Error in Traveller Core Rulebook

[Gaidheal]

I apologize if this has been found and an erratum printed but my quick search found no such discussion or correction.

The error is with the "Interplanetary Transit Times Table" on page 145 of the rulebook.

In short, the times are out by a factor of two for the appropriate "Thrust Rating", I.E. the time given for a TR of 2 is in fact the correct time for TR1 and the odd numbered TR columns are actually the times for a 0.5 g0 increment over the previous column (TR1 is TR1/2, TR3 is TR2.5, etc).

It appears that whoever did the maths forgot that the correct formula for the time is twice the displacement over the acceleration, all square rooted. This being derived from s = ut + (at^2)/2 so familiar to any Physics student, though usually more elegantly written - blame original ASCII.

 

[Gaidheal]

Whilst what I said above is correct, presumably a pilot wants to actually land or at least become stationary relative to whatever he is approaching, in which case the previous times work perfectly, of course (otherwise even a modest TR1 vessel is approaching its target with a speed of 4.5 km/s!).

If this was all thought through in precisely this manner, I shall stand in the corner in an embarassed silence, if not, well the 'error' has been fortuitous anyway, hasn't it? In either case, the table is clearly actually correct as I'd forgotten about flipover and deceleration.

:¬)

 

[Rikki Tikki Traveller]

The table is in error. The corrected table is in the Errata Files.

However, there are a couple of things to remember about the travel time tables: there are two different ways to travel and each will give a different table.

1. Constant acceleration
2. Constant acceleration to half-way point then constant deceleration to endpoint

The formulas for calculating travel times are different depending on how you are travelling.

If your endpoint is a planet, then you will want to use Method 2. If you are just trying to go as fast as you can (flyby), then Method 1 is the way to go.

Travel times in the TMB errata assume Method 2.

Hope that clears some things up.

 

[Gaidheal]

Well, mostly it repeats what I stated but the tables are related, as per the factor of two. If nothing else at least this thread and any other I may have missed (I did look but, oh well) bring the topic to others who might not have the same quick grasp of the maths.

Incidentally, the tables in the main book are correct for method 2 (accel - flip - decel).

 

[Rikki Tikki Traveller]

For interplanetary distances there is a pretty nice little conversion that works as a good estimate of travel times (within 10%).

T = 2 * sqrt(D/g)

WHERE:
T is is DAYS
D is distance in AU
g is acceleration in Gs.

This assumes accelerate for 1/2 distance, turn around and decelerate for 1/2 distance. All of the unit conversions from meters to AU, seconds to days and m/s^2 to Gs seem to pretty-much cancel each other out.

I use it all the time for interplanetary distances then ignore orbital burns and matching orbital speeds etc and assume that is all buried in the slop time.

Hope you find this useful.

 

[Gaidheal]

Aye, I'm aware of it, actually but thanks. It's easily close enough given all the other minor variations; order of magnitude is often considered 'close enough' for approximations over large distances and times, so a tenth is perfectly good most of the time.

For those with a calculator of some sort handy, the more formal equation amounts to "Find the square root of (d x 200 / a)" or "Find the square root of (d x 100 / a)" for the flipover-and-arrive-at-rest calculation, where d is in kilometres and a is in 'gees'.

The above is relatively easy for some of the common TRs, E.G. with a 4 'gee' M-drive, it's "root of 50d" for a constant acceleration all the way (the answer is in seconds, of course).

P.S. The quick and dirty method using AUs is much worse than a tenth for small numbers of AUs.