On 5/8/26 13:28, Richard Aiken - raikenclw at gmail.com (via tml list)
wrote:
> Dear All,
>
> I've lately been reading Timothy Zahn's Icarus novels. The stardrives
> in those books can be deliberately overpowered by burning extra fuel
> in exchange for extra speed. If you burn fuel at "+30%" of normal rate
> (the highest overpower rate mentioned), your journey time to the
> destination is reduced by the same amount.
>
> I am considering allowing something similar IMTU in regards to
> reactionless drives in real space. But I'm not great at math. Since
> I'm already using a version of the CT Sample Travel Times Table, would
> it be a reasonable ballpark to apply the same ratio? That is, burn X%
> extra reactor fuel (e.g. power) in exchange for the same percentage
> reduction in real space travel time?
>
> NOTE: Since I'm using that CT table, I'm obviously not concerned with
> knowing the precise accelerations involved.
>
> Sincerely,
> Richard Aiken

<snip>

Richard,

Since CT vessels, as far as I understand, are not reaction-mass limited
as a general rule, they follow brachistochrone trajectories (boost from
stationary relative to origin, tumble approx halfway, and boost in the
other direction until stationary relative to destination) rather than
the comparatively anemic Hohmann trajectories of our current era.  That
means constant acceleration.  In classic sci-fi terms, they are
_torchships_.

All else constant, travel time varies as the inverse square root of
acceleration - to halve the time, you need to quadruple the acceleration
(if that table has times listed at 1G and 4G, for example, then the 4G
time should be half the 1G time under this assumption).

So 1.3x power giving 1.3x acceleration, as you have posited, should
divide travel time by the square root of 1.3, relative to the original
acceleration.

Up to about 2x the power input, the travel time divisor can be taken as
1 + half the extra %age without *too* much error.  So your +30% "let 'er
rip" (Leslie Neilsen's epitaph, in case you're wondering) case would
divide travel time by 1.15, vs 1.1402 in the exact case.

If surface to orbit on Terra is 10,000 km, and at 1G it takes 33
minutes, at 1.3G it would take 33/1.15 = 28.7 minutes, rounded to 28.5
or 29 as you need to - assuming the extra juice can be maintained for
the full burn.  For simplicity on your part, I would suggest it can.  A
15% reduction would be 28 minutes, if that's easier to work with.

The error with the "half % boost as travel time reduction" gets bigger
with longer distances - such as boosting out 900 million kilometres (6
AU) to a gas giant - 117.9 h at 2G.  +30% "let 'er rip" would divide
that travel time by 1.15, giving 102.5 h.  A 15% reduction would give
100.2h.  If that's close enough for your game, run with it.

Alex