Launch to intercept target in orbit

[aluc24]

Hi all,

I'm sure this has been discussed before, but I really couldn't find any definitive answers to the issue except for "guess until it works".

I have build my first SSTO (level 6, with no upgrades to hangar), that is capable to reach 100x100km orbit with around 120m/s dV to spare (not including deorbiting burn). That is pretty tight. I want to use it for transportation of crew and stuff to the KSS (Kerbin Space Station) I've built before. It orbits Kerbin at 100x100km altitude.

My SSTO takes around 16min to reach apoapsis where it can perform circularization burn. The question now is - how do I correctly time the launch so that at the time of circularization burn, I'm as close to the target as possible (preferably under 5km).

I'm using simple target distance between my SSTO and target. Once it goes down to a certain number, I launch. But it will take my ages to determine the correct separation by trial and error.

 

How do I calculate how far away my target should be at the time I start up the engines on the runway so that I intercept it as close as possible? As I said, target orbit is 100x100km, and my SSTO reaches it's apoapsis in 16 minutes from the moment it starts rolling on the runway.

[Aser]

Find the point that your SSTO reaches Ap and time how long it takes you to get there. Then find a landmark below it on Kerbin. Go into map view while flying your KSS. Then set a maneuver node where your SSTO reaches Ap. When you are T-time it takes your SSTO to reach Ap,  you need to find another landmark.

 

When KSS reaches that landmark in its orbit, you launch your SSTO and you should be relatively close to it at Ap.

[aluc24]

10 minutes ago, Aser said:

Find the point that your SSTO reaches Ap and time how long it takes you to get there. Then find a landmark below it on Kerbin. Go into map view while flying your KSS. Then set a maneuver node where your SSTO reaches Ap. When you are T-time it takes your SSTO to reach Ap,  you need to find another landmark.

 

When KSS reaches that landmark in its orbit, you launch your SSTO and you should be relatively close to it at Ap.

That is very interesting solution! But could it be modified to use something else instead of landmarks? In my case, these landmarks happen to be in the middle of the ocean.

[Aser]

Well...let me think about it for a minute or two...

 

1. You could try lining up with land either to the direct north or south.

2. You could try visually taking a degree measurement from KSC (might not be very accurate)

3. You could plant a flag or dummy vehicle near KSC. Set it as your target. Launch the SSTO to Ap and record target distance. Fly KSS. Set the same flag or dummy as your target. Orbit until it matches your previously recorded value. Set a maneuver node right behind your craft in orbit. When you are T-(time of SSTO to Ap) from your maneuver node, check your distance to target. Save this number. Now when you target KSS from the SSTO, use that final number for your launch indicator. (I think this will work)

[Speeding Mullet]

I know you are trying to achieve something very specific, and I can't answer that better than has already been answered, but an alternative is obviously to get into LKO @ say 80km, then Hohmann transfer up to target @ 100km using maneuver nodes.  I've never been able to time launches very well so that's how I tend to go about it.  Otherwise if I am trying to do the above I do a test launch, see how close I am, the relaunch, adjusting.  The trial and error method in other words.

5thHorseman and Vanamonde, both well respected, prescribe to "trial and error", and "best nearly then adjust" in this thread so I don't think you are going to get a definitive way of hitting within 5km every single launch, especially with a space plane when your route to orbit is going to vary quite a lot depending on your launch profile.

I think just focusing on cleanly getting to orbit, then Hohmann transfer to target efficiently might even use less fuel than a constantly adjusted flight profile to hit target at apoapsis at exactly the right moment.

SM

[aluc24]

1 hour ago, Aser said:

Well...let me think about it for a minute or two...

 

1. You could try lining up with land either to the direct north or south.

2. You could try visually taking a degree measurement from KSC (might not be very accurate)

3. You could plant a flag or dummy vehicle near KSC. Set it as your target. Launch the SSTO to Ap and record target distance. Fly KSS. Set the same flag or dummy as your target. Orbit until it matches your previously recorded value. Set a maneuver node right behind your craft in orbit. When you are T-(time of SSTO to Ap) from your maneuver node, check your distance to target. Save this number. Now when you target KSS from the SSTO, use that final number for your launch indicator. (I think this will work)

The 3rd option sounds really good. But the Kerbin will rotate (and so will the KSC) when KSS makes one additional lap to record distance to the target as you described. That will throw off the calculations. Am I right, or am I missing something?

1 hour ago, Speeding Mullet said:

I know you are trying to achieve something very specific, and I can't answer that better than has already been answered, but an alternative is obviously to get into LKO @ say 80km, then Hohmann transfer up to target @ 100km using maneuver nodes.  I've never been able to time launches very well so that's how I tend to go about it.  Otherwise if I am trying to do the above I do a test launch, see how close I am, the relaunch, adjusting.  The trial and error method in other words.

5thHorseman and Vanamonde, both well respected, prescribe to "trial and error", and "best nearly then adjust" in this thread so I don't think you are going to get a definitive way of hitting within 5km every single launch, especially with a space plane when your route to orbit is going to vary quite a lot depending on your launch profile.

I think just focusing on cleanly getting to orbit, then Hohmann transfer to target efficiently might even use less fuel than a constantly adjusted flight profile to hit target at apoapsis at exactly the right moment.

SM

I perform very strict ascent profiles using precision autopilots. Ground-to-apoapsis takes 16min +/- 15 seconds on each attempt. I'd say that's close enough for a precision interception (if I know when to launch).

[Speeding Mullet]

5 minutes ago, aluc24 said:

The 3rd option sounds really good. But the Kerbin will rotate (and so will the KSC) when KSS makes one additional lap to record distance to the target as you described. That will throw off the calculations. Am I right, or am I missing something?

I perform very strict ascent profiles using precision autopilots. Ground-to-apoapsis takes 16min +/- 15 seconds on each attempt. I'd say that's close enough for a precision interception (if I know when to launch).

1 m/s = 2.24 mph = 3.6 kph

Orbital velocity at 100km = 2246.1 m/s x 3.6 = 8085.96 km/h = 2.2461 km/s

+- 15 seconds at 2.2461 km/s = Maximum missed distance of 33.69 km each way.  

Now let's take a moment to laugh at how massively oversimplified and hence pointless my maths is.......

It's certainly within the realm of possibility and obviously the above is an extreeeeemely simplified calculation that takes absolutely nothing into account, but if your profile is +- 15 seconds, and your going for an orbit of 100km, then you will travel possibly outside of your +-5km requirement each and every attempt, regardless how accurate the start of your launch is.  Then again the above useless calculation would also show you are easily in the realm of being able to adjust yourself to within a km on the way up to 100km without wasting loads of fuel, so it is a worthwhile exercise on your part trying to figure out a very well defined launch time.

Best luck with the accuracy, if you find a reliable way to do it let me know!  I'll stick to my Hohmann transfers in the mean time

SM

 

[aluc24]

7 minutes ago, Speeding Mullet said:

1 m/s = 2.24 mph = 3.6 kph

 

Orbital velocity at 100km = 2246.1 m/s x 3.6 = 8085.96 km/h = 2.2461 km/s

+- 15 seconds at 2.2461 km/s = Maximum missed distance of 33.69 km each way.  

Now let's take a moment to laugh at how massively oversimplified and hence pointless my maths is.......

It's certainly within the realm of possibility and obviously the above is an extreeeeemely simplified calculation that takes absolutely nothing into account, but if your profile is +- 15 seconds, and your going for an orbit of 100km, then you will travel possibly outside of your +-5km requirement each and every attempt, regardless how accurate the start of your launch is.  Then again the above useless calculation would also show you are easily in the realm of being able to adjust yourself to within a km on the way up to 100km without wasting loads of fuel, so it is a worthwhile exercise on your part trying to figure out a very well defined launch time.

Best luck with the accuracy, if you find a reliable way to do it let me know!  I'll stick to my Hohmann transfers in the mean time

SM

 

Well, 33.69km missed is only if I miss the launch window for these 15 seconds, e.g. the SSTO is stationary Usually, these extra plus or minus seconds happen somewhere in the middle or towards the end of ascent, so they won't contribute that much to missed distance. Well, maybe it will be hard to shave it down to 5km separation, but worth a try.

Aser gave a very smart and valid method. If he can clarify what to do about rotation of Kerbin when measuring the KSS-KSC distance once the dummy maneuver node is made, then we have a working method.

[Guest]

If orbital speed at a 100x100 km orbit is 2246m/s then +/-15s is equal to +/- 33.69km. Basically, the only way you could beat Speeding Mullet's suggestion on a regular basis with a direct rendezvous attempt is to either get lucky or use an automated pilot(KOS or mechjeb). Even with an automated pilot to precisely control the timing of the launch, you would still need to know the exact position of the target relative to the launch site, which again, would require KOS or mechjeb or KER. Even after all the figuring, DV gains are going to be minimal. Not worth the effort IMO.

Edited December 13, 2015 by Otis

[aluc24]

14 minutes ago, Otis said:

If orbital speed at a 100x100 km orbit is 2246m/s then +/-15s is equal to +/- 33.69km. Basically, the only way you could beat Speeding Mullet's suggestion on a regular basis with a direct rendezvous attempt is to either get lucky or use an automated pilot(KOS or mechjeb). Even with an automated pilot to precisely control the timing of the launch, you would still need to know the exact position of the target relative to the launch site, which again, would require KOS or mechjeb or KER. Even after all the figuring, DV gains are going to be minimal. Not worth the effort IMO.

+/- 33.69km miss is only possible if RELATIVE velocity between plane and the target is 2246m/s, and that is only possible if the plane is stationary for these entire 15 seconds. But if they add up during ascent, the relative velocity is already smaller, and hence the miss is smaller.

Even if I can't get it down to 5km, it is still worth time and dV to try to get as close as possible on the ascent. As for automated pilot, I'm using both Mechjeb and Pilot's Assistant (since I'm playing with FAR).

[Aser]

5 hours ago, aluc24 said:

The 3rd option sounds really good. But the Kerbin will rotate (and so will the KSC) when KSS makes one additional lap to record distance to the target as you described. That will throw off the calculations. Am I right, or am I missing something?

I believe you are correct. I'm working on a solution, but it's looking like things might be about to get slightly complicated.

 

Edit: Ok, I think I have something for you. Disclaimer: This requires math. The math it requires isn't too complicated, but I did just teach it to myself, so the possibility of this being incorrect exists. I suggest you go over and check to make sure I'm not leading you astray.

 

The answer I have is add 170,693km to your final number.

 

Here's how I arrived at that number...
 

Spoiler

 

I wanted to calculate how far the KSC would travel in one orbit of your KSS. First I calculated the orbital period of the KSS. T = 2pi ((kerbin diameter + orbit height)/velocity). Kerbin diameter = 600,000km. Your orbit height is 100,000km. Velocity is right around 2245m/s, so...

T=2pi(700,000/2245) = 1960 = 32.6 minutes

So, we know how long it takes KSS to orbit Kerbin. Now because of Kerbin's 6 hour day, it will rotate 1 degree per minute. 60*6 = 360 (degrees in a circle)

We can calculate the distance of an arc if we know the diameter of the circle. The formula I found was

arc = d*pi*(x/360)  Where d is the diameter of the circle and x is the angle in degrees. Plug in our diameter of 600,000km and angle of 32.6, and we get 170,693km.

I was able to test a 100km orbit and it does have an orbital period of 32.6 minutes. I was unable to test if the distance I arrived at is correct. KER is being somewhat of a b-.

 

You should be able to run a few tests to (dis)prove my solution. Good luck.

Edited December 13, 2015 by Aser

[GoSlash27]

aluc24,

 The method I use is to mark the passage of my spaceplane over KSC in it's first orbit. Time to passage overhead-orbital period= time lost due to launch.

 With this info, you know that you must launch when the target is that much early. Again, you can figure this out by marking the target's time of passage overhead KSC. Note the time, then add orbital period and subtract lead time. This gives you your launch window.

Fair warning though: spaceplanes have a lot of variance in their launch time loss.

Best,

-Slashy

[aluc24]

9 hours ago, Aser said:

I believe you are correct. I'm working on a solution, but it's looking like things might be about to get slightly complicated.

 

Edit: Ok, I think I have something for you. Disclaimer: This requires math. The math it requires isn't too complicated, but I did just teach it to myself, so the possibility of this being incorrect exists. I suggest you go over and check to make sure I'm not leading you astray.

 

The answer I have is add 170,693km to your final number.

 

Here's how I arrived at that number...
 

  Reveal hidden contents

 

I wanted to calculate how far the KSC would travel in one orbit of your KSS. First I calculated the orbital period of the KSS. T = 2pi ((kerbin diameter + orbit height)/velocity). Kerbin diameter = 600,000km. Your orbit height is 100,000km. Velocity is right around 2245m/s, so...

T=2pi(700,000/2245) = 1960 = 32.6 minutes

So, we know how long it takes KSS to orbit Kerbin. Now because of Kerbin's 6 hour day, it will rotate 1 degree per minute. 60*6 = 360 (degrees in a circle)

We can calculate the distance of an arc if we know the diameter of the circle. The formula I found was

arc = d*pi*(x/360)  Where d is the diameter of the circle and x is the angle in degrees. Plug in our diameter of 600,000km and angle of 32.6, and we get 170,693km.

I was able to test a 100km orbit and it does have an orbital period of 32.6 minutes. I was unable to test if the distance I arrived at is correct. KER is being somewhat of a b-.

 

You should be able to run a few tests to (dis)prove my solution. Good luck.

I tried it - measured my ascent time and distance again (14:45 (found a way to ascent quicker than before)), after creating maneuver right before apoapsis and orbiting to t- launch time, distance to KSC was 855. I then added 170.69km as you suggested, and the next time I launched when KSS was 1025.69km away. Even with perfect ascent, missed target by 600km... Something is not right, and I can't figure it out yet.

3 hours ago, GoSlash27 said:

aluc24,

 The method I use is to mark the passage of my spaceplane over KSC in it's first orbit. Time to passage overhead-orbital period= time lost due to launch.

 With this info, you know that you must launch when the target is that much early. Again, you can figure this out by marking the target's time of passage overhead KSC. Note the time, then add orbital period and subtract lead time. This gives you your launch window.

Fair warning though: spaceplanes have a lot of variance in their launch time loss.

Best,

-Slashy

That's very interesting solution. But does it account for Kerbin's rotation?

[GoSlash27]

Aluc24,

 It does not. You have to account for that in the math.

Best,

-Slashy

[Pecan]

Time, time, time ...

You can spend the time working out, for each combination of vehicle and payload, exactly when to launch and IF every flight goes exactly as planned (down to rounding-errors and other computer artefacts) through very unprefictable atmospheric launch you will have got your rendezvous.  Even with a SSTO rocket I wouldn't like to trust the accuracy though.  I assume you're using a spaceplane, since it takes so long to get to orbit, which means much more inherent flight-error.

Or you can do a lazy launch any time you like, with any vehicle/payload you like to a phasing orbit and spend the time on waiting for a very-predictable and much more accurate transfer manoeuvre.  Save yourself the launch worries,  Calculations from orbit are much more repeatable.

Edited December 13, 2015 by Pecan

[merendel]

My approach would be to aim for intercept after 1-2 orbits instead of a direct from launch.   Since your station is at 100km do your normal launch up to AP aiming to get there ahead of the station.  Once at AP raise your PE to 70+ and adjust so the station catches up after an orbit or two.   Much easier than precisely timeing the launch as its much easier to eyeball.   For a first launch of a new craft just go when the station is directly overhead and see how far around the planet it is when you reach AP.  On future launches make sure its that far plus a bit more from flyover and adjust to meet up after an orbit or two.

[aluc24]

All right... I'm giving up. I'll just do Hohman. If anyone finds an accurate and user-friendly solution, let me know...

[Plusck]

I was thinking about this problem earlier, and came to the conclusion that testing it in practice - then correcting forwards or backwards in time for subsequent launches - it is the only feasible solution because the maths is going to be horrible. You can approximate the maths for rockets since the acceleration increases over time at a relatively even rate, and you don't even need to consider the vertical distance and/or curvature of the planet since you can just consider the whole system as running along one dimension.

i.e. you have this system:  A-----B-------------C, where A= starting position of KSS, B= launch position of SSTO, C= meeting point.

However, since your acceleration is going to be changing quite significantly at different stages, it'll be a slog to determine your distance from B to C using maths since you'll have so many components to the equation.

On the other hand, since you know that it takes you a set time to get to C, you don't even need to make any calculations. You just need to set a flag at KSP, set it as target, climb to 100x100 orbit, note distance to target. Revert to the runway and leave your SSTO sitting there. Switch to KSS, set flag as target, and warp until your distance to target is the same. Set a manoeuvre node at that point on the KSS's orbit as soon as you've passed it, then go back to the tracking station and wait until your KSS's time to that node is exactly 16 minutes (or whatever your SSTO flight time is). You then hop in your SSTO on the runway, select KSS as target and see how far away it is. Theoretically, that should be the exact distance that you want to launch at every time.

 

[RokRoland]

On 13.12.2015 klo, aluc24 said:

Hi all,

I'm sure this has been discussed before, but I really couldn't find any definitive answers to the issue except for "guess until it works"
...

My SSTO takes around 16min to reach apoapsis where it can perform circularization burn. The question now is - how do I correctly time the launch so that at the time of circularization burn, I'm as close to the target as possible (preferably under 5km).

I'm using simple target distance between my SSTO and target. Once it goes down to a certain number, I launch. But it will take my ages to determine the correct separation by trial and error.

How do I calculate how far away my target should be at the time I start up the engines on the runway so that I intercept it as close as possible? As I said, target orbit is 100x100km, and my SSTO reaches it's apoapsis in 16 minutes from the moment it starts rolling on the runway.

After reading the initial question, then the answers, and then the original question again, I am unsure what you're actually asking. Whether you're asking "how to determine the correct separation in order to launch reliably", or "how to calculate how far away the target should be". Despite referring to calculation in the last paragraph, I do believe you're actually trying to find a method that will give you the correct time to launch on a reliable basis. Also, the method does not need to be mathematical but it should not be a "guess then correct until you hit it"-method.

The following method should give you the right point of reference to your launch with just a single attempt used for experimentation:

Line up your launch and wait until your space station is exactly overhead KSC, or whatever the closest point of separation is. At this time, launch your SSTO to the identical 100x100 orbit. No, you will not reach the space station this time. However, carry on and achieve the orbit with no regard to the space station.

Let the space station orbit around once. Once the space station again passes exactly overhead KSC, note the distance of KSC to your SSTO. Let time pass, bring your already-orbiting SSTO down if need be, and line up another launch.

Once the distance of KSC and space station is what you noted down in the previous step (outlined in bold font), launch your SSTO, and this time rendezvous with the space station in a coordinated fashion.

With this solution, you can keep on using your distance to target method as you currently are, without giving thought to orbital periods or mess about with maneuver nodes.

Finally, if you are having trouble eyeballing the distance of your reference SSTO to KSC at the proper time, jot down the distance between the SSTO and space station, put a satellite with sufficient delta-v to correct for position the identical distance in front of your space station on the identical orbit, and use the satellite for launch reference instead.

All in all it does sound like a bit of work considering that just one second delay in start will throw you off by over 2 km, but hey, this sounds like a very Kerbal way of doing things, so thumbs up, don't give up and why Hohmann if you can eyeball it?

[ForScience6686]

What I've done is set my ap above the target orbit until I get an intercept on the way back down.  So I do not complete my orbit until the rendezvous.  It's not always to efficient, especially if I'm too early on the launch.  But I've gotten a rescue down to 18 minutes with the rescued kerbal safely inside.  

This method is quite easy and repeatable, but you'll take a hit in efficiency as you usually need to burn radial to match the target.

 

[Plusck]

Why not do the opposite? Set Ap below the target orbit, make sure you're just slightly behind then transfer up? Zero efficiency losses, and I'm sure you could nail it within a quarter of an orbit every time so only a maximum of what, a 15-minute delay?

[Vegetal]

You know, even the Soyuz makes a transfer orbit before rendezvous with the ISS. They launch right when the ISS is overhead, get into a 150 something km orbit and from there, transfer into the station's higher orbit. Direct rendezvous is really complicated, even for real space programs.

[pokeman]

On 12/14/2015 at 6:43 AM, ForScience6686 said:

What I've done is set my ap above the target orbit until I get an intercept on the way back down.  So I do not complete my orbit until the rendezvous.  It's not always to efficient, especially if I'm too early on the launch.  But I've gotten a rescue down to 18 minutes with the rescued kerbal safely inside.  

This method is quite easy and repeatable, but you'll take a hit in efficiency as you usually need to burn radial to match the target.

 

This is the method I've been using too. Once you've got it just right the loses are very minimal i generally have an Ap only 1-2km above the target and am 90% of the way to orbit. To familiar targets like a LKO station I am usually docking by the T+8 min mark, that's with a rocket not a spaceplane though.

On 12/14/2015 at 9:39 AM, Plusck said:

Why not do the opposite? Set Ap below the target orbit, make sure you're just slightly behind then transfer up? Zero efficiency losses, and I'm sure you could nail it within a quarter of an orbit every time so only a maximum of what, a 15-minute delay?

It's not as fast and there's a much smaller window especially when the target Ap is <85km. A quarter of an orbit can take ages to catch up if you can only get 10km below your target. So it's more efficient yes (maybe ~25m/s to LKO) but less reliable and harder to meet a craft in less than one orbit, at least from my experience.

EDIT: 18 mins to target with a spaceplane is pretty damn good, any payload or just kerbals?

Edited December 21, 2015 by pokeman
Kerbs or Cargo?