Difference between revisions of "Elephants with spiderlegs"
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F_inertial = m ω^2 r = m v^2 / r | F_inertial = m ω^2 r = m v^2 / r | ||
with | with | ||
| − | + | m ∝ L^3 | |
and assuming | and assuming | ||
| − | ★ | + | ★ v ∝ L^0 |
| − | ★ | + | ★ r ∝ L^1 |
we get | we get | ||
| − | F_inertial | + | F_inertial ∝ L^2 |
with | with | ||
| − | A | + | A ∝ L^2 |
we get | we get | ||
| − | 𝜎 = F/A | + | 𝜎 = F/A ∝ L^0 |
| + | |||
| + | Good! works for all scales :) | ||
| + | But speeds stay constants so frequencies drop. | ||
| + | Not so good. Can we do something about it? Yes ... | ||
| + | |||
hollowing stuff out | hollowing stuff out | ||
(as is possible in low gravity) | (as is possible in low gravity) | ||
changes | changes | ||
| − | + | m ∝ L^2 | |
changes | changes | ||
𝜎 = ∝ L^-1 | 𝜎 = ∝ L^-1 | ||
| − | so we can do | + | so we can do what we wanted (increase speeds along with size) |
| − | + | v ∝ L^1 | |
and be back at | and be back at | ||
| − | + | 𝜎 ∝ L^0 | |
again | again | ||
| Line 48: | Line 53: | ||
When scaling to larger sizes forces from accelerations do NOT scale faster than the strength of the material. Given speeds are kept constant! <br> | When scaling to larger sizes forces from accelerations do NOT scale faster than the strength of the material. Given speeds are kept constant! <br> | ||
But if structures are hollowed out, as it is possible under low enough gravity, speeds can be scaled up along with the size. | But if structures are hollowed out, as it is possible under low enough gravity, speeds can be scaled up along with the size. | ||
| + | |||
| + | {{todo|How does this go together with the scale invariant [[unsupported rotating ring speed limit]]? Infinitesimally thin surfaces in the limit maybe?? To investigate.}} | ||
== Conclusion == | == Conclusion == | ||
| − | Machines shaped like | + | Machines shaped like Salvador Dalì's Elephants might actually work and exist in the future on asteroids. <br> |
| − | Salvador Dalì's Elephants | + | Heck, space-probes could probably do this in the foreseeable future (written 2021). |
| − | + | ||
| − | Heck space-probes could probably do this in the foreseeable future. | + | |
== Related == | == Related == | ||
Latest revision as of 08:48, 24 August 2021
Contents
In fiction and art
In "star wars", "war of the worlds", and Salvador Dali's pictures
it's likely just an artistic choice to make it look alien/surreal by making it look like something
that cannot be found by a long stretch (pun intended) in our world.
The artists probably have not thought deeply about the physics involved.
Making it work by by reducing gravity
Despite clearly not working here down on Earth with our crushing gravity
interestingly this "gargantuan spiderelephant anatomy" might actually practically work
on low but not too low gravity celestial bodies like e.g. big asteroids where the k in
» F_grav ∝ k * L^3 «
is sufficiently small.
Pros:
- no continuously depleting propellant needed
- more control than jumping
Math in more detail & making it work even better by "making the elephants hollow"
F_inertial = m ω^2 r = m v^2 / r with m ∝ L^3 and assuming ★ v ∝ L^0 ★ r ∝ L^1 we get F_inertial ∝ L^2 with A ∝ L^2 we get 𝜎 = F/A ∝ L^0
Good! works for all scales :) But speeds stay constants so frequencies drop. Not so good. Can we do something about it? Yes ...
hollowing stuff out (as is possible in low gravity) changes m ∝ L^2 changes 𝜎 = ∝ L^-1 so we can do what we wanted (increase speeds along with size) v ∝ L^1 and be back at 𝜎 ∝ L^0 again
In words:
When scaling to larger sizes forces from accelerations do NOT scale faster than the strength of the material. Given speeds are kept constant!
But if structures are hollowed out, as it is possible under low enough gravity, speeds can be scaled up along with the size.
(TODO: How does this go together with the scale invariant unsupported rotating ring speed limit? Infinitesimally thin surfaces in the limit maybe?? To investigate.)
Conclusion
Machines shaped like Salvador Dalì's Elephants might actually work and exist in the future on asteroids.
Heck, space-probes could probably do this in the foreseeable future (written 2021).
Related
External links
- "The Elephants" by Salvador Dali
- Originally posted here on twitter: [1]
