 # Unlimited thrust from ion drives?

Maybe I’m missing something here.

Ion drives carry maybe argon or hydrogen as a “fuel”. Inside the engine, an electron is stripped off each atom of fuel to form ions. Then these ions are accelerated from the engine by a linear accelerator, providing thrust.

So the thrust provided by each pound of fuel is limited only by the MEVs or BEVs of the linear accelerator. If the linear accelerator was powered by a really powerful multi-bigawatt nuclear reactor which could drive a 1,000 teraBEV linear accelerator, then the thrust of the ion drive could be virtually unlimited. All without increasing the fuel consumption, and without generating more of those pesky electroms to dispose of.

Note to NASA: build BIG!

True, sort of. Theoreticallyu the total change in velocity, aka delta V, for a given amount of propellant is not limited, given an unlimited amount of power. However, as you increase the specific impulse (efficiency) of the engine, you decrease thrust, so it takes much LONGER to acheive the same delta V.

Relaisitically, power is not unlimited. The more power you havey, the more mass you have in the power plant, whether it be nuclear, solar, or whatever. So, if you try to increase power you end up increasing the spacecraft mass whihc effectively DECREASES the total delat V, because the same amount of impulse needs to propel a more massive spacecraft.

If we had a very efficient power SOURCE whihc could produce lots and lots of power and not require a lot of mass to do that, this would be great. Unfortunately, even a nuclear power source, which can produce a LOT of power, tends to be very heavy and inefficient.

In other words, there is no free lunch.

However, as you increase the specific impulse…of the engine, you decrease thrust

“specific impulse n.
A performance measure for rocket propellants that is equal to units of thrust per unit weight of propellant consumed per unit time. Also called specific thrust.”

The specific impulse is just the thrust of a rocket (in pounds) divided by the pounds of fuel used per second.

There is no decrease in thrust implied by this equation. Welcome to the free lunch!

In fact, the specific impulse of a fuel is just the exhaust velocity divided by g, the universal gravitational constant.

See note 4 (near bottom of page)

http://www.nakka-rocketry.net/techs4.html

Nicht ausrichten, mein liebes Henry - that "g" is Earth's surface acceleration due to gravity. Useful for dealing with rockets from the Earth, hence its use in that equation.

"G" is the universal gravitational constant which gives rise to "g".

g = G*M/r2

Where "M" is the mass of the Earth, and "r" its radius.

...

Herr Einstein:

So glad you have joined the discussion, for I have a question for you.

Suppose we have virtually unlimited electrical power available aboard a spacecraft, and are using some of this electrical power to provide acceleration to a beam of ions.

We are conducting a set of experiments measuring the thrust of our ion propulsion vs. the kinetic energy in BEV’s which we are imparting to the ions exiting the craft. We have decided to hold the fuel use, in pounds/second constant during these experiments.

We are generating a graph of thrust (in Newtons) vs. ion acceleration energy (in BEVs), using a constant mass of one pound of ions/second ejected from our craft. [The mass of the ions being used is measured in the ship coordinate system, while the ion-making materials are at rest inside the ship.]

My question to you is: will this curve show a relativistic “flattening” as the velocity of the ions approaches the velocity of light?

My guess is that it will NOT: as the ions velocity approach C, their velocity increase is transformed into a relativistic mass increase. But their reactive force (thrust) acting on the ship will double every time the BEVs of the accelerator double.

What do you say, meine Herren?

Details of the thrust-measuring instrumentation is still classified, of course.

But it involves a small “force plate” on a load cell being suspended in the ion beam at the point of maximum beam energy, at the exhaust end of the accelerator tube. The force plate intersects only a small fraction of the total beam, and is constructed of a material which absorbs all ions impingent on it. The force seen by the load cell is linearly related to the thrust of the drive.

R. Lewis: The free lunch probably resides in the ratio (relativistic mass)/(rest mass) of the fuel used to provide the ions.

But their reactive force (thrust) acting on the ship will double every time the BEVs of the accelerator double.

On second thought, I think the thrust should double every time the BEVs quadruple. I still need to check on the relativistic effects, but the BEVs are a measure of the energy of the individual ions in the beam. The force (thrust) runs with momentum, which runs with the square root of the energy.

Guy's
The one thing you need to remember that with the ion drive we are using electrostatic effects to accelerate the ions from the gas we inject into the chamber. So using normal physics equations we can calculate the thrust from the reaction of hurling this mass out behind the engine. Once an energy level is achieved (max 90%sol) we are wasting our time in using giga watts to provide thrust as the SOL (speed of light) stops us achieving more usable thrust than physics allows. Remember that Einstein said that one you achieve 90% SOL then you need an infinite amount of energy to actually go at 100% SOL. If you could do this then the ship would shrink axially and become an atom long and infinitely wide and need more energy than is available in the universe to break through this barrier. This is how Einsteinian physics constricts our perception of FTL travel. Things are very different in the quantum universe. !! for time is no barrier and the SOL does not exist. You could slip int "hyperspace" and throw a banana out the back and arrive in Andromeda 1 second later removing the need to harness all the energy in the universe and dieing at the same time.
DM

http://laacg.lanl.gov/rfsc99/rfsc99_web/WEA/wea005.pdf

Thanks Dishman:

Using hydrogen for fuel to provide the ions, we have a proton accelerator. The above reference is for 450 MEV protons, which the article says only travel at a velocity of 0.65 of the velocity of light. Yet the total power delivered to the accelerator is already 100 megawatts!

The Space Shuttle’s three main engines, together, provide 1.18 million pounds of thrust, or 5.37 million Newtons thrust.

A pound of hydrogen contains 272x10^24 protons. If the above thrust is to be provided by one pound of hydrogen, each proton must provide about 2x10^-20 Nt of this thrust. So each proton must be accelerated for one second by a constant force of 2x10^-20 Nt. A proton’s mass is 1.67x10^-27 kilograms, so the acceleration experienced by the proton will be about 1.17x10^7 M/sec/sec. The terminal velocity of each proton will be acceleration*time, or 1.17x10^7 M/sec, or about 3.9% of the speed of light. Thus classical (nonrelativistic) calculations can be used, without introducing too much error.

The energy imparted to each proton will be about 1.52x10^-13 Joules. Each of the 272x10^24 protons in the pound of hydrogen will be treated equally, so a total of 413x10^11 Joules of energy must be provided to the ion beam. All this happens in one second, and requires a power of 413x10^11 watts drive (1 watt=1 Joule/sec): 41.3 billion watts!

And the linear accelerator tube would be HUGE: 5.85 million meters long!

I wonder what would happen if heavier nuclei were used, maybe iron, and if a circular accelerator were used…

Iron nuclei

The Space Shuttle’s three main engines, together, provide 1.18 million pounds of thrust, or 5.37 million Newtons thrust.

Each mole of iron weighs about 56 grams. In one pound of iron (454 grams) there are 8.1 moles, or 49x10^23 atoms of iron. Each atom of iron weighs about 9.3x10^-26 kilograms.

The total thrust of 5.37 million Newtons is shared equally by the 49x10^23 atoms of iron, so each atom sees a force of 1.1x10^-18 Nt. Each atom of iron sees an acceleration of 1.2x10^7 M/sec/sec, and in one second has a terminal velocity of 1.2x10^7 M/sec. This is about 4% of the speed of light.

Using classical (nonrelativistic) calculations, each atom of iron has a terminal energy of 6.7x10^-12 Joules, so the total 49x10^23 atoms have a total beam energy of 32.3x10^12 watts. That’s 32.3 billion watts!

And the linear accelerator tube would still be HUGE: about 5.85 million meters long!

So increasing the mass of the individual nuclei by a factor of about 56 didn’t make much difference in the size of the power source we would have to carry: both are around 50 billion watts.

However, the use of iron nuclei just might make a circular accelerator more practical, if the iron could somehow reduce the mass of the magnets required to hold the circular beam geometry. Circular beam geometry allows the 6 million meters of linear accelerator to be divided into, say, 1,000 orbits (of each nuclei) around a circular track of 1,900 meter diameter.

And linear accelerator tubes, which don’t require near as much mass be used for magnets, would make the craft at least 6,000 Kilometers long. Traveling at 100 Km/hr, it would require 2.4 Earth days just to get from one end to the other.

Oops: dropped a few decimal places in the power required to drive the ion beams: they actually require about 50 terawatts (50 mega-megawatts).

This is a LOT of power. For instance, the goal of India is to produce 0.25 terawatts of nuclear power by the year 2020.

http://www.assocham.org/prels/shownews.php?id=1057

Using 100 pounds of hydrogen per second

The Space Shuttle’s three main engines, together, provide 1.18 million pounds of thrust, or 5.37 million Newtons thrust. The Specific Thrust of the Space Shuttle’s engines is 453, so it uses 2,605 pounds of fuel per second. This consists of a combination of hydrogen and oxygen. This is said to be about 36 million horsepower:

http://www.boeing.com/defense-space/space/propul/SSME.html

A pound of hydrogen contains 272x10^24 protons, and 100 pounds of hydrogen contains 272x10^26 protons. If the above thrust is to be provided by one hundred pounds of hydrogen, each proton must provide about 2x10^-22 Nt of this thrust. So each proton must be accelerated for one second by a constant force of 2x10^-22 Nt. A proton’s mass is 1.67x10^-27 kilograms, so the acceleration experienced by the proton will be about 1.17x10^5 M/sec/sec. The terminal velocity of each proton will be acceleration*time, or 1.17x10^5 M/sec, or about 0.039% of the speed of light. Thus classical (nonrelativistic) calculations can be used, without introducing too much error.

The energy imparted to each proton will be about 1.14x10^-17 Joules. Each of the 272x10^26 protons in the one hundred pounds of hydrogen will be treated equally, so a total of 311x10^9 Joules of energy must be provided to the ion beam. All this happens in one second, and requires a power of 311x10^9 watts drive (1 watt=1 Joule/sec): 311 billion watts. This is 417 million horsepower.

And the linear accelerator tube would still be HUGE: 58.5 kilometers long. If a circular accelerator were used (remember that massive magnets are required) this linear track could perhaps be shrunk to a diameter of about 19 meters (1,000 orbits per ion).

I want to close out this thread with a brief summary of my findings.

First, large thrust ion drives, equivalent to the Shuttle’s three engines, are possible, using only 1/26 of the mass of fuel per second that the Shuttle uses.

However, such a drive is much less efficient, in terms of energy use, than the Shuttle. The Shuttle produces about 36 million horsepower to achieve its thrust, while using 2,600 pounds per second of fuel. An equal thrust ion drive would have to provide 417 million horsepower of electrical energy to the ion beam.

But if you are going space-cruising, and plan to carry along a 311,000 megawatt power source to have when you get there, you might as well use it for thrust production during the trip: it will provide 1.18 million pounds of “silent” thrust. The ion beam would use 100 pounds per second of “something”, maybe water, which could be replenished along the way.

Above, we said that 311,000 megawatts of power would be required to our electric-drive ion propulsion beam.

By comparison, an early NIMITZ-class nuclear aircraft carrier carried 194 megawatt nuclear reactors producing 260,000 horsepower.

http://www.naval-technology.com/projects/nimitz/

The Vogtle Electric Generating Plant, located near Waynesboro in eastern
Georgia near the South Carolina border, has a total capacity of 2,430 Mw.

http://www.southernco.com/southernnuclear/vogtle.asp

It would take 128 Vogtle-sized reactors to provide our 1.18 million pounds
of thrust.

It requires about six pounds of uranium to be “burned” every 24 hours to
produce 791 megawatts of power at the Cooper Nuclear Station reactor in

Thus our ion-drive engine’s 311,000 megawatt reactor would burn about 2,360
pounds of uranium every 24 hours, or 0.66 pounds of uranium per second of
thrust. If refueled every 18 months of full-thrust time, the refueling would
require 1.2 million pounds of uranium.

Of course, every full-thrust second also requires 100 pounds of something,
say water, be provided to our ion-beam. If we also carried an 18-month
(548-day) supply of water that would be 4,735 million pounds of water, or
about 2.37 million tons of water.

Say that we decided to build an unmanned prototype of this vehicle in Earth orbit. For testing purposes, we had decided to paint “Bye-bye Saddam” on the nose of it, fire it up, and head it out toward deep space. At the last minute we had to fight off a Russian attempt to put a dog on board, but we did throw in a few gooey Hallmark cards and several sheets of uncancelled postage stamps.

Well, our design goals were realized when the finished mass of the vehicle was just under twice the weight of water: the finished craft weighed just 5 million tons. Initial acceleration, in g’s was 0.000118, or 0.003776 ft/sec/sec. After running for one week, the velocity was 2,284 ft/sec. After 18 months, when it ran out of fuel, the velocity was about 178,130 ft/sec, or about 34 miles per second, or 54,294 meters/sec. This is about 0.00018 c: hardly relativistic.

It is true that you you can't accelerate the ions to faster than the speed of light, but
c (speed of light) is not a limitation to the thrust available from an ion drive. As the ion velocity approaches c, it's relativistic mass increases. So you don't get more thrust by squirting the ions out faster, you get more thrust because the ions have more effective mass. It takes thrust to accelerate the ions to anywhere near c, and whatever that thrust might be, it will appear as reaction force on the spacecraft.

The only effect of c is to make the ion velocity a non-linear function of the thrust produced at high power levels.