Solar powered Ion driven Space craft, theoretical limitations

[PB666]

Before I start I need to define my terms

F = force (measured in Newtons, N)
M = mass (as in vessel mass or fuel mass)
M* = mass ejection rate (M/sec)
kW = 1000 watts = energy production rate or 1000 joules per second.
Power = Power available (Kw) 
Power efficiency = Power not wasted
Heating = Power wasted
Irradiance = Solar output measured at 1 AU , 1361 Watts per sq. meter
Panel efficiency = percent of irradiance converted to electrical power
ISP = F_thrust / M* this value is 9.802 x ISPg (sec) which I will not use because basically it adds a term to every equation not needed, particularly for a craft that is interplanetary. ISPg is best applied to chemical thrusters, when you don't really care about where ejection force power comes from, you can wave your hands about bond energies, etc.

Given ISP:  M* = F_thrust / ISP         ION drive equation is F = ( 2 * Power efficiency * Power )  / ISP
 

Given: ION drives cannot shift ISP more than a 4 fold range
Given: HiPep produces 0.67 N (rated) at 39.3 kW at 9620s (94300 v) between .75 and .8 efficiency.  The form factor is .31 x .91 x .1? = Assuming density of 2 and a fill volume of 0.1 the M_thruster = ~5 kg. Thus one can estimate the following:
N/area = 2.37N/_m2     F/power input (N/kW) = 0.67/39.3 = 0.017 N/kw at 93000v. For the sake of simplification I will use 0.015 N/Kw at 100000v.

 

Thruster modification cost for on the fly down-ratable ISP (ISP_dr; arbitrary guess) = k * SQRT(100000/ISP_dr). The cost is paid assuming that the thruster is built for 100,000v (10202 s), and therefore added cost is to allow it to achieve lower ISP during the trip. This allows a significant burn say at Perigee allowing a kick then a higher ISP on a second pass and then most efficient ISP to reach Mars.

While these numbers appear not to have much value . . .we then can add solar panels
Maximum panel efficiency is 40% lets assume that this applies to non-atmospheric, then we can apply the following:
Irradiance (kW/_m2) * Panel efficiency = Output power per sq. Meter 1.361 * .4 =  0.544 kW/_m2 DC. If we assume this is 24V we have 22Amp so we need 10 gauge wire to feed the power center of the space craft.

We are going to take a base assumption that 1 square meter of panel weighs a kilogram. Therefore the space craft has a minimum of 1 * thruster weight.

So lets build an ion driven space craft, to keep things simple we will choose a spacecraft that with 1 meter squared solar panel

0.544 kW (panel output) x 0.015 N/kW (thruster input) =  0.00816 N. This then consumes M* of 0.00816N/100000v = 8.16E-8 kg/sec. We have alternatives. We have a theoretical weight per thruster of 5kg per .67N = 7.5 kg/n * 0.00816 = 0.0612 kg With our  panel we have 1.0612 (Assume the microelectronics the thruster is glued to the back of the panel)

ISP	Thrust (N)	M*x10E-9	duration/kgfuel
100000	0.00816	81.6	141d
50000	0.01632	326.4	35d
25000	0.03216	1305.6	9d
12500	0.06432	5222.4	53h
6250	0.12864	20889.6	13h

As of yet we do not know our dV. Two reasons for this I haven't added any fuel mass. Nor have I added any structure and control mass. 

Our theoretical acceleration is very close to thrust since solar panel of 1 kg dominates the mass.
Thus we can readily determine our theoretical maximum for each ISP. In this case I am going to add fuels and mass of 1.2 and tabulate the accelerations. To do this I am going to assume that for every kg of fuel added 0.2 kg of structure is added. With our theoretical ion drive we have then 1.0612 + Fuel*0.2 = dry mass, starting mass = dry mass + fuel mass + tunability cost mass. The equation is ISP * ln (full mass/dry mass)

ISP  (ISPgo)	0.1 kg	0.5 kg	1 kg	2.0 kg	4.0 kg
100k m/s    (10ks)	8845 C	35808	58383	86235	114713
50k     (5.1k)	4325 D	17581 B	28753	42622	56896
25k     (2.55k)	2143 F	8725 C	14288 B-	21210 B+	28353
12.5k   (1275)	1058 F	4317 D	7082 C-	10534 C+	14100 B-
6.25k   (637)	519   F	2127 F	3498 D-	5218 D+	7009 C-
3.125   (318)	253  F	1042 F	1719 F	2575 F	3472 D-

The first gets our craft from earth LEO to Mars LEO and back, but over a period of 200 days and of course the spacecraft does not carry any payload to speak of, the second gets us close to Mars, the third gets us to a geosynchronous orbit (or so). With 5 times as much fuel the third ISP gets our craft to Mars. In the second fuel column the starting mass is one/third fuel, and even with that mass the ship is unable to return from Mars with a decent ISPgo of 1275 sec (almost 3 times the SSME ISP). With 1 kg of fuel it makes it back to Earth's sphere of influence (however with any additional payload, its stuck at Mars). One of the things that I did was under-engineered a decoupler on the Gas tanks so that tanks are used serially and then discarded, this gets rid of 10% of the structural cost, but backbone cost still remain 10% of the tanks weight, this improves the ISP for heavier fuel loads a little. I have assigned a grade based upon the usefulness of each reaching Mars assuming it uses 1 ISP and does not refuel along the way. But we can pretty much assume that a ship that cannot even break earth’s orbit or reach L2 refueling or extra-lunar refuelling point is of little value and can be ignored. Consider than in a manned Mars mission at least 1/3 of the ships dry mass will be devoted to survival and other related activities. So at about 4500 dV even refueling will not help with humans onboard. 

The problem with more fuel loads, are two fold, the through put of the thruster (electrode wear and tear) and breaking Earth's orbit. So lets look at the (get the hell away from earth) accelerations. Lets keep in mind that unless we like leaving our astronauts for months in LEO and LMO for no particular reason, we need to be shooting for accelerations of at least 1mN per starting mass second. Lazily (and to control column widths) I will use the mm but you should assume that is mm/sec². Parenthesized numbers assume a humanized payload addition of 30% , the second number describes how many time the vessel would need to be refuelled to go to Mars enter its low orbit and return. 

ISP	0.1  (HPL) kg	0.5 kg	1.0 kg	2.0 kg	4.0 kg
100k m/s	6.9 mm (5.51, 1) C+	4.9 (4.1, 0), C	3.6 (3.2) D	2.4 (2.1) D-
50k	13.8 (12.9, 2+) B+	9.8 (8.3, 0) B-	7.2 (6.3) C+	4.7 (4.3) C	2.8 (2.6) D-
25k		20 (17, 0+*) B	14.4 (12.8) B+	9.4 (8.7) C+	5.6 (5.3) C
12.5k		39 (33, 3*) C-	29 (25.4, 1*) A-	18 (17*,0+) B	11 (10.5*,0+) B-
6.25k				38 (37*,1+) C+	22 (21*,0+) B
3.12k					44(42*, 2+) C

* if one pays the thruster cost here then the acceleration only need be used in LEO, and scale ISP to the dV need to alter a profile, possible to reduce the refuels. Based on this the very best choice here is a ship that can achieve 25000 to 100000 ISP (2750 to 10202 ISP) and keeps the humanized portion of the payload below 0.3 dry mass.  About the same amount of fuel as solar panel and the bare minimum of structure. I can Imagine a ball, with two bars sticking out and solar panels. Though I think probably given we need to add structural weight, 1.5x fuel might be better. 

So if this is the case suppose for a multiyear trip how much weight. Lets say 10 tons per astronaut, sounds pretty small. So our scale is 10000/0.3 = 33333, for 2 nauts that is 66666

How does this equate:

66666 meters of solar panel at 66 tonnes producing maximally 36 mW of Power. I should add that if one uses my 10 by 100 meter solar panel (KSP creation) that is 66 Solar panels.

The thrusters 11.5 tonnes produce 0.543 to 4.3 kN of thrust (double the PB-ION) and also produce 8.125 MW of waste heat, that needs to be dissipated. 

The thruster footprint at 0.1M height is 153 square meters (a circle of radius 6.9 meters radius).

Saturn V rocket has a radius of 5.1 meters.

Our payload in LEO weighs 190 tonnes. Saturn V = 140 tonnes to LEO.

Now judging by the structure, it has to be assembled in space.

 

 

 

Edited February 9, 2016 by PB666
and replaced diameter with radius

[Nothalogh]

Take the panels off, beam the power to it

[PB666]

 

1 hour ago, Nothalogh said:

Take the panels off, beam the power to it

That is the idea for the interstellar ship, but that is beyond the scope of this thread, this group, this century, and probably this millenium.

Beam of course means hv, which means collector, most panels can function at 10 times irradiance so all your doing is reducing the panels by a factor of 10.

[Bill Phil]

Just now, PB666 said:

 

That is the idea for the interstellar ship, but that is beyond the scope of this thread, this group, this century, and probably this millenium.

Beam of course means hv, which means collector, most panels can function at 10 times irradiance so all your doing is reducing the panels by a factor of 10.

And reducing the mass of the panels by the same factor. Which really helps.

And it also really helps if you don't have to carry your power source with you. 

[PB666]

18 minutes ago, Bill Phil said:

And reducing the mass of the panels by the same factor. Which really helps.

And it also really helps if you don't have to carry your power source with you. 

It all works well until you realize that the axis of the ship is facing the hv source, and it limits the number of panels, that you want a power that can accelerate at 1g for 1 year (or 0.1g for a year) and those ION thrusters waste most of the energy as reaction mass energetics, and you are lucky to get 0.001g and you would need to accelerate for 10 years, by which time your ship is way out of the resolution limit for the beam.

So I figured for a beam powered ship to work you would need a collective of light harvesters in the Inner solar system that beamed light to object near pluto's orbit, this is then stationary enough to beam light to a ship, it would send out polychromatic light so the ship could steer itself back to the center of the beam, when the beam ship moved far enough from ideal another orbiting ship would be employed. If we discount the ISP problem outlined in this thread (meaning no way to carry enough gas to reach anything close to c)

The critical problem with this is that when the ship finally reaches its speed.

1. Light reaching the deceleration zone would be tiny
2. Assumed that earth maintained interest 200 years later and kept sending light.

In fact this is the problem with nearly all near light speed how to stop if by some strange luck something 1/1000th c is achieved. They all have the same basic problems. Large slow ships can utilize celestials within the target system to help reduce velocity,
 

[Nothalogh]

That's why you build a railroad.

It seems you have your mind set on the locomotive, and less on the tracks

[batman78781]

IIRC the Ares V could lift 188 tonnes to LEO, so it's close enough. Unfortunately the constellation project was downscaled to the SLS program.

[Bill Phil]

7 minutes ago, batman78781 said:

IIRC the Ares V could lift 188 tonnes to LEO, so it's close enough. Unfortunately the constellation project was downscaled to the SLS program.

More like fortunately. If not for the downscaling, nothing would've happened at all.

On topic:

But there is a typical problem with electric propulsion: you need electricity. Which can be a blessing and a curse, as you all probably know.

[kerbiloid]

And in the limit we get that the easiest way is to take the Sun onboard: a fusion reactor.

Edited February 10, 2016 by kerbiloid

[Streetwind]

This thread contains a huge amount of numbers, a lot of assumptions not explicitly declared, and very little description of what you're actually doing. The thread title suggests you're exploring the theoretical limits of a rather unspecific grouping of technology, but it seems you're actually trying to design a crewed Mars mission?

[lugge]

1 hour ago, Streetwind said:

This thread contains a huge amount of numbers, a lot of assumptions not explicitly declared, and very little description of what you're actually doing. The thread title suggests you're exploring the theoretical limits of a rather unspecific grouping of technology, but it seems you're actually trying to design a crewed Mars mission?

Exactly what I was thinking.

It would be good if the thread starter drops a few sentences of what he's doing. Even a small conclusion what help.

Because I assume the starter has a scientific background: you don't write papers by just throwing in some random numbers without explaining the whole idea...

[Frozen_Heart]

Would a small fission reactor work better than solar panels for an ion spacecraft?

[wumpus]

I'm still wondering what assumptions you are making and how you are grading these devices.  My understanding is that ISPs tend to be 4000 or less, and there isn't much point in going higher.  Also expected burn times should be in months or years (at least one such drive fired for several years in the lab).  If the problem is that the mass of the solar panel dominates the mass, you need a smaller solar panel (and a smaller, presumably already designed ion drive) and more xenon (xenon is expensive, so try making the solar panels smaller before using too much xenon.  Or use argon (and much get much less Isp).

One thing that keeps getting ignored in such calculations is just how are you going through the Van Allen belts.  My guess is that the ship will be built in LEO, slowly trudge through the Van Allen belts and not be boarded until ready for Mars intercept (i.e. 3/4 of the burn to Mars).  [This gives at least one mission for SLS, or simply use Dragon/Orion/Soyez connected to some booster sent up that doesn't have boiloff issues (possibly by docking/burning fast enough).]

[fredinno]

14 hours ago, Bill Phil said:

And reducing the mass of the panels by the same factor. Which really helps.

And it also really helps if you don't have to carry your power source with you. 

Solar has a max. efficiency of 80% or so.

13 hours ago, Nothalogh said:

That's why you build a railroad.

It seems you have your mind set on the locomotive, and less on the tracks

How do you build a railroad without getting to the destination, and through the track zone a few times?

12 hours ago, batman78781 said:

IIRC the Ares V could lift 188 tonnes to LEO, so it's close enough. Unfortunately the constellation project was downscaled to the SLS program.

That was near the very end, when they changed the RS68 back to SSME- before, it was 130T, like SLS Block II.

1 hour ago, wumpus said:

I'm still wondering what assumptions you are making and how you are grading these devices.  My understanding is that ISPs tend to be 4000 or less, and there isn't much point in going higher.  Also expected burn times should be in months or years (at least one such drive fired for several years in the lab).  If the problem is that the mass of the solar panel dominates the mass, you need a smaller solar panel (and a smaller, presumably already designed ion drive) and more xenon (xenon is expensive, so try making the solar panels smaller before using too much xenon.  Or use argon (and much get much less Isp).

One thing that keeps getting ignored in such calculations is just how are you going through the Van Allen belts.  My guess is that the ship will be built in LEO, slowly trudge through the Van Allen belts and not be boarded until ready for Mars intercept (i.e. 3/4 of the burn to Mars).  [This gives at least one mission for SLS, or simply use Dragon/Orion/Soyez connected to some booster sent up that doesn't have boiloff issues (possibly by docking/burning fast enough).]

You can ignore this by staging the crewed vessel in MEO or Lunar Orbit, and making the cargo (as much as possible) from LEO.

And a Mars Mission will be made by SLS most likely anyways.

[PB666]

9 hours ago, Streetwind said:

This thread contains a huge amount of numbers, a lot of assumptions not explicitly declared, and very little description of what you're actually doing. The thread title suggests you're exploring the theoretical limits of a rather unspecific grouping of technology, but it seems you're actually trying to design a crewed Mars mission?

 

OK to make this blatantly obvious. Mass grows in three dimensions, volume space, but solar panels grow out in two dimensions and the discussion limits efficiency to 40% with an absolute limit of 100%, which drops output to 16 and 40% at Mars. To be blunt 66 1000 ft panels is not practical, therefore a 2 person ION driven trip is not possible. ION drives should be used to station fuel supplies which manned missions pick up and use but use different propulsion systems to reach those fuels supplies. ION drives should be used for transporting non-perishables only. Unless you design half height, 8th weight humans that don't mind living alone for years at a time in a coffin size vessel, solar efficiency and the neccesity of laying out panels in a 2D plane set the absolute limit in how useful solar can be for carrying weight. Even if we circumvent that problem, the ion drives themselves need to be layed out in a plane, so here again we reach the practical limitation. Structural rigidity in a 2D space is far less than in 3D. So some manner of stabilization in space needs to be improvised.

Of course, if we start talking about building structures in a space factory, whereby we are building 20 football field sized ships, then you can relax these restrictions a little, but you are never going to have crewes of a dozen people going to mars by ION drive, and we can rule out conventional nuclear because it has exactly the same problem with heat exchangers.

 

B O T T O M    L I N E

The limitations suggest that we build many low mass carriers and use the low mass carriers to ship fuel to drop off points where the fuel is condense into a refueling plug (hyperglolics right now appear to be the best option). These limitations suggest we do not ship humans with nuclear or solar panel powered spacecraft for thrust energy but use hyperglolics. In essence you are building a railway to mars, just like the railways of old, where the train stops, picks up fuel and supplies and goes to the next station. If you have alot of time to ship by ION drive then a 9000 ISP drive will be great for resupplying fuel. But the reality here is that we need to start designing multimission ships that once in space perform all future missions in space.

 

[PB666]

7 hours ago, wumpus said:

I'm still wondering what assumptions you are making and how you are grading these devices.  My understanding is that ISPs tend to be 4000 or less, and there isn't much point in going higher.  Also expected burn times should be in months or years (at least one such drive fired for several years in the lab).  If the problem is that the mass of the solar panel dominates the mass, you need a smaller solar panel (and a smaller, presumably already designed ion drive) and more xenon (xenon is expensive, so try making the solar panels smaller before using too much xenon.  Or use argon (and much get much less Isp).

One thing that keeps getting ignored in such calculations is just how are you going through the Van Allen belts.  My guess is that the ship will be built in LEO, slowly trudge through the Van Allen belts and not be boarded until ready for Mars intercept (i.e. 3/4 of the burn to Mars).  [This gives at least one mission for SLS, or simply use Dragon/Orion/Soyez connected to some booster sent up that doesn't have boiloff issues (possibly by docking/burning fast enough).]

Think about it. 9000 ISP is actually the HiPep highest output flat panel ION drive. Second I gave alternative drive capabilities. So that issue is dealt with, the choice of drive was one that went from 2500 ISP to 10000.  This fits all the capacity requirements,

1. Able to use alot of power
2. Power to momentum conversion is efficient
3. The footprint is reasonably small (.31 x .91) or about a quarter of a square meter./
4. Because we are talking about how to get people to Mars we need speed, to get speed you sacrifice Xenon mass.

I think I made is quite clear, Solar panels are the limiting factor, and the mass of the solar panel I got off of NASA web pages, 1 kg per meter^2. The efficiency was set at the highest available. Ultimately however its not the MASS of the

I know alot of you guys out there are trying to WISH up a way to Mars, let me remind everyone of the saying, If Wishes were horse beggars would ride. There aint a ride out there. Getting ION drive to Mars, no problem, getting the dV required to go to LMO and back, not a problem, getting humans to mars with 66 1000 foot panels is a big problem. We might wish we could build such a craft, it aint going to happen.

Let me state this as I was designing a panel for the game, . . . . . . .1000 feet recieves 1340000 watts of power from the sun, at 40 percent that is 450 kW right so that basically means that producing 24 volts, that translates into  18750 Amps