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What's the absolute minimum time in which spacecraft docking can be achieved?

EDIT:

This question isn't so much about the time to match orbits as it is about the time it takes to maneuver into the proper orientation and execute the individual docking steps.

For a better example than my original one -- suppose you have a Dragon V2 approaching the ISS when they suddenly realize that their CO2 scrubbers have failed. They need to dock as rapidly as possible; every second counts. The capsule is already on a course which will take it right up into alignment for docking, but it will still have to be oriented, mated, and so forth. If they act as rapidly as they possibly can, how long will it take before they can breathe fresh air again (ignoring the remaining time it takes to close the distance with the ISS)?

Obviously there would be redundancies in place for the failure of the CO2 scrubbers (if the Dragon V2 even has those). This scenario is just for the sake of discussion.

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    $\begingroup$ Are you asking about existing craft and existing machinery (I doubt Dragon capsules can dock together at all today), or about what could be achieved with time to design new equipment? $\endgroup$ – BowlOfRed Jan 27 '16 at 22:16
  • $\begingroup$ I think the only times we could establish reliably are the times needed to pressurise the space between vessels' doors, and get the doors open, closed and sealed. That would depend a lot on the vehicles in question I suspect... $\endgroup$ – Andy Jan 28 '16 at 13:23
  • $\begingroup$ Dragon capsules have full OMS and possess the androgynous ports used by the ISS, so they can dock together easily; that's actually the case I was interested in. But I'm not worried about the mechanical side of things or pressurization; I'm more interested in the amount of time it would take to maneuver together into the right orientation. $\endgroup$ – sevenperforce Jan 28 '16 at 14:59
  • $\begingroup$ "close together and on the same trajectory" implies that you'd need to adjust the orbit of either sufficiently to achieve actual physical rendezvous within the allowed time; the time to do that is likely to be heavily dependent on the specific orbit and distance involved. Because they are "already on an aerobraking trajectory" my guess is you are going to have an awful hard time doing that quickly enough. Why did the crew of the leaking craft not just seal the leak to the best of their ability before attempting aerobraking? Entry interface is not the time for last-minute fixes... $\endgroup$ – a CVn Jan 29 '16 at 10:44
  • $\begingroup$ You would need to know the following: do the capsules have full translational thrusters (references are unclear - if not, are the service modules still attached); what is the acceleration provided by these; what is the distance between the two spacecraft. It's impossible to answer the question in its current form. $\endgroup$ – Andy Jan 29 '16 at 10:55
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This primarily depends on starting distance and relative velocity, but nevertheless, it's so dangerous as to point of total impracticality.

Total delta-V of Dragon V2 is hard to find, but some estimates put it at about 390m/s.

First, the capsule accelerates up to half of its delta-V, so to speed of 195m/s. We might try to get the time taken from thrust and mass of the capsule, but Wikipedia conveniently provides us with "Burn time - 25 seconds" for the engines, let's run with it - so acceleration takes 12.5s. At 15.6m/s^2 we've covered 1218m out of initial distance.

Then there's inert flight at 195m/s until we're 1218m away from the station. The time in seconds is the distance in meters divided by 195

Then we brake for 12.5s and just gently bump right into the docking port as the engines go off.

Of course if we made any slightest mistake along the way, we either crash into ISS or float inertly in space with no propellant.

Generally, for a distance $d$ greater than 2436m the time will be $t = 25+(d-2436)/195 [s]$. For a lower distance it will be correspondingly less than 25s, you can find it yourself for 15.6m/s^2 acceleration. And of course any minimal mistake will end with a disaster.

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  • $\begingroup$ Aish -- good math, but not really what I was looking for. I was assuming that the intercept trajectory is already set. What I'm trying to figure out is the minimum time for orientation, mating, and docking steps. When I've seen video of free capsules docking with the ISS, there's always a slow, gradual puffing of the RCS thrusters to gradually nudge the capsule into position, then slow mating. How much faster can THOSE steps be completed? $\endgroup$ – sevenperforce Feb 2 '16 at 20:29
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    $\begingroup$ @sevenperforce: Pretty much arbitrarily shorter. There's the short fixed sequence of docking - the probe contact and locking, then establishing a hard dock, pressure equalization and opening the hatch. Some of these can be rushed, so there's only the matter of bringing the speed near zero (and spraying whole ISS with copious amounts of propellant in the process, definitely not welcome but it will survive, if a little worse for the wear) and maintaining the trajectory, which is all down to pilot skills. This whole slow dance is effect of caution and sparing ISS extra sprays of propellant. $\endgroup$ – SF. Feb 3 '16 at 1:16
  • $\begingroup$ So with a skilled pilot...or, perhaps, a skilled autopilot...what sort of minimum timeframe are we looking at from the point that they begin orienting for docking to when the hard dock is established? Ten minutes? Five minutes? Thirty seconds? $\endgroup$ – sevenperforce Feb 3 '16 at 13:03
  • $\begingroup$ @sevenperforce: Something like my above calculations modified with non-zero initial speed, to shorten the approach time as allowed by available fuel, plus less than a minute since the probe makes the connection to when the hatch is open. There's enough time to perfect the x,y, roll, pitch and yaw during the approach, while bringing z to zero. so the approach time is still the final roadblock overcame by accelerating towards and then decelerating against the station. $\endgroup$ – SF. Feb 3 '16 at 13:37
  • $\begingroup$ Although I'm not sure how the androgynous port performs comparing to the Soyuz port, e.g. how much inaccuracy it allows. Soyuz port allows for a lot, and is pretty fast. Supposedly the new one should be better. (Plus the Soyuz port requires a relatively high approach speed - it won't make a good hard dock if you bump too gently! It was a problem with the first dockings where the pilots would make too perfect, too gentle approach.) $\endgroup$ – SF. Feb 3 '16 at 13:38

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