However, the original post is a first-order approximation of the required energy. It is meant to highlight that one system's required fuel weight is exponential while the other's is not. Let's not let excessive details (which apply similarly to both vehicles) obfuscate the elegant simplicity of the rocket equation.
Your statement that a reduction in fuel by a factor of ten is not possible is very wrong. For a given orbit, provided exhaust velocities are equal, a rocket which does not carry its fuel will always use less fuel. How much less? Well, given that one has an exponential dependence on fuel and the other does not, it stands to reason that for high orbits a factor of ten could be conservative.
A better way for you to argue against a power savings is to point out that there's no way super heated air could ever achieve the exhaust velocity equal to that of kerosine and liquid oxygen. Thus the linear function may for a range of orbits be more expensive than an exponential function.
I knew this was a large subject, when I started it, but wanted present the concept of the exponential rocket equation. I'm working on a full write up on my site and should have something up by the next slashback.
A propulsion system such as this can provide a tremendous reduction in required energy.
Conventional rockets, which carry their own fuel are large consumers of energy, as not only must they lift a payload into space but all
the fuel as well.
The total weight of a rocket including fuel is given by an exponential function known as the rocket equation.
Stated simply, a rocket of mass m0 requires fuel of mass m1 to lift it; that fuel of mass m1 requires more fuel of mass m2 to lift
it; the fuel of mass m2 requires fuel of mass m3; and so on, ad infinitum.
The rocket equation is given by
m = m0 exp(Vf/Vex)
where m is the total required mass, m0 is the mass of the payload, Vf is the final velocity,
and Vex is the exhaust velocity of the combusting fuel.
This exponential increase in initial mass can be huge.
For example a low earth orbit requires a change in velocity,
Vf, of about 8 km/s.
Kerosine and liquid oxygen provide an exhaust velocity of about 2.5 km/s.
Thus, m/m0 = exp(Vf/Vex) = 24.5.
It would take 25 times the original weight of a given payload mostly in fuel
to achieve a low earth orbit with kerosine and liquid oxygen!
Assuming a payload of 1000 kg and an energy density of 10^7 J/kg for
the fuel, the total energy would be E = (25*10^3 kg)(10^7 J/kg) =~ 250 GJ!
The wonderful thing about rockets that don't carry fuel with them is that there
is no exponential dependency on initial mass.
The energy required is simply the orbital energy, given by half the gravitational potential
energy (derivation mercifully omitted) of the payload, given by E = -(G m0 M)/2r.
The energy in this case, omitting concerns of efficiency, would be
E = (6.67*10^-11 Nm^2/kg^2)(5.98*10^24 kg)(1000 kg)/(2*6400 km) =~ 30 GJ
This article, like most articles that tout LEDs as a replacement
for light bulbs, confuses efficacy and efficiency.
Luminous efficacy is defined as the power of radiated visible light
(visible luminous flux) divided by the dissipated electrical power.
Given in lumens per watt, efficacy provides a useful means of comparing
which source provides the most useful illumination for a given power.
Efficiency on the other hand is defined as the power of
radiated visible light (visible luminous flux) divided by the
power of all radiated light (total luminous flux).
Ideally given as a unit-less ratio, efficiency provides the ratio
of useful light to wasted light and does not necessarily correlate
with efficacy.
It is possible to have simultaneously high efficiency and low efficacy.
The question of why LEDs haven't already replaced all lights can be answered
quickly by comparing the efficacy of different sources of light.
All numbers below are approximate.
Filament light: 10 lm/W
White LED: 20 lm/W
Halogen light: 25 lm/W
Red LED: 40 lm/W
Florescent light: 100 lm/W
Sodium light: 150 lm/W
It can be seen why red LEDs have replaced halogen bulbs
with red filters in stop lights -- red LEDs have a much higher efficacy.
Note that the efficacy of LEDs are still well below that of florescent lights.
If you feel frustration in seeing how far LED technology still has to go
to compete with the boring lighting technologies of yesteryear, assuage your
sorrows in the knowledge that you can save billions in energy costs right
now, simply by switching to florescent lighting.
Often omitted in the discussion of alternative or modified
energy sources is the concept of energy return on investment (EROI).
It's defined as the ratio of energy provided for useful work
divided by the energy required to extract and process the fuel source.
If one expends energy overprocessesing the fuel,
the net energy contributed to the system is reduced.
For example, it's been
published
that ethanol requires 70% more energy to produce than it provides.
Given that the global economic system exists almost exclusively on the
ever-diminishing stored
potential energy
of the earth,
it seems that reducing the EROI of an energy source should be avoided.
All I know is I saw some kid outside sitting outside talking to it.
I heard it say that it's just a bill, yes it's
only a bill, and as I stated before it's sitting on Capitol Hill.
It went on to describe a long, long journey
followed by a long, long wait and I believe it
summarized its feeling by saying that it hoped and prayed that it will, but today it is still just a bill.
My assumption is that it wants to become a law,
undoubtedly motivated by their fancier ribbons.
Every once in a while, I'm really motivated by a Slashdot post,
and explore the problem further with some quick and light
research and writing.
By the time I've finished, most readers and moderators
have long since left the post for fresher news and I'm left with
a relatively small audience.
In the spirit of Slashback I thought I could reincarnate
those old posts for a second viewing.
While risking my Karma for something that could be seen as off topic,
I do think it adds value to Slashdot and really doesn't fit anywhere else.
Ecosystem and Economy:
In response to the standard environmentalist-versus-economist
arguments that were flying about in a previous Slashdot
post
in reference to a Daily Telegraph
article,
I sought out a fresh
viewpoint
based on reductionism and the conservation of energy.
Social Network Theory:
A Slashdot
post
led to a Register
article,
which was steeped in an unusual amount conspiracy theory.
Suggesting that Google was gamed by a group of A-list bloggers,
perhaps it is all simply just a result of
social networks.
This is a new topic to me, so if you know anything about
social network theory, I'd love it if someone could take me to school.
First-Generation TiVo:
In a
discussion
concerning second-generation TiVos
I thought I'd whip up a
quick script
that would allow people
to see what I'm currently watching as proof that my
house wields the mighty sword of TiVo modding.
Mystery Treasure:
I also put a not-so-well hidden page on my site to see if anyone
would gravitate towards it, but it as of yet remains undiscovered.
Hint: MSIE users will not get far.
Consider it pay back for not doing PNG
transparency.:P
I know only of the properties of diamond,
as I've used it for a substrate in planar
microwave active antenna arrays.
As a dielectric it provided very low loss
and an amazing thermal conductivity.
(The only complaint is that the relative
permittivity was a bit low.)
I am unfamiliar with the concept of phonon
conduction but will add it to my queue of
things to research.
I find material science very interesting.
I'll be waiting for the DirecTiVo version of these services as well.
I was surprised to see that caller-id display on the screen isn't
a standard feature yet.
I've implemented on-screen caller id by means of the ncid daemon,
which receives broadcast information from my Linux server.
It's a very useful feature.
If you're interested, you can even see what I'm
watching
on my TiVo right now.
As an experiment I've grown wheatgrass and catnip for my evil cat,
as incentive for him to stay out of the other plants.
I've found that I had good results if I let the seeds do their
initial sprouting and growth underneath a sheet of clear plastic wrap.
The trick is not to get too eager and remove the plastic wrap to soon.
The plastic wrap is a perfect way to even out the sporatic waterings
that are inevitable when you're slashdotting.
High electrical conductivity and high thermal
conductivity tend to run together.
For instance copper has an electrical conductivity of 5.8x10^7 S/m
and a thermal conductivity of 200 W/mK.
A notable exception is diamond
with a low electrical conductivity on the order of 1 S/m
and a high thermal conductivity of 700 W/mK.
Because of diamond's superior thermal conductivity
and low electrical conductivity,
it functions as an excellent material for use in a
heat sink.
What interests me is, that by adding free electrons by doping
the diamond with oxygen is he seeing actual superconductivity
or just the high conductivity one would expect, if diamond
had free electrons.
The specific energy of a NiMH battery is
approximately 70 Wh/kg (250 kJ/kg).
In comparison a realistic methanol fuel cell
has a specific energy of
700 Wh/kg (2.5 MJ/kg).
A methanol fuel cell has roughly ten times the specific energy. However I've heard that the
energy density in (J/L) is only on the order of
a factor of two better. Can anyone speak to this?
The
size
of a dollar bill is 6.6294 cm wide, by 15.5956 cm long, and 0.010922 cm in thickness.
A stack of one dollar bills worth $97.8 trillion
would be 10 billion meters high or slightly more than 25 stacks of bills that each would reach to the moon.
Laid end-to-end the bills would stretch 15.25 trillion meters. That's long enough to stretch
from the sun to
pluto
almost three times over.
That many dollar bills would cover the entire 68 square miles of the District of Columbia in a pile of bills two feet deep.
there once was a man-made rocket
that was built with funds out of pocket
three were shot into space
and vanished without trace
the hatch they forgot to lock it
A trick that really improved the performance of my PC was replacing it with a Sun Blade 2000 with dual processors, 8 GB of memory, and a 24.1-inch LCD display.
The unexpected bonus was the tricked out "Sun" headlight in front and color shifting paint.
Slashdot Mirror
Good points.
However, the original post is a first-order approximation of the required energy. It is meant to highlight that one system's required fuel weight is exponential while the other's is not. Let's not let excessive details (which apply similarly to both vehicles) obfuscate the elegant simplicity of the rocket equation.
Your statement that a reduction in fuel by a factor of ten is not possible is very wrong. For a given orbit, provided exhaust velocities are equal, a rocket which does not carry its fuel will always use less fuel. How much less? Well, given that one has an exponential dependence on fuel and the other does not, it stands to reason that for high orbits a factor of ten could be conservative.
A better way for you to argue against a power savings is to point out that there's no way super heated air could ever achieve the exhaust velocity equal to that of kerosine and liquid oxygen. Thus the linear function may for a range of orbits be more expensive than an exponential function.
I knew this was a large subject, when I started it, but wanted present the concept of the exponential rocket equation. I'm working on a full write up on my site and should have something up by the next slashback.
Michael.
A propulsion system such as this can provide a tremendous reduction in required energy.
Conventional rockets, which carry their own fuel are large consumers of energy, as not only must they lift a payload into space but all the fuel as well. The total weight of a rocket including fuel is given by an exponential function known as the rocket equation. Stated simply, a rocket of mass m0 requires fuel of mass m1 to lift it; that fuel of mass m1 requires more fuel of mass m2 to lift it; the fuel of mass m2 requires fuel of mass m3; and so on, ad infinitum. The rocket equation is given by
m = m0 exp(Vf/Vex)
where m is the total required mass, m0 is the mass of the payload, Vf is the final velocity, and Vex is the exhaust velocity of the combusting fuel.
This exponential increase in initial mass can be huge. For example a low earth orbit requires a change in velocity, Vf, of about 8 km/s. Kerosine and liquid oxygen provide an exhaust velocity of about 2.5 km/s. Thus, m/m0 = exp(Vf/Vex) = 24.5. It would take 25 times the original weight of a given payload mostly in fuel to achieve a low earth orbit with kerosine and liquid oxygen! Assuming a payload of 1000 kg and an energy density of 10^7 J/kg for the fuel, the total energy would be E = (25*10^3 kg)(10^7 J/kg) =~ 250 GJ!
The wonderful thing about rockets that don't carry fuel with them is that there is no exponential dependency on initial mass. The energy required is simply the orbital energy, given by half the gravitational potential energy (derivation mercifully omitted) of the payload, given by E = -(G m0 M)/2r. The energy in this case, omitting concerns of efficiency, would be
E = (6.67*10^-11 Nm^2/kg^2)(5.98*10^24 kg)(1000 kg)/(2*6400 km) =~ 30 GJ
The savings in energy is almost a factor of ten!
Michael.
P.S. - Lots of derivations late at night. Be merciful in the event of errors.
This article, like most articles that tout LEDs as a replacement for light bulbs, confuses efficacy and efficiency.
Luminous efficacy is defined as the power of radiated visible light (visible luminous flux) divided by the dissipated electrical power. Given in lumens per watt, efficacy provides a useful means of comparing which source provides the most useful illumination for a given power.
Efficiency on the other hand is defined as the power of radiated visible light (visible luminous flux) divided by the power of all radiated light (total luminous flux). Ideally given as a unit-less ratio, efficiency provides the ratio of useful light to wasted light and does not necessarily correlate with efficacy. It is possible to have simultaneously high efficiency and low efficacy.
The question of why LEDs haven't already replaced all lights can be answered quickly by comparing the efficacy of different sources of light. All numbers below are approximate.
Filament light: 10 lm/W
White LED: 20 lm/W
Halogen light: 25 lm/W
Red LED: 40 lm/W
Florescent light: 100 lm/W
Sodium light: 150 lm/W
It can be seen why red LEDs have replaced halogen bulbs with red filters in stop lights -- red LEDs have a much higher efficacy. Note that the efficacy of LEDs are still well below that of florescent lights. If you feel frustration in seeing how far LED technology still has to go to compete with the boring lighting technologies of yesteryear, assuage your sorrows in the knowledge that you can save billions in energy costs right now, simply by switching to florescent lighting.
Michael.
there once was a power mac
on the net i thought i'd hack
i was stunned to see
it ran bsd
my plans were thus set back
Michael.
sh:
Jeden Tag verlieren wir immer mehr unserer Rechte, die Profite der großen Firmen zu schützen.
Michael.
Often omitted in the discussion of alternative or modified energy sources is the concept of energy return on investment (EROI). It's defined as the ratio of energy provided for useful work divided by the energy required to extract and process the fuel source.
If one expends energy overprocessesing the fuel, the net energy contributed to the system is reduced. For example, it's been published that ethanol requires 70% more energy to produce than it provides.
Given that the global economic system exists almost exclusively on the ever-diminishing stored potential energy of the earth, it seems that reducing the EROI of an energy source should be avoided.
Michael.
My attempt at Israel-perl-code humor pales in significance to such a statement.
What's the point of having Excellent Karma, if one does not put it on the line?
Remember Rachel Corrie.
Michael.
while (<ID_LIKE_TO_GO>){
if(in("Israel") == 1){
$too_expensive = 1;
}
}
return("Michael.")
Ha! That's the lazy-bones mouse trap. You don't think I'd make the treasure found by means of the seach function do you?
Michael.
All I know is I saw some kid outside sitting outside talking to it.
I heard it say that it's just a bill, yes it's only a bill, and as I stated before it's sitting on Capitol Hill. It went on to describe a long, long journey followed by a long, long wait and I believe it summarized its feeling by saying that it hoped and prayed that it will, but today it is still just a bill.
My assumption is that it wants to become a law, undoubtedly motivated by their fancier ribbons.
The full story can be found here.
Michael.
Every once in a while, I'm really motivated by a Slashdot post, and explore the problem further with some quick and light research and writing. By the time I've finished, most readers and moderators have long since left the post for fresher news and I'm left with a relatively small audience. In the spirit of Slashback I thought I could reincarnate those old posts for a second viewing.
While risking my Karma for something that could be seen as off topic, I do think it adds value to Slashdot and really doesn't fit anywhere else.
Ecosystem and Economy: In response to the standard environmentalist-versus-economist arguments that were flying about in a previous Slashdot post in reference to a Daily Telegraph article, I sought out a fresh viewpoint based on reductionism and the conservation of energy.
Social Network Theory: A Slashdot post led to a Register article, which was steeped in an unusual amount conspiracy theory. Suggesting that Google was gamed by a group of A-list bloggers, perhaps it is all simply just a result of social networks. This is a new topic to me, so if you know anything about social network theory, I'd love it if someone could take me to school.
First-Generation TiVo: In a discussion concerning second-generation TiVos I thought I'd whip up a quick script that would allow people to see what I'm currently watching as proof that my house wields the mighty sword of TiVo modding.
Mystery Treasure: I also put a not-so-well hidden page on my site to see if anyone would gravitate towards it, but it as of yet remains undiscovered. Hint: MSIE users will not get far. Consider it pay back for not doing PNG transparency.
Michael.
Fascinating!
I know only of the properties of diamond, as I've used it for a substrate in planar microwave active antenna arrays. As a dielectric it provided very low loss and an amazing thermal conductivity. (The only complaint is that the relative permittivity was a bit low.)
I am unfamiliar with the concept of phonon conduction but will add it to my queue of things to research. I find material science very interesting.
Thank you for your comment.
Michael.
Viral gene chips, betcha' can't eat just one.
Michael.
I'll be waiting for the DirecTiVo version of these services as well.
I was surprised to see that caller-id display on the screen isn't a standard feature yet. I've implemented on-screen caller id by means of the ncid daemon, which receives broadcast information from my Linux server. It's a very useful feature.
If you're interested, you can even see what I'm watching on my TiVo right now.
Michael.
As an experiment I've grown wheatgrass and catnip for my evil cat, as incentive for him to stay out of the other plants.
I've found that I had good results if I let the seeds do their initial sprouting and growth underneath a sheet of clear plastic wrap. The trick is not to get too eager and remove the plastic wrap to soon. The plastic wrap is a perfect way to even out the sporatic waterings that are inevitable when you're slashdotting.
Michael.
Treasure
High electrical conductivity and high thermal conductivity tend to run together. For instance copper has an electrical conductivity of 5.8x10^7 S/m and a thermal conductivity of 200 W/mK.
A notable exception is diamond with a low electrical conductivity on the order of 1 S/m and a high thermal conductivity of 700 W/mK.
Because of diamond's superior thermal conductivity and low electrical conductivity, it functions as an excellent material for use in a heat sink.
What interests me is, that by adding free electrons by doping the diamond with oxygen is he seeing actual superconductivity or just the high conductivity one would expect, if diamond had free electrons.
Michael.
Visit das Schlößl.
The specific energy of a NiMH battery is approximately 70 Wh/kg (250 kJ/kg).
In comparison a realistic methanol fuel cell has a specific energy of 700 Wh/kg (2.5 MJ/kg).
A methanol fuel cell has roughly ten times the specific energy. However I've heard that the energy density in (J/L) is only on the order of a factor of two better. Can anyone speak to this?
Michael.
Previous Slashdot Science post on Ecologoy and Economy
Excellent. Perhaps during the EVA they could collect Steve Bennett's body.
Michael.
The size of a dollar bill is 6.6294 cm wide, by 15.5956 cm long, and 0.010922 cm in thickness.
A stack of one dollar bills worth $97.8 trillion would be 10 billion meters high or slightly more than 25 stacks of bills that each would reach to the moon.
Laid end-to-end the bills would stretch 15.25 trillion meters. That's long enough to stretch from the sun to pluto almost three times over.
That many dollar bills would cover the entire 68 square miles of the District of Columbia in a pile of bills two feet deep.
Oh, wait. Now I get it.
Michael.
Strange. The link above doesn't work without a slash at the end. Try this or add your own slash to the end of the URL.
This site provides information on the current monopolies that dominate media due to the deregulations in the early 1990s. Extrapolate from there.
Michael.
there once was a man-made rocket
that was built with funds out of pocket
three were shot into space
and vanished without trace
the hatch they forgot to lock it
Michael.
I have no idea. I was aiming for funny!
Coding standards:
Another word of advice, "C#" is a bad name for your perl script. I hear there's already something named that.
Michael.
A trick that really improved the performance of my PC was replacing it with a Sun Blade 2000 with dual processors, 8 GB of memory, and a 24.1-inch LCD display.
The unexpected bonus was the tricked out "Sun" headlight in front and color shifting paint.