Cataphract performance numbers

At 60% of To End in Fire, <person name redacted to avoid spoilers> provides us with the following performance numbers for the last flight of Cataphracts provided to the SLN:

• Maximum acceleration time: 255 seconds (two drives of 180 + 75)
• Range without ballistic phase: 33.8 light-seconds (10.14 million km)
• Final velocity: 84176 km/s

I was in doubt from the text whether 84176 km/s was the final velocity after two stages or after just the first. The text says: "<pronoun> could inject a ballistic phase at 180 seconds, [...] but velocity at that point would only be 84,176 KPS."

Only one of two interpretations is physically possible. If that velocity is at 180s at the end of the first drive, the first drive accelerates at 84176 / 180 ≅ 467.6 km/s² or 47686 gravities, which is a decent acceleration for a missile. It would have crossed 7,575,840 km. But then if the missile does nothing and coasts for the next 75 seconds, it'll cover another 6,313,200 km. For it to cover only 2,564,160 km, it would need to have a negative acceleration.

The other interpretation is that the combined acceleration of both stages results in a speed of 84,176 km/s. This one results in a physically valid pair of acceleration numbers, but it's equally unlikely. 84,176 km/s is a decent Δv for a single stage; for two stages, it would mean that both stages are actually pretty poor, at around 30,000 gravities each.

I think the range here is the wrong number and I think I know where the math went wrong: David forgot to add the base velocity of the first stage when calculating the range. If instead we were to calculate the acceleration of the second stage from a standing start to cover the remaining 2.56 million km, it would have an acceleration of 911.7 km/s² or 93000 gravities. That's pretty much the acceleration of everyone's stage in high-power mode for 60 seconds. They've managed to extend it to 75 (though I expect the Manticoran Mk14 ERM can do 90).

If I'm right, the correct calculation would be that the missile covers nearly 8.9 million km during the second stage's powered phase, making the missile have a full range without ballistic phase of nearly 16.5 million km. Or 54.9 light-seconds.

Or did I get my math wrong somewhere? I've corrected myself already half a dozen times...

ThinksMarkedly wrote:At 60% of To End in Fire, <person name redacted to avoid spoilers> provides us with the following performance numbers for the last flight of Cataphracts provided to the SLN:

• Maximum acceleration time: 255 seconds (two drives of 180 + 75)
• Range without ballistic phase: 33.8 light-seconds (10.14 million km)
• Final velocity: 84176 km/s

I was in doubt from the text whether 84176 km/s was the final velocity after two stages or after just the first. The text says: "<pronoun> could inject a ballistic phase at 180 seconds, [...] but velocity at that point would only be 84,176 KPS."

Only one of two interpretations is physically possible. If that velocity is at 180s at the end of the first drive, the first drive accelerates at 84176 / 180 ≅ 467.6 km/s² or 47686 gravities, which is a decent acceleration for a missile. It would have crossed 7,575,840 km. But then if the missile does nothing and coasts for the next 75 seconds, it'll cover another 6,313,200 km. For it to cover only 2,564,160 km, it would need to have a negative acceleration.

The other interpretation is that the combined acceleration of both stages results in a speed of 84,176 km/s. This one results in a physically valid pair of acceleration numbers, but it's equally unlikely. 84,176 km/s is a decent Δv for a single stage; for two stages, it would mean that both stages are actually pretty poor, at around 30,000 gravities each.

I think the range here is the wrong number and I think I know where the math went wrong: David forgot to add the base velocity of the first stage when calculating the range. If instead we were to calculate the acceleration of the second stage from a standing start to cover the remaining 2.56 million km, it would have an acceleration of 911.7 km/s² or 93000 gravities. That's pretty much the acceleration of everyone's stage in high-power mode for 60 seconds. They've managed to extend it to 75 (though I expect the Manticoran Mk14 ERM can do 90).

If I'm right, the correct calculation would be that the missile covers nearly 8.9 million km during the second stage's powered phase, making the missile have a full range without ballistic phase of nearly 16.5 million km. Or 54.9 light-seconds.

Or did I get my math wrong somewhere? I've corrected myself already half a dozen times...

I haven't read To End in Fire yet, but those numbers seem closer to what we've seen before for just the 1st stage of the initial Cataphract.

Duckk told us, from the tech bible ages back (I'd have to dig to find the post) that "Cataphracts go 467 KPS^2 for 180 seconds, then 961 for 75” - that's the 1st gen ones (by UH they'd improved a vast amount). Translated into gees, that's 47,653 g and 98,061 g. (Though I'd have to go back and reread UH because I thought those vastly improved Cataphracts were getting launched by SLN -- which seems like it might contradict what TEIF is saying about how capable their Cataphracts were)

The numbers for the initial Cataphracts give a range and burnout velocity from rest, after 225 seconds, of 16.5 million km and 156,135 KPS. (Burnout of the 1st stage is at 7.5 million km and 84,060 KPS)

So reading your quote, and crunching numbers, I think that velocity is just for the 1st stage, during its ballistic coast. BTW you did make a math mistake converting KPS^2 into gees; 467.6 km/s² is 47,719 gees (not 47686). (I noticed because my missile accel spreadsheet works in gees; and the 1st stage terminal velocity didn't come out right when using your lower number; but when I worked out the right number and converted back to KPS^2 it matched your calc there)

That's a slightly better acceleration (0.14%) on the first stage than the initial cataphracts Duckk quoted.

But if the 2nd stage, from rest, only covers 2,564,160 km; then it's got a worse acceleration than Duckk quoted. And I basically matched your numbers for 911.7 km/s² or 93000 gravities (give or take a little rounding on the gees); which is 5.41% worse than the initial Cataphracts.

I guess arguably the SLN might have been given plans for a somewhat downrated "export" version. (And we know those initial Cataphract's first stages were using a SLN Javelin missile's drive and performance, so it wouldn't make sense to downrate those; any fudging would need to be in the 2nd stage) However we also know that Filareta brought improved cataphracts in Raging Justice; and again the ones we saw during UH were significantly better than even though (though the snipped I pasted into my spreadsheet mentions them being bigger; with now only 6 per pod)

But either way it appears that the range value did get messed up in this book. And I concur that forgetting to include the base velocity imparted by the 1st stage seems a very plausible scenario for such a mistake.

ThinksMarkedly wrote:At 60% of To End in Fire, <person name redacted to avoid spoilers> provides us with the following performance numbers for the last flight of Cataphracts provided to the SLN:

• Maximum acceleration time: 255 seconds (two drives of 180 + 75)
• Range without ballistic phase: 33.8 light-seconds (10.14 million km)
• Final velocity: 84176 km/s

I was in doubt from the text whether 84176 km/s was the final velocity after two stages or after just the first. The text says: "<pronoun> could inject a ballistic phase at 180 seconds, [...] but velocity at that point would only be 84,176 KPS."

Only one of two interpretations is physically possible. If that velocity is at 180s at the end of the first drive, the first drive accelerates at 84176 / 180 ≅ 467.6 km/s² or 47686 gravities, which is a decent acceleration for a missile. It would have crossed 7,575,840 km. But then if the missile does nothing and coasts for the next 75 seconds, it'll cover another 6,313,200 km. For it to cover only 2,564,160 km, it would need to have a negative acceleration.

(SNIP)

ThinksMarkedly wrote:Or did I get my math wrong somewhere? I've corrected myself already half a dozen times...

If it is coasting for 75 seconds, then the missile has a ballistic phase. The 10.14 million Kilometer range is without a ballistic phase.

Jonathan_S wrote:So reading your quote, and crunching numbers, I think that velocity is just for the 1st stage, during its ballistic coast. BTW you did make a math mistake converting KPS^2 into gees; 467.6 km/s² is 47,719 gees (not 47686). (I noticed because my missile accel spreadsheet works in gees; and the 1st stage terminal velocity didn't come out right when using your lower number; but when I worked out the right number and converted back to KPS^2 it matched your calc there)

I am not sure of all the math, but I am of that one. The reason for the discrepancy is because I used the non-rounded number I had in my calculator. 467.6 is rounded down from 467.6444444444444 km/s².

But if the 2nd stage, from rest, only covers 2,564,160 km; then it's got a worse acceleration than Duckk quoted. And I basically matched your numbers for 911.7 km/s² or 93000 gravities (give or take a little rounding on the gees); which is 5.41% worse than the initial Cataphracts.

Well, the point of a second stage is that it isn't used from rest. It's used after the first stage has accelerated to 84176 km/s. So the number 2.56 million km is completely irrelevant.

I guess arguably the SLN might have been given plans for a somewhat downrated "export" version. (And we know those initial Cataphract's first stages were using a SLN Javelin missile's drive and performance, so it wouldn't make sense to downrate those; any fudging would need to be in the 2nd stage) However we also know that Filareta brought improved cataphracts in Raging Justice; and again the ones we saw during UH were significantly better than even though (though the snipped I pasted into my spreadsheet mentions them being bigger; with now only 6 per pod)

But either way it appears that the range value did get messed up in this book. And I concur that forgetting to include the base velocity imparted by the 1st stage seems a very plausible scenario for such a mistake.

There's not much indication that the SLN had received "export" versions. If nothing else, at the time, the Alignment had realised that holding back would have backfired, so it doesn't look they did. They kept on doing improvements.

So it's likely they had more in the pipeline that went undeployed by the end of the war.

Robert_A_Woodward wrote:If it is coasting for 75 seconds, then the missile has a ballistic phase. The 10.14 million Kilometer range is without a ballistic phase.

That's not what I meant. I meant that if the first stage of roughly 47500 gravities accelerated for 180 seconds and the second stage of 75 seconds accelerated at 0 gravities, it would have a greater range than 10.14 million km. ANY acceleration would give it even more. The only way to get to 10.14 is if the acceleration were negative, which is pointless.

TBH, this person made another questionable decision in the simulator just after this. They had the Mk23 RMN missiles use up all three stages to accelerate to about 80% the speed of light, and then coast to attack the target. I thought one wouldn't do that because, despite arriving at very high speed and superb ECM, they'd have almost no ability to evade, so they'd be easy pickings. One would question this person's skills because of that, but the credentials presented put actually into question what we don't know.

But the 33.4 light-second range makes no sense.

Pretty much ALL the numbers are wrong. Or... Senior moment, Or, GA better surrender.

Distance 20Mkm -a 1.6Mkm ballistic phase in ... 150s...

IF you punch in 173,000 number for acceleration at 150s you get ~19Mkm... which matches some numbers as written.

RFC had a massive senior moment, as it appears he punched in end velocity as his acceleration and then achieved RANGE???

*******EDIT: Doh, should have figured this out already... The number is NOT 150s but rather it is SUPPOSED to be 250s.

180s @48,000g
25-->30s Ballistic phase (Actually just did calc and it requires 19s for 1.6Mkm ballistic, but now is only 18Mkm... So, WTH? I give up)
75s@96,000g

His end velocity of 173,000 km/s is still baloney but...

******* End EDIT I'll leave the rest for everyone humor to read... Hrmm talking of senior moment, should have figured typo first.

150s @92,000g's = 10.1Mkm...
THIS lines up with his 10.1Mkm earlier in book which is CLEARLY wrong but how,.... good question Or, MALIGN have missiles 2X greater acceleration than the GA in same size...

GA better surrender if MALIGN ever get ships built.

Or, his ~19Mkm = 180s @69,000g and 60s@69,000g ... Of course last we checked Cataphracts were supposed to have a slower first stage... and a 75s 2nd stage...

As Cataphracts??? Which version??? are supposed to have 180s@48,000g and 75s@69,000g??? for ~16Mkm range. If 92,000g 2nd stage only increases range by ~0.7Mkm or so... Requires 173,000g 2nd stage for 75s to hit 18.7Mkm and then if there was a 1.6Mkm ballistic phase gets it out to 20Mkm as stated in book???... None of it makes any sense.

Which also does not make sense as gargantuan Hasta missiles are flying along at 700kps(69,000g) as well so...

Mass/Acceleration scaling seems to not exist as a problem for MALIGN missiles. Nor energy density for nuclear weapons/Capacitors as we have 3SECOND graser fire. Lets state that again... 3 SECOND Graser fire from capacitors in missile bodies when the best 2000 year advanced NUCLEAR 50Gt warheads produce weaker X-ray lasers for only 0.005s. Its "ONLY" 600X longer duration + massively increased throughput...

I don't know. I give up. None of the numbers make any sense. At this point I just want the last book and ignore the physics as it has left the rails.

Relax wrote:RFC had a massive senior moment, as it appears he punched in end velocity as his acceleration and then achieved RANGE???

Well, to be fair, I think I know what term in the equation of motion he forgot because I had made the same mistake before. From High School, we know that:

ΔS = v₀t + at²/2

For the first stage, v₀ = 0, so the equation reduces to the acceleration component. We didn't know the acceleration for sure, so I used the other equation which said that

Δv = at

That gave us a = 84176 / 180 = 467.64444 km/s². Plugging back into the other equation gives us the distance travelled of 7.56 million km.

The mistake was calculating the range of the second stage, because v₀ is not zero. The difference is 84176*75 = 6.3 million km.

ThinksMarkedly wrote:
That gave us a = 84176 / 180 = 467.64444 km/s². Plugging back into the other equation gives us the distance travelled of 7.56 million km.

The mistake was calculating the range of the second stage, because v₀ is not zero. The difference is 84176*75 = 6.3 million km.

We are talking apples/oranges here. He had SEVERAL senior moments when writing this book regarding missiles. I was specifically addressing the missiles at end of book which I thought was obvious from the 150s and 19Mkm numbers being used. The 10.1Mkm is just um yea...

Relax wrote:We are talking apples/oranges here. He had SEVERAL senior moments when writing this book regarding missiles. I was specifically addressing the missiles at end of book which I thought was obvious from the 150s and 19Mkm numbers being used. The 10.1Mkm is just um yea...

I'm still trying to wrap my bacon around the sudden accel jump of the SLN capital single drive missile to from 48K Gs to 86K Gs for LONG term endurance (then also as the first stage of the latest Cataphract) in UH - interesting that we did not see that here.

Theemile wrote:I'm still trying to wrap my bacon around the sudden accel jump of the SLN capital single drive missile to from 48K Gs to 86K Gs for LONG term endurance (then also as the first stage of the latest Cataphract) in UH - interesting that we did not see that here.

I haven't reached the end of the book yet, so I don't know any numbers other than those I posted above.

93000 G for 75 seconds is nothing revolutionary. We know the RMN missiles of the turn of the century could do that for 60 seconds. Extending to 75 is interesting, but the RMN had already extended the Mk14 ERM to 90 seconds. I don't think this was explicit because no one fires missiles in the high-power setting, but the Mk14 low-power setting is 270 seconds, 150% of the regular 180 s. With the same 1:3 ratio, that would make the Mk14's high power setting 90 seconds.

270 seconds is the flight time in Hypatia. From a standing start, 270 s @ 46000 gravities covers 16.44 million km. And we know from the text that that's about the engagement range, because the Cataphracts could reach them in turn. And I think the 270-second ERM time was established elsewhere too, but even if it's just 240 seconds (4 min), it's still better than 3 x 75s.

Now, the question is why the Cataphract doesn't run the second stage ERM in low-power mode. I think the answer is obvious: it can't, because otherwise they would be using it. Not only that, if they had a stage that could run 225 seconds at 47500 gravities instead of 180, they'd also be using that.