To End In Fire wrote:The range was down to barely twenty million kilometers, and the upgraded Cataphracts had a powered range of over nineteen million.
Even with a 1,630,000-kilometer ballistic phase, total flight time was only a hundred and fifty seconds.
150 seconds is shorter than the normal drive endurance on an SDM, and a Cataphract 1st stage is built on an SDM drive.
But after crunching through the numbers it seems clear that they actually launched with their first stage in it's full power, 60 second endurance mode. And further, that at that distance, with those drive numbers, it made sense to do so as it shaved about 35 seconds off their flight time.
With a half-power first stage all Cataphracts have a powered endurance of 180+75=255 seconds.
The improved Cataphracts Filareta's 11th fleet launch had a first stage with 701 KPS^2, meaning even if the 2nd stage hadn't been improved over the original design they'd have a continuous powered range of 23,500,000 km.
The "The latest, tweaked version of the Cataphract" from Uncompromising Honor improved that first stage accel to 840 KPS^2, so again even with zero improvements to the 2nd stage they should now have a continuous powered range of 27,600,000 km.
But with a full power first stage they'd only have 60+75 = 135 seconds of powered endurance (less than the 150 second flight time of the sucker punch). And the ballistic phase is actually not wildly far off for those UH cataphracts first stage in full power mode. 840*2 = 1680 KPS^2 (171,400 gees) for 60 seconds gives you 100,800 KPS, coast at that for 15 seconds gives you 1,512,800 km; only about 8% short of the 1,630,000 km the book quoted.
It'd actually need an accel of 1811 KPS^2 (184,800 gees) But then to have the stated range of "over nineteen million" the 2nd stage would need need an acceleration of around 2,800 KPS^s (326,500 gees) for its 75 seconds.
That'd make the first stage about 2x quicker than a Mk23 and the second stage about 2.2x quicker than a Mk30 or Mk31 CM.
So let's say those cataphract numbers are true. It can run at either:
905.5 KPS^2 for 180 seconds, then 2,800 KPS^2 for 75, or
1811 KPS^2 for 60 seconds, then 3,200 KPS^2 for 75
In the half-power launch they'd use the first stage for 110.5 seconds then cut over to the 75 second second stage, for 20.9 million km range in 185.5 seconds.
In the full-power launch they'd use the first stage for 60 seconds, coast for 15, then cut in the 75 second second stage, for 20.9 million km range in 150 seconds.