# Physical properties of just a giant tower of solid metal **URL:** \ **Category:** Factual Questions\ **Created:** [November 14, 2022, 8:02pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906 "2022-11-14T20:02:20Z")\ **Posts on this page:** 13\ **Page:** 2
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [November 20, 2022, 1:56pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/21 "2022-11-20T13:56:09Z")
In general, one bound on the height of a cylindrical tower is that the yield strength at the base must be greater than the pressure. If you crunch the numbers, this works out to be \text{max. height} = \frac{\text{compressive yield strength}}{\text{(density)} g} where g is the acceleration due to gravity. Note that this is independent of the cross-sectional area (though of course changing the cross-sectional area will affect this tower’s stability to other failure modes.) This means that you can place a bound on the height of a tower just by knowing the properties of the material it’s made of. For [copper](https://www.copper.org/resources/properties/144_8/) this works out to be anywhere between 500 and 5000 meters depending on the alloy in question (see Table 2). ---
**Author:** ![3AxisCtrl](https://avatars.discourse-cdn.com/v4/letter/3/ecd19e/32.png) [@3AxisCtrl](https://boards.straightdope.com/u/3AxisCtrl)\ **Post date:** [November 20, 2022, 2:34pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/22 "2022-11-20T14:34:08Z")
> [@Chronos](#): > > Uneven heating, though, would be an issue. If the Sun is shining on one side of the tower, for instance, that side would get hotter than the shaded side, and so the sunward side would expand more, and so you’d get a slight curvature. But it wouldn’t take much curvature for a 240-meter-tall tower to put its center of mass outside of its footprint. My back-of-the-envelope calculation indicates that a 20-degree F temperature difference between the two sides (unlikely in a metal that conducts heat as well as copper) would make the sunny side around an inch longer. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [November 21, 2022, 6:39pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/23 "2022-11-21T18:39:43Z")
There’s also self-buckling to consider, when a column experiences buckling under its own weight. A free standing column with density p , Young’s modulus E, and cross-sectional area A, will buckle under its own weight if its height exceeds a certain critical value defined by: max height = (7.8373 \* (E_I / p_g\*A))^1/3 , where g is gravitational acceleration and I is the second moment of area of the cross section. ---
**Author:** ![Sunspace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sunspace/32/1250_2.png) [@Sunspace](https://boards.straightdope.com/u/Sunspace)\ **Post date:** [November 22, 2022, 12:41pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/24 "2022-11-22T12:41:07Z")
What units are those in? ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [November 22, 2022, 3:28pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/25 "2022-11-22T15:28:32Z")
That magic number 7.83735 is just a dimensionless constant, unless I misunderstood something. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [November 22, 2022, 3:30pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/26 "2022-11-22T15:30:08Z")
Correct. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [November 22, 2022, 3:35pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/27 "2022-11-22T15:35:10Z")
> [@Sunspace](#): > > What units are those in? Just keep the units consistent, Si or English for everything. 7.8373 is a dimensionless constant. ---
**Author:** ![Dorjan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dorjan/32/12440_2.png) [@Dorjan](https://boards.straightdope.com/u/Dorjan)\ **Post date:** [November 22, 2022, 4:18pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/28 "2022-11-22T16:18:38Z")
I went ahead and ran the self buckling calculations for a 5m (16.4ft) solid copper cylinder. If my math is mathing, the critical height before it will buckle under its own weight (all other factors notwithstanding) is approximately 303m (995 ft). ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [November 22, 2022, 4:24pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/29 "2022-11-22T16:24:17Z")
I’m getting there. My copper tower is at 275 metres. ---
**Author:** ![Retzbu\_Tox](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/retzbu_tox/32/11829_2.png) [@Retzbu\_Tox](https://boards.straightdope.com/u/Retzbu_Tox)\ **Post date:** [November 27, 2022, 3:05am UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/30 "2022-11-27T03:05:30Z")
Remove the bottom layer of blocks and place them at the top, leaving the entire 52 million kilogram structure hovering in the air like some Wile E. Coyote project, violating everyone’s OCD. When they complain, tell them it’s a space elevator in geostationary orbit. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [November 27, 2022, 3:09am UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/31 "2022-11-27T03:09:41Z")
The joys of Minecraft. Copper: 298 metres Gold: 47 metres Iron: 139 metres Coal is at 98 metres but the concept of cubic metre blocks of solid coal doesn’t make as much sense. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 27, 2022, 4:20pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/32 "2022-11-27T16:20:42Z")
Aside: Minecraft Steve can carry 45,660 tons, based on inventory, stack limits, and the mass of a cubic meter of gold. There are heavier calculations out there on the Internet, but they’re all based on the (IMO unfounded) assumption that a crafted item weighs as much as the sum of all of its ingredients. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [November 27, 2022, 6:00pm UTC](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906/33 "2022-11-27T18:00:33Z")
The addition of shulker boxes means you can carry way, way more than that. They are in effect portable chests, so each can carry 27 more stacks. [Previous page](https://boards.straightdope.com/t/physical-properties-of-just-a-giant-tower-of-solid-metal/974906.md?page=1)