Newtonian or relativistic equations of motion

Does anyone know whether the Honorverse books take Special Relativity into account when calculating the motion of ships and missiles? I've noticed a couple of places where the Newtonian equations for uniformly accelerated motion give results that seem inconsistent with the narrative. Since the terminal velocity of missiles, especially multi-drive missiles, are large fractions of the speed of light I'm wondering whether relativistic calculations are being used.

Also, what values are used for the speed of light and standard gravity? I've been using the textbook values of
Standard gravity = 9.80665 metres per second squared
Speed of light = 299792458 metres per second
in my calculations.

Expanding on my question, the performance figures specified for the proposed multi-drive missile in Chapter 2 of In Enemy Hands appear to have been calculated using Newtonian mechanics, i.e.
range from rest = 0.5 * acceleration * (time of flight) ^ 2
and
terminal velocity from rest = acceleration * (time of flight).
However, the figures in the text for the Manticoran MDMs used at the Battle of Barnett and the Battle of Manticore show slightly lower performance than I'd expect based on these equations.

Ashes of Victory
Chapter 35

"Agreed. Agreed." White Haven rubbed his chin some more. The final—or currently "final"—version of the long-range missiles could reach 96,000 gravities of acceleration, four thousand more than the ones Alice Truman had deployed at Basilisk. That gave them a powered attack range from rest of almost fifty-one light-seconds at maximum acceleration. By stepping the drives down to 48,000 g, endurance could be tripled, however, and that upped the maximum powered envelope to well over three and a half light-minutes and a terminal velocity of .83 c. That was crowding the very limits of the fire control technology available even to the Royal Manticoran Navy, however.

I couldn't find an explicit statement of the maximum flight time at half power for the MDMs used at Barnett so I assumed it would be three times that of a single drive missile, i.e. 540 seconds. In that case terminal velocity would be nearly 0.85c. It's a small discrepancy and could easily be a typo but ...

At All Costs
Chapter 65

Although Tourville's command was still almost half an hour from its turnover point for a zero/zero intercept of Sphinx, the range between the opposing forces had fallen to just a shade over 84,000,000 kilometers, and their closing speed was up to 45,569 KPS. That geometry gave Tourville's MDMs an effective range of better than 85,369,000 kilometers, which, as Frazier Adamson had just observed, meant they were in extreme missile range of Home Fleet.

But Manticoran MDMs' acceleration rate was just over thirty-four KPS2 higher than his birds could pull. That gave them a current effective range of better than 90,370,000 kilometers, which meant he'd been in their effective range for over two minutes.

Assuming that Tourville is assuming that Manticoran MDMs have an acceleration of 48,000 gravities (that would be consistent with the Battle of Barnett) my calculations give a maximum powered flight time for the MDMs of just under 530.4 seconds. Taking the value of 530.4 seconds and calculating the terminal velocity from rest for an MDM I get 0.83c, which is the value given in Ashes of Victory.

So there are three possibilities:-
1) I've made a mistake somewhere in my calculations.
2) Manticoran MDMs in production have a maximum flight time at half power of approximately 530 seconds and I'm mistaken in my assumption that it should be 540 seconds. (In this case, where are the definitive performance figures given? House of Steel?)
3) Non-Newtonian mechanics are being used.

Since missiles with four drive stages are in the pipeline near the start of Storm from the Shadows it seems that relativistic mechanics are required. The terminal velocity from rest for the Mark 23-D, assuming an acceleration of 48,000 gravities and a drive endurance of 720 seconds, would be 1.13c using the Newtonian equation.

Storm From the Shadows
Chapter 12

"This is the system-defense variant, the Mark 23-D, for the moment, although it's probably going to end up redesignated the Mark 25. It's basically an elongated Mark 23 to accommodate both a fourth impeller drive and longer lasing rods with more powerful grav focusing to push the directed yield still higher. Aside from the grav units and laser rods, this is all off-the-shelf hardware, so production shouldn't be a problem, although at the moment the ship-launched system has priority.

If it is the case that non-Newtonian equations are being used are the actual equations given anywhere? I've only got as far as Mission of Honor in the series so it's possible that the answers to my questions appear in a later book when Mark 23-D / Mark 25 missiles get fired in anger.

Good questions that I have touched on previously. I know that relativistic effects are mentioned, in that crew are a little younger than their chronological ages.
I started discussion on how at extremes tau factors could add greatly to the kinetic energy of missiles, but most don't discuss it.

I don't think David bothers too much with the effects of relativity. He certainly didn't through he first 4 books. But Bu9 includes people who could do the analysis for him and they may do it.

I believe it was a a book signing a while back where he said he had to ignore things like the increasing energy required for acceleration to allow missiles to get the velocities they do.

ericth wrote:I believe it was a a book signing a while back where he said he had to ignore things like the increasing energy required for acceleration to allow missiles to get the velocities they do.

Bingo. Not a snowball's chance in hell.

kzt wrote:I don't think David bothers too much with the effects of relativity. He certainly didn't through he first 4 books. But Bu9 includes people who could do the analysis for him and they may do it.

The figures given in In Enemy Hands, the seventh book, seem to be ignoring relativity. I'd been wondering whether in later books, once MDMs are being used in combat, that some sort of relativistic correction was applied. For example with the closing speed mentioned in the Battle of Manticore the effective terminal velocity for the MDMs would be 0.99988c without relativistic effects.

ericth wrote:I believe it was a a book signing a while back where he said he had to ignore things like the increasing energy required for acceleration to allow missiles to get the velocities they do.

Do you recall how long ago that book signing was?

Since it seems likely that Newtonian mechanics are used in all the books does anyone know if definitive performance figures are given for the missiles used at the Battles of Barnett and Manticore? I've checked the figures for the Havenite missiles and they also seem to have a maximum flight time at half power of roughly 530 seconds.

pi_r_squared wrote:Does anyone know whether the Honorverse books take Special Relativity into account when calculating the motion of ships and missiles? I've noticed a couple of places where the Newtonian equations for uniformly accelerated motion give results that seem inconsistent with the narrative. Since the terminal velocity of missiles, especially multi-drive missiles, are large fractions of the speed of light I'm wondering whether relativistic calculations are being used.

Also, what values are used for the speed of light and standard gravity? I've been using the textbook values of
Standard gravity = 9.80665 metres per second squared
Speed of light = 299792458 metres per second
in my calculations.

David seems to use 9.8 m/s^2 for gravity; though he (or his characters) round off for readability - so a ship accelerating at 504 gees would probably be said to accelerate at 4.9 KPS squared rather that 4.9392.

I did a lot of looking at missile performance a while back (see the thread Missile Spreadsheets) and they always seemed to follow newtonian acceleration. (Though a few times David got gees and KPS^2 mixed up; and there were a few where ship motion might have gotten added in incorrectly)


To the little I've looked at is ships seem to be the same. Sure, he'll look up the time dilation factor to throw in the odd statement about ship time passing slower, but relativity doesn't seem to impact acceleration time in the Honorverse. (Though possibly he could ret con that by having that be a magic property of impeller wedges and sails - with other kinds of propulsion having to follow the rules).
I'm interested to see how he'll handle the 'top speed' of the 4 stage system defense MDMs. Even from rest, using Newtonian acceleration, their straight line max velocity exceeds c. My bet is on a fiat top speed of at or just over 0.9c (shielding or some such excuse). That's compatible with the early book discussion about frac-c bombardment but avoids the problem of an impossible top speed or flight time.

Jonathan_S wrote:<snip>

I did a lot of looking at missile performance a while back (see the thread Missile Spreadsheets) and they always seemed to follow newtonian acceleration. (Though a few times David got gees and KPS^2 mixed up; and there were a few where ship motion might have gotten added in incorrectly)

Thank you for the link to the thread on missile spreadsheets. I've been working on my own missile spreadsheet over the last couple of days. The Battle of Barnett was the first inconsistent value I came across but I've found several more since and I'm starting to think that it's a coincidence that an endurance of 530 seconds solves the inconsistent values for the Battles of Barnett and Manticore.

Jonathan_S wrote:<snip>

I'm interested to see how he'll handle the 'top speed' of the 4 stage system defense MDMs. Even from rest, using Newtonian acceleration, their straight line max velocity exceeds c. My bet is on a fiat top speed of at or just over 0.9c (shielding or some such excuse). That's compatible with the early book discussion about frac-c bombardment but avoids the problem of an impossible top speed or flight time.

A limit imposed by the missiles' particle screens is certainly a neat way to dodge the problem. The limit would need to be considerably more than 0.9c though or it would invalidate Tourville's projected figures at the Battle of Manticore. Depending on exactly how the limit worked tactical officers might need to dial down the acceleration of an MDM below the standard half power setting so that the missile arrives at the target while still under power without exceeding the capability of its particle screen.