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Author Topic: The physics of fusion power  (Read 1753 times)

Lagrange

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The physics of fusion power
« on: 09 September 2018, 12:19:00 »
Alsadius and I have been discussing the physics of fusion power by PM and I wanted to lay it out clearly in case anyone wants to use the actual physics.

Fusion starts with Hydrogen and turns it into Helium.  In theory, you could keep fusing beyond Helium to Iron, but the energy gain is only modest and anyways "mostly Helium" is the stated output.  Hydrogen-1 yields the most energy with an atomic mass of 1.007825.  This is fused into Helium-4 with an atomic mass of 4.002602.  The mass lost when fusing 4 hydrogen atoms into a helium atom is therefore d=0.028698 = 4 * 1.007825 - 4.002602.  Using E=d c2 this yields the energy of fusion where c is the speed of light.

Using the energy to accelerate the Helium created we can solve for the velocity v using the kinetic energy equation: d c2 = 0.5 mass_helium v2 .  Solving, we get v = (2  d c2/ mass_helium)0.5 = 35.9*106 meters / second.    Plugging this into the Rocket Equation
with a 1e-3 fraction of mass for fusion + reaction mass then implies the ship moves at about 52 hexes/minute.  Rounding down slightly, this suggests 50 thrust points per 1e-3 fraction of total mass used as fuel.

So, if you wanted to maintain a thrust of 1g for a day, it would require 5.8% of the vessel mass and a 1g transit form Earth to Zenith transit point would require 53% of the vessel mass.  At this level of mass consumption, the Rocket Equation starts to matter so we should look for cheaper options.

The mass use of a constant-g transit can be decreased by simply accelerating slower---at 1/10th g, it takes only a factor of 100.5~=3.16 longer, reducing the overall fuel mass requirements by 100.5 to about 17% of the initial mass.  This square root relationship holds generally.

When traveling at station-keeping drive scales, another obvious trick comes up.  You can just transit with the jumpship, but when outbound, there is no need for a turnover since you can do a jump with an arbitrary velocity.  Unfortunately, jumping sheds velocity so this trick cannot be used in-bound.  Not turning over saves a factor of 20.5 in time and hence in fuel use.

It is also possible to increase the thrust generated from fusion by accelerating additional mass (Hydrogen/Carbon/Oxygen/Iron/whatever) other than the Helium leftovers.  The general equation here is again a square root, so increasing the mass lost by a factor of 10 yields a 100.5 increase in thrust.  Given this, ship designs allowing "overthrust" by burning a factor of 4 more fuel to achieve a factor of 2 more thrust seem reasonable. 

Overall, it seems feasible to run the game using something consistent with the physics of fusion, but fuel use becomes a much more important part of the process at transit scales.   No constraints from the physics are imposed on ASF, but even a 200 ton smallcraft burning fuel at the "strategic" rate violates the physics---at 1g it uses up a burn-day's fuel after about 9 hours.  A 30 ton smallcraft using strategic fuel rules however is consistent with the physics of fusion.

Edit: fixed a factor of 2 error in the kinetic energy equation and used rocket equation to figure out thrust.
« Last Edit: 13 September 2021, 07:32:49 by Lagrange »

Starfox1701

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Re: The physics of fusion power
« Reply #1 on: 09 September 2018, 12:37:17 »
I don't think anyone is going to take you up on this as its kinda game breaking in a you can't conquer the galaxy sort of way. For my part based on what I know about jump drives I accept that physics just don't work exactly the same in this universe.

Lagrange

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Re: The physics of fusion power
« Reply #2 on: 09 September 2018, 13:15:52 »
I don't think anyone is going to take you up on this as its kinda game breaking in a you can't conquer the galaxy sort of way.
I'm not actively proposing a game here, just laying out what the rules would look like.

However, I disagree a bit about conquering the galaxy.  Only warships and dropships would be seriously impacted and they have plenty of mass that could be used for fuel instead.  The logistics of refueling would also add some complexity, but this is nowhere near the diminishing returns part of the rocket equation.
For my part based on what I know about jump drives I accept that physics just don't work exactly the same in this universe.
The difference here is that the jump drive is supposed to be "new physics" in game while the fusion drive is not supposed to be. 

Alsadius

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Re: The physics of fusion power
« Reply #3 on: 09 September 2018, 13:40:15 »
My original numbers were much more generous than this, and implied that tactical fuel use was roughly correct even for WarShips, but it seems I botched the math(I used conservation of energy, not conservation of momentum, which is grossly oversimplified for any kind of plausible rocketry. Also, I got an efficiency of fusion that was 3x too high).

Basically, we're deep into alternate universes for this to work. In that case, the right solution might be simply shrinking hyper limits around objects substantially to make up for the slower accelerations. In BT, the jump limit for Sol is beyond the orbit of Saturn. If you don't have to go as far(perhaps somewhere around the asteroid belt?), then the transit times don't change substantially even at these lower accelerations.

Otherwise, you need to go up to antimatter-based power systems. Fusion just doesn't cut it after a certain point.

Lagrange

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Re: The physics of fusion power
« Reply #4 on: 09 September 2018, 14:48:20 »
Routine us of L1 points for jumps would presumably become much more common.  It's a 2 hour transit from Earth to Earth's L1 point at 1G so only 0.3% of the starting mass would be needed.   

The rules make transiting from L1 point to another L1 point prohibitively difficult so maybe adding an extra jump to short interstellar trips would be the primary consequence.

Sabelkatten

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Re: The physics of fusion power
« Reply #5 on: 09 September 2018, 14:54:13 »
Interesting tidbit: The canon jump distance limits are based on reading PART of MechWarrior 1ed's description of interstellar travel. It said that transit to a jump point took about a week at 1G - 1G during acceleration, most of the transit spent drifting. The implied numbers put jump points at 1-2 AU and makes fuel consumption far more reasonable.

IIRC it's also not gravity that was the problem, but the presence of debris that would damage a jump drive. Pirate points were based around knowing exactly where everything was so that nothing got to close.

Of course when people learned just how much stuff there actually is up there the idea of any debris being a problem gets kind of silly... ::)

Lagrange

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Re: The physics of fusion power
« Reply #6 on: 09 September 2018, 16:43:51 »
With respect to L1 transits:

a) Every planet has them, so they are universal.
b) They are near to, but not quite on top of the L1 point itself.   Hence, a space station at the L1 point requires very little energy to stay on station.
c) An average astrogator (skill 5) working an 8 hour shift with computer assistance requires an average of about 5 shifts to compute an L1 solution according to SO.   This is less than the time to charge for a jump so it's reasonably feasible.

Overall, merchant traffic through L1 points seems reasonably feasible.

Daryk

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Re: The physics of fusion power
« Reply #7 on: 09 September 2018, 18:05:47 »
I went through much the same math way back in college.  You're missing the Lorentz transformations for relativistic exhaust velocity.  Even with that advantage, I remember matter/anti-matter annihilation being insufficient for rules as written accelerations. I've long held strategic thrust should be dialled down by a factor of 10, for much the same reasons you're proposing.  Glad to know there are other folks interested in the physics of things.  Hopefully Cray will be along shortly...

Lagrange

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Re: The physics of fusion power
« Reply #8 on: 09 September 2018, 20:14:04 »
You're missing the Lorentz transformations for relativistic exhaust velocity.
You're right, but I don't think it matters.  The Lorentz factor on the exhaust seems to be about .35%, but the momentum of the exhaust with a relativistic correction cancels the relativistic velocity correction.  This is discussed briefly here.

Antimatter is much more powerful although it's slightly tricky as the annihilation leaves nothing but energy behind so you need to decide how much exhaust to use.  A reasonable choice is something like 3/4 matter + 1/4 antimatter which seems to provide at least a factor of 10 more thrust.

Daryk

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Re: The physics of fusion power
« Reply #9 on: 09 September 2018, 20:33:50 »
It's been over twenty years since I did that math, but after a quick skim, that Wikipedia page seems to be talking about relativistic speeds for the vehicle itself, not the exhaust.  I'll take a closer look at it tomorrow after work.

Sabelkatten

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Re: The physics of fusion power
« Reply #10 on: 10 September 2018, 15:45:42 »
IIRC for a 1,000,000 ton cruising warship I got an exhaust velocity of about 5 C assuming a 100% effective drive (i.e. all the fuel is used as reaction mass, and it has to leave the ship at five times the speed of light - or at the speed of light but weighting 5 times as much as it did in the tanks). Making it a drive with 500% efficiency - that's pretty decent... ::)

Daryk

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Re: The physics of fusion power
« Reply #11 on: 10 September 2018, 17:46:38 »
After a more thorough read, I'm 99% certain that wikipedia page refers to cases where the vehicle itself is travelling at relativistic speeds, which is different from a typical transit.  As the page itself states, "A 0.1c velocity interstellar rocket is thus considered to be a non-relativistic rocket because its motion is quite accurately described by Newtonian physics alone."  Dropships are definitely in that regime, but their exhaust is not.

Lagrange

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Re: The physics of fusion power
« Reply #12 on: 10 September 2018, 19:28:03 »
After a more thorough read, I'm 99% certain that wikipedia page refers to cases where the vehicle itself is travelling at relativistic speeds, which is different from a typical transit.  As the page itself states, "A 0.1c velocity interstellar rocket is thus considered to be a non-relativistic rocket because its motion is quite accurately described by Newtonian physics alone."  Dropships are definitely in that regime, but their exhaust is not.
I should have been more specific---I was referring to this:
Quote from: Relativistic Rocket
The specific impulse of relativistic rockets is the same as the effective exhaust velocity, despite the fact that the nonlinear relationship of velocity and momentum as well as the conversion of matter to energy have to be taken into account; the two effects cancel each other...
Also, the (uncorrected) velocity of fusion exhaust is only .085c so Lorentz corrections are essentially negligible.  You could choose to accelerate only a small fraction of the helium to get more relativistic exhaust, but that is undesirable from a thrust generation point of view.

Daryk

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Re: The physics of fusion power
« Reply #13 on: 10 September 2018, 19:30:39 »
Undesirable, but absolutely necessary to achieve the minuscule fuel consumption in the rules.  The calculations I remember running started with that, and determined the necessary exhaust velocity from there.

Lagrange

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Re: The physics of fusion power
« Reply #14 on: 10 September 2018, 21:35:56 »
Undesirable, but absolutely necessary to achieve the minuscule fuel consumption in the rules.  The calculations I remember running started with that, and determined the necessary exhaust velocity from there.
If I understand correctly, the idea is that if you accelerate a much reduced amount of mass to near light speed then you can more efficiently translate energy into velocity.

But, the general rule is that if you increase the amount of exhaust you more efficiently translate energy into velocity.   Decreasing the amount of exhaust does the opposite and the quote I gave from wikipedia indicates the lorentz correction for velocity cancels the lorentz correction for momentum (as makes sense).  Can you recover the equations to look at?

Daryk

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Re: The physics of fusion power
« Reply #15 on: 11 September 2018, 03:34:42 »
Digging through the piles of boxes that are 300 miles away is untenable, but I may have time to take another crack at the math this coming weekend.  We'll see how it goes.  Again, my general approach was to start with the fuel consumption rates, and try to find both the energy and the momentum necessary to achieve the stated accelerations.  Tactical thrust was no problem.  Strategic, on the other hand, broke down quickly.  I ultimately tried fusing all the way to iron, and when that yielded insufficient energy, looked at matter/anti-matter, which still didn't have enough.  Dropping strategic thrust by a factor of 10 only roughly triples transit times (as you noted above), and brings things closer to the realm of possibility.

Sabelkatten

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Re: The physics of fusion power
« Reply #16 on: 11 September 2018, 05:17:21 »
You don't actually need to calculate exact exhaust velocities...

10% of the ship is fuel? A perfect antimatter photon rocket gets your ship up to ~10% of C max (~36 burn-days at 1G). 1% fuel means about 3½ day at 1G.

If you're actually using fusion the output is way less. IIRC about 5% max. So 1% fuel means about 4 hours at 1G.

Daryk

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Re: The physics of fusion power
« Reply #17 on: 11 September 2018, 16:44:19 »
As the wiki page points out, at anything less than around 10% of c, you don't need Lorentz transformations for the ship.

Lagrange

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Re: The physics of fusion power
« Reply #18 on: 13 September 2021, 07:35:53 »
I ended up examining this one closely and found a couple flaws in the equations.  Fixing these, it's 50 (not 80) thrust points per .1% of mass.

glitterboy2098

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Re: The physics of fusion power
« Reply #19 on: 13 September 2021, 09:24:21 »
It is worth noting that K-F hyperspace drive theory developed out of observations made by Kearny and Fuchida of anomalous readings during fusion reactor development.
To me this suggests that the ridiculous fuel efficiency of BT fusion drives is not only in universe Canon, but stems from some sort of hyperspace interaction inside the reactor. That the reactions are somehow leeching energy out of higher dimensional space and as a result their performance can appear to violate conventional 3d physics. Figuring out how and why is what led to the ability to move ships through that same higher dimensional space.

VhenRa

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Re: The physics of fusion power
« Reply #20 on: 13 September 2021, 11:11:45 »
And their pointing out these observations got them essentially unpersoned by the scientific community and their role in the development of the fusion reactor instead publicly attributed to another team.

monbvol

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Re: The physics of fusion power
« Reply #21 on: 13 September 2021, 11:40:36 »
I have started thinking the K-F Boom may do more than it says on the product description label and would make a bit more sense for why Dropships fully displaced their more primitive forebearers.

Daryk

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Re: The physics of fusion power
« Reply #22 on: 13 September 2021, 17:11:42 »
More how?  What the tin says they do is a LOT!  ???

monbvol

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Re: The physics of fusion power
« Reply #23 on: 13 September 2021, 19:23:50 »
More how?  What the tin says they do is a LOT!  ???

Considering how far one fuel point moves a Behemoth in one minute for how little it masses in comparison I am reasonably certain they include some dark magics not listed on the tin.

Daryk

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Re: The physics of fusion power
« Reply #24 on: 13 September 2021, 19:31:25 »
Oh totally, but it does say that in the rules, so I was a little confused... :)

DevianID

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Re: The physics of fusion power
« Reply #25 on: 14 September 2021, 01:54:19 »
So 50 instead of 80 per .001 of ship mass?  Still close to tactical fuel, but again the way brackets work make any attempt to use brackets break as the brackets are too wide.  A % based system is much cleaner with less charts and brackets, by choosing your ships allocated % fuel reserve.

In real life, 10% for an independent battleship wet navy was a standard fuel load, with 5% being a low endurance and 20% being a high endurance.  We trend towards low endurance with tanker ships nowadays, but in btech a mix of low endurance ships with fleet tenders, normal endurance solo operators, and high endurance scouts/raiders makes total sense still.

The trip to earth from a [zenith/nadir] is a good metric to measure the more realistic fuel versus bt transit fuel.  With transit magic endurance, we have an earth to [zenith] at 1g constant of 9.1 days and 1.5 billion kilometers.

With a 5% round trip fuel load, spending 1.25% there and back again twice, the trip takes 92 days there and 92 more back, so half a year for the worst endurance ships that cant refuel in space to make the 4 burns necessary from one planet to another.
With a 5% 1 way fuel load, spending 2.5% speeding up and 2.5% slowing down, this trip takes 46 days.  This is very reasonable for civilian bulk commerce, with a point to point time from one planet to another in roughly 3-4 months depending on how many jumps the cargo makes.  Since current btech bulk shipping still takes 3 weeks to 2 months, the impact here is minimal.
With a 10% round trip fuel load, this trip takes 46 there and 46 days back, per the 5% fuel load, though with 5% less mass starting out on the way back the return trip is a little faster.  Bulk cargo ships that cant refuel in space will need a 10% fuel capacity.
With a 10% 1 way (or 20% round trip) fuel load the trip from [zenith] to earth is 23 days.  This 23 days is pretty close to the 9 days the physics breaking transit drives provide, and managing to put a 10% fuel capacity on existing btech ships is trivially easy. 
With a 20% 1 way fuel load (for those scout/raider type ships) we can get the transit time down to 15 days.

The cool part about % based fuel is that we get interesting decision points from a gameplay and narrative perspective.  Is the 8 days saved burning at a 20% fuel rate worth not having the redundancy of being able to return home without refueling?  Do you have to scour known pirate points regularly since they save so much time?  Acquiring star charts to unlock star systems is a video game thing, but it is an actual reality when you have some systems with massive [zenith distances]--systems with large [zenith distances] and few planetoids to generate pirate points might be off limits except to those with secret pirate point system charts; the safety of which are of the highest importance and the most top secret things a star empire might have.

An existing leopard has a 7% fuel capacity, enough for 5% travel options and 2% combat options.  A union has only 5.9%, so it's combat fuel load is a mere .9%, though that tracks with how they are used to more or less just land when they get to a planet instead of fly around like a leopard.  An overlord has only a 3% fuel load... this thing needs tankers flying alongside it, or over a month to make planetfall--which fits it's fluff as a planetary invasion dropper as part of a fleet versus the union which is a more solo operative.

If you wanted a leopard raider, you only need to rip out the aerospace bays [or use 50 ton mechs and fighters instead of 100 tonners saving 300 tons] and now you have a 23% fuel load, enough for a quick burn to a planet and a 3% reserve.  A union with its aerospace bays removed for fuel has a 14% fuel capacity, giving it the ability to make a 10% in system burn and 2.5% out system return; with 10% of your previously fuel tonnage freed up for that sweet pirate loot.

EDIT: A convoy example is also interesting.  A 3 dropship invader jumpship could disembark an overlord military transport, an avenger destroyer escort, and a mule tender ship.  The combined convoy weighs 22.3k tons, with an onboard 785 tons of fuel for a 3.5% fuel capacity with an extra 36% convoy weight in the mule's cargo hold, allowing for the combined convoy to make a 20% insystem burn and 10% out system burn with no issues.  A 3.2k danais tender in place of a 11.2k mule makes for a 11% danais convoy cargo hold, making it okay for suppling the 3 ship fleet for a 10% insystem burn, getting an overlord to a planet much faster than it could without a tender.
« Last Edit: 14 September 2021, 08:01:57 by DevianID »

Lagrange

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Re: The physics of fusion power
« Reply #26 on: 14 September 2021, 07:01:58 »
The trip to earth from a LaGrange is a good metric to measure the more realistic fuel versus bt transit fuel.  With transit magic endurance, we have an earth to LaGrange at 1g constant of 9.1 days and 1.5 billion kilometers.
I think you mean Zenith/Nadir?  The L1-Terra point requires about 3 hours thrust at 1g.

Anyways, I completely agree about real fuel use opening up interesting tactical situations.  In addition to endurance & convoy questions, you have several other tactically interesting possibilities:
  • A variant on the convoy has the tender only slow down once (as it exits the system) to mate with a jumpship.
  • A variant on the variant has the tender with a tug so that it can take the jumpship with it.  Then, the tender need never slow down (since jumps bleed away kinetic energy).
  • Another tactic is utilization of L1 points around orbiting bodies.  L1 points are small enough to defend, so it creates interesting force allocation questions for a system defender.
All of these are decisions which become much sharper when fuel is nontrivial.

DevianID

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Re: The physics of fusion power
« Reply #27 on: 14 September 2021, 07:57:40 »
Yeah, sorry total brain fart on the lagrange versus zenith points vocabulary lol.  Math is good, words less so...  So using the 50 thrust points per .001 of ship tonnage, 5.76% ship weight is about 1 day of 1 g transit time using 2 thrust/min for 24 hours.  Thus ships with ~6% fuel weight (leopard/union) can use all the published 1g transit times in strategic operations of 1 day or less with no change.

On the tug idea, a custom mule with a tug can have 7000 tons of fuel total.  So when combined with a 152k ton invader, 9.7k ton overloard and 1400 ton avenger you have a 4% convoy fuel load using just the Mule's fuel, before detaching the overlord and avenger to retrograde burn while the mule and invader jump out.
« Last Edit: 14 September 2021, 08:28:28 by DevianID »