The Mechanical Rocket Motor. I

This page gives the energy storage capacity for a flywheel given the
tensile strength of the material and its density:

Flywheel Basics Tutorial.
http://rpm2.8k.com/basics.htm

The energy storage per weight is best when the mass is concentrated as
a thin hoop of rotating material, though the energy stored per volume
is less in this configuration.
If you want to maximize the energy stored per weight criterion, then:

(energy stored)/mass = (1/2)*(tensile strength)/density .

For the thin hoop configuration this is also equal to
(1/2)*(velocity)^2. So

velocity = sqrt(tensile strength/density).

The tensile strength of multiwalled carbon nanotubes has been
measured to be 150 GPa:

Direct mechanical measurement of the tensile strength and elastic
modulus of multiwalled carbon nanotubes.
B.G. Demczyk et al.
Materials Science and Engineering A334 (2002), 174, 173-178.
http://www.glue.umd.edu/~cumings/PDF...334demczyk.pdf

This was for micron-scale samples. It is not known if this stength
will still hold for macro-scale nanotubes, but it has been confirmed at
the micro-scale.
The density of carbon nanotubes is in the range of 1300 kg/m^3. Then
the possible speed of the hoop could be:

velocity = sqrt(150 GPa/1300 kg/m^3) = 10,740 m/s.

This is a tremendously high speed. This raises the possibility they
could be used for rocket propulsion. What you would want to do is
convert this rotational velocity to linear velocity to be able to
impart momentum to the rocket.
However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
So another possibility would have the nanotube material rotate around
as a thin rod attached at one end. Then if we broke the connection at
this end the rod could be made to fly off in the desired direction by
breaking the connection at the right time in its rotation. However the
rod will not attain the full velocity of its rotational speed at the
free end. The reason is the rod will still retain some rotation because
of conservation of angular momentum. So some of the energy will go into
rotation and some will go into linear translational motion.
This report by Jerome Pearson calculates the velocity possible at the
tip of a thin uniform rod according to its tensile strength and
density:

ASTEROID RETRIEVAL BY ROTARY ROCKET.
http://www.star-tech-inc.com/papers/.../asteroids.pdf

The speed calculated is U = sqrt(2σ/�) , σ the tensile strength and
� the density. Pearson refers to this as the materials characteristic
velocity. For the carbon nanotube material it would be U = sqrt(2*150
GPa/1300 kg/m^3) = 15,200 m/s.
However, as I said this would not be the linear speed of the rod
flying off because some of the energy will be retained as rotational
motion. The linear speed of the rod when it flies off should instead be
the speed of the center of mass, which is at the midpoint for the
uniform rod, because of conservation of linear momentum.
The speed of this midpoint half-way along the rod will be half the tip
speed or 7600 m/s, giving an ISP of 760 s. This compares to the best
liquid hydrogen/liquid oxygen chemical rockets of 450 s. The carbon
nanotubes would also take up much less space since they are denser than
liquid hydrogen. However, the volume would not be found simply from the
density of the carbon nanotubes. This is because you would need space
for the rods to rotate freely before they are released. So the
effective density would be less than 1300 kg/m^3, but still better than
that of liquid hydrogen. You also would not have the volume of the
liquid oxygen to carry.
You could probably also design the rod in a tapered configuration to
maximize the linear translational velocity. Pearson in his report
calculates the degree of tapering to attain the maximum tip velocity.
The intent of his report was to propose a method of propulsion in the
form of a large 'sling' that could propel mass from an asteroid as a
means to retrieve the asteroid. But the calculations still work for a
tapered rod at the micro-scale.
This page describes the idea in the form of a launching method for
payloads from Earth:

TAPERED SLINGS.
http://www.nas.nasa.gov/About/Educat...ki/SPBI1SL.HTM

To use this idea instead to calculate the speed the tapered rod would
fly off if released, you need to calculate the position of the center
of mass. Using this you can find the speed for the center of mass from
the proportion of its distance from the fixed end to the tip. From
conservation of linear momentum this will be the speed the tapered rod
will receive when released. The center of mass calculation for the
center of mass is rather complicated but I wind up with a speed for the
released rod of v =(characteristic velocity)/sqrt(Ï€) = 8570 m/s, an
ISP of about 860 s. I would like to receive some confirmation on this
calculation though.
This tapered rod does give a better ISP but you would have the problem
of binding the nanotubes together to result in the right taper. It is
not known whether nanotubes bound together will retain the same
strength of individual nanotubes.
One possibility would be to use the single atomic layer graphene
recently produced. This has been made in micron-scale sizes which is
sufficient for the purpose. You could cut this in the shape to have the
right taper. I've been informed by one of the scientists who produced
it that it should have the same strength as individual nanotubes.
This speed though is still less than the speed of the thin rotating
nanotube hoop at 10,400 m/s. One possibility to convert this rotational
motion fully into linear motion in a single direction might be to have
a fixed low friction flat slab with one end very close to and
tangential to the rotating hoop. You cut the hoop at the point closest
to the slab. This point will fly off in a tangential direction then
will move linearly along the surface of the slab. But we want the rest
of the hoop to also move linearly along the surface of the slab. To
insure this you might have the hoop be rotating inside another hoop
kept fixed of a slightly larger diameter.
This though would increase the weight of the material that has to be
carried along, thus effectively reducing the ISP. However, if this
material is also made of strong nanotube material you might be able to
get a higher velocity of the rotating hoop thereby cancelling out the
effect of the increased weight that has to be carried.
Both the tangential slab and the containing hoop would have to be made
of very low friction material at the velocities to be used. Carbon
nanotubes remarkably have been found to have very low friction:

Low-Friction Nanoscale Linear Bearing Realized from Multiwall Carbon
Nanotubes.
Science 28 July 2000: Vol. 289. no. 5479, pp. 602 - 604.
http://www.sciencemag.org/cgi/conten...t/289/5479/602

Then the rotating hoop, the containing hoop and the fixed slab could
all be made of nanotube material or perhaps of single atomic layer
graphene.


Bob Clark

Robert Clark wrote:
However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
So another possibility would have the nanotube material rotate around
as a thin rod attached at one end. Then if we broke the connection at
this end the rod could be made to fly off in the desired direction by
breaking the connection at the right time in its rotation.

No, that can't work. If you have something rotating, it has to have no
net momentum, or it won't rotate if it isn't bolted down. It will move
around, with its center of mass staying in the center, not what you
choose as a pivot.

Have you ever seen what happens when the clothes are all on one side of
a washing machine?

To avoid violating conservation of momentum, you *can* do this:

Have two counter-rotating flywheels. Then, slow them both down, taking
energy from both, so that the total angular momentum is constant.
Impart that energy to your reaction mass, separate from the flywheels.

Then, with the reaction mass being shot off in one direction,
conservation of momentum becomes your friend, and your rocket moves in
the other.

You *were* going to acknowledge and obey conservation of momentum in
your design, weren't you?

John Savard

wrote:
Robert Clark wrote:
However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
So another possibility would have the nanotube material rotate around
as a thin rod attached at one end. Then if we broke the connection at
this end the rod could be made to fly off in the desired direction by
breaking the connection at the right time in its rotation.

No, that can't work. If you have something rotating, it has to have no
net momentum, or it won't rotate if it isn't bolted down. It will move
around, with its center of mass staying in the center, not what you
choose as a pivot.

Have you ever seen what happens when the clothes are all on one side of
a washing machine?

To avoid violating conservation of momentum, you *can* do this:

Have two counter-rotating flywheels. Then, slow them both down, taking
energy from both, so that the total angular momentum is constant.
Impart that energy to your reaction mass, separate from the flywheels.

Then, with the reaction mass being shot off in one direction,
conservation of momentum becomes your friend, and your rocket moves in
the other.

You *were* going to acknowledge and obey conservation of momentum in
your design, weren't you?

John Savard

You're plan might work. However, a rod rotating around one fixed end,
not in the center, will also work. You can confirm this by tying a
short string around one end of a pen and twirling it around. When you
release it, the pen will fly off, but it will be rotating. So some of
the kinetic energy will be in the form of rotation and some in the form
of linear translational motion.


Bob Clark

Robert Clark wrote:
wrote:

Robert Clark wrote:

However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
So another possibility would have the nanotube material rotate around
as a thin rod attached at one end. Then if we broke the connection at
this end the rod could be made to fly off in the desired direction by
breaking the connection at the right time in its rotation.

No, that can't work. If you have something rotating, it has to have no
net momentum, or it won't rotate if it isn't bolted down. It will move
around, with its center of mass staying in the center, not what you
choose as a pivot.

Have you ever seen what happens when the clothes are all on one side of
a washing machine?

To avoid violating conservation of momentum, you *can* do this:

Have two counter-rotating flywheels. Then, slow them both down, taking
energy from both, so that the total angular momentum is constant.
Impart that energy to your reaction mass, separate from the flywheels.

Then, with the reaction mass being shot off in one direction,
conservation of momentum becomes your friend, and your rocket moves in
the other.

You *were* going to acknowledge and obey conservation of momentum in
your design, weren't you?

John Savard


You're plan might work. However, a rod rotating around one fixed end,
not in the center, will also work. You can confirm this by tying a
short string around one end of a pen and twirling it around. When you
release it, the pen will fly off, but it will be rotating. So some of
the kinetic energy will be in the form of rotation and some in the form
of linear translational motion.


Bob Clark


The mechanics of spinning the rod or rotor probably require energy in
some form (ultimately) other than plain mechanical.

So, the system approach to be taken would involve more than the simple
considerations of the "throw-away" fragmentation. At least, to be credible.

--
1) Eat Till SATISFIED, Not STUFFED... Atkins repeated 9 times in the book
2) Exercise: It's Non-Negotiable..... Chapter 22 title, Atkins book
3) Don't Diet Without Supplemental Nutrients... Chapter 23 title, Atkins
book
4) A sensible eating plan, and follow it. (Atkins, Self Made or Other)

Robert Clark wrote:

This page gives the energy storage capacity for a flywheel given the
tensile strength of the material and its density:

Flywheel Basics Tutorial.
http://rpm2.8k.com/basics.htm

The energy storage per weight is best when the mass is concentrated as
a thin hoop of rotating material, though the energy stored per volume
is less in this configuration.
If you want to maximize the energy stored per weight criterion, then:

(energy stored)/mass = (1/2)*(tensile strength)/density .

For the thin hoop configuration this is also equal to
(1/2)*(velocity)^2. So

velocity = sqrt(tensile strength/density).

The tensile strength of multiwalled carbon nanotubes has been
measured to be 150 GPa:

Direct mechanical measurement of the tensile strength and elastic
modulus of multiwalled carbon nanotubes.
B.G. Demczyk et al.
Materials Science and Engineering A334 (2002), 174, 173-178.
http://www.glue.umd.edu/~cumings/PDF...334demczyk.pdf

This was for micron-scale samples.
[snip]

Scaling up to tonnes will be linear and material deffects will not
appear in bulk. A (million-fold)^3 scaleup is just a mouse click
away. Riiight.

Bob Clark

http://www.mazepath.com/uncleal/analysis.jpg

What you have is crap. What NASA has is crap, Space Scuttle or
Orion. A two-day experiment verifies or falsifies a remarakable
empirical loophole in the basic physics.

Contemporary physics offers no expedient solution to serious space
travel. The best specific impulse to be had is a nuclear reactor and
an ion engine - a profligate waste of energy (mv^2)/2 to get
/_\(momentum) mv. It is a disgusting radiation source because
shielding is massively payload parasitic. Astronomers will scream.
Go price a tonne of xenon. Mercury and cesium were disasters for
condensing, corroding, and shorting everything. SF6 ate out the
insides.

Oooooh.... We could ion engine shoot out buckminsterfullerene
separately as both cations and anions (to balance spaceship charge),
MW=720.64 vs. xenon MW= 131.29. Go price a tonne of C60/70 crude mix.

If NASA wants to go anywhere serious NASA needs a loophole. Nature is
not shy about providing one: General Relativity through the symmetry
of its maths fails to allow Earth-moon spin-orbit momentum transfer
powering observed 3.8 cm/year lunar orbit recession,

http://en.wikipedia.org/wiki/Einstein-Cartan_theory

The simple patch introduces a chiral vacuum pseudoscalar background.
If you want lunar recession then you get an Equivalence Principle
parity violation. Metaphoric left and right shoes will vacuum
freefall along non-parallel minimum action trajectories (right shoes
will be the majority anomaly). Inertial and gravitational mass will
uncouple for parity-divergent masses. There's a cheat code for
squirting around space.

Or there isn't. Somebody should look. It's a two-day experiment in
commercial apparatus using $100 in consummables,

http://www.mazepath.com/uncleal/lajos.htm

Cut the crap, Clarke. Columbus had to sail west.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz3.pdf

"Jbuch" wrote in message
...
Robert Clark wrote:
wrote:

Robert Clark wrote:

However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
So another possibility would have the nanotube material rotate around
as a thin rod attached at one end. Then if we broke the connection at
this end the rod could be made to fly off in the desired direction by
breaking the connection at the right time in its rotation.

No, that can't work. If you have something rotating, it has to have no
net momentum, or it won't rotate if it isn't bolted down. It will move
around, with its center of mass staying in the center, not what you
choose as a pivot.

Have you ever seen what happens when the clothes are all on one side of
a washing machine?

To avoid violating conservation of momentum, you *can* do this:

Have two counter-rotating flywheels. Then, slow them both down, taking
energy from both, so that the total angular momentum is constant.
Impart that energy to your reaction mass, separate from the flywheels.

Then, with the reaction mass being shot off in one direction,
conservation of momentum becomes your friend, and your rocket moves in
the other.

You *were* going to acknowledge and obey conservation of momentum in
your design, weren't you?

John Savard


You're plan might work. However, a rod rotating around one fixed end,
not in the center, will also work. You can confirm this by tying a
short string around one end of a pen and twirling it around. When you
release it, the pen will fly off, but it will be rotating. So some of
the kinetic energy will be in the form of rotation and some in the form
of linear translational motion.

The mechanics of spinning the rod or rotor probably require energy in some
form (ultimately) other than plain mechanical.

That's not the problem, anyone with a shred of
sense can see that the spinning a rod round by
holding it at one end with the other moving at
several km/s will tear the machine apart with
the vibration of such an off-axis load.

George

Uncle Al wrote:

Robert Clark wrote:

This page gives the energy storage capacity for a flywheel given the
tensile strength of the material and its density:

Flywheel Basics Tutorial.
http://rpm2.8k.com/basics.htm

The energy storage per weight is best when the mass is concentrated as
a thin hoop of rotating material, though the energy stored per volume
is less in this configuration.
If you want to maximize the energy stored per weight criterion, then:

(energy stored)/mass = (1/2)*(tensile strength)/density .

For the thin hoop configuration this is also equal to
(1/2)*(velocity)^2. So

velocity = sqrt(tensile strength/density).

The tensile strength of multiwalled carbon nanotubes has been
measured to be 150 GPa:

Direct mechanical measurement of the tensile strength and elastic
modulus of multiwalled carbon nanotubes.
B.G. Demczyk et al.
Materials Science and Engineering A334 (2002), 174, 173-178.
http://www.glue.umd.edu/~cumings/PDF...334demczyk.pdf

This was for micron-scale samples.

[snip]

Scaling up to tonnes will be linear and material deffects will not
appear in bulk. A (million-fold)^3 scaleup is just a mouse click
away. Riiight.


Bob Clark


http://www.mazepath.com/uncleal/analysis.jpg

What you have is crap. What NASA has is crap, Space Scuttle or
Orion. A two-day experiment verifies or falsifies a remarakable
empirical loophole in the basic physics.

Contemporary physics offers no expedient solution to serious space
travel. The best specific impulse to be had is a nuclear reactor and
an ion engine - a profligate waste of energy (mv^2)/2 to get
/_\(momentum) mv. It is a disgusting radiation source because
shielding is massively payload parasitic. Astronomers will scream.
Go price a tonne of xenon. Mercury and cesium were disasters for
condensing, corroding, and shorting everything. SF6 ate out the
insides.

Oooooh.... We could ion engine shoot out buckminsterfullerene
separately as both cations and anions (to balance spaceship charge),
MW=720.64 vs. xenon MW= 131.29. Go price a tonne of C60/70 crude mix.

If NASA wants to go anywhere serious NASA needs a loophole. Nature is
not shy about providing one: General Relativity through the symmetry
of its maths fails to allow Earth-moon spin-orbit momentum transfer
powering observed 3.8 cm/year lunar orbit recession,

http://en.wikipedia.org/wiki/Einstein-Cartan_theory

The simple patch introduces a chiral vacuum pseudoscalar background.
If you want lunar recession then you get an Equivalence Principle
parity violation. Metaphoric left and right shoes will vacuum
freefall along non-parallel minimum action trajectories (right shoes
will be the majority anomaly). Inertial and gravitational mass will
uncouple for parity-divergent masses. There's a cheat code for
squirting around space.

Or there isn't. Somebody should look. It's a two-day experiment in
commercial apparatus using $100 in consummables,

http://www.mazepath.com/uncleal/lajos.htm

Cut the crap, Clarke. Columbus had to sail west.


If it's so cheap and easy, show us.

All those other 'bad examples' have at least one virtue: They've all
been demonstrated at least once. Most of them, out in vacuum, where it
really matters.



--

Frank

You know what to remove to reply...

Check out my web page: http://www.geocities.com/stardolphin1/link2.htm

"Man who say it cannot be done, should not interrupt man doing it."
- Chinese Proverb

The spinning of rotors at the micro-scale and the nano-scale has
already been accomplished so this is within the range of what is
currently possible:

Nanomotors realise visionary's dream.
Thursday, 30 October, 2003
"Researchers at Berkeley at the University of California created the
world's smallest electrical device earlier this year - one hundred
million of which could fit on the end of a pin."
http://www.scienceagogo.com/news/200...runc_sys.shtml

Using Nanotubes and Etched Silicon, UC Berkeley Physicists Build
World's Smallest Motor.
Berkeley, CA. July 23rd, 2003.
http://www.nanotech-now.com/ucb-release-07232003.htm

The spinning motion of the rotor is initiated by electrostatic charge.
You would have to have quadrillions to quintillions of them though at
the nanoscale if they were to amount to thousands of kilos of reaction
mass.
An automated process would be needed for making the rotors, such as
for example used for integrated circuits.
Another problem is that the spin of the rotors would have to be
maintained in vacuum. So additional mass for the vacuum chamber would
have to be carried along.


Bob Clark



Robert Clark wrote:
This page gives the energy storage capacity for a flywheel given the
tensile strength of the material and its density:

Flywheel Basics Tutorial.
http://rpm2.8k.com/basics.htm

The energy storage per weight is best when the mass is concentrated as
a thin hoop of rotating material, though the energy stored per volume
is less in this configuration.
If you want to maximize the energy stored per weight criterion, then:

(energy stored)/mass = (1/2)*(tensile strength)/density .

For the thin hoop configuration this is also equal to
(1/2)*(velocity)^2. So

velocity = sqrt(tensile strength/density).

The tensile strength of multiwalled carbon nanotubes has been
measured to be 150 GPa:

Direct mechanical measurement of the tensile strength and elastic
modulus of multiwalled carbon nanotubes.
B.G. Demczyk et al.
Materials Science and Engineering A334 (2002), 174, 173-178.
http://www.glue.umd.edu/~cumings/PDF...334demczyk.pdf

This was for micron-scale samples. It is not known if this stength
will still hold for macro-scale nanotubes, but it has been confirmed at
the micro-scale.
The density of carbon nanotubes is in the range of 1300 kg/m^3. Then
the possible speed of the hoop could be:

velocity = sqrt(150 GPa/1300 kg/m^3) = 10,740 m/s.

This is a tremendously high speed. This raises the possibility they
could be used for rocket propulsion. What you would want to do is
convert this rotational velocity to linear velocity to be able to
impart momentum to the rocket.
However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
So another possibility would have the nanotube material rotate around
as a thin rod attached at one end. Then if we broke the connection at
this end the rod could be made to fly off in the desired direction by
breaking the connection at the right time in its rotation. However the
rod will not attain the full velocity of its rotational speed at the
free end. The reason is the rod will still retain some rotation because
of conservation of angular momentum. So some of the energy will go into
rotation and some will go into linear translational motion.
This report by Jerome Pearson calculates the velocity possible at the
tip of a thin uniform rod according to its tensile strength and
density:

ASTEROID RETRIEVAL BY ROTARY ROCKET.
http://www.star-tech-inc.com/papers/.../asteroids.pdf

The speed calculated is U = sqrt(2σ/�) , σ the tensile strength and
� the density. Pearson refers to this as the materials characteristic
velocity. For the carbon nanotube material it would be U = sqrt(2*150
GPa/1300 kg/m^3) = 15,200 m/s.
However, as I said this would not be the linear speed of the rod
flying off because some of the energy will be retained as rotational
motion. The linear speed of the rod when it flies off should instead be
the speed of the center of mass, which is at the midpoint for the
uniform rod, because of conservation of linear momentum.
The speed of this midpoint half-way along the rod will be half the tip
speed or 7600 m/s, giving an ISP of 760 s. This compares to the best
liquid hydrogen/liquid oxygen chemical rockets of 450 s. The carbon
nanotubes would also take up much less space since they are denser than
liquid hydrogen. However, the volume would not be found simply from the
density of the carbon nanotubes. This is because you would need space
for the rods to rotate freely before they are released. So the
effective density would be less than 1300 kg/m^3, but still better than
that of liquid hydrogen. You also would not have the volume of the
liquid oxygen to carry.
You could probably also design the rod in a tapered configuration to
maximize the linear translational velocity. Pearson in his report
calculates the degree of tapering to attain the maximum tip velocity.
The intent of his report was to propose a method of propulsion in the
form of a large 'sling' that could propel mass from an asteroid as a
means to retrieve the asteroid. But the calculations still work for a
tapered rod at the micro-scale.
This page describes the idea in the form of a launching method for
payloads from Earth:

TAPERED SLINGS.
http://www.nas.nasa.gov/About/Educat...ki/SPBI1SL.HTM

To use this idea instead to calculate the speed the tapered rod would
fly off if released, you need to calculate the position of the center
of mass. Using this you can find the speed for the center of mass from
the proportion of its distance from the fixed end to the tip. From
conservation of linear momentum this will be the speed the tapered rod
will receive when released. The center of mass calculation for the
center of mass is rather complicated but I wind up with a speed for the
released rod of v =(characteristic velocity)/sqrt(Ï€) = 8570 m/s, an
ISP of about 860 s. I would like to receive some confirmation on this
calculation though.
This tapered rod does give a better ISP but you would have the problem
of binding the nanotubes together to result in the right taper. It is
not known whether nanotubes bound together will retain the same
strength of individual nanotubes.
One possibility would be to use the single atomic layer graphene
recently produced. This has been made in micron-scale sizes which is
sufficient for the purpose. You could cut this in the shape to have the
right taper. I've been informed by one of the scientists who produced
it that it should have the same strength as individual nanotubes.
This speed though is still less than the speed of the thin rotating
nanotube hoop at 10,400 m/s. One possibility to convert this rotational
motion fully into linear motion in a single direction might be to have
a fixed low friction flat slab with one end very close to and
tangential to the rotating hoop. You cut the hoop at the point closest
to the slab. This point will fly off in a tangential direction then
will move linearly along the surface of the slab. But we want the rest
of the hoop to also move linearly along the surface of the slab. To
insure this you might have the hoop be rotating inside another hoop
kept fixed of a slightly larger diameter.
This though would increase the weight of the material that has to be
carried along, thus effectively reducing the ISP. However, if this
material is also made of strong nanotube material you might be able to
get a higher velocity of the rotating hoop thereby cancelling out the
effect of the increased weight that has to be carried.
Both the tangential slab and the containing hoop would have to be made
of very low friction material at the velocities to be used. Carbon
nanotubes remarkably have been found to have very low friction:

Low-Friction Nanoscale Linear Bearing Realized from Multiwall Carbon
Nanotubes.
Science 28 July 2000: Vol. 289. no. 5479, pp. 602 - 604.
http://www.sciencemag.org/cgi/conten...t/289/5479/602

Then the rotating hoop, the containing hoop and the fixed slab could
all be made of nanotube material or perhaps of single atomic layer
graphene.


Bob Clark

Robert Clark wrote:
This page gives the energy storage capacity for a flywheel given the
tensile strength of the material and its density:

Flywheel Basics Tutorial.
http://rpm2.8k.com/basics.htm

The energy storage per weight is best when the mass is concentrated as
a thin hoop of rotating material, though the energy stored per volume
is less in this configuration.
If you want to maximize the energy stored per weight criterion, then:

(energy stored)/mass = (1/2)*(tensile strength)/density .

For the thin hoop configuration this is also equal to
(1/2)*(velocity)^2. So

velocity = sqrt(tensile strength/density).

The tensile strength of multiwalled carbon nanotubes has been
measured to be 150 GPa:

Direct mechanical measurement of the tensile strength and elastic
modulus of multiwalled carbon nanotubes.
B.G. Demczyk et al.
Materials Science and Engineering A334 (2002), 174, 173-178.
http://www.glue.umd.edu/~cumings/PDF...334demczyk.pdf

This was for micron-scale samples. It is not known if this stength
will still hold for macro-scale nanotubes, but it has been confirmed at
the micro-scale.
The density of carbon nanotubes is in the range of 1300 kg/m^3. Then
the possible speed of the hoop could be:

velocity = sqrt(150 GPa/1300 kg/m^3) = 10,740 m/s.

This is a tremendously high speed. This raises the possibility they
could be used for rocket propulsion. What you would want to do is
convert this rotational velocity to linear velocity to be able to
impart momentum to the rocket.
However, you also want the material to all exit in a single direction
to impart the momentum of the rocket in the opposite direction. But if
you induced the hoop to fly apart the materials would fly off in all
directions in the plane of rotation.
...
[Snip]
...
One possibility to convert this rotational
motion fully into linear motion in a single direction might be to have
a fixed low friction flat slab with one end very close to and
tangential to the rotating hoop. You cut the hoop at the point closest
to the slab. This point will fly off in a tangential direction then
will move linearly along the surface of the slab. But we want the rest
of the hoop to also move linearly along the surface of the slab. To
insure this you might have the hoop be rotating inside another hoop
kept fixed of a slightly larger diameter.
This though would increase the weight of the material that has to be
carried along, thus effectively reducing the ISP. However, if this
material is also made of strong nanotube material you might be able to
get a higher velocity of the rotating hoop thereby cancelling out the
effect of the increased weight that has to be carried.
Both the tangential slab and the containing hoop would have to be made
of very low friction material at the velocities to be used. Carbon
nanotubes remarkably have been found to have very low friction:

Low-Friction Nanoscale Linear Bearing Realized from Multiwall Carbon
Nanotubes.
Science 28 July 2000: Vol. 289. no. 5479, pp. 602 - 604.
http://www.sciencemag.org/cgi/conten...t/289/5479/602

Then the rotating hoop, the containing hoop and the fixed slab could
all be made of nanotube material or perhaps of single atomic layer
graphene.


Bob Clark

You could probably use the same containing hoop for very many of the
rotating hoops, since it would only have to contain a rotating hoop
when the rotating hoop is cut in order for it to fly off. You could for
instance have a large number of rotating hoops arranged one above the
the other in a column. As this "propellant" is expended the hoops can
be pushed lower down in the column (or you could instead have the
containing hoop pushed further up.) Then the same containing hoop would
be used for all the rotating hoops in the column. Then the containing
hoops would only amount to a small portion of the mass of the
propellant hoops.
Potentially then you could have an ISP that nearly fully corresponds
to an exhaust velocity of 10,740 m/s. The question is how much the
speed of the rotating hoop would be reduced by friction when it is
rotating while rubbing against the containing hoop.


Bob Clark