Flight Question Orbital Mechanics - cheapest plan to the moon?

[johan]

So I've been reading the descriptions and pros & cons of various different orbits on this page: http://www.orbitermars.co.uk/stdorbit.htm

To check my understanding, can somebody please help me out with some comments on the following?

If I had just undocked with the ISS and wanted to go to the moon (so I have a large relative inclination to deal with), I'd have to do something like the following?

1. Turn on Align Planes MFD and target the moon, wait near the ISS until we reach one of the nodes... let's say we reach the AN first, for the sake of my example.
2. Turn prograde, and burn until my orbit around Earth is quite elliptical (so let's say I raise ApA to what, 1000km's or so?)
3. Wait until Apoapsis (which should co-incide with the DN, since Periapsis co-incides with the AN).
4. Turn orbit-normal and burn main engines to change my orbital plane very efficiently.
5. Whilst still near Apoapsis, turn retrograde and drop my PeA slightly, so that I will just brush the upper atmosphere (perhaps PeA=75km or so will do the trick?).
6. Use aerobraking to drop Apoapsis to LEO. If I can see that air friction alone won't slow me enough, use retro rockets and/or airbrake (or just go around twice if I have the time). Wait for Apoapsis, then burn prograde to lift PeA out of the atmosphere, to ensure we don't de-orbit accidentally or mess up the eject burn.
7. Now set up eject plan to the moon, the burn should be maximally efficient since we're in LEO and properly aligned with the moon's orbit.

I thought of just doing the eject burn from the Periapsis of the elliptical orbit for maximum efficiency, but the timing isn't very likely to be correct, so we have to circularize first.

 

[Jarvitä]

Or, you could just wait for a proper alignment (every ~14 days) and make a direct, off-plane lunar transfer from ISS orbit, no plane changes or secondary parking orbits required.

 

[johan]

Or, you could just wait for a proper alignment (every ~14 days) and make a direct, off-plane lunar transfer from ISS orbit, no plane changes or secondary parking orbits required.

Right.

Should'a thought of that!:facepalm:

For the sake of exercising my new knowledge though, let's say the next alignment is 12 days away and I just can't wait that long? Let's say I'm off to resupply the moon base with LOX, and just stopped by the ISS to drop off a new ammonia pump module , and if I don't get to the moon in the next 10 days, 6 people will perish for lack of breathable air.

 

[flytandem]

Right.

Should'a thought of that!:facepalm:

For the sake of exercising my new knowledge though, let's say the next alignment is 12 days away and I just can't wait that long? Let's say I'm off to resupply the moon base with LOX, and just stopped by the ISS to drop off a new ammonia pump module , and if I don't get to the moon in the next 10 days, 6 people will perish for lack of breathable air.

This could be a fun challenge. I was going to ask you to post a scenario with the ship in LEO off plane to the moon and not in good position to go immediately to the moon. But I opened up the stock scenario, Delta-glider/DG Mk IV in orbit and it appears to be a convenient facsimile of what you are asking. It is not a full 12 days out but maybe 10.

So I propose we use that scenario as a starting point and see what we can come up with for minimizing fuel use and getting to the moon (docking with Luna-ob1) within 7 days (168 hours) of the start of the scenario. I am going to be busy with work for several days but will probably have a chance to play with the task Monday or Tuesday.

 

[Tommy]

So I propose we use that scenario as a starting point and see what we can come up with for minimizing fuel use and getting to the moon (docking with Luna-ob1) within 7 days (168 hours) of the start of the scenario.

Sounds a lot like the Lua Challenge #3 with a time limit.

 

[Jarvitä]

Right.

Should'a thought of that!:facepalm:

For the sake of exercising my new knowledge though, let's say the next alignment is 12 days away and I just can't wait that long? Let's say I'm off to resupply the moon base with LOX, and just stopped by the ISS to drop off a new ammonia pump module , and if I don't get to the moon in the next 10 days, 6 people will perish for lack of breathable air.

If that situation happened in real life, it would probably be cheaper to launch two separate missions to ISS and the moon than a single one capable of performing a 70° plane change in LEO and a TLI. Also, the person responsible for such a mishap would never be allowed to hold responsibility for anything more critical than grocery shopping.

 

[johan]

Sounds a lot like the Lua Challenge #3 with a time limit.

Ok, I used the Lua Challenge to do some initial investigation. I ran the scenario a bunch of times, each time stopping as soon as I had fixed the RInc so as to have preliminary results sooner.

This scenario has an RInc of 50.06'.

I wasn't flying terribly efficiently :embarrassed:... I usually dropped PeA before raising ApA, until I realized this is silly and wastes ~50Kg of fuel - you should drop PeA only after fixing RInc. Also, I wasn't properly accounting for my burn time when raising ApA, so my actual ApA tends to be a couple thousand seconds after the node... however, this doesn't seem to make a huge difference, see scenario 6.1 and 6.2.:thumbup:

(I couldn't find out how to make a proper table in this post, so I'm abusing the CODE tags, any help would be much appreciated...)

#    Raised ApA to    Final RInc    Total Fuel used after fixing RInc
1    02.5 Mm            0.21'            3423.48 Kg
2    05.0 Mm            0.16'            3130.09 Kg
3    10.0 Mm            0.18'            2778.89 Kg
4    15.0 Mm            0.07'            2601.10 Kg
5    30.0 Mm            0.14'            2332.45 Kg
6.1  60.0 Mm            0.03'            2165.53 Kg
6.2  60.0 Mm            0.25'            2142.14 Kg (Set up ApA closer to node)
7    70.0 Mm            0.25'            2103.45 Kg

By these results, it looks like it will get somewhat more efficient still, if we continue to raise ApA some more.:hmm:

Oh, and, of course... the higher ApA numbers come with a time penalty, but we'll have to see how that pans out. By the time I had fixed the RInc in the 70 Mm scenario (#7), it had taken something like 5 or 6 simulated hours. That's just to get to ApA and do the plane change burn... so getting back to PeA so we can circularize will probably take another 6 hours or so, which means we've already spent half a day.

 

[Tommy]

With the Lua challenge you don't need to make the Plane Change before TLI. As Jarvita pointed out, there are windows for an off-plane transfer. In that scenario, the moon is at about the correct distance from the node for an off-plane intercept. The harder part is getting the plane alignment with OB-1. There are a couple methods for that.

Sometimes it's possible to solve the plane alignment during the transfer. When stting up the transfer, care is taken to ensure that a node with the target will occur just before entering the Moon's SOI, and an alignment burn is done there. THis is trickiesnt, and not always possible.

The easier way is to try to place your Pe at a point on the target's orbital path. Then when you make your first insertion burn stop as soon as your Ecc is low enough that you are fully captured by the moon. IIRC, for the Moon, that's about .7 to be safe (any "drifting" caused by the Earth will ruin the alignment) and make the PlC at the node at your new Ap.

I've made that challenge with just under 2500kg fuel used - and know I can do better with a bit of practice and experimentation.

However, while these windows come every 14 days, and actually last for a day or two each side of the node (the higher the RInc the shorter the window), there may be times where you can't wait for one. In this case, elevating your Ap enough to save a really significant amount of fuel will make your period grow to a few days at least, so there is only so uch to be saved by this method if you have time to spend - in which case you could simply wait for the off-plane window.

If you can't wait, the quickest way to efficiently make a large plane chang is an aerodynamic plane change. In a stock DG, a PlC this size can be made for about 3k dV if flown well. This is about the same savings (over a normal PlC) that you would get if you raised your Ap to the point that your orbital period was about 2 days - not counting the cost of recircularizing (only a couple hundred dV if you use your aerodynamic method to lower the Ap again). Ideally, if your node was near enough to the node, you could skip the recircularization and have a much cheaper TLI since you'l be using the velocity that you used to raise the Ap.

 

[flytandem]

I made a quick run of the deltaglider/DG Mk4 in orbit. Got to docking with Luna Ob1 with 6 hours to spare from the 7 day limit. Used 2954 Kg of fuel from scenario start. It was first doing a partial TLI with a ~2800 m/s of both pro and plane change. Then after a couple of days, another burn with a mix of inward, pro and plane change to time arrival at the moon ~10 hours ahead of the deadline (enough for a couple orbits or more to rendezvous. I planned the arrival Pe to be on a node with Luna-ob1. Arrival had the insertion burn at Pe with a little bit of plane change to flavor. Then at Ap (also at node) did the final plane change so that rendezvous happened at next Pe making just 1 orbit to rendezvous. It was just seat of pants navigating with a bit of eyeballing based on experience as to what's important and when.

 

[johan]

It was just seat of pants navigating with a bit of eyeballing based on experience as to what's important and when.

Yeah... I tried that, but due to lack of experience, got to use almost 4 tons of fuel...:embarrassed: see below...

With the Lua challenge you don't need to make the Plane Change before TLI. As Jarvita pointed out, there are windows for an off-plane transfer.

Let me just check that I understand these windows you guys are talking about. If I'm in LEO with a nonzero RInc to the moon's orbit, each time I make a full orbit around the Earth, I'll pass through the Moon's plane twice. If my only objective was to get to the same orbital path as the Moon, I could use either of these two points for an off-plane "intercept". However, if I want the Moon to also be there when I reach it's orbit, I have to wait for the right time, then use one of the nodes to do the same off-plane burn? Which one I use, would depend on which side the moon finds itself.:hmm: This would explain why you say the windows are 14 days apart, since the moon's period is 28 days, isn't it.

It strikes me though, that if I could fly accurately enough, I could do an off-plane intercept no matter where the moon is, provided I time my eject burn correctly. I'm sure transX can plan work out a plan like this? It would mean I would get to the moon from an "odd" direction, but once I'm there I could do an orbit insertion burn to make sure the moon's gravity captures me, right?

In that scenario, the moon is at about the correct distance from the node for an off-plane intercept. The harder part is getting the plane alignment with OB-1.

Doesn't that scenario use your current system time? This would explain why I was able to do the off-plane intercept so easily on the weekend, the moon just happened to be in the right spot . I did it with 3932.80 Kg in total, which tells me I have a lot of room for improvement! I messed up the final plane change (to align with Lna-OB1), horribly... I tried eyeballing it before doing my insertion burn for lunar orbit, this was a very bad idea! It changed my RInc from ~20' to something stupid, which was very expensive to fix.:huh: Cost (quite literally) a ton of fuel.

If you can't wait, the quickest way to efficiently make a large plane chang is an aerodynamic plane change. In a stock DG, a PlC this size can be made for about 3k dV

Do you mean I can get a 3k dV plane change done for free, or do you mean a 50' plane change will cost 3k dV with this method? Good idea by the way, thank you very much - I'll be sure to use it in future.

Ideally, if your node was near enough to the node, you could skip the recircularization and have a much cheaper TLI since you'l be using the velocity that you used to raise the Ap.

Yeah, I thought I was being super clever when I realized I could do this, but of course it's only because the moon happened to be in the right spot (as compared to where the DG starts in orbit), this weekend

 

[Tommy]

Let me just check that I understand these windows you guys are talking about

The windows occur when the moon will be at a node when you get there (and you'll eject at the opposite node). The simple way to find a window is to transfer to a vessel landed at the moon (use scenario editor to add one landed a BB if needed). Open AlignplanesMFD and change the reference to Earth. Now target the vessel you'll be using, and you get a pretty good idea when the moon will reach a node, and which node.

It strikes me though, that if I could fly accurately enough, I could do an off-plane intercept no matter where the moon is, provided I time my eject burn correctly.

Not always, and not cheaply. It will work best if the RInc is 90 degrees - at around 50 degrees no matter how you time the burn youll still be getting to the moons orbital altitude without getting very close to it's path, unless yo either incorporate a significant plane change or inward/outward velocity to the TLI (very expensive) or make a very large correction burn (also expensive). But keep in mind that the "window" lasts for a couple days either way - the moon is big enough to pull you in if you get close enough.

Doesn't that scenario use your current system time?

I hadn't realized, but yes. Since that challenge doesn't have a time limit I never paid much attention to how long I had to wait for a window, or that it was different on different days.

Do you mean I can get a 3k dV plane change done for free, or do you mean a 50' plane change will cost 3k dV with this method?

The second option. An aerodynamic plane change always cost some fuel - you have to rebuild the orbit after you do it. This cost varies with how much velocity you lose to drag during the PlC, The higher the RInc, the longer you'll need to stay in the atmo, so the more expensive it can be. It's not usually cost effective for PlC's much under 30 degrees, and depends a lot on your skill as a pilot. The idea is to get RInc and TN both down to zero simultaneously. If the TN stops dropping (you are "pushing" the node away ahead of you) it means you are turning to tightly and need to lower your closure rate by either lowering AoA or gaining altitude. Keep in mind that the closure rate will increase as you lose velocity. It's tricky, and will take some practice to get it efficient.

 

[flytandem]

I reflew the DG Mk 4 in orbit scenario, this time dropping into the atmosphere to do a plane change using vehicle lift and supplying thust to offset the drag. It was cheaper deltaV than in space only but not by a huge amount.
Space only= 6887 m/s dv.
Using atmosphere = 6492 m/s dv. (saved 395 m/s)
Maybe I can retry the non atmospheric method to see if I can shave off some of the difference.

Edit: another refly of non atmospheric and this time only prograde from LEO. Raising Ap about half way to the moon, then at Ap doing another burn to arrive 12 hours early. The usual 1 orbit with plane change at Ap to docking with wheel. The result had even more savings than atmospheric. It used only 5831 m/s total dv which is 661 less than the previous best.

 

[dgatsoulis]

This sounds a really nice challenge! I'd like to give it a shot.
Just to get it straight though...
You guys are using the stock Orbiter 2010 scenario (Delta-glider\DG Mk4 in orbit)
And the goal is to use the least amount of fuel to dock with Luna-ob1, within 168 hours from the beginning of the scenario? (So that the docking MUST occur the LATEST on MJD 51989.5293?) Or 168 hours from what ever time you choose to initiate the TLI?
(From what i've read, it's the first... just want to make it clear.)

 

[flytandem]

This sounds a really nice challenge! I'd like to give it a shot.
Just to get it straight though...
You guys are using the stock Orbiter 2010 scenario (Delta-glider\DG Mk4 in orbit)
And the goal is to use the least amount of fuel to dock with Luna-ob1, within 168 hours from the beginning of the scenario? (So that the docking MUST occur the LATEST on MJD 51989.5293?) Or 168 hours from what ever time you choose to initiate the TLI?
(From what i've read, it's the first... just want to make it clear.)

168 hours from start of scenario. You can wait for the TLI if you like but it's using up your 168.

 

[Tommy]

It was cheaper deltaV than in space only but not by a huge amount.
Space only= 6887 m/s dv.
Using atmosphere = 6492 m/s dv. (saved 395 m/s)

The aerodynamic PlC can be done much cheaper. The main thing is do NOT use thrust to maintain speed. Letting the velocity reduce makes the PlC much easier (higher rate of closure), and allows less time spent in the atmosphere - and the lower speed means less drag. This means that the total velocity lost to drag will be less. For a PlC of this magnitude, expect velocity to drop down to about 4.5k to 5k, and altitude no lower than 55k to 60k. Toward the end, let the altitude climb up over 60k - 65k, and rebuild the orbit from there. Above 75k, velocity losses to drag are very slight, so you can roughly calulate dV by subtracting the minimum velocity reached from orbital velocity, and then add about three hundred for de-orbit and drag during the re-build.

I've done the ISS - Mir trip for just under 4k dV, this should be quite similar. As with most things, timing is crucial. De-orbit too soon and you will lose more velocity due to drag since you have lower the closure rate so you reach the node. De-orbit to late and you;ll need a higher AoA to get a high enough closure rate - and drag increases significantly at AoA's above 4 - 5 degrees. I try to use about .6 to .7 up trim, and change altitude to control the closure rate as required.

 

[flytandem]

The aerodynamic PlC can be done much cheaper. The main thing is do NOT use thrust to maintain speed. Letting the velocity reduce makes the PlC much easier (higher rate of closure), and allows less time spent in the atmosphere - and the lower speed means less drag. This means that the total velocity lost to drag will be less. For a PlC of this magnitude, expect velocity to drop down to about 4.5k to 5k, and altitude no lower than 55k to 60k. Toward the end, let the altitude climb up over 60k - 65k, and rebuild the orbit from there. Above 75k, velocity losses to drag are very slight, so you can roughly calulate dV by subtracting the minimum velocity reached from orbital velocity, and then add about three hundred for de-orbit and drag during the re-build.

I've done the ISS - Mir trip for just under 4k dV, this should be quite similar. As with most things, timing is crucial. De-orbit too soon and you will lose more velocity due to drag since you have lower the closure rate so you reach the node. De-orbit to late and you;ll need a higher AoA to get a high enough closure rate - and drag increases significantly at AoA's above 4 - 5 degrees. I try to use about .6 to .7 up trim, and change altitude to control the closure rate as required.

I agree, actually I did just let the speed drop as I banked and changed planes to align with the moon. I felt that if the speed were slower it would help get more change in alignment per second at the same banked G loading. I only mentioned thrust to offset drag as itin effect is what was done even if done at the end of all the slowing due to drag.

So what did you get for the trip to the wheel at the moon? You said much cheaper than 6400 m/s. Then you said you can do the ISS to Mir in a bit under 4K. The ISS Mir trip is about 77 degrees plane change. The challenge here is only a 51 degree plane change. So instead of about 4K m/s it's probably about 2/3rds of that or about 2650 m/s. Then you still have to do a TLI at about 3100 making usage at 5750 and you still have to do the orbit insert. To make it challenging, the arrival from what I've seen has the ship coming in at about 90 degrees required plane change if arriving at a node with the wheel. So there's more than just doing a 800 m/s insert. Even if just the 800 m/s and no plane change we have an estimated total deltaV now at about 6550 m/s. So my 6492 result was probably a pretty good representation of the aerodynamic method.

 

[Tommy]

The lower dV value was for the "challenge # 3", where you can wait for a window. I haven't had time to work on the stock scenario you used, looks like the nearest window is at least 3 - probably four days away so I would expect some plane change is required.

As for the aerodynamic plane change, I would expect about 3300 - 3500 m/n, not 2650. It's not a linear relationship between RInc and dV. It seems that the higher the angle the more (relatively) efficient it gets - due to the faster closure rate (degrees per second). Plus, theres sort of a "fixed" cost, at least about 800m/s minimum. The longer you are in the atmo, the higher this gets, of course, but the difference between a PlC of 70 degrees vs 60 degrees isn't as large as the difference between 6 degrees vs 50 degrees - if you can follow that explanation!

Once I finish my part of the IMFD Full Manual update, and take a break, I'll see if I can't get a decent annotated flight recording of this maneeuver. I still need to refine the technique quite a bit. At this time I'm still doing a lot of guessing on altitudes, etc, so I'm not sure exactly what I'm doing that gives me the efficiency I've been able to achieve.

And I misunderstood, and thought the 6550 number was just for the PlC, not the whole trip. I'd agree that that is a pretty good representation of the method.

 

[Kyle]

Shoot, all I did to learn how to go to the moon was look at a tutorial, looked at the map it showed the spacecraft was over Hawaii, the moon over Africa. Took a ruler and put it on my computer, estimated the length in inches on my screen board the moon and the spacecraft are on the Map MFD and I just fire my engines and go. Works every time.

EDIT: Look how close I get too, I always get in the wrong orbit though

 

[dgatsoulis]

Edit: another refly of non atmospheric and this time only prograde from LEO. Raising Ap about half way to the moon, then at Ap doing another burn to arrive 12 hours early. The usual 1 orbit with plane change at Ap to docking with wheel. The result had even more savings than atmospheric. It used only 5831 m/s total dv which is 661 less than the previous best.

Wow, 5831 m/s of total dV for this challenge is very impressive.:thumbup:
Of course... it's flytandem who did it!

I tried a similar approach to this, using IMFD. But instead of burning prograde to half the moon's altitude, i burned all the way.
(IMFD Tangenial Transfer, time of arrival 105 hours later)
dV for burn from LEO 3157.74 m/s
When i had covered about 2/5ths of the distance (Alt 165M), i made another burn, this time Target Intercept program, off-axis, arrival 160 hours from begining of the scenario. dV 795.09 (+ 2.7 m/s for a correction a bit later).
Then, when i was inside the moon's weak SOI (G=0.10) i used about 190 m/s of RCS thrust to try and allign myself better and also to set my Perilune. Got my Rinc with Luna-OB1 down to about 35 degrees and my Perilune Alt to about 180 km. (manually making the burns, with IMFD's Map program on the left and Orbit MDF on the right).
Used another 5 m/s for corrections and when i reached Luna-OB1's orbit (at a node, Alt 498 km) i used the Target intercept/two plane program to set up a rendesvouz with the station in one orbit. dV used 1608 m/s + 37.92 m/s for the PIC burn a little bit later.
On the final approach i used 191.6 m/s to match my velocity about 15 Km away from the Station. Total dv= 5988,05 - fuel spent 2665kg (Main+RCS). Time: 163 hours.
There is some room for improvement, i'll give it another shot to try and save ~160 m/s, to match flytandem's dV.