# Delta-V with unlimited fuel?

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#### tosse

##### Guest
I was wondering how much delta-v would be practical to achieve if you can have "unlimited" fuel avaiable in orbit?<br /><br />Lets say we use lunar regolith to fabricate liquid hydrogen and oxygen, and then send it to orbit. When done automated and routinely it would be very cheap, at least compared to sending it up from earth surface (let's not discuss the feasibility of this plan, lets just say it's possible).<br /><br />Then lets say we want to send a 10-tonnes craft to Mars. How long would it take if we used 100 tonnes of fuel? A 1000 tonnes? 10 000 tonnes? Where would it not be practical anymore (because of the weight of the fuel)?

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#### najab

##### Guest
Unlimited fuel implies unlimited dV.

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#### henryhallam

##### Guest
Although in theory unlimited dV is attainable, the Isp of a given fuel means that after a certain point you get diminishing returns.<br /><br />With a vacuum Isp of around 450 seconds for LH2 and LOX let's try to calculate what would happen:<br /><br />The relevant equation is "the" rocket equation, dV = g * Isp * ln(initial mass / final mass)<br /><br />The faster you want to go, the greater the fraction of rocket mass that must be fuel. You can try to make this fraction as close to 1 as possible, but it can start to get ridiculous. Remember the mass of the propellant tanks etc. counts as payload. Existing mass ratios tend to be about 10:1 to 20:1 but imagine we can increase this to as much as 100:1 (which might be doable given that the structure doesn't have to support launch accelerations). <br /><br />Then we have dV = 9.8 * 450 * ln (100) = 20.3 km/s. Quite respectable. I won't go into the maths to derive a trip time to Mars (mainly because I don't understand enough of it) but using the Orbiter simulator with the "TransX" planning tool it looks like it would take approx. 115 days (nearly four months) assuming 7.6 km/s dV used to inject into the transfer orbit and then another 12.7km/s used to slow down for Mars orbit capture. If you're willing to do some aerobraking you can use more dV for injection and less for capture - at the extreme case, using all 20.3 km/s for injection this would reduce trip time to less than 60 days but then you have an encounter velocity of almost 30km/s. Dumping all that with aerobraking without burning up is quite a challenge and I don't think it's really feasible.<br /><br />p.s. Looking around on Google I found a graph to illustrate dV as a function of mass ratio halfway down this page: http://www.pma.caltech.edu/~chirata/deltav.html

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#### henryhallam

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By the way, increasing the mass ratio to 1000:1 (10000 tonnes fuel, 10 tonne craft) gives you about 30 km/s dV, which only reduces the trip time to 40 days (full aerobraking) or 71 days (full rocket braking).<br /><br />I don't think this justifies lugging up ten times as much fuel from the moon.<br /><br />10:1 ratio (100 tonnes fuel, 10 tonne craft) = 10.1 km/s dV, 170 day trip time (rocket braking), 85 day trip time (aerobraking). You have to lose 15km/s aerobraking - maybe doable?<br /><br />For reference, a Hohmann transfer uses about 3.5 to 4 km/s injection dV and takes ~280 days (depends a lot on the launch window chosen)

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#### vogon13

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Maybe a scenario to help visualize a practical experiment:<br /><br />Imagine an empty space shuttle main fuel tank in space. It is refilled with liquid oxygen and liquid hydrogen from your lunar facility or a 'depot' on the ISS. A single space shuttle main engine is bolted on the bottom of this tank. Light off the engine and away it goes. A single engine on an fully fueled external tank will burn for approximately 24 minutes. With a suitably small payload, and considering the small mass of the tank, you have something that is going to accelerate to a pretty amazing velocity in just those 24 minutes. Final 'burn out' velocity will depend on where you start burn, low earth orbit, lunar orbit, or in solar orbit at earth's distance from sun. A small probe (like New Horizons) and just working this out in my head so I'm probably off a bunch, might be going in excess of 100000 miles per hour. <br /><br />Not bad for a system that seems 'doable' if funded extravagantly. <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

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#### tosse

##### Guest
Thank you all for the input.<br /><br />Let us say that we build a ridicilously big ion engine (let's say an isp of 3000) which could use ridicolously much fuel, how much could we then cut off the traveling time?<br />And would it be practical to build a ridicilously big ion engine? I guess it would be too much mass to just build a 100 "normal" small ones and "connect" them..?

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#### spacester

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Nice posts. Those numbers look good, as you say it's hard to pin down numbers because it depends on your parking orbits and launch window (due to Mars' eccentric orbit)<br /><br />My understanding is that the maximum dV you can get by Aerobraking at Mars is around 1.5 km/s maybe 2.0 km/s with a fancy ballute. So a robust infrastructure would have rocket engines in any case.<br /><br />The Shuttle ET is about the best we'll ever do in mass ratio of the tank itself (in a gravity field). When full, it masses 95% fuel. So that lets you set an upper limit on max possible dV from a single stage.<br /><br />Everything else in your spacecraft is inert weight (engines, everything else but payload), so you know you can't do much better than say 90% propellant fraction for your finished launch vessel. Maybe 92% . . .<br /><br />Actually, we've pinned down the maximum dV in the sense that we've found out that SSTO (Single Stage To Orbit) is very hard to do. That's right around 10.0 km/s. Things are easier in space and to build huge propellant fraction ships, over 98% or something, is conceivable.<br /><br />I'm too lazy to do the math right now, but I'd be surprised if a craft could theoretically, with current materials, be built with chemical propulsion (maximum Isp ~ 475 sec) that can do more than, um I'll say 16 km/s <div class="Discussion_UserSignature"> </div>

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#### henryhallam

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With respect, Vogon, I don't think that is correct. A shuttle external tank has a dry mass of 30 tonnes and carries 721 tonnes of fuel. A single SSME is 3.2 tonnes and provides a vacuum Isp of 454 seconds.<br />Thus total ship dry mass = 33.2 tonnes, fueled mass = 754.2 tonnes for a mass ratio of 19.7.<br /><br />From the rocket equation, dV = 454 * 9.8 * ln(19.7) = 13300 m/s or 13.3 km/sec. This is just under 30000 miles per hour, a bit short of your estimate. If you try to attach a modest-sized spaceship as well, you'll be down in the 8 km/sec range. Still, this is quite viable as a way of getting to mars - just the slight problem of getting that 720 tonnes of fuel up into orbit! <br /><br />Tosse, I have to go to work now but I'll try to run some numbers for an ion drive vessel when I get back. On the face of it, it would appear that the Isp is 8 times as much so you'll get 8 times the dV, but as I'm sure you know this is complicated by the pathetic thrust, so an enormous engine would be required which would raise the vessel's dry mass a lot.

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#### tosse

##### Guest
Thanks in advance henryhallam <img src="/images/icons/smile.gif" /><br /><br />And i just want to clarify that i am only talking about a orbit-to-orbit vessel (that will never touch any planet surface). I am just curious how quick a mars-trip (or a jupiter-trip, or an astreoid-trip) could be done without nuclear engines, if you have a fuel-infrastructure in orbit. To me it seems that it would be reasonable simple to extract H and O from for example regolith.

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#### henryhallam

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I'm afraid to say after thinking it through a bit more and doing some research on the 'net, I really don't have enough experience to give any numbers for a large ion drive with any confidence. Basically:<br /><br />* I can't find any numbers for an Isp of an ion drive that uses hydrogen, rather than xenon. Does anyone know if there's a reason why xenon is always the reaction mass used? Maybe storage?<br /><br />* Hydrogen itself is very rare in lunar regolith, xenon even rarer.<br /><br />* Nobody has built a large ion drive yet. Maybe I'm not using the right search terms, but I can't even find an estimate on mass / thrust / Isp for anything bigger than the DS1 probe's engine. I do suspect that a very large ion drive, complete with nuclear reactor to power it, would mass a lot more than a rocket engine for the same thrust.<br /><br />* Even a large ion drive will still have comparatively tiny thrust compared to a conventional rocket. This means the "burn" must take place over weeks or months compared to minutes. For as short a trip as one to Mars, this may mean it is impractical as a way to reduce trip time, since the time saved by a higher velocity is lost by spending ages accelerating / decelerating.<br /><br />* The same reason makes it much harder to calculate trajectories, because all the standard equations / programs assume instant burns. If it takes a few minutes this doesn't make much difference, but when it takes weeks and months this requires more complicated maths that I don't have a grasp of yet.<br /><br />I'm not saying that an ion drive is necessarily impractical for a trip to Mars, just that I can't confidently claim whether it is or not!

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#### henryhallam

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Ah, makes sense.<br />Let's see:<br />Assume a constant energy imparted to each of two ions, one massing 1 unit and the other massing 100 units.<br /><br />Light ion:<br /><br />m=1<br />KE=1 = 0.5 mv^2<br />v^2 = 2<br />v= 1.4<br />mv = 1.4<br /><br />Heavy ion:<br />m=100<br />KE = 1 = 0.5 mv^2<br />v^2 = 2/100 = 0.02<br />v = 0.14<br />mv = 14.1<br /><br />So the heavier ion gives much greater momentum, i.e. thrust, per ion, for the same energy. However of course the fuel has greater mass. So presumably when energy is the limiting factor, as it is on current small probes running on solar power or RTGs, a heavier fuel is better, but when lots of energy is available, lighter ions give more thrust per unit mass, i.e. greater Isp. <br /><br />p.s. Ions accelerated in an electric field gain kinetic energy equal to the potential they fall through, so for power consumption purposes it's the kinetic energy given to the ions that matters, not just the velocity.

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#### exoscientist

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Newsgroups: sci.astro, sci.space.policy, sci.physics <br />From: "Robert Clark" <rgregorycl...@yahoo.com /> <br />Date: 28 Feb 2005 06:54:30 -0800 <br />Local: Mon, Feb 28 2005 6:54 am <br />Subject: About the "Mars in two weeks" nuclear rocket. <br />http://groups-beta.google.com/group/sci.astro/msg/ccb5ebe44a13da71 <br /><br />Bob Clark <br /><br /> <div class="Discussion_UserSignature"> </div>

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#### spacester

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About three years ago I researched ion engines extensively. Maybe I'm out of date, but it sounds like there's not much new in the field.<br /><br />My understanding is that Xenon's unique property is that it does not erode the wires in the exit grid. Everything else does.<br /><br />My research conclusion was that with lots of energy, the limiting factor in building an interplanetary ion drive was the flux density - how concentrated you can make the ions within the, uh, reaction chamber. If you get all that power and you want some serious thrust, you're either going to have to increase the density of the ion stream of make really really large diameter engines. At some point the large diameter makes it impractical.<br /><br />But even with Xenon, IIRC high flux density will erode the wires. So I remain hopeful but skeptical that ion engines will be a big part of near-term space infrastructure.<br /><br />Actually, it is also my understanding that the <i>lighter</i> the ion the better. Your math is flawless except for the assumption that the KE is equal. The logic is, IIRC, that the lighter the ion, the higher velocity it can achieve in a given engine geometry. The higher the exhaust, the higher the specific impulse (by definition), and Isp is the primary performance criteria, along with thrust of course. <br /><br />Calculating constant thrust trajectories is very difficult. My understanding is that it can only be solved with computer simulations, and once you've done that, you parameterize the calculations. But even then it's not simple. I'll have to go check my links if I can find them . . . <div class="Discussion_UserSignature"> </div>

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#### vogon13

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At SRB separation, ET is ~75% full of fuel. 80-90 tons (the 2000 pound kind) of orbiter and payload accelerates through 20 mach numbers to achieve orbit (or very nearly, neglecting OMS burn). Figured loosing 75% of mass to accelerate, no air drag, all ready in LEO (at least), and having a fully fueled ET would really make a big bump in the performance of shuttle derived system I was playing around with. Titan III C performance from earth's surface to escape velocity with Voyager craft on board beats or equals a fully fueled ET already in orbit with negligible payload? I am thunderstruck, or have really messed up the guestimation process. <img src="/images/icons/frown.gif" /> <div class="Discussion_UserSignature"> <p><font color="#ff0000"><strong>TPTB went to Dallas and all I got was Plucked !!</strong></font></p><p><font color="#339966"><strong>So many people, so few recipes !!</strong></font></p><p><font color="#0000ff"><strong>Let's clean up this stinkhole !!</strong></font> </p> </div>

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#### henryhallam

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I think (without doing any more maths) that even though the shuttle tank + SSME combination wouldn't get a much greater dV than the Titan, it would be able to give this dV to a considerably heavier payload.

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