The Lens was perhaps the newest feature of the interstellar cruisers of the day. Actually, it was a complicated computer which could throw on a screen a reproduction of the night sky as seen from any given point of the Galaxy.
Channis adjusted to co-ordinate points and the wall of lights of the pilot room were extinguished. In the dim red light at the control board of the Lens, Channis' face glowed ruddily. Pritcher sat in the pilot seat, long legs crossed, face lost in the gloom.
Slowly, as the induction period passed, the points of light brightened on the screen. And then they were thick and bright with the generously populated star-groupings nearer the Galaxy's center. [Book Three, p. 29-30]
Before I go on, I have to wonder at why Asimov happened to call this new technology the (capitalized) "Lens". Is it a call-out to E.E. Smith's somewhat earlier Lensman stories which also featured hyperspace travel? Or is it simply in reference to the projected galaxy's disk-shape, which Asimov referred to in an earlier story as the "Galactic Lens"? But let's dig into the several pages of detail on its operation to which Asimov now treats us:
The ship bounded through the Galaxy, its path a widespaced dotted line through the stars. The dots, referred to, were the scant stretches of ten to sixty light-seconds spent in normal space and between them stretched gaps of many parsecs that represented the Jumps through hyperspace.
Bail Channis sat at the control panel of the Lens and felt again the involuntary surge of near-worship at the contemplation of it. He was not a Foundation man and the interplay of forces at the twist of a knob or the breaking of a contact was not second nature to him.
Not that the Lens ought quite to bore even a Foundation man. Within its unbelievably compact body were enough electronic circuits to pinpoint accurately a hundred million separate stars in exact relationship to each other. And as if that were not a feat in itself, it was further capable of translating any given portion of the Galactic Field along any of the three spatial axes or of rotating any portion of the Field about a center.
It was because of that, that the Lens had performed a near-revolution in interstellar travel. In the younger days of interstellar travel, the calculation of each Jump through hyperspace meant any amount of work from a day to a week -- and the larger portion of such work was the more or less precise calculation of "Ship's Position" on the Galactic scale of reference. Essentially that meant the accurate observation of at least three widely-spaced stars, the position of which, with reference to the arbitrary Galactic triple-zero, were known.
And it is the word "known", that is the catch. To any who know the star field from one certain reference point, stars are as individual as people. Jump ten parsecs, however, and not even your own sun is recognizable. It may not even be visible.
The answer was, of course, spectroscopic analysis. For centuries, the main object of interstellar engineering was the analysis of the "light signature" of more and more stars in greater and greater detail. With this, and the growing precision of the Jump itself, standard routes of travel through the Galaxy were adopted and interstellar travel became less of an art and more of a science.
And yet, even under the Foundation with improved computers and a new method of mechanically scanning the star field for a known "light signature", it sometimes took days to locate three stars and then calculate position in regions not previously familiar to the pilot.
It was the Lens that changed all that. For one thing it required only a single known star. For another, even a space tyro such as Channis could operate it.
The nearest sizable star at the moment was Vincetori, according to Jump calculations, and on the visiplate now, a bright star was centered. Channis hoped that it was Vincetori.
The field screen of the Lens was thrown directly next to that of the visiplate and with careful fingers, Channis punched out the co-ordinates of Vincetori. He closed a relay, and the star field sprang to bright view. In it, too, a bright star was centered, but otherwise there seemed no relationship. He adjusted the Lens along the Z-axis and expanded the Field to where the photometer showed both centered stars to be of equal brightness.
Channis looked for a second star, sizably bright, on the visiplate and found one on the field screen to correspond. Slowly, he rotated the screen to similar angular deflection. He twisted his mouth and rejected the result with a grimace. Again he rotated and another bright star was brought into position, and a third. And the he grinned. That did it. Perhaps a specialist with trained relationship perception might have clicked first try, but he'd settle for three.
That was the adjustment. In the final step, the two fields overlapped and merged into a sea of not-quite-rightness. Most of the stars were close doubles. But the fine adjustment did not take long. The double stars melted together, one field remained, and the "Ship's Position" could now be read directly off the dials. The entire procedure had taken less than half an hour. [Book Three, p. 35-38]
Commentary: To start with, I'm unable to resist remarking on the breathless description of the Lens as a device able to "pinpoint accurately a hundred million separate stars... capable of translating any given portion of the Galactic Field along any of the three spatial axes or of rotating any portion of the Field about a center". Obviously, while this was surely an amazing leap of imagination to 1940's readers, this could be a free app on any pocket smartphone today. (Think about what that says about our advances in computing technology -- outstripping Asimov's view of a 50,000-year future in less than a century.) Easy guess: I'm sure if this were included in a Hollywood film today, then control of the Lens would be depicted not by "knob... contact... visiplate" but by the standard "holo-view floating touchscreen" effect that's been part of every sci-fi movie since Minority Report, it seems.
One great thing about this passage is that the traditional time for computing interstellar jumps is absolutely identical to that found in the Star Frontiers: Knight Hawks game. From Second Foundation above: "In the younger days of interstellar travel, the calculation of each Jump through hyperspace meant any amount of work from a day to a week". In the Star Frontiers game: all established routes are from 4 to 14 light-years, i.e., days of travel time (SF Alpha Dawn p. 51). So that's interesting, but the rationale given above of hunting stars wouldn't apply, I think, because in the Frontier only 20 known routes exist, and you'd always know where you were and what the closest stars were (excepting perhaps misjumps to unknown systems, but that's not the standard situation).
Of course, the upthrust of this passage from "Search by the Mule" is that the time spent on search-calculations has been radically reduced to only about 30 minutes for a fairly inexperienced user like Channis. Part of the explanation here is the "growing precision of the Jump itself". But does this indicate some irreducibly random element on even the best jumps, or simply an improvement in the preparatory calculations?
The other novella in Second Foundation, "Search by the Foundation" (originally "-- And Now You Don't" when presented in 1950) has just a few tidbits on interstellar travel, such as a restatement of the internal experience, and the fact that even with excellent charts, some calculations are still needed:
... she met the initial acceleration with equanimity and the more subtle nausea that accompanied the insideoutness of the first jump through hyperspace with stocism. [Book Three, p. 155]
The calculations were not difficult. The "Space Route Handbook" was quite explicit on the Foundation-Kalgan route. There was the momentary twitch of the timeless passage through hyperspace and the final light-year dropped away. [Book Three, p. 161]
Finally, there is a scene describing a major spacefleet battle which turns on an apparently novel tactic: half of the Foundation fleet lures an opposing navy into a predetermined sector of space, at which point the other half of the force performs a hyperspace jump into the rear of the enemy, and thus devastate them from an undefended direction. So apparently a hyperspace jump is now (perhaps for the first time?) accurate enough to succeed at that, at least from a relatively short distance away, and with some precise pre-planning as to time and location. [Book Three, p. 239-243]
So I think that concludes our monograph on Asimovian hyperspace and the connection points it has to the Star Frontiers: Knight Hawks game. The limitation options for narrative/gameplay purposes seem to be: (1) requiring days of advance time for calculating a jump, (2) not being able to jump from the vicinity of a large gravitational mass, and (3) needing to achieve a certain base velocity before a jump. Asimov's Foundation series focuses mostly on items #1-2, with a single whisper of a suggestion to #3 (one character mentions "building up take-off speed" in Book Two, p. 226). Niles' Knight Hawks game relies on items #1 and #3, with no mention of #2 -- and likewise disposes of the term "hyperspace" (in favor of "Void"), as well as any special technology for "hyperspace motors".
Much of the language, and interestingly the traditional time frame for the calculations, is identical between the two works. But in general the Asimovian explanation seems not only more widespread in works of SF, but (to put cause after effect) more satisfying and not so self-evidently preposterous. I think if I were to revise the Knight Hawks campaign setting information, then the first and foremost fix that I'd make would be to switch to a more fully Asimovian view of the interstellar travel mechanism.