To address the buckling issue. There are two forms of buckling that are
relevant for this tower. One is a local buckling that would cause
wrinkling of the outer surface. I agree that inflated toroidal tubes
can be arranged to resist this. But the more serious buckling, which
the inflated tubes will not help, is global buckling.
Imagine a long thin element, like a plastic ruler or a bamboo cane. If
you put an axial load onto the ruler it will buckle without local
wrinkling of the surface, and is what we know as Euler buckling. The
material does not fail (it is purely elastic) and the cross-section is
maintained. In this illustration, the load is external, but if you make
a long enough and thin enough tall pole, it will buckle under its own
self weight.
That was the issue that we found to be the killer when considering the
20 km tower for the SPICE project, and which I addressed in an earlier
post. (http://www-civ.eng.cam.ac.uk/cjb/papers/cp94.pdf) The equations
there apply to the space tower: the inflation of the tube does not
alter the buckling load because it is an internal self-equilibrating
system.
It is the same logic that stops a Bowden cable, as used in a bicycle
brakes, buckling. In these systems, the central wire is under very high
tension when you apply the brakes, and this is in equilibrium with a
compressive force in the external coil that forms the outer tube of the
cable. Ordinarily, a force of that magnitude would cause the tube to
buckle, but it doesn't. The reason is that if the tube moves to the
side it takes the internal cable with it. The internal cable causes a
restoring force to be applied to the tube. The overall effect is that
the self-equilibrating force in the internal wire has no effect on
buckling capacity of the outer tube.
Exactly the same logic applies to the inflated tower, although in
reverse. The internal compression in the air takes the place of the
internal wire in the Bowden cable. In the same way that the force in
the wire does not cause the brake cable to buckle, the internal air
pressure in the tube will not prevent the inflated tower from buckling.
You don't need to build a 1 km tower to show that it won't work. Make a
tube out of polythene (the thinner the better to show the difference,
block one end, and inflate it. If its quite short, you will be able to
stand it on end, but if it is long, it will buckle under its own
weight. It won't matter how hard you inflate it.
Chris Burgoyne
On 20/08/2015 19:58, Julia Calderone wrote:
Hi all,
Brendan Quine, the inventor of the space tower, has followed up with
some responses to a few of your thoughts (his responses are bolded
below). I have included his statements in an updated version of the
story:
http://www.techinsider.io/thoth-12-mile-space-tower-elevator-astronauts-travel-major-flaws-2015-8
If anyone has any thoughts or responses to his comments, please feel
free to shoot me a response here.
Thanks again.
Best,
Julia
*External forces* would be an issue:
“This is a big fat tower, and it's under *compression*. The
graphics don't
show any tethers or taper, and the sides are not obviously wind
permeable.
This means the torque [twisting force] at the base will be
enormous. It's
just not clear how it will actually stay up.”
*We agree that the tower will require very substantial foundation
however this requirement is similar to that of existing massive steel
and concrete construction structures. The patent describes a harmonic
control strategy and actively guided structure concept where the
attitude of the building is constantly monitored and its vibration
modes controlled (see FIG. 4 a schematic diagram showing active
stabilization control of the elevator core structure, US9085897).*
“Thunderstorms and icing would be a big problem. Construct[ing] a
tower to take wind gusts and turbulence arising from deep tropical
convection looks very problematic to me.”
Ice build-up hampers proper functioning of planes and drones at
such high
altitudes. Unlike aircraft that can fly, a giant tower wouldn’t be
able to
navigate around those regions.
*The structure may require de-icing in the same way that aircraft
wings are sprayed with antifreeze during operation in winter. This
function can be facilitated within the elevator structure however it
is likely that icing will be occasional as event will be isolated and
the solar radiation environment will rapidly heat and melt ice buildup
during the day. It is likely that the elevators would be equipped with
a de-icing capability also cleaning the outer surface as the pass up
and down the core. There is some significant research developments in
materials finishes that prevent ice build-up that could also be
deployed in lower structural sections. It is unlikely that the mass of
any ice buildup would be significant by comparison to the overall mass
of the structure.
The structure is designed to withstand a Category 5 hurricane with
wind speed of 156 mph with significant safety margin and so the sheer
and turbulent forces of a thunder storm are within this design envelope.*
Problem with *buckling* under it's own weight:
"The problem with this, assuming you could design one that you could
actually build, is that it would be subject to the same problems of
self-weight buckling. When one part of the internal cell starts to
buckle,
the volume of the gas inside does not change, which means that it
would not
resist the collapsing action"
*The problem of structural wrinkling (the onset to buckling) has been
addressed by previous research (see Experimental investigation of
inflatable cylindrical cantilevered beams ZH Zhu, RK Seth, BM Quine, S
Okubo, K Fukui, Q Yang, T Ochi, JP Journal of Solids and Structures 2
(2), 95-110, 2008). In fact there is a volume change during the
buckling event. Also the commentator may be assuming that the core is
comprised of a single gass cell the diameter of the structure however
the structure is comprise of many cells arrange in a torus and there
is a significant volume change between the sides of the structure
during buckling. The research paper lays out experimentally derived
guidelines for pneumatic structures to avoid the onset of wrinkling
which we have adopted in our design.*
*Material and cost* limitations:
The most feasible type of tower that could reach such heights is a
cylindrical tower made out of plastics reinforced with carbon fibers,
called Carbon Fibre Reinforced Plastic, or CFRP, which would cost
about
$500 billion and need 250 million tons of the carbon material. Of
course
new materials may become available, but nothing much is on the
horizon that
is substantially better than CFRP."
*Our patent proposes the use of polyethylene reinforced with Kelvar 49
(both widely available in industrial quantity). We agree that there
would be a need for a significant increase in industrial manufacturing
capability of these materials and consequently we are proposing the a
1.5 km demonstrator be constructed first in order to grow production
capacity before embarking on the 20 km tower.*
Not much fuel savings:
"Less than 1% of the energy required for orbit is saved by
launching from a
height of 20km. There doesn't seem to be much benefit."
*As we describe in A free-standing space elevator structure: a
practical alternative to the space tether BM Quine, RK Seth, ZH Zhu
Acta Astronautica 65 (3), 365-375, 2009, rockets consume approximately
30% of their fuel during the initial ascent phase to 20 km. The
reduction in fuel usage comes with a corresponding benefit in the
number of stages needed to reach orbit (only one stage is required for
a launch at 20 km versus 3 or 4 for conventional launch). The 1%
energy estimate claim does not take into account the staging aspect of
rocketry (the rocket is extremely heavy with stages and fuel at launch
and very light by orbit). Rocketry is extremely energy inefficient
with only about 3% of the chemical energy going into raising to
payload to orbit. Thus massive amounts of fuel and hardware must be
raised initially to have enough left to propel the final injection
stage. Electrical elevators are %50-%60 efficient leading to a
significant fuel saving advantage that enables single stage to orbit
space planes to fly from the top of the tower. These planes can also
be completely reusable like a passenger jet as opposed to being single
use like current rockets. This reaps the a very significant hardware
cost advantage which will dramatically reduce the cost of space access.*
On Thu, Aug 20, 2015 at 12:11 PM, Julia Calderone
<[email protected] <mailto:[email protected]>> wrote:
Hi all,
Thanks to everyone for your extremely helpful responses. I have
included quite a few of them into my article.
http://www.techinsider.io/thoth-12-mile-space-tower-elevator-astronauts-travel-major-flaws-2015-8
Take a gander, and please let me know if you see any glaring
errors or issues! Hope you enjoy it.
Thanks again for everyone's help.
My best,
Julia Calderone
On Wed, Aug 19, 2015 at 12:30 PM, David Appell
<[email protected] <mailto:[email protected]>> wrote:
Greg Rau wrote:
"Anyway, couple of thoughts. If the tether is made of carbon,
that's more than a few dollars worth of carbon sequestration..."
Except the mass of a space elevator is only ~10^5 kg.
David
--
David Appell, freelance science writer
e:[email protected] <mailto:[email protected]>
w:http://www.davidappell.com
b:http://davidappell.blogspot.com
t: @davidappell
m: Salem, OR
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