how to calculate intercept speed when the game does not cooperate?

[king of nowhere]

bit of a complex situation here, and i will need to explain in some details.

i have a spaceship at jool, it needs to get back to duna. i cannot launch refueling missions because it's supposed to be a grand tour, so the mission has to make it on its own. the ship actually has isru, but it can use it only at duna, as a self imposed challenge - looong story. that's why i want to go to duna.

in my current orbit, 100k x 150k around jool, i need some 2000 m/s to get back to duna, already including a discount for some aerobraking. I only have about 1500 m/s. i am trying to find gravity assists to get there.

i explored in depth ways to use tylo. unfortunately, while tylo is great for lowering periapsis down to 40M km, lowering it further all the way to duna does not work. it becomes more expensive. i spent a couple hours simulating trajectories there, no success. the very first thing i explored was a duna flyby with gravity assist, but it only lowered apoapsis from 70 to 55M km, not enough.

furthermore, i am using kerbalism so i have to provide life support. my ship has supplies for between 10 and 20 years, depending on malfunctions; i can make a convoluted trajectory with multiple orbits, but only to some extent. i can't gradually lower periapsis over 20 orbits.

next i tried a kerbin gravity assist, and this looks more promising. getting in a kerbin intercept costs me some 1350 m/s, but the first pass lowers my apoapsis to 35M km. from there direct insertion to duna would still be too expensive, over 1000 m/s. but I can, without additional manuevers, set my first kerbin flyby so that it will send me en route for a second kerbin flyby on the next orbit, and that will lower my apoapsis to 20M km, at the level of duna. periapsis instead will be 9M km. And i still have 150-200 m/s for course corrections.

at this point, i would like to know what's my intercept speed for Duna. is it low enough that i can aerobrake it? (I can aerobrake up to 200 m/s on a duna flyby). unfortunately, after 2 gravity assists the game cannot calculate the trajectories precisely anymore, so the exact line keeps shifting every time i try to set a new manuever. i can't even start forcing a duna intercept from here. I know i can get one with limited cost within a few years, but i have no way of knowing how expensive would be the injection. and this is what i hope somebody can help me solve.

My best estimate is that my final orbit is similar to an Eve-Duna transfer, so i can expect a similar injection deltaV. and that would be 600 m/s (for elliptic orbit, not counting circularization). too much, even using my remaining fuel for braking. but then, eve has a lot of plane difference with duna, so maybe it will be cheaper?

i certainly would rather not fly my ship all the way to the second kerbin flyby to discover it. kerbalism has some issues with time warp, and some events that require my attention, so that i can't just time warp my way there; it would take weeks of real time. i'd hate to do all that before finding out if my trajectory is even feasible.

so, anyone knows some way to calculate an intercept speed on duna? in theory orbital mechanics should allow that, but i am not so good at using those.

 

[Spricigo]

Well, I just just drop link for some tools that are useful for this kind of calculations and back away slowly. (That is more calculation than I care to do for my own game)

16 minutes ago, king of nowhere said:

kerbalism has some issues with time warp, and some events that require my attention, so that i can't just time warp my way there;

I was under impression that setting KAC alarms for such events was possible. If that is not part of the  challenge maybe you should take a look at that.

[king of nowhere]

38 minutes ago, Spricigo said:

I was under impression that setting KAC alarms for such events was possible. If that is not part of the  challenge maybe you should take a look at that.

the problem is not alarms. the first problem is that resource converters and radiation shielding have bugs at time warp above x1000. and my ship is huge (a manned grand tour taking into account life support and possible malfunctions requires a big ship), so it lags, so the actual time is more like x300. and then there are solar storms, at every solar storm i must protect the crew from radiations by turning the engines towards the sun. but this way the solar panels are not exposed, so after the storm has passed i must turn the ship again to maximize solar panel coverage. and again, big ship + lag means several minutes to rotate it. and every once in a while i must send a kerbonaut in eva to inspect every part and repair those that are close to malfunctioning... even after figuring out the rythm, it took me a real life week to pass the 2-year trip to jool.

i will look at those links tomorrow. thanks

[theAstrogoth]

Planning gravity assist flybys is really tricky, and the tools that Spricigo linked are probably the best/easiest ways of doing it.  I highly recommend KSPTOT.

4 hours ago, king of nowhere said:

but i have no way of knowing how expensive would be the injection. and this is what i hope somebody can help me solve.

If you have a rough idea of the details of your transfer orbit (the one you're in before entering Duna's SoI) then it's not too hard to calculate  the Δv needed for insertion. You can take a look a guide I recently wrote up for planning comet intercepts (which can also be used to plan other transfers). You can ignore all of the stuff about phase and ejection angles, and just look at Step 3, where I calculate the Δv for ejection out of an SoI. It turns out the math for insertion is exactly the same! I'm happy to help you make sense of the math if you'd like.

Also, I think that my other web app, the KSP Transfer Illustrator, could be helpful here. You can upload orbits to it in a similar way to the Trajectory Illustrator (which you've already seen), and it will tell you the details of a transfer (ejection/insertion Δv, time, and direction).  If you want to fiddle around with the apps, I'd suggest getting the parameters of your future orbits with the Trajectory Illustrator (you can hover over orbits in the plots to see their details) and then feeding them into the Transfer Illustrator to find out how much Δv you'll need for insertion at Duna.

Edited February 3, 2021 by theAstrogoth

[king of nowhere]

10 hours ago, theAstrogoth said:

Planning gravity assist flybys is really tricky, and the tools that Spricigo linked are probably the best/easiest ways of doing it.  I highly recommend KSPTOT.

If you have a rough idea of the details of your transfer orbit (the one you're in before entering Duna's SoI) then it's not too hard to calculate  the Δv needed for insertion. You can take a look a guide I recently wrote up for planning comet intercepts (which can also be used to plan other transfers). You can ignore all of the stuff about phase and ejection angles, and just look at Step 3, where I calculate the Δv for ejection out of an SoI. It turns out the math for insertion is exactly the same! I'm happy to help you make sense of the math if you'd like.

Also, I think that my other web app, the KSP Transfer Illustrator, could be helpful here. You can upload orbits to it in a similar way to the Trajectory Illustrator (which you've already seen), and it will tell you the details of a transfer (ejection/insertion Δv, time, and direction).  If you want to fiddle around with the apps, I'd suggest getting the parameters of your future orbits with the Trajectory Illustrator (you can hover over orbits in the plots to see their details) and then feeding them into the Transfer Illustrator to find out how much Δv you'll need for insertion at Duna.

ok, let me see if i got this straight: to adapt the formula, i need to calculate the hyperbolic eccess velocity from my high point in the transfer orbit to the orbit of duna. duna is orbiting kerbol, so i use the mu factor for kerbol (luckily the wiki provides them, because i'm not sure how to calculate those when the game uses a different G constant). so, V=radq(mu/ap), and duna's orbit is about 2,1*10^10 m. i get 1.17*10^18/2.1*10^10 = radq(5.5*10^7)=7400 m/s. which is right for duna's orbital velocity

as for my transfer orbit, it has apoapsis of 21M km and periapsis of 9M km, semiaxis 15M km, so i have radq(1.17*10^18*((2/21G)-(1/15G)).... ewww, such ugly numbers... i get 9.5*10^-11 - 6.7*10^-11... total is radq(3.3*10^7)=5700 m/s.

1700 m/s of intercept? this looks completely wrong. i don't get such a high intercept speed on a direct jool-duna transfer. unless that speed already includes the orbital speed around duna (roughly 1 km/s), making the intercept deltaV 700 m/s to circularize orbit, or 350 m/s to enter elliptic orbit....

is my math correct?

except taking two big and approximate numbers and making the difference between them is not a very accurate method. i fear this whole procedure was no more accurate than just eyeballing it.

 

 by the way, why that formula make no mention of inclination, despite it being a huge factor in trasfer costs? shouldn't be relevant in my case because i mostly take care of inclination with gravity assists, but i fear that mathematical procedure may be an approximate one taking into account only coplanar orbits

 

 

edit: no wait, i skipped part of the calculus. so i got 1700 m/s of hyperbolic excess. now i have v1=radq(1700^2 + 2*3*10^11(1/r0 - 1/rSoI). this factor goes to 0 if i have a periapsis at the edge of SoI, so it really seems 1700 m/s is the speed at which i enter the sphere of influence... in which case, without further calculus, i can determine i'd be screwed, as i can barely tolerate 1700 m/s when entering duna's atmosphere... anyway, let's call 400 km r0, it becomes 2,5*10^-6 -[negligible] and it all adds up to radq(2,89*10⁶+1,5*10^{6 hey, i just noticed i can actually write apices)}) =2090 m/s. which should be my speed at periapsis. which basically gives me a 600 m/s to enter elliptic orbit, which is the same exact value i could have gotten by just eyeballing it

i'm still suspicious of those equations, by the way. they fail to take into account too many parameters, they must be approximated in some ways. EDIT: oh, it is written that plane changes must be accounted for separately

well, anyway, it's probably worth a shot anyway. i may be able to use a duna gravity assist to raise periapsis and get a better intercept the next time. and if all else fails, i have escape pods, i can save my crew when i pass near kerbin. i spent hours trying all conceivable trajectories i could think of, i don't think i can find anything better in any case.

Edited February 3, 2021 by king of nowhere

[theAstrogoth]

2 hours ago, king of nowhere said:

 by the way, why that formula make no mention of inclination, despite it being a huge factor in trasfer costs? shouldn't be relevant in my case because i mostly take care of inclination with gravity assists, but i fear that mathematical procedure may be an approximate one

That's right. The biggest assumption is that the craft's velocity is aligned with the planet's velocity across the SoI change, which is seldom true, but can still be pretty close. 

2 hours ago, king of nowhere said:

oh, it is written that plane changes must be accounted for separately

Yup. If you know all your orbital parameters and choose a particular place to do a plane change, it's not too hard to calculate.

2 hours ago, king of nowhere said:

... =2090 m/s. which should be my speed at periapsis. which basically gives me a 600 m/s to enter elliptic orbit, which is the same exact value i could have gotten by just eyeballing it

You have a much better eye for these than I do! I think you did all the calculation right. I used a slightly more accurate value for Duna's atmosphere height and got a similar answer:

So probably too fast to aerobrake, unfortunately, since you said 200 m/s is probably the most velocity you can shed per pass.

 

Edited February 3, 2021 by theAstrogoth

[Zhetaan]

On 2/2/2021 at 7:42 PM, king of nowhere said:

the very first thing i explored was a duna flyby with gravity assist, but it only lowered apoapsis from 70 to 55M km, not enough.

[snip]

my ship has supplies for between 10 and 20 years, depending on malfunctions; i can make a convoluted trajectory with multiple orbits, but only to some extent.

[snip]

next i tried a kerbin gravity assist, and this looks more promising.

[snip]

I can, without additional manuevers, set my first kerbin flyby so that it will send me en route for a second kerbin flyby on the next orbit

[snip]

My best estimate is that my final orbit is similar to an Eve-Duna transfer, so i can expect a similar injection deltaV. and that would be 600 m/s (for elliptic orbit, not counting circularization). too much, even using my remaining fuel for braking. but then, eve has a lot of plane difference with duna, so maybe it will be cheaper?

You considered using a Duna flyby to raise your periapsis after all of this; after two Kerbin flybys to get your solar apoapsis down to Duna's altitude, it makes sense--provided that you have the life support--to use Duna to raise your solar periapsis so as to slow your velocity on your next encounter.  I went a little mad with FlybyFinder and a J-K-E-D trajectory, that being roughly what you initially proposed.  My numbers largely agree with yours; I haven't yet found a way to get the braking delta-V down to a manageable value for your vessel.  However, the most efficient assist trajectory I know to get to Jool from Kerbin is the K-E-K-K-J assist; it would not surprise me to see that a good way to Duna from Jool is a J-K-K-D-D assist.  It shouldn't be terribly difficult to set up, since your K-D transfer will have Duna catching up to you from behind; your main need at that point will be to course correct to get the second encounter, and possibly also to boost for an encounter within your life support window.

[king of nowhere]

16 minutes ago, Zhetaan said:

You considered using a Duna flyby to raise your periapsis after all of this; after two Kerbin flybys to get your solar apoapsis down to Duna's altitude, it makes sense--provided that you have the life support--to use Duna to raise your solar periapsis so as to slow your velocity on your next encounter.  I went a little mad with FlybyFinder and a J-K-E-D trajectory, that being roughly what you initially proposed.  My numbers largely agree with yours; I haven't yet found a way to get the braking delta-V down to a manageable value for your vessel.  However, the most efficient assist trajectory I know to get to Jool from Kerbin is the K-E-K-K-J assist; it would not surprise me to see that a good way to Duna from Jool is a J-K-K-D-D assist.  It shouldn't be terribly difficult to set up, since your K-D transfer will have Duna catching up to you from behind; your main need at that point will be to course correct to get the second encounter, and possibly also to boost for an encounter within your life support window.

i wasn't able to use flyby finder. when i tried to find a second kerbin flyby, it returned no results.

Currently I am uncertain whether to use the J-K-K-D trajectory, or a J-D-D trajectory. The first has a greater cost up front (1450 m/s), but it looks like it has a better chance of reducing intercept speed. I am also considering to go directly to duna and do some partial rocket braking there, with 300 m/s i would slow enough to get some decent assists from duna. it looks promising on paper, but the orbital times are longer, so it would probably stretch the mission too much. I am also still looking for ways to save a little bit by going in tylo orbit for a while and leave, with oberth effect, when the orbital alignments are more favorable.

A more acculate calculation shows i have 1700 m/s, which are still not enough for the direct trajectory, but much closer

[Zhetaan]

1 hour ago, king of nowhere said:

i wasn't able to use flyby finder. when i tried to find a second kerbin flyby, it returned no results.

FlybyFinder won't do multiple passes of the same body.  It can calculate a J-D-K-D trajectory, for example, but not a J-K-K-D trajectory.  It has to do with the  fact that solutions to Lambert's problem break down when considering transfers from a point to the same point (actually from a radial distance from the centre of attraction to the same radial distance, but it's the same issue as in a repeat flyby).  There are ways to perform that calculation, but I've found them all to be far less than user-friendly.

2 hours ago, king of nowhere said:

Currently I am uncertain whether to use the J-K-K-D trajectory, or a J-D-D trajectory.

Were I given the choice, I'd exhaust the possibilities with the J-K-K-D path first, even after accounting for the higher up-front cost, because it allows one to either append a second Duna flyby to it if needed, or escape to Kerbin should it turn out to cost too much.

[king of nowhere]

well, i did manage to find a better trajectory. from my current jool orbit i could spend 300 m/s to get captured by tylo in a very elliptic orbit. From there, getting the timing right to launch again is tricky, because the elliptic orbit only saves energy if you burn prograde at periapsis, strongly constraining your trajectories. But i found one where the alignment is just right, that will let me reach Duna intercept with only 200 m/s. The timing is not good for meeting Duna, but i still have over 1000 m/s, which are enough to make a course correction at periapsis to reach Duna in the second orbit. From there it's 700 m/s for capture, which i now have, because i saved 500 m/s on leaving jool.

this manuever would force me to spend 30 days around tylo, which in kerbalism is bad because tylo is inside jool's radiation belts, but i tackled this by putting my crew in an escape pod. Those pods have an ion engine with plenty of deltaV, so it won't be a problem to rejoin with the main ship after it's left tylo.

 

I can still probably improve this manuever if i go for kerbin instead of duna, but in any case, i now have a workable solution. it feels much better to look for gravity assist when you know you have a working trajectory to fall back on

Edited February 6, 2021 by king of nowhere