Tuesday, August 29, 2023

The 1000D Limit

Hfoileiiau, a small gas giant in the New Sol (MAGY 0503 D501956-7) outer system. The semi-major axis of Hfoileiiau is 8.49 AU, placing its orbit inside the 1000D limit of Aeetes, the system’s G3 V primary star.

The maneuver drive is the standard means of sublight movement in Traveller. A remarkable piece of near-magical tech, the M-drive is a reactionless system providing constant acceleration to the ship with virtually unlimited range and no fuel requirements, instead being powered directly by energy from the ship’s power plant.

Traveller is notable as a game that usually presents referees and players with a series of tradeoffs at every turn, whether it is in character generation, ship design, or combat. In most editions, including Classic Traveller and Mongoose Traveller, the maneuver drive requires few tradeoffs, and over the years many creative minds have proposed various setting-breaking exploits and hacks using the technology.

Perhaps as a way to prevent such shenanigans, both T4 and Traveller5 impose a 1000D limit on maneuver drives, which is an extension of a 10D limit placed on anti-gravity units in MegaTraveller. T4 Starships (1994) explains how this 1000D limit works. At TL12, advances in gravitics leads to the invention of thruster plates:

Gravity drives use the stellar system itself as their reaction mass (much as a train pushes against its track, and the planet below, rather than by expelling exhaust). A small change in a star’s momentum translates to a huge velocity change for the much smaller spacecraft. … Beyond a certain point, quantum-gravitic effects drastically reduce the efficiency of a gravitic-drive ship by a factor of a hundred or more, and thus they cannot maneuver effectively in deep-space unless they have an auxiliary drive, though they can remain there while, for example, computing jump parameters. The cutoff parameter turns out to be around 2,000 solar radii. Beyond this point, thruster plates are virtually worthless for anything beyond stationkeeping, and some alternate form of propulsion is needed (71).

This concept is continued in Traveller5. As explained in Book 2: Starships, “Maneuver is the standard in-system ship drive. It interacts with gravity sources to produce vectored movement. M-Drives are subject to the 1000D limit: beyond 1000D from a gravity source, the drive operates at only about 1% efficiency” (101).

I think I understand the rationale behind this rule: it creates a limitation on what is otherwise a seemingly limitless technology. On its face the 1000D limit appears to be an innocuous change, but upon further examination, this change has some far-reaching and maybe unintended implications on the Traveller universe.

But first, let’s consider where the 1000D limit falls with some common types of stars:

1000D Limits for Main Sequence Stars
TypeStellar
Diameter (km)
1000D Limit
(AU)(Orbit No.)
A0 V3,739,947258
A5 V2,543,164178
F0 V2,243,968157
F5 V1,944,772137
G0 V1,645,577117
G5 V1,226,7038.27
K0 V1,062,1457.16
K5 V927,5076.26
M0 V762,9495.16
M5 V478,7133.25
M8 V209,4371.44

In general, the 1000D limit falls well beyond the habitable zone of main sequence stars. The 1000D limit for Sol would be 9.3 AU or 1.391 billion km, encompassing the entire inner system plus Jupiter, but falling short of Saturns’s orbit of 9.5388 AU. This means that maneuver drives in Sol’s outer system operate at only 1% efficiency. Under such circumstances a speedy System Defense Boat with 6g acceleration has its acceleration reduced to only 0.06g, or 0.588399 m/s2.

Consider the Starjammer’s journey to the outer system of Desolation. This trip consisted of two distinct segments. In the first segment, the Starjammer constantly accelerated at 3g until the halfway point was reached. In the second segment the Starjammer decelerated at 3g until it arrived at the derelict liner Speedwell with a velocity of zero. The total time for this trip was 141.86 hours.

If we instead applied the 1000D limit to this trip, the Starjammer could only use constant 29.41995 m/s2 acceleration until it hit the 1000D limit of Dross, the M2 V system primary, which is about 18.26% of the total travel distance. For the remaining 81.74% of the journey the Starjammer would be limited to only 0.2942 m/s2 acceleration.

If I remembered enough calculus and functions I could probably produce a formula for incorporating the 1000D limit into the Starjammer’s trip. But I don’t, so I had to brute-force this problem using the nifty Uniformly Accelerated Motion Calculator at CalculatorSoup.

Let’s assume the Starjammer’s journey now consists of three segments: the first begins in orbit around Desolation and stretches to ½ the distance between Desolation and Dross’s 1000D limit. The second segment stretches from this point to the 1000D limit. And the third segment stretches from the 1000D limit to the location of the Speedwell in the outer system.

The Starjammer begins in orbit around Desolation and then fires up the M-drive, moving with constant 3g acceleration through the entire first segment. Then the Starjammer begins to decelerate at a little less than 3g through the second segment. At the end of the second segment the Starjammer’s M-drives efficiency drops to 1%. The trick here is to finish the second segment with a velocity just low enough so that the Starjammer can decelerate at 0.2942 m/s2 all through the entire third segment and still arrive at the Speedwell with a velocity of zero.

We know the distance of each of these three segments. We know the starting velocity of the first segment and the ending velocity of the third segment are both zero. And we know the maximum and minimum acceleration rates in each segment.

Let’s tackle the third segment first. We know the distance from Dross’s 1000D limit to the Speedwell (1,566,856,472 km), we know the final desired velocity (0 m/s), and the maximum deceleration rate (-0.2942 m/s2). Using the online calculator, we can solve for the time (3,263,672 seconds, or over 906 hours) and the velocity at the 1000D limit (960,175 m/s).

So let’s try the first segment next. We know the initial velocity (0 m/s), distance (175,050,000 km), and acceleration (29.41995 m/s2). Using the calculator, we can solve for the final velocity of the first segment (3,209,350 m/s) and time (109,088 seconds).

This leaves the second segment. We know the initial velocity (3,209,350 m/s), final velocity (960,175 m/s), and distance (175,050,000 km). We can solve for acceleration (-26.79 m/s2) and time (83,966 seconds).

Trip Summary with 1000D Limit
SegmentDistance
(km)
Acceleration
(m/s2)
Initial Velocity
(m/s)
Final Velocity
(m/s)
Time
(s)
1175,050,00029.411003,209,350109,088
2175,050,000-26.78663,209,350960,17583,966
31,566,856,472-0.2941960,17503,263,672
Total1,916,956,4723,456,726

Add all of this together, and the time for the Starjammer to reach the Speedwell considering the 1000D limit on maneuver drives increases from a little less than 6 days to a little over 40 days. But perhaps even more importantly, these calculations are far too complicated to use at a game table for too little benefit. For both in-game and metagame reasons, you’d be crazy not to just fire up the jump drive for an intra-system jump.

So the first implication of imposing the 1000D limit: travel within the inner system of most star systems is unchanged, but travel to and within most of the outer system will almost always be via jump drive. Alternative propulsion systems for deep space maneuver, like fusion drives or High Efficiency Plasma Recombustion (HEPlaR) drives, are not nearly as efficient as classic thruster plates.

If no gas giants orbit within the 1000D limit, the old trader trick of refueling at a gas giant on the cheap and then motoring to the mainworld using the maneuver drive really doesn’t work so well, does it? Conversely, any gas giants inside the 1000D limit, such as Jupiter in the Sol system, would likely become the locus for additional starship traffic.

I think this is a fairly big change to the OTU setting: I’ve always pictured sublight ships regularly shuttling back and forth from the outer system with raw fuel and ores, with microjumps of less than one parsec reserved for rare trips to the extreme outer system.

With a 1000D limit microjumps are probably quite common in star systems with any sort of activity in the outer system. If the main world has a low hydrographic percentage or no surface water at all—and all sources for hydrogen are outside the 1000D limit—fuel suddenly becomes a much more dear commodity.

Maybe in a universe with a 1000D limit ships circumvent the restriction by using a slingshot effect to island hop between worlds in the outer system. Ships might use their maneuver drive to accelerate around and around a gas giant to build up momentum and then “hurl” themselves at the next closest gas giant.

Naval doctrine around system defense probably also shifts with 1000D limits in place, possibly giving more of an advantage to the native force occupying the system. A classic intruder scenario is an enemy fleet jumping into the outer system, refueling at a gas giant, then making for the main world at top speed in normal space. A native force defending a system therefore has to protect both the main world as well as the gas giants, forcing some tough choices if there are multiple gas giants. Does the native commander concentrate all assets at one strong point or spread them out over several, diluting their effectiveness?

If no gas giants were inside the 1000D limit the native force would probably see an intruder force jump into the outer system and refuel. Messengers seeking reinforcements could be dispatched to a neighboring system. The intruder would either need to “waste” fuel on an intra-system jump to the main world, still giving the native force at least a week to prepare, or make way using manuever drives. This would take multiple weeks and provide extra-system reinforcements time to arrive.

So possibly defense of any gas giants beyond the 1000D limit becomes a much lower priority with this restriction in place? This might be just as well, as SDBs and monitors cannot be easily transferred between gas giants in the outer system. A SDB jump-shuttle becomes a near necessity for moving defense boats around the system.

If any gas giants were inside the 1000D limit, the native commander could concentrate defenses on a much smaller number of points, and transfering assets between strong points is easier: the distances are necessarily shorter and maneuver drives can be used at full efficiency.

This might force some intruders to just jump directly to the main world’s 100D limit and lay siege without refueling, which is a huge gamble given the inherent command and control lag of jump. A 1000D limit forces an intruder to commit assets with no certainty as to what defenses will be found when it emerges out of jumpspace. A native force might only have its standard picket of SDBs and monitors at the end of the jump, or maybe this picket has been reinforced by a BatRon or an entire task force. As is sometimes said in these parts, “Hard tellin’, not knowin’.”

I don’t think any of these changes outright break the Official Traveller Universe, but all told, I’m not sure adding the 1000D limit into my MgT game is really worth the effort. As setting background the concept provides some nice handwavium, but as a game mechanic it seems to just make travel in the outer system a bit too messy and inefficient for my taste.

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