When do I launch?

[Box O'Pots]

I have gotten docking down some what okay. However it seems that when ever I want to dock with my space station, you know to bring Jeb home or refuel before I crash into [insert name of planet here], I end up orbiting many many many many... many times before I can achieve a rendezvous. So my question is when do I launch so I can have a rendezvous with my space station in one or two orbits?

Edited November 20, 2013 by Box O'Pots

[allmhuran]

Short answer: You want to launch when the station is just about passing over KSC.

Long answer: It depends on how high the station is compared to how high your parking orbit is.

Objects in lower orbits complete an orbit faster than objects in higher orbit. The bigger the difference in altitude, the bigger the difference in the orbital period. To reduce the number of orbits needed for a launch window, put your second ship into an orbit that is very different from the orbit of the space station.

If you launch to a lower orbit than the station then you want to enter orbit with the station is in somewhat in front of you, since you will catch up to it. But getting into orbit in the first place takes time, so you want to launch when the station is just behind you, or directly over you.

[Vanamonde]

Save the game, launch and fly to an orbit at the station's height, and note the time it took. Load your save, wait until the station is that far to the west of KSC, and launch for a rendezvous then.

[700NitroXpress]

Generally, you want to launch when the space station is a little behind the KSC by like 5 degrees or so. By the time you get into orbital altitude the station will have caught up to you and you still have to do your inclination burn and get your nodes even with the orbit of the station. Your apoapsis should be matching the orbit of the station and the peri should be under the stations orbit. This way you'll catch up to it. Usually, you can plan one maneuver node and get a good intercept within 1km, which is all you need, then just do the visual approach.

[Traches]

See that little desert peninsula to the west of KSP? Launch when your station's about there.

If you've got a little fuel to spare, you can vary the period of your orbit to match up with your station in a single time around.

Set up in a circular orbit at the same altitude as the station. If you're ahead of the station, then you need a longer orbit to match up with it. Burn prograde (you can use a maneuver node to see how much dV it'll take) until your intercept markers line up. Wait till you get close (which will take one orbit), then kill your relative velocity.

If you're behind the station, burn retrograde. If you're in LKO and there's a decent separation, that'll take a little longer though. Probably won't be able to get it in one orbit.

[voneiden]

I'm going to expand a little bit what others have already suggested.

Direct rendezvous from launch. Assumes target has roughly constant velocity (=circular orbit)

1. Through experimenting, measure the time (t) in seconds it takes to reach apoapsis from launch. Also estimate the angle between apoapsis and KSC (α).
   
2. (Optional? Assumes launch towards East!) For greater accuracy: mark down the elapsed time (t_α) when measuring α. While our ascent vehicle is flying, Kerbin is also rotating. This means the angle between apoapsis and KSC looks smaller when it is measured than it would look at launch time. Angular velocity of Kerbin is (É_kerbin = 2pi/21600 = 0.0002908882 rad/s = 0.0166666667 deg/s). Thus it can be calculated α₂ = α + É_kerbin*t_α
   
3. Solve the angular velocity of the rendezvous target: ̉ۡ_target = v / r, where r = 600 000 m + h
   
4. Calculate how many degrees rendezvous target moves during ascent: β = É_target * t
   
5. To get the angle x you should have between your target and KSC at launch time: β - α or β - α₂
   

Example case 1 (not a real test case, arbitrary numbers chosen):

Space station is orbiting on a circular orbit at 250 km with a velocity of 2038 m/s.

Step 1: The launching vehicle is tested with the following traits:

• Time to apoapsis t = 10 min = 600 s
  
• Angle to apoapsis α = ~40 degrees (measured at 7 min = 420 s)
  

Step 2: Kerbin's rotation: 0.0166666667 deg/s * 420 s = 7 degrees. Thus α₂ = 40 + 7 = 47 degrees

Step 3: B]̉ۡ_target = v / r = 2038 m/s / (250 000 m + 600 000 m) = 0.00239764706 rad/s = 0.137375057 degrees/s

Step 4: 0.137375057 degrees/s * 600 s = 82 degrees

Step 5: x = 82 degrees - 47= 25 degrees

So, the launch should occur when target is 25 degrees away from KSC.

I'm going to test this now to see if I wrote complete nonsense. BRB.

Example case 2 (tested in KSP):

Step 1: The launching vehicle is tested with the following traits:

• Time to apoapsis t = 7 min 49 s = 469 s
  
• Angle to apoapsis α = ~47 degrees (measured at 2 min 39 s = 159 s)
  

Step 2: Impact of Kerbin's rotation is about 2 degrees. So α₂ is 49 degrees.

Step 3: The rendezvous target is at 200 km circular orbit flying 2101 m/s. Angular velocity 0.15 deg /s.

Step 4: During the ascent the target moves 70 degrees.

Step 5: 70-47 = 21 degrees.

I used Kerbal Engineering Redux to see the phase angle to the target ship before launching. When the phase angle hit 339 degrees (21 degrees before 360) I slammed launch and followed my ascent profile:

1. Full thrust to 150 m/s
   
2. 50% thrust to 6 km
   
3. 75% thrust to 10 km, pitch 45 degrees east, thrust 100%
   
4. After staging, pitch 25 degrees east. 100% thrust until apoapsis hits 200 km
   

The result:

I'm pretty sure if your angles are +- 5 degrees you will still get a decent intercept so there's no need to be as meticulous as I was. Also step 2 doesn't seem to make much of a difference for low kerbin orbits.

Edited November 20, 2013 by voneiden

[Kasuha]

I have gotten docking down some what okay. However it seems that when ever I want to dock with my space station' date=' you know to bring Jeb home or refuel before I crash into [insert name of planet here'], I end up orbiting many many many many... many times before I can achieve a rendezvous. So my question is when do I launch so I can have a rendezvous with my space station in one or two orbits?

I rarely have to wait more than two orbits to make a rendezvous even though I usually don't wait for the right time to launch. The more different the two initial orbits are, the shorter time it takes. If your space station is on high orbit, put your lifter on low Kerbin orbit first, then set up a maneuver to meet with the station on its high orbit. If your space station is in low orbit, just overshoot and wait for it on high orbit first. But in general I recommend putting the station in high orbit (>600 km) because it's way more convenient both to reach from Kerbin and to access/start from for interplanetary missions. I have two stations at the moment, one at 100 km and one at 650 km and the lower one is almost abandoned now because it's impractical to use it.

Edited November 20, 2013 by Kasuha

[capi3101]

In practice (for me anyway), I wait until the target craft is around 500,000 meters uprange of KSC (this involves going to my KSC ground beacon, targeting the craft, and waiting until its distance is around 500,000 and still decreasing) before launching. That generally works and it's a good ballpark figure for targets between 70,000-120,000 meters or so (I occasionally wait to 475,000 for lower targets, and it's never a precise value).

[Box O'Pots]

Thank you everyone that posted you threw down some good knowin!

[explosions happen]

On 11/20/2013 at 3:58 AM, voneiden said:

I'm going to expand a little bit what others have already suggested.

Direct rendezvous from launch. Assumes target has roughly constant velocity (=circular orbit)

 

1. Through experimenting, measure the time (t) in seconds it takes to reach apoapsis from launch. Also estimate the angle between apoapsis and KSC
2. ...

This is an awesome answer!

So I get the input variables are the Time To Apoapsis TTA and Angle To Apoapsis ATA of the launch vehicle, which is great for an orbiter going for a direct-intercept of a space station where you can restart it.

But anyone know about predicting a certain launch vehicle's TTA and ATA for a direct-intercept with a orbiting vehicle's altitude? Like an Apollo-style mission on the moon, lander going to intercept orbiter?

[Snark]

Here's one thing that can help: if you get in the habit of designing your craft with a consistent TWR, they will follow very consistent ascent curves to orbit, and pretty soon you'll get a good feel for when to launch. Plus you can adjust your trajectory slightly on the way up.

For example, I always design my craft to have a launchpad TWR of exactly 1.5. When I need to launch, I just go straight to immediate intercept, and nail it pretty much every time, because all my ships follow the same curve.

[Snark]

12 hours ago, explosions happen said:

But anyone know about predicting a certain launch vehicle's TTA and ATA for a direct-intercept with a orbiting vehicle's altitude? Like an Apollo-style mission on the moon, lander going to intercept orbiter?

So, you've got a lander on the Mun, and you want to launch to intercept an orbiter.

What you do is, you wait until the orbiter is directly overhead, and then wait a "little while" longer, and then you launch.  The question is, just how long is that "little while"?  Glad you asked. 

Let's say you're on a moon with gravitational parameter μ and radius r, and you want to intercept a craft in circular orbit at altitude h.  How much time t should you wait after the craft passes directly overhead before you launch?

It's given by this formula:

t = π[(r + h)^1.5 - (r + h/2)^1.5] / μ^0.5

So, just to take an example.  Let's say you're on the Mun (μ and r available here, or in-game in the map window), and your target ship is orbiting at an altitude of 40 km.  In this case,

• μ = 6.5138398×10¹⁰ m³/s²
• r = 200,000 m
• h = 40,000 m

Plugging in these numbers to the formula above, we get t = 177 seconds.

So, let's talk TWR.  The number above glosses over the fact that we haven't taken TWR into account-- it assumes we can just instantly go to the needed velocity upon takeoff.  In reality, it takes some time to get up to speed.  For most vacuum worlds, that won't be a lot of time; vac worlds (Tylo excepted) tend to be much smaller than Kerbin and have much lower orbital velocities, so ships can get up to orbital speed pretty quickly.  The extra time you need to allow to get up to speed will be approximately half the time it takes your ship to accelerate from 0 m/s to orbital velocity.  So, let's say your Mun lander can do 10 m/s² of acceleration.  On the Mun, orbital velocity at the surface is a bit over 500 m/s.  So it takes around 50 seconds to accelerate to that speed, so we need to allow extra time of about 25 seconds to account for acceleration.  This is subtracted from our earlier number (since you have to launch earlier, to allow for acceleration).  177 - 25 = 152.

Therefore, in the above example, you'd want to launch your ship about 152 seconds after the target ship is directly overhead.

Note that there's some approximation there-- this is assuming you have a high TWR relative to local gravity.  That's usually a safe assumption for landers on low-gravity worlds.  However, if your ship has a low acceleration compared with local gravity, then the math gets a lot uglier and the acceleration time will be significantly longer, in a non-linear way.  Also, I've made the approximation that your acceleration will be constant, which isn't the case-- you accelerate faster as you burn off fuel mass.  We could delve into Tsiolkovsky formulae to give a more accurate value that takes into account your engine's I_sp and so forth, but honestly it's not worth the bother.  The above approximation will generally be good to within a few seconds, and in any case the lion's share of the time is determined by the orbital mechanics (i.e. the mass and radius of the Mun, and the altitude of the target ship) rather than the time to accelerate.  And you don't need to have the launch pinpointed to the nearest second; even if you're off by half a minute, it's no big deal, you just make a small correction burn while you're en route to rendezvous.

Anyway, there's the math, if you want it.    Personally, I never bother with it-- I just launch when it "looks right" and it generally does well enough.  I'm fine with wasting a couple of dozen m/s of dV, if it saves me a minute or two of calculations.