There are numerous references to spacials in the series, but it's frustratingly hard to calculate just how far a spacial is. Aside from various anomalies from writer to writer, there is also a difficulty in resolving the various distances implied by various situations. This is one attempt at solving the problem. The reader is asked to bear in mind the response of White Dwarf magazine's SF games editor to certain readers who queried his theories on certain technical matters: "If you knew how starships really worked, you'd be writing to the patents office, not to White Dwarf." And if the Blinovitch Limitation Effect is good enough for Dr Who...
The first reference to spacials seems to be in Cygnus Alpha, where Liberator took up orbit 1,000 spacials above the penal colony. In Time Squad the programmed guardians' capsule was first detected drifting at a range of 1,073,000 spacials. Orbit was established over Saurian Major at 1000 spacials. Jenna noted in The Web that Federation pursuit ships could detect Liberator at a range of two million spacials. In Mission to Destiny, where Blake ordered Zen to bring the Liberator to within 200 spacials of the drifting Ortega. The first references in a tactical situation occurred in Duel where it was stated that Liberator had taken up orbit 1,000 spacials (again) above the planet. Travis later ordered an attack with a 1500 spacial trajectory. Liberator, boxed in, could not break orbit without crossing the fire of pursuit ships with a speed and range of SB-4 and eight million spacials.
In Project Avalon Zen reported interceptors approaching at SB-2, two million spacials. In Redemption a planet was bypassed at a range of 1000 spacials. The Spaceworld pursuit craft were ranged at 50,000 spacials and closing.
In Horizon the Federation freighter was first detected at 500 spacials (beyond the freighter's own detector range). In Hostage the attacking pursuit ships were ranged between two and nine hundred spacials, though these ships were fitted with detector shields. (In both of these episodes, detector ranges are exceptionally low. Both were written by Allan Prior. Because of their dicrepancy with other references, I am not considering them to be authoritative.)
In Voice From the Past, Asteroid PK-118 had a stated diameter of 0.102 spacials.
I know of two previous attempts to guess the value of a spacial. Tony Attwood, in his Blake's 7: The Programme Guide (W H Allen, 1982) uses the diameter of Asteroid PK-118. Assuming this to be somewhere in the region of 100 miles (a common daimeter for asteroids), a spacial is estimated at about 1000 miles (1600 km). The reasoning here is by no means unsound.
Bruce Parks, in his article A Question of Scale (Horizon Newsletter #26, May 1991) uses the Liberator floorplans in the Horizon Technical Manual (scaled in millispacials) to arrive at a value of some 21.7 miles. In fact he implicitly arrives at two values, 21.7 and 21.77 miles, which average out at - surprise! - 21.735 miles or 35.19 km. Unfortunately the Technical Manual is not a canonical source.
These two values can be translated into the various canonical
references. The three important references, as I see them, are:
(a) Liberator's standard orbit of 1000 spacials.
(b) the detector range of Federation pursuit ships, implied in Duel
to be up to eight million spacials.
(c) the diameter of asteroid PK-118.
(a) If we take a spacial to be in the order of 1500 km, only marginally smaller than Attwood's putative 100 miles, then Liberator's orbit is in the region of 1.5 million km (5 light seconds). This is about four times the average distance from Earth to the Moon, a much higher orbit than that suggested by sfx shots in various episodes (eg Pressure Point).
(b) Detector ranges work out at 12 billion km, which might seem a lot. This is, however, only about eleven light hours. If, as I've suggested elsewhere, pursuit ships can travel at speeds of some 30,000c, they can cover this distance (40,000 light seconds) in 1.3 seconds. This doesn't give Blake and his crew much time to react. Come to think of it, it doesn't give the Federation pilots much time to lay in an attack course. Liberator would be gone and out of range within a second of being detected.
(c) Asteriod PK-118 would have a diameter of just over 150 km, which is not unreasonable. Assuming a density comparable to that of Mars (about 20% lighter than Earth), the asteroid would have a surface gravity of about one hundredth that of Earth, which ties in with Blake's remarks on the subject.
(a) With a 35.2 km spacial, Liberator's standard orbit would be 35,000 km, somewhat under one tenth of the distance from Earth to the Moon, and more in line with the various sfx shots.
(b) Detector ranges plummet to just over 280 million km at eight million spacials, 933 light seconds. At 30,000c, they would have 0.03 seconds to deploy, which is possibly expecting a bit too much from their finely honed reflexes.
(c) Asteroid PK-118 becomes a ball of rock 3.5 km in diameter, and one careless sneeze could send Blake spinning into orbit.
A third approach is to use detector ranges to calculate the value of a spacial. This is tricky because even if you assign a reasonable deployment window (say five minutes), you then have to consider the possible variations implied by target speed and direction. The easiest and quickest way out is to assign a time to intercept a stationary target. We'll assume this is at 30,000c (TD-10) since the pursuit ships are going for an all-out attack, not sidling up to wave hello.
A five minute (300 second) journey at 30,000c will cover 9 million light seconds. That's 2,700 billion km - 0.285 light years. If that's eight million spacials, then a spacial is 337,500 km.
But if that's the case, then Liberator's orbit is at something over 300 million km from the planet - that's somewhere between Mars and Jupiter from the Sun. And Asteroid PK-118 has a diameter of 33,750 km - nearly three times that of Earth, so a bit on the large side for an asteroid and low gravity is out (unless it's made of expanded polystyrene or something).
The problem in trying to calculate the value of a spacial lies in squaring the distances implied by orbital altitude with those implied by detector range. Either the former is ludicrously large, or the latter ludicrously small. (Asteroid diameter becomes less of a problem if you're prepared to slide the decimal point one way or the other.)
Detector ranges weighing in at significant fractions of a light year might also seem ridiculously large, but I feel we have to assume them to give ships a reasonable chance of detecting anything in the first place.
One possible way out is to cheat. A spacial isn't always a spacial. Either orbital ranges are in (say) millispacials, or detector ranges are in kilospacials. I favour the latter option because standard orbit is 1000 spacials. If that's actually 1000 millispacials, why not simply call it one spacial?
If we take a spacial to be 1500 km, then - as already shown - pursuit ships have a detector range of 12 billion km, or 1.3 seconds at TD-10. If detector ranges are actually in kilospacials, they then have a deployment window of 1300 seconds, more than 21 minutes. And they can pick up a target from 12 trillion km, well over a light year (about 1.26 ly).
With a 35 km spacial and changing spacials to kilospacials, pursuit ships have a deployment window of about 30 seconds. Range is 280 billion km, which is about 0.3 light years. However, Asteroid PK-118 is still a bit on the small side.
If that 35 km is considered to be a millispacial, then orbital ranges must also be taken to be millispacials. Asteroid PK-118 gets a diameter of 3,500 km, slightly smaller than the Moon. Either it's a big asteroid, or diameter is actually 0.0102 spacials - 350 km, within credible bounds.
An alternative to blatant cheating is subtle cheating. Why should a spacial have a fixed value? And what is a spacial anyway? (Not 'how long is a spacial?' but 'what is a spacial?') Time for some doubletalk Let's say...
'A spacial is the radius of the temporal distortion field induced by a body moving at a given supraluminal velocity'
... which sounds neatly authoritative without actually meaning all that much. Note the careful absence of any reference to mass, since that would introduce a hideously unguessable variable into the equation. So we only have speed to deal with, and the faster you go, the longer a spacial becomes.
This is not too fanciful, since mass, length and time are all dependent on sublight velocity, as given by the tau equation. Tau is the square root of (1-(v2/c2)). It means, for example, that at half the speed of light, tau is 0.866. Ship time is less than seven eighths of 'normal', and ship mass is 15% heavier than it is at rest. It would also be a shorter ship - 86% of its normal length, to be precise.
The reference to the London's voyage being 'eight months ship time' suggests that some comparable measure of distortion occurs during supraluminal flight. Applying the tau equation to speeds faster than light leads to some mathematical difficulties, such as finding the square root of a negative number (since v, ship velocity, now exceeds c, the speed of light). Also, passing the light barrier means passing the point where tau reaches zero and ship's mass becomes infinite, needing infinite energy to make it go faster. The traditional SF cheat here is not to go through the light barrier, but to sidestep it via the hyperdrive, warp drive or - in B7 - the Time Distort drive.
Given that the TD drive, like most if not all of its counterparts elsewhere in SF, is merely a fanciful means of explaining away the highly improbable, it can have any effect we damn well like. Any time dilation effect can be contrived to suit ease of calculation and aesthetic whim, though it should also - at least in B7's case - allow for journeys that are not only relatively short according to the subjective experience of those travelling, but also fairly short by some hypothetical 'absolute time'. Suppose, for example, that time distortion reduced subjective time to one thousandth of 'actual'. The flight to Cygnus Alpha would then take 8,000 months, or 667 years. Since such a period did not actually pass outside the London, the degree of time dilation must be relatively small. It might be something like that implied by Hoffal's Law, which I'm just about to make up. Hoffal's Law states that:
t = T*L
Subjective time (t) is objective time (T, distance divided by speed) multiplied by L. L is the Lye Coefficient, which is:
(SQR[1000/V]*1.978)
(1.978 is the Falschmann-Lugner Constant, which is .... er ... a constant determined by messrs Falschmann and Lugner. It is close enough to 2 for ready reckoning, but three decimal places looks classier. The fact that B7 first aired in 1978 is, of course, quite coincidental).
At 1000c, V is 1000 and L is therefore 1.978. Ship time is actually close to twice 'real' time. But at 10,000c, L shrinks to 0.62. A 100-day journey will seem like just two months to those on board. And at 30,000c, L is 0.36, and for each day on board, nearly three days will pass in the outside universe.
You will notice that at relatively slow speeds, ftl travel takes longer. There is actually some advantage in this - not in terms of travel, but in determining a value for TD-1. TD-1, we can say, is the velocity at which t=T, which also happens to be the speed at which L=1. This happens to be 3,900c, and if we apply the TD:SB=5:3 principle, then SB-1 is 6,500c and SB-6 (=TD-10) is 39,000c. At this speed, L has a value of 0.317
So much for time. What about distance, as measured in spacials? Keeping the maths fairly simple, we could say that spatial distortion is inversely proportional to temporal distortion, or 1/L. At 39,000c 1/L is 3.157.
With a 1500 km spacial, the eight million spacial Federation detector range becomes equivalent to about 38 billion km, or some 35 light hours. A hefty distance, but not nearly enough for my satisfaction. Something considerably larger would be better. How about the Noe-Bogues formula, which defines spatial (as opposed to temporal) distortion as...
(V/1000)2/1.978
At 39,000c, this is 804, and those 8 million 1500 km spacials amount to 1.02 light years. Now we're talking! This is a long way - a very long way - but it needs to be if Federation patrols are to stand more than a snowball's chance of ever finding anything. And a pursuit ship at TD-10 could cross a light year in about 13 minutes - a reasonable time period in tactical terms. Better than 1.3 seconds, anyway.
(With a 35 km spacial, 8 million spacials becomes a mere 0.024 light years, and the deployment window shrinks to about 18 seconds. I don't consider either of these values terribly reasonable.)
Note that halving the speed quarters the range. Detectors, communicators and ships' gunnery all have greater effective ranges at faster speeds. Fast ships, therefore, have an immense tactical advantage. And because speed determines weapon and detector range, it then makes sense to give target ranges in spacials rather than an absolute distance. But if you and the target are moving at different speeds (very likely), then their distance from you is going to be different to your distance from them - something the spacewar tactician always needs to bear in mind. (Note that B7 differs from a lot of other space operas in that accelerating to ftl speed does not offer a convenient escape route from lumbering space dreadnoughts. Han Solo might be in for a nasty shock if he ever gets the pursuit ships on his tail.)
(Another point the observant - or pedantic - may have noticed, is that giving the Noe-Bogues equation a value of 1 gives a speed of 1,406c, less than half TD-1. At 1406c, L is 2.345 - spatial and temporal distortion are misaligned, an effect noted as the Spurios Divergence Effect.)
What, however, is a spacial at sublight speeds, or indeed when a ship isn't moving at all? In the case of a stationary ship, V is zero and the Lye Coefficient breaks down. More precisely, the Falschmann-Lugner and Noe-Bogues principles become inapplicable when no Time Distort field is in operation. But ftl detector systems still remain operational, and since these are by convention calibrated in spacials, there is such a thing as a real-time 'virtual spacial'. It works out at about 1500 km.
Liberator's standard orbit, therefore, is 1,500,000 km, though there is a reference towards the end of Seek-Locate-Destroy that suggests the teleport might have been functional at up to 250,000 spacials, or nearly 4 million km. (Alternatively, Liberator might have merely been 250,000 km from the planet, about 150 spacials). And Asteroid PK-118 becomes a humdrum typically-sized asteroid about 150 km in diameter.
As far as the Worlds Edge subcanon is concerned:
A spacial is 1500km as measured by any vessel at rest or travelling at sublight speed (though still subject to the tau equation at significant fractions of c).
TD-1 is 3,900c, SB-1 is 6,500c.
Temporal distortion is calculated via Hoffal's Law (t=T*L), L being the Lye Coefficient (SQR[1000/V]*1.978)
Spatial distortion is calculated via the Noe-Bogues Coefficient ([V/1000]2/1.978) which leads to effective detector, communicator and weapon ranges increasing with speed.