a great time like riding in an elevator and listening to "In-A-Gadda-Da-Vida".... twice.

 

[Alpha_Geek]

Perhaps if you played InnaGaddaDavida at incredible volume from multiple speakers placed around the bottom of the elevator...

No, that's crazy. Nevermind.

 

[sojourner]

Right, so what you're all saying to me is that "orbit" has no actual height/distance from the Earths surface and would therefore need some kind of clarification, a clarification that I put into my original post when I said that by orbit I meant 75 miles up where the atmosphere borders the vacuum of space.

Well, again, there's no border "cut off point" between the atmosphere and the vacuum of space. The air just gets thinner and thinner as you go up until it gets so thin that it isn't there no more. But there's no instant cut-off point.

I understand what you are saying but really there is a cut off the point, the cut off point is where the last of the gas molecules/atoms are and thereafter it becomes vacuum. A guestimate would be 75 miles up.

Your guesstimate is way off. As has been mentioned the ISS still needs reboosts of it's orbit at a height of over 200 miles due to atmospheric drag. So there are still peltny of gas molecules/atoms at 75 miles.

 

[All Seeing Eye]

Well, again, there's no border "cut off point" between the atmosphere and the vacuum of space. The air just gets thinner and thinner as you go up until it gets so thin that it isn't there no more. But there's no instant cut-off point.

I understand what you are saying but really there is a cut off the point, the cut off point is where the last of the gas molecules/atoms are and thereafter it becomes vacuum. A guestimate would be 75 miles up.

Your guesstimate is way off. As has been mentioned the ISS still needs reboosts of it's orbit at a height of over 200 miles due to atmospheric drag. So there are still peltny of gas molecules/atoms at 75 miles.

It's not even my guestimate. Go take it up with Wikipedia if the guestimate is wrong.

 

[Trekker4747]

Probelm #1 with your understanding of science and why things will or will not work:

Using Wikipedia as a reliable information source.

 

[All Seeing Eye]

I did a search to find out how high the atmosphere goes, wiki said between something or other and 75miles up. I had no reason to doubt that information.

 

[Scout101]

Given 2 minutes, Wikipedia can be made to say that the atmosphere ends at 75 feet, too. That's why it's not a good resource.

Still not a good question, anyway. Something can be made to 'orbit' at 100 ft off the ground, it'll just take a LOT of thrust/energy to maintain that orbit. What's special about putting something at a height where the atmosphere is extremely thin?

Either way, not sure what else can be said here. You asked if it could be done, and the general answer (including some math and physics) seems to be that the simple crushing weight of this thing would answer No, not without collapsing under its own weight. And that says nothing about its effect on the surface of the earth, weather patterns, etc. Nor could anyone come up with a benefit of having a structure at this altitude, certainly not for the crushing cost of this thing in time, resources, and money. Can't even think of a USE for the thing, as the height isn't useful, introduces a million problems, and wouldn't even be desireable to live in.

next question?

 

[sojourner]

I did a search to find out how high the atmosphere goes, wiki said between something or other and 75miles up. I had no reason to doubt that information.

Well, now you do.

 

[TheMasterOfOrion]

space elevators are a great dream but it won't happen for another 100 yrs

 

[chardman]

space elevators are a great dream but it won't happen for another 100 yrs

The folks at The Spaceward Foundation might well take issue with that.

In his last years, Sir Arthur C. Clarke predicted that the space elevator will be built "about 10 years after everyone stops laughing". We believe people will stop laughing once a proper tether is demonstrated, and we think that this will happen within 5 to 10 years.

http://www.spaceward.org/

And from what I've heard, the Japanese maintain that they've recently had a breakthrough that may allow them to fabricate a working tether as early as next year!

I'm over 50, and I truly believe that Space Elevators will become a reality in my lifetime. Atmosphere breaching pyramids and Apocalyptic cataclysms foretold by Mayans? Not so much!

 

[Trekker4747]

Ok here's some quick and dirty stuff...

The WTC Tower 1 was 1,355 Feet tall and had an area/footprint of an acre (43,560 sq feet.) a volume of 59 million cubic feet. ( a floor area of about 4.8 million sq. ft.)

Each tower took about six years to build.

Now. Assuming a pyramid with a square base:

Area of base as calculated by JB2005 was 5625 sq.miles.

Volume of a Square-based Pyramid:

Length of Base * Width of Base * Height * 1/3.

So 5625 (miles) * 5625 (miles) * 75 (miles) * 1/3 = 2,373,046,875 miles.

Cubic Miles. Or 12,529,687,500,000 cu. feet.

12.5 trillion square-foot volume. Or a "floor area" of about (assuming the same "ratio" of volume to floor-area as the WT1) 968,992,248,062 sq. feet.

215,000 times the WTC.

If we're to also assume the same "ratio" of volume to construction time it'd pretty much take half the length of the entirity of human history to construct this thing.

 

[Jadzia]

out by a factor of 5625

and you dont convert cu-miles to cu-feet that way

 

[Trekker4747]

out by a factor of 5625

and you dont convert cu-miles to cu-feet that way

Dammit. I KNEW I'd mess the math up!

Ok.

2.3 Billion cu. miles to cubic feet is 3,500,000,000,000,000,000,000 cu. feet.

Divide by the volume of the WTC = 7.3^13

73,000,000,000,000 so that's 73 trillion times the volume of WTC?



Or have I buried my self in bad math and need to start over?

Ok. I'm starting over.

Base of pyramid: 5625 miles (29,700,000 feet)

Height of pyramid: 75 miles (396,000 feet)

Volume of a pyramid: L*B*H*1/3

29700000 * 29700000 * 336000 * 1/3 = 98,794,080,000,000 (98.8 Trillion)

A "floor space" of 8,233,333,333,333 (8.2 Trillion)

8.2 Trillion / 4.8 million = 1708x the "floor space" of the WTC. (1.8m times the volume)

WTC Volume: 59m cuft in 6 years. = 9.8m cuft/year
WTC "Floor Area": 4.8m sqft in 6 years = 800,000 cuft/year

Hyper Space Pyramid Volume: 98.8t cuft = 10m times the WTC.

I know I'm messing something up in the math, being tired and trying to do this with Windows calculator isn't easy, not mention working with such large numbers.

I think it's simple to say that constructing such a thing would take eons to do.

 

[Scout101]

I think my favorite part is that even if we ignore the insurmoutable problems of construction (time, energy, cost, and materials), there's still not a single positive reason to build the damned thing. And, of course, a fairly glaring negative:

it would destroy the planet.

If you somehow keep it from crushing itself (unsure how), the sheer mass of the thing would probably sink right into the core. And seriously screw with weather patterns, wrecking anything within about a continent or two...

 

[All Seeing Eye]

[joke] Now for the killer question: What if we were to build this thing and then fit huge rockets underneath it to blast it into space.............[/joke]

 

[Scout101]

[joke] about the same result as if you built it from your original specs. not only can't be done, but it would crush itself into oblivion long before 'liftoff'. And that's ignoring the fact that there probably isn't enough fuel if you used every once of oil on the planet, and fired every nuke you could build, to get it high enough to slide a sheet of paper underneath[/joke]

 

[trekkiedane]

The last couple of posts actually gave me this idea:

How about building it in orbit and then putting it down somewhere, you know where there's a country/continent we might like to destroy anyway, Wouldn't that be easier?