Harnessing the Power of Photons: A Closer Look at Photon Space Propulsion

[Runei]

Hello, another thread had discussed this, and I have been contemplating the idea for a while, whether it would be possible to use photons to propel a spaceship.

I did some calculations to see how it would work and what energy levels we are talking about, and so I'd like if someone who has a little more insight migt review it and tell me whether its completely wrong?

c = 299792458 m/s

$p_{photon} = \frac{E_{photon}}{c}$

And for the spacecraft (sc)

$p_{sc} = m_{sc}\cdot v_{sc}$

So for a single photon shot out with a given energy we have

$\frac{E_{photon}}{c} = m_{sc}\cdot Δv_{sc}$

A lot of photons will give rise to a total energy E and the final velocity

Giving us

$E = m_{sc}Δv_{sc}\cdot c$

If we have a spacecraft of 500 000 kg and a final velocity of 10.000 m/s we get

E = 1.4990e+18 J = 1.5e+9 GJ

If we say we have a powersource that cna deliver 300 MW to the propulsion system we would have that it would take approximately 58 days to accelerate to this speed, is that correct?

:D

 

[jbriggs444]

Yes, a quick check indicates that your numbers are correct.

1.5e9 GJ involves the conversion of about 17 kg of mass to energy.

17 kg of mass equivalent at 300,000,000 meters/sec ~= 500,000 kg of mass at 10,000 meter/sec.

If your fuel supply is anything less exotic than matter-antimatter annihilation then you will have used up more than 17 kg of fuel and produced more than 17 kg of [presumably] useless byproducts. You can improve your propulsion efficiency by using the energy to eject those byproducts at something less than c rather than ejecting photons at c.

 

[D H]

If we say we have a powersource that cna deliver 300 MW to the propulsion system we would have that it would take approximately 58 days to accelerate to this speed, is that correct?

[strike]
No. This is completely wrong.

You are ignoring relativity. The Newtonian ideal rocket equation is a mean and nasty equation. The relativistic ideal rocket equation is even nastier and meaner.

You are also ignoring that that 300MW has to come from somewhere. Unless the photons are generated by antimatter/matter annihilation, photons are just about the worst form of propulsion imaginable, and an antimatter/matter is pure science fiction.[/strike]

I completely misread your post. For some reason I thought you were trying to make your light-powered rocket accomplish something significant as opposed to a mere 10 meters per second delta V.

You still have a math error, though. It will only take 49.57 days. 500000 kg * 10 m/s * c is 1.499e15 joules, or 1.499e6 gigajoules. Dividing by 350 megawatts yields 49.57 days.

Note that you need a laser, or something that acts just like a laser in the sense of producing a highly collimated output. A 350 megawatt light source that radiates uniformly in all directions will produce a lot of light but zero thrust. A couple of side points:

• A 350 megawatt continuously operating laser is huge. We don't know how to do that other than with a whole bunch of smaller continuously operating lasers.
• Lasers consume a whole lot more than energy than they output in the form of light. You'll need a lot more power production than 350 megawatts if you want to use lasers.

 

[jbriggs444]

It appears to me that OP is using the convention of periods as separators between sets of three digits. So he writes the speed as "10.000" meters per second but us folks in the U.S. need to read it as "10,000" meters per second.

 

[D H]

Ahh. If that's the case, there's still a problem. A 500000 kg vehicle would need 135.7 years to attain a Δv of 10000 meters/second of from a thruster that ejected 350 megawatt in the form of perfectly collimated light as the propulsive mechanism. And that's ignoring the rocket equation.

Light as a propulsive mechanism is, at least for the foreseeable future, a downright silly idea. Unless you're using matter/antimatter annihilation, that is. And then you have a slew of new problems. One is that the world's total annual antimatter production is in the nanograms. Another is that the output has to be collimated to be of any use as thrust. Matter/antimatter annihilation produces high energy gammas, and we don't know how to focus high energy gammas for any extended period of time.

 

[jbriggs444]

Agreed on the feasibility.

I hadn't reviewed the 300 MW figure. I think he needs a 300 GW engine.

 

[Runei]

Ah yes when I used the power source I mistakenly wrote 300 GW. 300MW gives me 158 years. So yes, an unfeasable solution I guess unless you get up to maybe 1 TW or something like that. And of course then there's all the engineering aspects of it.

Thanks for the reviewing :)

 

[Vanadium 50]

Photons are the worst thing to use in a rocket.

You want to give your rocket a momentum p. That means that the exhaust needs momentum -p. The energy it takes to give the exhaust a momentum p is p²/2m. So to keep the energy low, you want m to be high, not low.

(This is a non-relativistic equation, but the same feature exists in the relativistic one)

 

[Runei]

I see that, but that equation

p²/2m doesn't fit with the proton momentum equation does it?

But doesn't matter since it's quite clear to me now that they won't work.

I was simply interested in finding concepts for propulsion that wouldn't involve rocket fuel. I have been thinking about (not trying to design - simply just curious) ways to make spaceships maneuverable. For that you would need several exhaust pipes and I guess rocket fuel in that sense would be problematic, since you would have many different exhaust directions.

I know the ISS uses Ion engines to stay in orbit, but they have so low thrust that it's not really maneuverability :)

 

[Vanadium 50]

but that equation p²/2m doesn't fit with the proton momentum equation does it?

Please see above:

(This is a non-relativistic equation, but the same feature exists in the relativistic one)

 

[D H]

Photons are the worst thing to use in a rocket.

You want to give your rocket a momentum p. That means that the exhaust needs momentum -p. The energy it takes to give the exhaust a momentum p is p²/2m. So to keep the energy low, you want m to be high, not low.

I agree 100% with your first statement, that photons are the worst thing to use in a rocket.

The sentiment of your p²/2m is correct: The goal is to get the greatest Δp per unit of energy. That p²/2m is a bit simplistic. This would suggest that one should burn a LOX/LH₂ rocket fuel-lean so as to piggyback unconsumed O[/sub]2[/sub] onto that hot exhaust. LOX/LH₂ rockets are run very fuel-rich. Those unburnt H₂ molecules in the exhaust make the average mass of an exhaust particle considerably less than a stoichiometric mixture in which the exhaust is pure water vapor.

I was simply interested in finding concepts for propulsion that wouldn't involve rocket fuel.

Unless the light source is external (e.g., a solar sail), you still have what is essentially a rocket. You need to consume something to generate that energy that's being pumped out as photons.

I have been thinking about (not trying to design - simply just curious) ways to make spaceships maneuverable. For that you would need several exhaust pipes and I guess rocket fuel in that sense would be problematic, since you would have many different exhaust directions.

You do need many exhaust directions. Plus and minus x, y, z, and plus and minus roll, pitch, yaw. To make matters worse, you need dual, maybe triple redundancy in all directions. If your vehicle isn't triple redundant in all directions and involves people, you had better be very well prepared to argue why that triple redundancy isn't needed.

I know the ISS uses Ion engines to stay in orbit, but they have so low thrust that it's not really maneuverability :)

No, it doesn't. You're talking about VASIMR, and that won't be used until 2014, and that's just a demo mission, a test. There are no official plans yet to make the use of VASIMR operational. How can there be? It's not even know whether it will work. That's what that first flight test is supposed to demonstrate.

 

[Vanadium 50]

I'm a nuclear physicist, not a rocket scientist, but I suspect that a real-life rocket would have design considerations that might move you away from maximum specific impulse. Things like control, temperature and safety. So I am not surprised that real rockets run rich (and I wouldn't be surprised if it were the other way around).

The minimum number of maneuvering thrusters is six. But for redundancy I wonder if it makes sense to make the redundant thrusters offset to the "regular" ones - i.e. push at 45 degrees relative to x, y or z. I suspect that will minimize fuel, given a uniform set of required corrections. I'd have to think about that.

 

[D H]

I'm a nuclear physicist, not a rocket scientist, but I suspect that a real-life rocket would have design considerations that might move you away from maximum specific impulse. Things like control, temperature and safety. So I am not surprised that real rockets run rich (and I wouldn't be surprised if it were the other way around).

Specific impulse isn't quite the right metric. It's used because it's easy and generic. The right metric is fuel-specific, and isn't quite so easy to derive. The goal is to get the biggest bang for the buck: maximize the thrust per unit energy. The reason for burning LOX/LH₂ fuel-rich is that this increases thrust even though it reduces specific impulse.

The purpose of a rocket nozzle is to convert that random thermal energy that results from combustion into non-thermal (collimated) translational energy. A water molecule has three degrees of freedom in translation, three in rotation, and two in vibration. Those non-translational degrees of freedom get in the way of the nozzle doing its job. Exiting water molecules will have some, but not all, of that non-translational thermal energy transformed to collimated translational energy as the exhaust cools on the way out of the nozzle. Now look what happens when the combustion is fuel-rich. Because hydrogen is so light, that extra hydrogen doesn't reduce specific impulse all that much. Hydrogen molecules have but one vibrational and two rotational degrees of freedom. Right off the bat, that added hydrogen helps achieve the goal of increasing thrust because of those two fewer non-translational degrees of freedom. Another factor is that because hydrogen is so light, those non-translational modes lose energy much more dramatically as the exhaust cools. Compare that to running lean instead of rich. You'll get the same loss of degrees of freedom, but you lose that cooling effect and you also lose a lot on specific impulse.

The optimal mass mixing ratio with respect to maximizing specific impulse is the stoichiometric 8:1 oxygen to hydrogen ratio (1:2 in terms of number of atoms). The optimal mass mixing ratio respect to maximizing thrust per unit of consumed energy is about 3.5:1. Typically the ratio used is a suboptimal 5:1 to 6:1. The problem isn't safety. The problem is density, or lack thereof. Packing extra hydrogen means larger fuel tanks.

The minimum number of maneuvering thrusters is six.

More than that. You need translation and rotation, and you need to vehicle to be controllable. With only six thrusters, you're going to always get an undesired rotation when you just want to translate, and undesired translation when you just want to rotate. That undesired rotation / translation needs to be compensated, and the only way to do that is to cancel the desired translation / rotation that was just gained.

Coming up with an optimal thruster design is a bit of an art. Some amount of undesired rotation / translation is tolerable, as is some loss of efficiency. The goals are to ensure controllability in all directions without having thrusters poking out everywhere, and to do so with a reasonable amount of efficiency.

But for redundancy I wonder if it makes sense to make the redundant thrusters offset to the "regular" ones - i.e. push at 45 degrees relative to x, y or z. I suspect that will minimize fuel, given a uniform set of required corrections. I'd have to think about that.

That's one of the pieces of the puzzle used in the art.

 

[mfb]

I would expect that in theory, 6 maneuvering thrusters allow to get any position, velocity and orientation (and maybe even rotation) - but as they can only push and not pull, some maneuvers might be too messy, so more thrusters are used.
As alternative, you could use internal mechanics to change the orientation.

 

[D H]

I would expect that in theory, 6 maneuvering thrusters allow to get any position, velocity and orientation (and maybe even rotation) - but as they can only push and not pull, some maneuvers might be too messy, so more thrusters are used.

"In theory" are a dangerous pair of words. In reality, nothing is perfect. It can't be. There's always some error. Those imperfections make it theoretically impossible to be able to get by with only six thrusters.

Let's suppose you don't care about orientation. Your perfect design means that you will never build up an undesired orientation; all thrusters are perfectly aligned so that the thrust vector is in line with the center of mass. This is of course impossible. Nothing is perfect. But even if they were perfectly aligned, the center of mass moves as the vehicle burns fuel. What was a perfect alignment is now imperfect. Even if you overcame that with gimbaled thrusters that whose pointing is perfect, you still have a problem: The exhaust gas is not at 0 kelvin. What this means is that in one instant the thrust will be pointing this way, the next, in some other way. The only way to overcome this is to have perfectly designed thrusters with an infinitely long nozzle.

You need to care about orientation, so you need extra jets. Six won't do.

As alternative, you could use internal mechanics to change the orientation.

That works to some extent. That's what momentum wheels and control moment gyros do. There's a problem here: Those things saturate or develop gimbal lock. You still need attitude jets.

 

[mfb]

"In theory" does not imply "with perfect alignment".

Neglecting position and in a 2D environment: With 2 thrusters towards the same side, mounted at opposite sides of the spacecraft , you can rotate and change your velocity freely. A pure rotation looks like that: "Fire thruster A (gives angular momentum+linear momentum), wait, fire thruster B (cancels momentum+linear momentum) - if they are not balanced, one of those parts needs some thrust from the other thruster, too. This allows to rotate into an arbitrary direction, fire both thrusters until you reach the designed velocity, and rotate in an arbitrary direction afterwards.
The combination of "rotation, velocity change, rotation, velocity change, rotation" allows a translation, therefore you can reach a specific location, too.
The thrusters do not need a perfect alignment - it is sufficient that they change the angular velocity and the linear velocity at the same time.

4 more thrusters allow the same things in 3D.
Highly impractical and extremely fuel-consuming, of course, but possible with real equipment.

 

[K^2]

Photons are the worst thing to use in a rocket.

Depends on your $\Delta v$. If you want to achieve relativistic velocities, you'll have to use photons or matter accelerated to velocities where it might as well be photons in terms of E/p ratio.

Specific impulse isn't quite the right metric. It's used because it's easy and generic. The right metric is fuel-specific, and isn't quite so easy to derive. The goal is to get the biggest bang for the buck: maximize the thrust per unit energy. The reason for burning LOX/LH2 fuel-rich is that this increases thrust even though it reduces specific impulse.

If you want to optimize for total quantity of propellant used, you maximize I_sp. The mass of fuel monotonically decreases with higher I_sp. Yes, that does not optimize energy, and in some cases, reducing I_sp might reduce energy requirement. However, that would increase the amount of propellant used. If you reduce I_sp by running fuel-rich, you end up wasting more H2, which is the expensive part of the LOX/H2 combination. You also increase the mass of the tanks, so you can't save there either.

Whatever considerations for running engines fuel-rich may be, it is not to save on fuel costs.

 

[mfb]

H₂ gives a higher I_sp at the same temperature (same kT).
Running fuel-rich decreases the released energy, but I_sp can increase a bit. Nuclear thermal rockets would use hydrogen for exactly that reason.

 

[D H]

A pure rotation looks like that: "Fire thruster A (gives angular momentum+linear momentum), wait, fire thruster B (cancels momentum+linear momentum) - if they are not balanced, one of those parts needs some thrust from the other thruster, too. This allows to rotate into an arbitrary direction, fire both thrusters until you reach the designed velocity, and rotate in an arbitrary direction afterwards.

That's not pure rotation, and it's not a controllable system. There is no translation in a pure rotation. Pure rotation results from a couple. A single thruster cannot give pure rotation.

To see why this is problematic, you need to look at why this full 6DOF motion capability is needed. This capability comes at a fairly high cost, a cost that is justified only if the intended use mandates that capability. A rocket that carries a scientific payload to some other planet doesn't need this. All that this kind of vehicle needs is complete control over rotation (+roll, -roll, etc.) and translation control in one direction only (typically +x). What typically justifies that extra expense is a vehicle that is to actively operate in close proximity to some other vehicle. When a vehicle in close to proximity another vehicle needs to change its orientation for some reason, the rotation needed to accomplish that change had better be close to pure.

There are other problems with your proposed solution. Let's suppose that the force and torque from firing thruster B point exactly opposite to the force and torque from firing thruster A. (Note this only happens with a perfect alignment and placement of the two thrusters.) We have a big problem if the force ratio (the ratio of the force from thruster B to that from thruster A) and torque ratio are not identical. Your proposed scheme makes for an uncontrollable vehicle because you can't cancel both the angular momentum and translational momentum.

Now let's suppose that the torque and force are not perfect, that instead there's torque or force in some undesired (orthogonal) direction. You can't just handwave this problem away. What's going to happen is that an attempt to fix this undesired rotation/translation is going to result in yet some other undesired rotation/translation. A system is controllable if this cascading sequence of undesired effects always tends to zero. A system in which some error cannot be addressed or in which this cascading sequence grows unbounded is not controllable.

A vehicle with only six jets is inherently uncontrollable. There's too much coupling between rotational motion and translational motion.

If you want to optimize for total quantity of propellant used, you maximize I_sp.

Not true.

Burning LOX/LH₂ fuel rich, or LOX/alcohol fuel lean enables a vehicle to attain some desired delta v for a given payload mass while consuming less propellant mass. Alternatively, reducing the quantity of the more dense of the oxidizer or fuel will enable a vehicle to attain the same desired delta v for a larger payload mass. For some oxidizer/fuel combinations, the increase in payload mass can be quite significant by moving toward a fuel rich mixing ratio when the oxidizer is denser than the fuel, or a toward fuel lean ratio when it's the fuel that has greater density.

 

[mfb]

There is no translation in a pure rotation.

As I wrote in the post, I neglected translation at that point - and handled that afterwards.

What typically justifies that extra expense is a vehicle that is to actively operate in close proximity to some other vehicle. When a vehicle in close to proximity another vehicle needs to change its orientation for some reason, the rotation needed to accomplish that change had better be close to pure.

True. As I said, highly impractical.

There are other problems with your proposed solution. Let's suppose that the force and torque from firing thruster B point exactly opposite to the force and torque from firing thruster A. (Note this only happens with a perfect alignment and placement of the two thrusters.) We have a big problem if the force ratio (the ratio of the force from thruster B to that from thruster A) and torque ratio are not identical. Your proposed scheme makes for an uncontrollable vehicle because you can't cancel both the angular momentum and translational momentum.

You can reduce the torque/thrust ratio by using both thrusters at the same time - to anything which can be handled by a single thruster.

It ignores the 3rd dimension, but we have 4 more thrusters there.