The Space Station Rendezvous Challenge

[MaxSchram]

Here comes something new, but i'm not sure if it can be done. It's the first step towards a space station and has to do with timing and fine feeling.

The idea is: Deploy something in an orbit, leave the orbit and return to do a rendezvous maneuver.

Here are the rules:

1. Jettison the space station (The last stage of your spacecraft) into an orbit around kerbin.

2. Leave the orbit and do whatever you want.

3. Return to the original orbit and rendezvouz with the station. (Proof is a picture with ur pod and the station on one screen)

4. You can use whatever parts, from every mod you want.

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My first try failed, but i want to discuss my consideration here to verify their correctness. It's gets a little mathematical and i'm not sure if my calculations are right, but read on:

I left the station in an nearly circular orbit at 40576m altitude (Orbit period: T1 = 28.567min). Then i did a Hohmann Transfer to an orbit at 150000m altitude (Orbit period: T2 = 36.2min). The transfer time was Ttrans = 16.157min. Here i had to wait for a specific time interval Twait until i could do a second Hohmann Transfer back to the initial orbit.In order to estimate Twait i did the following calculations:

Since there are two transfers involved, the number of full orbits of the station is

n1 = (Twait + 2 * Ttrans) / T1

One transfer performs half an orbit. The number of full orbits of the spacecraft is

n2 = 2 * 0.5 + Twait / T2

An orbit is a periodical motion so i get modulo 1 for both numbers and define a value

V(t) = (n1 mod 1) - (n2 mod 1)

With V(t) = 0, for t = Twait

This is a non-differentiable problem so i solved it numerically. There are multiple solutions, but the one with the smallest Twait was arround 117.7 minutes.

Wenn i came back to the first orbit the station wasn't anywhere near, but it's really hard to get all the timings and velocities correct.

[plazmaXIII]

Warringer should put this into his next KSP calculator . . .

i would imagine if your just the tinyest bit off you would miss by quite some distance, maybe its not possible to do manually . . .

keep trying

[Warringer]

Interesting idea...

I will think about it, but truth be told, I cannot think of any other application for that safe for this single challenge.

[MaxSchram]

I just did some tests in an orbit, flying away from the last stage and getting back. I have to admit: It's already pretty difficult without doing any orbit changes and stuff. But one can spot an object from quite far away, especially if antialiasing is turned of, since the the pixel flickering does help.

But as you say, it's really easy to miss it by some ten thousend meters by just not hitting the right velocity or the exact timing.

[plazmaXIII]

Interesting idea...

I will think about it, but truth be told, I cannot think of any other application for that safe for this single challenge.

if it can be proven to work then its a new challenge for KSP players to sink there teeth into.

however, how much momentum does a decoupler add to the final stage/station? can we be sure that its not going to add momentum. even if the final speed was like 0.1m/s off, for 100mins or so that could make a huge difference! and thats without the human error involved in the timings and speed . . .

guess we need to wait and see if it will work . . .

[Entroper]

Wow, this will be incredibly difficult without good instrumentation. Color me interested.

[Herra Tohtori]

I'd go out on a limb and say it cannot be done (consistently and on purpose) with current instrumentation.

Even on a few kilometres' range, simply getting a visual observation of the target is really really hard without a radar (especially the way the cameras work). If you can get within visual range with calculated manual burns. And when you get within visual range, there's still the problem of approaching it while trying not to overshoot it.

Rendezvous maneuvers will need the following instrumentation to be feasible:

-own and target orbit parametre display

-own and target locations on respective orbits

-orbital synchronization utilities (plane, altitude and finally phase of orbit synchronization)

Heck, even on Orbiter this would be nearly impossible without said instrumentation, and even then it's challenging to rendezvous with a space station on target orbit with something more realistic than a Delta Glider - trying to do it with Space Shuttle is rather hard.

The easiest vaguely possible way to do the challenge would be to limit the orbit change to a small orbital plane change, so that the orbital period stays as close as possible to original; that way you could perhaps re-synch the orbit later. ???

[Rocket Surgeon]

I'll concur with Herra.

[DoctorEvo]

My hat goes off to whoever manages to do this. I'm not even going to TRY until we at least have some more rendezvous-oriented instrumentation. (Well, okay... I *might* TRY.)

[MaxSchram]

I adjusted my goals to something more easy. As Herra stated that a small plane change would be the easiest to manage i tryed it.

First of all i modified the 'Mun' part from the lunar smackdown challenge. It's bright orange now and very light, so it's easily spottable.

I brought it into an circular orbit around 66265m, did a plane change of around 4° and met it again ~30min later. At this altitude the maximal distance is around 46km, but we can improve it step by step.

Unfortunally i was messed up the slowdown maneuver by misscalculating the burn direction and overshoot it. Had a hard time closing in afterwards.

1st picture is before takeof.

2nd at initial orbit.

3rd at plane change

4th at rendezvouz point, ~30 min later.

Btw: May someone tell me how to insert images properly? Like using spoiler tags?

[plazmaXIII]

how dou calculate this with the plane change, i wanna give it a try

[MaxSchram]

Look at the figure i attached to this post.

It shows the initial velocity vector v0 and the target velocity vector v1, as well as the desired plane change angle alpha. The viewpoint is directly from above, to the planets center.

Both vectors have the same length, because we don't want to change the orbits altitude. In order to achieve this, we have to apply a velocity change deltav. It's direction is given by the angle beta, relative to the initial velocity vector

beta = (180 - alpha) / 2.

This equation holds, because we have an isosceles triangle and the sum of all interior angles ist 180°.

The magnitude of deltav we have to spend is

|deltav| = |v1 - v2|.

In praxis you establish an orbit and orientate your spacecraft to the right angle. As soon as you fire your engines you'll notice, that your velocity decreases. Eventually it increases again and as soon as you hit your initial velocity the plane change maneuver is done.

[DoctorEvo]

I brought it into an circular orbit around 66265m, did a plane change of around 4° and met it again ~30min later. At this altitude the maximal distance is around 46km, but we can improve it step by step.

Hmm... less impressive than what I was hoping for, but still...

(Did it ever completely leave visual range?)

Now, who can manage an orbit-sync?

In praxis you establish an orbit and orientate your spacecraft to the right angle. As soon as you fire your engines you'll notice, that your velocity decreases. Eventually it increases again and as soon as you hit your initial velocity the plane change maneuver is done.

Ooor, you can just hold orbit-normal (90 degrees flat to your flightpath) and rotate a little bit as your flight path bends, while keeping an eye on your velocity... for small plane-changes, it doesn't cost that much, and it doesn't require any math.

[Rocket Surgeon]

Hahaha. The one time I thought I'd see how easy it would be to change my plane I just pointed where I wanted to go and fired until I swung around to that direction. And here are you with your charts and numbers and fancy stuff.

(Seriously, I did a poor job of it)

[MaxSchram]

I simulated the example from my first post in Matlab and also did some acceleration experiments. The result was disillusioning.

If only the two transfer velocities for the orbit changes are missadjusted by just 1m/s, the final rendezvous position is missed by over 100km. This is an unclosable gap. Even if we get thoose velocities right, the change isn't instant. While accelerating a simple spacecraft (Pod, LFT, LFE, SAS) with 25% thrust, the transfer orbits apogee is changed by ~5km. This distance is somewhat equivalent to ~5m/s, which is already more than the error in the first example.

The only chance to possibly do this, is to fly the maneuver with a minimal orbit difference about less than 5km. The velocity changes are smaller, so they can be adjusted quicker and more easy. But the orbit period differences are also smaller, so it takes for ever to re-sync them. The wait time for the same maneuver with 40km and 45km orbit altitudes would be around 2440 minutes, which is nearly 2 days !!!. I don't do this before there is some time acceleration tool

[MaxSchram]

I'm not really sure and the proof i've got isn't worth much, but if you guys trust me: I DID IT

After thoose pretty depressing last thoughts i went out for meeting a friend. On the way and back i thought about that problem and had the final idea:

If i overshoot by such huge distances, why not intentionally undershoot it, establish a lower orbit and than slowly overtake it?

For doing so i first did some tests to estimate the maximal view distance, which is about 30km. At this range the pixel flickering is barely spottable, but can be done. I also did some trigonometric math and came to a method for estimating the current orbit position relative to the space center indicator on the nav ball. With the help of this to things i did all the calculation again an gave it it try.

I established an orbit around ~55.7km and transfered to an orbit at ~150km. There i recalculated all the values to take the deviations into account, and waited for 146.67 minutes. Than i transfered back, landing behind the target and also 3km lower. I waited another 30 minutes, while slowly closing in. At this time the flickering started to occure. Finaly i lost patience and tryed to burn towards the target, what was a big mistake - and i lost track of it.

I'll think about a closing-in maneuver and try it again eventually. At the picture you see the closest point i could reach. I know it's not more than a pixel and is easily done with paint or photoshop but it had the right heading and altitude and got closer.

[FoC400]

Wow, mix this with the lunar smack down and life will be complete

[DoctorEvo]

Wow, mix this with the lunar smack down and life will be complete

Or...

-Lunar smackdown

-Orbit-land-orbit

-Rendezvous challenge

-Finish with a precision deorbit and landing

Whoever does this is the God of Kerbal.

[MaxSchram]

I did another one:

I used three elliptical orbits, all with perigee at ~66.7km. The first orbit was the targets orbit the other two had a slightly smaller / bigger eccentricity. They were designed in the way, that the sum of both secondary orbits periods matched two times the target orbits period. I also created three different solid booster parts, each producing a exact calculated amount of delta v and burned 0.1 seconds. By using them i minimized adjustment errors during orbit changes.

The apogees were:

target = 72858m

secondary1 = 75196m

secondary2 = 70556m

The result worked ot pefectly fine,as you can see in the images:

1st: Shot after launch, notice the three colored boosters.

2nd: Decoupling the target.

3rd: After first orbit change, the target slowy starts to get distance.

4th: Rendeuvous after the maneuver and a few burns for closing in. (I actually bumped in it )

[Armstrong]

8) Cool stuff!!

But makes me realize how important an easy guidance system will be in the final game; if you take off a few minutes too early or too late you can miss your rendez vous with whatever is flying in space (let alone find it in the first place....)

[DoctorEvo]

8) Cool stuff!!

But makes me realize how important an easy guidance system will be in the final game; if you take off a few minutes too early or too late you can miss your rendez vous with whatever is flying in space (let alone find it in the first place....)

If you end up doing that, the key is to slide into a slightly higher or lower (usually elliptical) orbit than the target so that it/you can catch up again. Oddly enough, this means you have to fire retro and slow DOWN in order to catch up (thus dropping down a bit and 'cutting the corner' to catch up), or fire forwards and speed UP in order to let it catch up. Depending on how badly you missed, it may take several orbits to merge with your target - that is, IF you even realize which way it is.

[Lee2011]

'First successful rendezvous

Gemini 7 photographed from Gemini 6 in 1965

Rendezvous was first successfully accomplished by US astronaut Wally Schirra on December 15, 1965, who maneuvered the Gemini 6A spacecraft within 1 foot (30 cm) of its sister craft Gemini 7. The spacecraft were not equipped to dock with each other, but maintained station-keeping for more than 20 minutes. Schirra later commented:

Somebody said ... when you come to within three miles (5 km), you've rendezvoused. If anybody thinks they've pulled a rendezvous off at three miles (5 km), have fun! This is when we started doing our work. I don't think rendezvous is over until you are stopped - completely stopped - with no relative motion between the two vehicles, at a range of approximately 120 feet (37 m). That's rendezvous! From there on, it's stationkeeping. That's when you can go back and play the game of driving a car or driving an airplane or pushing a skateboard — it's about that simple.'

LOL

[DoctorEvo]

Somebody said ... when you come to within three miles (5 km), you've rendezvoused. If anybody thinks they've pulled a rendezvous off at three miles (5 km), have fun! This is when we started doing our work. I don't think rendezvous is over until you are stopped - completely stopped - with no relative motion between the two vehicles, at a range of approximately 120 feet (37 m). That's rendezvous! From there on, it's stationkeeping. That's when you can go back and play the game of driving a car or driving an airplane or pushing a skateboard — it's about that simple.'

Yeah, well HE didn't have to navigate his way to that three-mile milestone... Though I agree that rendezvous isn't completely over until relative velocity is killed, but I disagree with him about the range at which this must be achieved. If you've killed velocity at three miles, even closing from there is relatively straightforward.

Though for us Kerbonauts, with no translational RCS whatsoever, this terminal closing and deceleration is actually more difficult because we can't really steer.

[Jack wooster]

If you build a space station with a hole at one end you can dock with it and stay together, have done this but I do not have any pictures at work!

[DoctorEvo]

If you build a space station with a hole at one end you can dock with it and stay together, have done this but I do not have any pictures at work!

I'm picturing a command pod just rammed in between three liquid engines attached to a tricoupler...