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Let's assume the flight rules don't prohibit you from going to the ISS in a malfunctioning craft and don't force you to land on next orbit, unlike the real life ones.

Let's also assume you have an Apollo era slide rule, sextant, watch, pen and paper, and the most recent orbital elements for the ISS. Can you still implement the propellant-efficient fast "Soyuz scheme" rendezvous (launch-to-docking in six hours) while doing all the calculations manually? For the sake of the argument, we can state that there's no other workload for all three crew members, and the transfer craft's initial orbital elements are fully known.

  • Will it be possible to calculate all burn times, angles and durations in time?
  • What nomograms can drastically reduce calculation times?
  • How will adding a navigation radar into the instrument mix ease up the calculation burden?

Notes:

Possibly useful: Wertz, Bell (2003).

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    $\begingroup$ Wow. This is a particularly precise question. I like it, but I do wonder what scenario planning came up with it... $\endgroup$
    – Rory Alsop
    May 3 '15 at 23:22
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    $\begingroup$ A slide rule? Seriously? The precision and accuracy of slide rules was very, very low. Three to four places of precision, and with lots of calculations, I would hazard three or less. This is the 21st century. What's wrong with a laptop or a smartphone? $\endgroup$
    – David Hammen
    May 4 '15 at 16:16
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    $\begingroup$ Only just maybe if you were Neil Armstrong - and probably not then. Neil (and I imagine a few others) seemed to have what it took to intuitively vector sum the real world (or real out of this world) dynamics and produce a human response. Failing that or magic the errors are large enough that you may get within sight but with excess delta v and probably wrong plane and more. Having flown relatively trivial orbital simulations long long ago I was appalled at how a fuel reserve that the computer could turn into a rendevous was essentially always turned into flaming ruin by manual control. $\endgroup$
    – Russell McMahon
    May 5 '15 at 12:18
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I'm going to hazard and say it's not very likely, more to human reaction time than anything. If one has to assume that the computers are not available for the quick launch sequence, one also has to accept that they are not available to control timing. Here's a blurb about the thruster capacity in the various nodes, from Spaceflight 101.

SKD, the Soyuz Main Engine, provides a thrust of 2,942 Newtons. The entire Soyuz Attitude Control System is comprised of 28 DPO Thrusters. Two clusters of 14 DPO Thruster are mounted on the spacecraft with 12 of these jets providing 26.5 Newtons of Thrust and the remaining 16 providing 130 Newtons.

Assuming a mass of around 7150 kg, as the same site indicates, that means that even with the smallest thruster, there's an acceleration of around 3.7mm/ second^2. Given a human reaction time of even a tenth of a second, that could result the in the delta-V being off by .3mm/s How much of a difference does that make? In 6 hours, that's only 6.5m. That doesn't sound so bad really, until you consider how long of a thrust is likely required. It's hard to know exactly, but I have found that to support a close orbit like this, a 30 degree phase angle or less is required. I don't have the exact delta v required, but I'm going to guess that it is around 10 m/s. For that length of time, one would have to do a burn with the smallest thruster around 45 minutes. I suspect the reaction time would be far worse for that length of time, but it could still theoretically be done. I'm sure the main engine is used more than the small ones, greatly reducing the thrust time required (By a factor of 100), but that would leave more uncertainty in the location.

Okay, so let's say you get your angle off by 1 degree, which would be an easy thing to do without assistance. What does that do? That would given an error of around 1.6%. That means the planned 10m/s burn could be off by as much as 16 cm/s, which over 6 hours would mean an error of around 5km, fairly significant!

Also keep in mind that the thrust requirements grow the longer the thrust takes to plan, and things get very complicated very quickly!

Bottom line, unless you have access to some kind of a computer, it seems very unlikely that you could pull this off. There might be a person or two who could pull this off, but I doubt it.

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    $\begingroup$ You can however as person much more easily use adaptive configuration: where you will get closer and closer to the object you wish. It is not really unfeasible to do that by hand: people can operate by hand surgery lasers on a much higher accuracy. And given good visual feedback humans are really good at increasing their accuracy over time. (IE you'll need to have a feedback of the relative speeds and distance, and then get closer and closer). 5Km I think is close enough for actual feedback. $\endgroup$
    – paul23
    May 18 '15 at 11:09
  • $\begingroup$ The problem is it's somewhat counter-intuitive. I suppose one could do it with lots of practice, I would just hope one does that ahead of time. $\endgroup$
    – PearsonArtPhoto ♦
    May 18 '15 at 21:03
  • $\begingroup$ It is actually no more counter intuitive than driving a car. - It is the same level of abstraction (Given a good interface). When driving a car you also only influence power/forces. Yet at the same time you are very well capable of making a smooth turn or braking in a smooth way for a traffic light. Similar to a rendez vous: getting closer to an object in orbit is continuous up to many derivatives. And humans are amazing at extrapolation/differentiation. $\endgroup$
    – paul23
    May 23 '15 at 10:03
  • $\begingroup$ Been done by hand once in direct radar contact with target, but getting to that point is nasty hard. $\endgroup$
    – Joshua
    Aug 15 '16 at 17:33

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