Energy production that converts Hydrogen to Iron?

[Devin-M]

On rocket equation calculator, 37,474,057m/s exhaust velocity, initial mass 556600kg, final mass 38200kg, change in velocity 100,393,423m/s or 0.33c.

Proxima Centauri: 4.24ly
Travel Time: 12.8yrs @ 0.33c

 

[Devin-M]

It's amazing what you'd be able to do with just a tiny amount of fuel.

I tried the same dry mass with only 100kg of fuel. Initial mass 38300kg, final mass 38200kg, exhaust velocity 37474057m/s...

97km/s delta v for getting around Earth or the Solar System with only 100kg of fuel in a 38200kg craft!

 

[PeterDonis]

It's amazing what you'd be able to do with just a tiny amount of fuel.

If it's fusion fuel, sure, since the energy per unit mass is about 5 orders of magnitude larger than for chemical fuel. The hard part is actually getting the fusion reaction to go.

 

[Devin-M]

It seems possible to do even better still:

We start off the same:
Dry Mass: 38200kg (of which 12000kg is useful payload)
Wet Mass: 556600kg
Propellant Mass: 518400kg
Propellant Energy: 719TJ/kg

But, before we do any thrusting, we use all the energy in the Deuterium to make matter-antimatter:
518400kg deuterium * 0.008kg/kg = 4147kg matter-antimatter
518400kg-4147kg = 514253kg iron

Now we dump overboard non-energetically 510106kg of iron leaving us with:

4147kg matter-antimatter
4147kg iron

The propellant mass is now:

4147kg + 4147kg = 8294kg

This changes the pre-thrust mass of the rocket to:
Dry Mass: 38200kg (of which 12000kg is useful payload)
Wet Mass: 46494kg
Propellant Mass: 8294kg (1/2 matter-antimatter, 1/2 iron)
Propellant Total Energy: 372EJ

But this becomes difficult to put into the rocket equation because pre-thrust the propellant mass is 8294kg, but only half of that mass actually comes out of the engine, because the other half turns to pure energy.

So we're back to the scenario in which an astronaut has a 0.5kg ball in his left hand, a 0.5kg ball in his right hand, and he's letting go of one ball while throwing the other...

 

[PeterDonis]

It seems possible to do even better still

The best possible scenario in terms of propellant usage is a photon rocket, which is the scenario discussed in the article on the relativistic rocket equation that I referenced. That scenario assumes that all of the propellant mass is converted to photons that are ejected as exhaust with perfect collimation.

The downside of this method is that you can't just magically convert matter to photons. You have to find actual reactions that do it.

 

[Devin-M]

Actually, I’ll have to retract my last post. It isn’t quite clear that converting all the energy to antimatter and then dumping much of the iron would actually improve the delta-v.

 

[PeterDonis]

converting all the energy to antimatter

Doesn't make sense anyway. The energy is what it is. You can't make it more energy by converting it to antimatter. You might as well just use it directly.

 

[Devin-M]

I thought by reducing total mass before thrust begins (with the same energy on board) it would be beneficial, but isn’t clear whether that’s truly the case.

 

[PeterDonis]

I thought by reducing total mass before thrust begins (with the same energy on board) it would be beneficial

Which would work the same even if you didn't turn the energy into antimatter. And I've already shown you that it doesn't make things any better.

 

[Devin-M]

I guess it makes sense. It's not like a car so decreasing the propellant mass (and by extension total mass) with the same total energy won't make it faster.

If we increase the mass of the ball the astronaut throws for the same throw energy, the astronaut always goes faster.

1kg Ball, 100J, 100kg Astronaut:
Astronaut: 0.14m/s
Ball: 14.08m/s

2kg Ball, 100J, 100kg Astronaut:
Astronaut: 0.198m/s
Ball: 9.9m/s

1kg Ball, 100J, 100kg Astronaut:
Astronaut: 0.14m/s
Ball: 14.08m/s

0.1kg Ball, 100J, 100kg Astronaut:
Astronaut: 0.044m/s
Ball: 44.7m/s

A=(sqrt(2)*sqrt(B)*sqrt(E))/sqrt(D*(B+D))

C=(D/B)*A

A=Astronaut_Final_V_m/s
B=Ball_Mass_kg
C=Ball_Final_V_m/s
D=Astronaut_Mass_KG
E=Total_Energy_J=100J

 

[PeterDonis]

If we increase the mass of the ball the astronaut throws for the same throw energy, the astronaut always goes faster.

I already gave a general argument for why that is the case.

 

[Devin-M]

On rocket equation calculator, 37,474,057m/s exhaust velocity, initial mass 556600kg, final mass 38200kg, change in velocity 100,393,423m/s or 0.33c.

Proxima Centauri: 4.24ly
Travel Time: 12.8yrs @ 0.33c

0.33c in flat space. Better still… oberth effect near sag a*?

 

[snorkack]

0.33c in flat space. Better still… oberth effect near sag a*?

No. Because then you have to travel the 25 000 ly TO sag a* BEFORE using Oberth effect (and then back). AND spare fuel to use the Oberth effect at sag a*, which means that you´ll for the first leg be travelling slower than if you were not planning on using Oberth effect.

 

[Devin-M]

For a destination such as Andromeda (2.5 Mly) would it be quicker to take this detour?

 

[mfb]

That depends on your spacecraft and its propulsion system. It's possible.

 

[sophiecentaur]

As I stated, nuclear physics isn't my forte: I've been unable to find another source of error in my math, however I have no formal education in the subject and am not confident none exist. I would appreciate anyone deeply knowledgeable in the subject reviewing the math and identifying any further errors made.

Imo, this thread would better have been put quietly to sleep immediately after its birth. Only the fourth post should have been enough to save all this effort

Not to rain on your parade, but while this fusion engine would not facially violate any laws of physics, as a practical matter, it is basically an engineering impossibility.

What follows in that post should be enough.