ESA ATL Plausibility Checks and Development

[su_liam]

SSME's are awfully expensive to use as expendable rockets(not to say NASA isn't suggesting the same damn idea for SLS). Also adapting Titan to hydrogen with much lower impulse density than its current aerozine50 seems like a painful and pointless hurdle. It seems easier to re-adapt the LR-87 to kerosene. The thrust difference isn't too great and you could possibly use three or four engines to bridge the gap. Four engine version might look a bit like this bastard only with kerolox.

Again, that's not to say NASA wouldn't do this. They have a bit of an obsession with hydrolox first stages and they sure ain't too frugal to burn RS-25s left and right.

Still, frugality-wise, expending SSMEs may still be a better bet than praying for the PW 1000000 lb thruster to get off the drawing board and kerosene-burning LR-87s might still take more time than they'd like.

[e of pi]

Originally Posted by su_liam

SSME's are awfully expensive to use as expendable rockets(not to say NASA isn't suggesting the same damn idea for SLS). Also adapting Titan to hydrogen with much lower impulse density than its current aerozine50 seems like a painful and pointless hurdle. It seems easier to re-adapt the LR-87 to kerosene. The thrust difference isn't too great and you could possibly use three or four engines to bridge the gap. Four engine version might look a bit like this bastard only with kerolox.

The LR-87 is just not a great engine. It's only about 304s ISp even in the improved versions, and switching to kerosene (a propellant it hasn't been fired on in about 35 years by the time this is being designed)...it's a lot of investment in a kinda lousy engine. SSME is a known quantity, and they probably already are planning on a revised expendable SSME variant, since they're expending them on Shuttle-C at a rate of 3/flight...with a production rate of 6/year, or in batches every few years, the cost/engine will go down agood bit, espeically if there's a version optimized for expendability. Or maybe it'll be more like the RS-68, where it's an SSME-derived expendable as opposed to a straight SSME variant, but still with good manufacturing commonality.

Still, frugality-wise, expending SSMEs may still be a better bet than praying for the PW 1000000 lb thruster to get off the drawing board and kerosene-burning LR-87s might still take more time than they'd like.

That was roughly my thought when I was advising Bahamut on this design. There's no good off-the-shelf American kerolox option (though I suppose one option would be to borrow the European's Argo engines--they weren't too proud to borrow RD-180 OTL for Atlas V after the wall came down), so the higher per-flight cost (which may not be terribly higher with an engine common between Shuttle itself, the expendable Shuttle-C side-mount cargo booster, and now Titan V) may be balanced by essentially no engine development cost, unless you want to throw a few hundred mill after an expendable-optimized version you've probably been studying by then. The ISp boost you're almost getting for free. Save a billion there, and even if it costs an extra $20 million per flight you're still ahead of the game for 50 flights.

[su_liam]

is the Isp bonus enough to make up for the dryweight costs of the large volume tankage?


But if it comes to really steep development costs or long delays, then by all means burn up some SSMEs, if only as an interim solution.

Lack of decent kerosene-LOX engines after the glory days of Apollo is one of the great shames of NASA history IMO. RS-IC forever baby!


Also, does the Shuttle-C actually expend its engines. I thought there was something about the tail pod being recoverable. At least in some variants.

I need to research the Argo engine. Man, my research schedule has gotten dense and I still need to get back to my poor neglected blog. The curse of interesting things...


EDIT: Somehow missed an important part of the preceding post.

[e of pi]

Originally Posted by su_liam

is the Isp bonus enough to make up for the dryweight costs of the large volume tankage?

Oh yes. It's far less than the 35% increase in sea-level ISp, and way, way less than the 45% improvement in vacuum ISp. Maybe from 5% of fuel mass to 8%. On the other hand, for the same delta-v, you need on the order of 35% less fuel (calculated for a delta-v of 4 km/s with ISp=304 and ISp=450), and the added dry mass of the stage disappears into a rounding error.

Also, does the Shuttle-C actually expend its engines. I thought there was something about the tail pod being recoverable. At least in some variants.

There were some proposed that did, some that didn't, and some that started as the former and evolved to the latter. I couldn't recall which Bahamut was planning on, so I used the one I'd pick--just expend 'em.

I need to research the Argo engine. Man, my research schedule has gotten dense and I still need to get back to my poor neglected blog. The curse of interesting things...

Luckily you needn't search too much further than this thread to start, it's a Bahamut original design (for the rocket), so you can find the specs there.

[su_liam]

Originally Posted by e of pi

Luckily you needn't search too much further than this thread to start, it's a Bahamut original design (for the rocket), so you can find the specs there.

Suddenly, I feel really stupid.

[Bahamut-255]

Originally Posted by e of pi

There were some proposed that did, some that didn't, and some that started as the former and evolved to the latter. I couldn't recall which Bahamut was planning on, so I used the one I'd pick--just expend 'em.

Initially using the same SSMEs that are used on STS is my initial plan, to accelerate development. In any case, this Shuttle-C I'm planning expends the engines after use - simpler IMHO - so expendable SSME engine research and development will have some serious merit ITTL. Especially with the Titan V coming online.

Luckily you needn't search too much further than this thread to start, it's a Bahamut original design (for the rocket), so you can find the specs there.

And I just realised that I haven't actually put the key engine specs for the Argo LV up yet! So here are the basics of it:


Core Stage: 4x Rolls-Royce RZ.9 - 190,000 Kgf (sl). 270s Isp (sl). 304s Isp (vac).

2nd Stage: 4x Rolls-Royce RZ.12 - 35,000 Kgf (vac). 329s Isp (vac).

The Argo LRBs use one Rolls-Royce RZ.9 each.


I know the specs may look rather medicore by today's standards, but it was built in the 1980s ITTL. Using early 1980s tech.


EDIT: Don't worry about it su_liam. I've been making quite a few errors here myself, and I'm the Author of this Thread!

[e of pi]

Originally Posted by Bahamut-255

Initially using the same SSMEs that are used on STS is my initial plan, to accelerate development. In any case, this Shuttle-C I'm planning expends the engines after use - simpler IMHO - so expendable SSME engine research and development will have some serious merit ITTL. Especially with the Titan V coming online.

I think, looking at the cost, it's a project that would be worth doing almost as soon as Shuttle-C is over its own funding peak--so about a year or so after first flight, I guess? That's what, '86? Three or four years of work, and I think it's doable (which would bring the expendable SSME online pretty close to the date for the Titan V proposal, yeah?). It may end up being a bit more RS-68 than RS-25E, but it should be possible to achieve significant cost reductions. (Indeed, it might be worth looking at what the cost/flight turnaround on Shuttle engines was--is it cheaper to just switch shuttle itself to expendable SSME, pulling and disposing of them after flights?)

EDIT: Don't worry about it su_liam. I've been making quite a few errors here myself, and I'm the Author of this Thread!

Hey, somewhere up-thread there's a post where I made about six paragraphs of speculation about introduction dates for Argo, but it was all invalidated when Bahamut pointed out that Europa had worked, and thus all my discussion of Ariane was so much wasted speculation...

EDIT: A few estimates about SSME-E development. RS-68 development OTL cost about $500 million, and ended up with an engine that cost about $15 million per instead of $40 million per for SSME. Such a dev program would pay for itself over 20 engines, or about 7 Shuttle-C flights. Alternately, one could pursue a development program that made fewer changes from SSME, and keeping more of the pressure and ISp benefits of that engine. This might cost less, but with correspondingly lower reductions in per-engine cost. Say...$250 million for dev, but an engine cost of $20 million or $25 million instead of $15? The payoff there would in 12.5-16.7 engines--just 4 or 5 Shuttle-C!

[Bahamut-255]

Originally Posted by e of pi

I think, looking at the cost, it's a project that would be worth doing almost as soon as Shuttle-C is over its own funding peak--so about a year or so after first flight, I guess? That's what, '86? Three or four years of work, and I think it's doable (which would bring the expendable SSME online pretty close to the date for the Titan V proposal, yeah?). It may end up being a bit more RS-68 than RS-25E, but it should be possible to achieve significant cost reductions. (Indeed, it might be worth looking at what the cost/flight turnaround on Shuttle engines was--is it cheaper to just switch shuttle itself to expendable SSME, pulling and disposing of them after flights?)

But don't forget that Shuttle-C won't be in real use until Freedom/Alpha construction begins, where it can send up the heavy - 50+ Tonne - segments. So it seems perfectly reasonable to me to assume that the Titan V will use existing SSMEs initially - during development and the early few flights. Afterwards, they can design an expendable variant of it which carries lower production costs. And possibly be ready for when Station construction begins - especially if NASA has a few words about it IMHO.

EDIT: A few estimates about SSME-E development. RS-68 development OTL cost about $500 million, and ended up with an engine that cost about $15 million per instead of $40 million per for SSME. Such a dev program would pay for itself over 20 engines, or about 7 Shuttle-C flights. Alternately, one could pursue a development program that made fewer changes from SSME, and keeping more of the pressure and Isp benefits of that engine. This might cost less, but with correspondingly lower reductions in per-engine cost. Say...$250 million for dev, but an engine cost of $20 million or $25 million instead of $15? The payoff there would in 12.5-16.7 engines--just 4 or 5 Shuttle-C!

I would say option 2. Go for the Isp retention benefits.


Another point. I looked again at the diameter of the Titan V. It does looks like 570cm with a drop in the length would work best. If I need a larger diameter payload fairing, I can always do an Atlas V with it if you get my drift.

It was either that or making a UA1208. And that did not seem like a very smart move to me.


And finally for now. Thanks to everyone who took this thread past the 11,000 mark! It's very much appreciated.

[e of pi]

Originally Posted by Bahamut-255

But don't forget that Shuttle-C won't be in real use until Freedom/Alpha construction begins, where it can send up the heavy - 50+ Tonne - segments. So it seems perfectly reasonable to me to assume that the Titan V will use existing SSMEs initially - during development and the early few flights. Afterwards, they can design an expendable variant of it which carries lower production costs. And possibly be ready for when Station construction begins - especially if NASA has a few words about it IMHO.

I've kind of lost track of when Freedom's development and launch is happening in your TL--I keep getting it muddled with Eyes' equivalent station. Shuttle-C will be online in, what, late 80s, and Freedom's launched in...the early 90s? Anyway, I guess it's mostly a money question as to when they start SSME-E development. To me it makes sense to do it early so you can see the benefits in total cost earlier, but maybe they can't shake loose the $250 mill among all the other development until Titan V is also trying to spec the engine.

I would say option 2. Go for the Isp retention benefits.

That would be my preference as well.

And finally for now. Thanks to everyone who took this thread past the 11,000 mark! It's very much appreciated.

Ah! I noticed that it had passed the mark and meant to mention it in my last post but...I guess I forgot.

[Bahamut-255]

Originally Posted by e of pi

I've kind of lost track of when Freedom's development and launch is happening in your TL--I keep getting it muddled with Eyes' equivalent station. Shuttle-C will be online in, what, late 80s, and Freedom's launched in...the early 90s? Anyway, I guess it's mostly a money question as to when they start SSME-E development. To me it makes sense to do it early so you can see the benefits in total cost earlier, but maybe they can't shake loose the $250 mill among all the other development until Titan V is also trying to spec the engine.

I'm looking at final development being given the go-ahead in 1992/3. With the first launch occurring in 1997. Being completed by 2000.

But yes. Financial considerations will stall SSME-E development until the Titan V is developed. That and until Freedom segments are launched, there will be very few missions where Shuttle-C is of any unique use.

One other consideration I need to know. The TJI payload of Shuttle-C - and by extension, Argo and Titan V. Since that would likely influence missions to the Outer Planets.

Ah! I noticed that it had passed the mark and meant to mention it in my last post but...I guess I forgot.

I did too so no worries!

[e of pi]

Originally Posted by Bahamut-255

But yes. Financial considerations will stall SSME-E development until the Titan V is developed. That and until Freedom segments are launched, there will be very few missions where Shuttle-C is of any unique use.

All right, given that Freedom schedule it makes sense to delay SSME-E development, I suppose.

One other consideration I need to know. The TJI payload of Shuttle-C - and by extension, Argo and Titan V. Since that would likely influence missions to the Outer Planets.

Well, that' relatively easy if you know the delta-v profile to TJI. Which...I don't. Not of the top of my head. Truth would know, but he's been busy with finals. Perhaps 14 km/s on top of the 10 km/s to get to orbit? Once you pick a TJI estimate, you can back-figure what payload your launcher can take to that with the rocket equation. Or if you can find a C3 value in km^2/s^2, Schillings has a setting for that.

This is another tool we've been using for Eyes (well, Truth's been using), though it requires MatLab to run.

[Bahamut-255]

Originally Posted by e of pi

Well, that' relatively easy if you know the delta-v profile to TJI. Which...I don't. Not of the top of my head. Truth would know, but he's been busy with finals. Perhaps 14 km/s on top of the 10 km/s to get to orbit? Once you pick a TJI estimate, you can back-figure what payload your launcher can take to that with the rocket equation. Or if you can find a C3 value in km^2/s^2, Schillings has a setting for that.

Well this source says 6,300m/s of delta-v is needed for a Hohmann Transfer from Earth to Jupiter. Though, obviously, this does not assume Planetary Flyby's which can cut the delta-v requirement, at the cost of significantly increased flight duration. But at least it gives me a number that I can use.

[Shevek23]

There would be tradeoffs depending on what you want. A Hohmann orbit would be the minimum energy needed to reach Jupiter, but you can only access it during a brief window that opens up when Earth and Jupiter are in the right relative positions, which would happen at intervals a bit longer than an Earth year. (Earth returns to the same place it was in at the last window in one year, but by then Jupiter has moved on. A Jovian year is a bit under 12 Terran years so I guess the window is about every 13 months. Also since both planets are in slightly elliptical orbits, some windows are more advantageous than others (and their timing won't be at a constant interval either).

There might be some advantage launching around the Moon, but the Moon has to be in the right relative position which would often not be the case when the window opens; also there's the "Oberth Effect" to consider--it's better to apply delta-V low in a gravity well because it results in more energy accruing to the spacecraft, Earth's well is much deeper than Luna's, so it's a tradeoff between possibly gaining something from Luna's orbital speed versus burning for delta-V at a higher potential.

Anyway if you want to get to Jupiter sooner, or launch at a more convenient time, we are looking at higher energy orbits, which cost more delta-V, and also if the goal is to reach Jupiter orbit and stay there instead of a flyby, the more energetic the transfer orbit the more velociy we have to lose at that end. If atmospheric braking at Jupiter is an option, that might be OK, though such maneuvers are going to be at very high speeds compared to familiar Earth reentry speeds, since Jupiter is so massive hence the approach speed will be great.

Jupiter is great for gravity assist orbit changes to other goals though the window for the "Grand Tour" taken by the Voyager probes OTL will be closed by now. But if one can reach Jupiter first and be satisfied with a flyby there, I suppose just about any outer planet can then be reached at just about any time, if one is not insisting on visiting a third and then a fourth and fifth...

So if you can send something to Jupiter I suppose that means you can reach any outer planet as the final goal, and get a free flyby of Jupiter into the bargain, if your craft can take the rather adventurous conditions of a close approach to the big planet with its powerful magnetic field, radiation flux, fast-moving orbital junk, and so on.

One approach might be to design a standard Outer-System launch system that can launch a fixed payload on a Hohmann path to Jupiter, and fine-tweak the close approach to Jove so that a perihelion burn of a final stage carried all that way as part of the standard-mass payload sends it out on the best approach to whatever outer planet is the final goal; burning low gets maximum benefit from available delta-V and one ought to get some angular momentum from the encounter too. So the final payload probe mass will depend on just how much rocket you need at periJove, but I suspect the delta-V required there would typically be in one ballpark so the detailed probe designs would be around one typical mass.

I am not sure a hydrogen-oxygen final stage can store the fuel on the long arc from Earth to Jupiter, so we might be stuck with lower ISP propellants. But those have their advantages offsetting their inefficiency to consider--much more compact, minimal maintenance, in the case of hypergolics easier rocket engine design, in the case of ker-lox (assuming oxygen at least can be kept liquid on the way out) a lower combustion chamber temperature.

I'd think then that designing around being able to reach Jupiter in a standard way would open up the whole outer system for exploratory probes. A standard rocket stack designed to send a standard outer-planet packet to Jupiter at Hohmann optimum window time might also send a smaller payload to Jupiter or even a second, final destination by using some or all of the final Jovian-maneuver rocket mass allocation for final increments on the escape orbit from Earth instead, thus enabling trips to Jupiter at non-window times.

And if your program can support multiple launches of the standard outer system launch vehicles at the same time, or in very fast succession, a whole cluster of different probes can be sent to Jupiter in a salvo, there to scatter to different final destinations.

I've lost track of whether this mission is to be one of the standard ones the Argo series is to be capable of, or if this is another specialized variation. The naming of names matters to you and so I've been trying to track down whether Odysseus's ship had a name; I sure don't recall one.

Besides, his return expedition to Ithaca started out with a dozen ships, all but his being soon destroyed, and his own ship is wrecked too, so perhaps even if someone can turn up the name of his flagship, it wouldn't be the most auspicious!

Maybe I can think of some other mythic track referencing a Europe-relevant culture hero famed for far-flung exploration of the most distant lands?

I believe there was a whole genre of Celtic poetry about far voyages, of which the tale of Saint Brendan's expedition is the most famous, "Imre" or something like that.

But based on my track record, I'm guessing if I do find some name or generic term that thrills me, you'll want some variant of it instead.

Maybe, if these rockets are a distinct variant of the Argo series, these versions can be the ones called "Argosy?" That's not really appropriate because the Argosy name suggests a more bread-and-butter workhorse for everyday use, not far ranging-adventure.

But if you'd started with Argosy for the whole series, these deep-space variants could well be the Argos!

[Michel Van]

Originally Posted by Bahamut-255

Well this source says 6,300m/s of delta-v is needed for a Hohmann Transfer from Earth to Jupiter. Though, obviously, this does not assume Planetary Flyby's which can cut the delta-v requirement, at the cost of significantly increased flight duration. But at least it gives me a number that I can use.

this source give more Math on question
http://www.aa1zb.net/space/orbits/CentaurThrust.html

and yes Planetary Flyby's reduce the needed Delta-v

best example was Galileo
the Jupiter Orbiter had to be launch with Shuttle and Centaur-G.
but it was launch with Shuttle and Inertial Upper Stage solid-fuel booster
so with lower Delta-V of IUS, Galileo needed several Planetary Flyby's called
"VEEGA" or Venus Earth Earth Gravity Assist maneuvers
It works well but it need allot of time
Voyager 1&2 needed direct around one year to get flyby Jupiter
Galileo needed FIVE years to get in Jupiter orbit

Cassini–Huygens Planetary Flyby's is a special case
first the probe have to reach Saturn, (needed six years to take twice the distant of jupiter)
second its mass of 5600 kg (Galileo 3132 kg, Voyager 722 kg)

[Shevek23]

How much delta-V can taking advantage of Venus save us?

If it's a whole lot (and even a little bit can amount to "a whole lot" in terms of the launched payload mass, considering the exponential nature of the rocket equation!) then it might be worthwhile to make the sacrifice of a long delay in travel time to Jupiter as a tradeoff for the bigger payload.

The philosophy of making a standard deep-space launcher would still be the same only now it's designed around the requirements of a mission to Jupiter via Venus.

The big problem I'd foresee would be the issue of windows. If we can in principle send something bigger to Jupiter (and hence, via Jupiter gravity assist and strong Oberth effect, shaping a new exit orbit at periJove, onward to other planets) via gravity assist at Venus, great--but now we need not for just Earth and Jupiter, or just Earth and Venus, to be in the right alignment--we need all three bodies to be in the right relative places, and I fear that would happen at intervals far greater than one Terran year and change.

Venus and Earth coming into optimum alignment I suspect happens at longer intervals than one year, because the two inner planets have years so close to one another. The odds are Jupiter will then be in entirely the wrong place.

Of course I'm talking about ideal trajectories; if we can fudge the windows by using more delta-V we open them up a lot, and if we can gain enough benefit from Venus (or Mars? Is Mercury relevant here too?) we might still come out ahead of a direct launch to Jupiter I guess.

But going straight for Jupiter seems more foolproof to me, considering it can then be the gateway to the rest of the system, depending on the exact close approach to the giant planet.

So it all depends--does Venerian gravity assist allow a very large increase in payload arriving at Jupiter, or is it only marginal? And how wide open is the window for using Venus to get to Jupiter before the additional delta-V to approach Venus on a non-optimum path reduces payload to equivalent to a direct launch to Jupiter, and how long is the interval between those windows?

Can we use Mars or Mercury in a similar way? That would open up more windows but I'm sure the gravity assist from them would be much less due to their lower mass.
-----
If the suggestion of designing deep-space missions around direct fly-bys of Jupiter is a good one, perhaps the rocket family that does this job could be called Zeus? Or Olympian?

Changing European mythoi, the name Thor is of course pre-empted by American 1950s rocketry! Valhalla?

I can't think of anything appropriately Celtic, Arthurian, or from medieval or Early Modern European history or literature.

Galileo might do!

[Bahamut-255]

Gravity-Assisted Flyby's may be cheaper in terms of delta-v requirements, but are a lot more complex. Not only do you have to approached the flyby target with great accuracy, as so to place you on the correct subsequent trajectory, but the opportunities are limited. For example, Cassini/Huygens used two Venus Flybys, followed by an Earth Flyby, then a Jupiter Flyby to reach Saturn, dependant on a unique Planetary Alignment that would not reoccur for another ~600 years.

What it ultimately boils down to is this:

1) Direct path with either a very large - and expensive - booster.

2) Direct path with a small - and limited capability - payload on a smaller LV.

3) Flyby assists to reduce the delta-v requirement from propellant. At the cost of increased mission time and complexity.

In the end. Those are the three basic means of Outer Planet Exploration.

[Shevek23]

So if your ESA launcher can launch something substantial to Jupiter encounter, I think you've got a reliable strategy. Jupiter system itself is a destination worthy of many scientific investigations, and it's first rate as a gravity-assist. I suspect from a close Jupiter flyby you can go anywhere, and the minimum-energy window opens every 13 months, so missions can be launched every year, or more often if there's some margin to widen the window. Jupiter's deep gravity well can redirect craft coming in at wide deviations from the ideal minimum-energy Hohmann approach I'd think.

Of course going to other destinations indirectly from Jupiter would add time, but I think the transit to Jupiter would be a matter of just a few years at most; how long it adds to the final destination leg depends on how out of alignment the destination is from Jupiter. Also the way I understand how gravity assist works, you can't achieve just any trajectory out; it would be limited to a cone and at that you'd need a periJovian burn to fully exploit even that limited range, but I'd think that every planet beyond Jupiter's orbit would be reliably reachable at some time within Jupiter's 12-Earth-year orbit, so a missed opportunity could be redeemed 12 years later, which strikes me as within the planning horizon of a space agency.

Is this why your question was focused on Jupiter?

[e of pi]

If Jupiter injection requires a delta-v of about 6.7 above orbital, then that means that for a vehicle with an orbital launch mass of X, you could appromixate the trans-Jupiter mass by dividing the orbital payload by the mass ratio required for a hydrolox stage performing 6.7 km/s of boost. This is a mass ratio of 4.5 or so. So the 10 metric ton Argo base core can do about 2.2 tons dry mass through TLI, the 37 ton max version maybe 8.2. These are masses to TJI, of course, stage masses would have to come out of this, plus any propellant for maneuvers at flybys down the line.
Titan V: 3.7 tons to 9.7 tons.
Shuttle-C: a staggering 16.8 tons. Though, of course, this means rustling up a 60 ton hydrolox stage. A kinda nutty alternative approach would be to just take a Castor 120 or similar and bolt that to a smaller hydrolox stage. Reduced payload due to smaller ISp on the solid doing the majority of the work, but it'd work and you'd need reduced new hardware. And when it's not being used for TJI launches, this upper stage package might make a dandy small launch vehicle on its own. Perhaps 2.5 tons or so to LEO?

[Michel Van]

Originally Posted by Shevek23

Is this why your question was focused on Jupiter?

Jupiter is biggest Gasplanet in Solarsystem and has 4 big Moons, a Fascinating place to explore
next to that is Jupiter a large "slingshot" for Space probe
the Voyager 2 probe use this to get to Saturn faster and from there to the outer planets
the ESA Ulysses probe used Jupiter to get in a Solar polar orbit

also are proposal for Solar probe who goes very close to Sun
the German HELIOS needed a powerful Titan IIIE to get to sun,
the 370 kg spacecraft reach a record speed of 70.22 km/s but got only to 0.29 AU to Sun
to get closer we need Jupiter as "slingshot" to get a probe closer to Sun

Originally Posted by Shevek23

How much delta-V can taking advantage of Venus save us?

the DV to Venus is with 3900 m/s much lower as needed 6300m/s for Jupiter.
Jupiter probe Galileo was launch to Venus with 3900 m/s
at fly by it gain 2230 m/s onto its cumulative speed to reach Earth first time
there it got wide orbit to cross Earth in 2 years later
on second Earth fly by, the probe adding 3700 m/s to its cumulative speed to get to Jupiter

[Shevek23]

So, the same rocket engine for a TJI requiring 6700 meters/sec delta-V from an Earth parking orbit could instead send a larger mass toward Venus; achieving a multiple set of passes by Earth and eventually on to Jupiter that way. The question was how much larger a mass? If injection to Venus requires only 3900 m/sec then I figure, about 1.87 times as much, using e of pi's implied ISP of 454 for the hydrogen engine.

Well, that sounds great, but of course out of that extra 87 (plus) percent has to come maneuvering propellant for tweaking the passages past Venus and Earth, not to mention any adjustments for slingshotting on past Jupiter. And assuming the planets are aligned correctly it takes many many years to get where it's going. And the planets are rarely aligned conveniently.

Unless it's not a problem storing liquid hydrogen for years (and it is around Earth orbit, and using Venus for slingshotting means the probe spends a lot of time even closer to the Sun than Earth is) the subsequent maneuvers have to be done with storable propellants that have much lower ISP so the efficient hydrogen engine has shot its bolt upon interplanetary injection, along with its tankage. The mass of the LH2/LOX tankage and their engine comes out of that 87 percent advantage; sufficient storable propellant, its tankage and a suitable thrust engine have to be deducted as well. The same is true of a direct Jovian passage of course! But deep in Jupiter's gravity well a given amount of delta-V counts for a lot more energy change than it does skimming the atmospheres of Venus or Earth--to be fair, it also accounts for a much lower change in angular momentum.

I still think the thing to do is aim for something that can consistently reach Jupiter directly every year, and use Jupiter's mass to accomplish other goals.

Clearly we can only send smaller probes for a given launch system, but we can send them reliably and they'll get where they are going sooner. I think a factor of 2 reduction in the payload is a reasonable price to pay for those advantages; I was just afraid it would be more like a factor of 10!

The more probes we route via Jupiter, the more experience the space agency involved gets with the quirks of such a route and the more reliably future probes can be sent that way. Meanwhile we are getting frequent close observations of the Jovian system and perhaps we'd even want to set up a long-term Jupiter orbiter to serve both as a long-term scientific observation platform and as a monitor of other spacecraft routed past Jupiter.

The speed of light delay is such that I wouldn't suggest such a monitor can usefully guide the transiting probe, but it can pick up and relay telemetry from it and if something goes wrong we've got a virtual downloadable "black box" to analyze, plus direct observations from the monitor's distant perspective.

Obviously for planets that require less than 6700 meters/sec to reach directly, one should launch straight for them and use the increased payload.
----
But it occurs to me, while Venus and Earth will rarely be in a given alignment to a third planet, they are reliably in any desired alignment to each other; the strategy seems to be to loop around both Venus and Earth for free energy; sending it on to Jupiter from there is probably not something that can be done just any old time but probably a good percentage of the time; the "window" problem might not be nearly as severe as I was thinking. But certainly such a strategy will add years to each probe's travel time. That's the tradeoff then; years versus nearly twice the payload capability.