On MDM Flight Profiles

[Edit: RFC later said here that "Unfortunately, because of the nature of the "splitter plate" technology used in the current generation MDM, you can't set different acceleration rates on the sequenced drive nodes." so this whole post is moot for the moment.]

As a follow up to my earlier analysis of the Mk16 DDM flight profiles: On DDM Flight Profiles I crunched the numbers on 3 drive MDMs and found a surprising outcome.




And to make the differences more visible here is it plotted on a logrithmic x-axis


Up to 17 million km the fastest profile is all 3 drives at full power (92,000 gees for 60 seconds each), with a coast phase if necessary before the final drive.

Then up to 41 million km the fastest profile is keeping the first 2 drives at full power, but stepping the final drive down to half (low) power.

But then, surprisingly, all the way out to 70 million km the best profile is High-Low-Low (first drive at 92,000 gees for 60 seconds and the next 2 at 46,000 gees for 180 second each). Even though you have to add a ballistic phase (at ~17 million km) to get powered terminal attacks beyond 50 million km the extra velocity going into your coast still wins the race.
At 50 million km HLL is 52.4 seconds sooner than LLL, and 35.2 seconds faster than LHL (2nd best profile)
At 55 million km HLL is still 39.3 seconds ahead of LLL
At 60 million km HLL is 24.3 seconds ahead of LLL
At 65 million km HLL is 8.4 seconds ahead of LLL
And at 70 million km HLL is 0.8 seconds ahead of LLL

It's not until 71 million km (6 million beyond max powered range) than the LLL flight profile finally edges out the HLL one!

The books always seem to describe using the Low-Low-Low (all 3 drives at 46,000 gees for 180s each) even though number crunching shows that's not actually the fastest time to target at common battle ranges...

Because I was calculating for minimum time to target I always put the ballistic segment after the 2nd drive burnout (to give the highest coasting velocity). But it's not impossible that a tactical situation would cause a commander to take a much longer flight time in order to have both 2nd and 3rd drives available for terminal maneuvering.

Hmm. I didn't look at combinations, but a while back I came up with these:

[Duration] @ [accel] gives: [powered range], [final speed], [time till burnout]
1 * 1 min @ 96k gee: __1.7 e9m, __56 e6m/s (0.19 c),_ 1.0 min
2 * 1 min @ 96k gee: __6.9 e9m, _108 e6m/s (0.36 c),_ 2.0 min
3 * 1 min @ 96k gee: _15.7 e9m, _153 e6m/s (0.51 c),_ 3.2 min
4 * 1 min @ 96k gee: _28.4 e9m, _191 e6m/s (0.64 c),_ 4.4 min

1 * 3 min @ 46k gee: __7.35 e9m, __79 e6m/s (0.26 c), __3.0 min
2 * 3 min @ 46k gee: _30.0_ e9m, _148 e6m/s (0.49 c), __6.3 min
3 * 3 min @ 46k gee: _69.5_ e9m, _201 e6m/s (0.67 c), _10.0 min
4 * 3 min @ 46k gee: 129.__ e9m, _238 e6m/s (0.79 c), _14.5 min

Using those, I looked at a few long ranges (with the ballistic phase before the last drive):

Shooting at a target 30 e9m away,
the 2DM (46kgee) takes 6.3 min,
the 3DM (96kgee) takes 5.4 min (ballistic: 2.2 min),
the 4DM (96kgee) takes 4.6 min (ballistic: 0.2 min).

Shooting at a target 70 e9m away,
the 2DM (46kgee) takes 14.7 min (ballistic: 8.4 min),
the 3DM (46kgee) takes 10.1 min (ballistic: 0.1 min),
the 4DM (96kgee) takes 8.9 min (ballistic: 4.5 min).

Shooting at a target 150 e9m away,
the 2DM (46kgee) takes 31.6 min (ballistic: 25.3 min),
the 3DM (46kgee) takes 19.1 min (ballistic: 9.1 min),
the 4DM (46kgee) takes 16.2 min (ballistic: 1.7 min).

The third drive gives a significant improvement, but the hypothetical 4th adds surprisingly little (since the missile is already pushing up against lightspeed).

Fourth stage would be more for endurance than speed as its already going about as fast as it can.

Bill Woods wrote:Hmm. I didn't look at combinations, but a while back I came up with these:

[Duration] @ [accel] gives: [powered range], [final speed], [time till burnout]
1 * 1 min @ 96k gee: 1.7 e9m, 56 e6m/s (0.19 c), 1.0 min
2 * 1 min @ 96k gee: 6.9 e9m, 108 e6m/s (0.36 c), 2.0 min
3 * 1 min @ 96k gee: 15.7 e9m, 153 e6m/s (0.51 c), 3.2 min
4 * 1 min @ 96k gee: 28.4 e9m, 191 e6m/s (0.64 c), 4.4 min

1 * 3 min @ 46k gee: 7.35 e9m, 79 e6m/s (0.26 c), 3.0 min
2 * 3 min @ 46k gee: 30.0 e9m, 148 e6m/s (0.49 c), 6.3 min
3 * 3 min @ 46k gee: 69.5 e9m, 201 e6m/s (0.67 c), 10.0 min
4 * 3 min @ 46k gee: 129. e9m, 238 e6m/s (0.79 c), 14.5 min

Using those, I looked at a few long ranges (with the ballistic phase before the last drive):

Shooting at a target 30 e9m away,
the 2DM (46kgee) takes 6.3 min,
the 3DM (96kgee) takes 5.4 min (ballistic: 2.2 min),
the 4DM (96kgee) takes 4.6 min (ballistic: 0.2 min).

Shooting at a target 70 e9m away,
the 2DM (46kgee) takes 14.7 min (ballistic: 8.4 min),
the 3DM (46kgee) takes 10.1 min (ballistic: 0.1 min),
the 4DM (96kgee) takes 8.9 min (ballistic: 4.5 min).

Shooting at a target 150 e9m away,
the 2DM (46kgee) takes 31.6 min (ballistic: 25.3 min),
the 3DM (46kgee) takes 19.1 min (ballistic: 9.1 min),
the 4DM (46kgee) takes 16.2 min (ballistic: 1.7 min).

The third drive gives a significant improvement, but the hypothetical 4th adds surprisingly little (since the missile is already pushing up against lightspeed).

Looks like you did the hard work of factoring in relativity.

Except that for whatever reason (and keeping the math simple for author and readers isn't an insignificant possible reason) wedges seem to ignore the mass increase and consequent reduction in acceleration caused by approaching the speed of light).

If you compare the numbers in the books you see things like a 3 drive MDM at half power (46,000 gees) has a burnout range of 65 million km at 0.8 c. (or if it's exactly 46,000 gees I get 65,726,640 km and 0.812c) which is what Newton would calculate.

Which actually gives you the insane answer than the new 4 drive system defense MDMs, with their CM derived final drive, have a top speed in excess of light.
So, as I believe I mentioned before, I'm betting RFC ends up declaring a hard limit around 0.99 c


That would seem to match with the apparently artificial limit described in FiE; "if the Peeps launched at .8 c, their birds' drives would boost them to .99 c before burnout." That math doesn't work for cleanly for either Newtonian (3 minutes at 46,000 gees would put them in past c) or relativistic (takes like 26 minutes at 46,000 gees to boost from .8c to .99c vastly longer than the 180 second drive lifetime) acceleration calculations; hence apparently artificial velocity limit.

Jonathan_S wrote:Looks like you did the hard work of factoring in relativity.

Not hard actually, once I'd set up a spreadsheet as a calculator, using the appropriate formulas.
viewtopic.php?f=1&t=7150&hilit=cheatsheet&start=32

Except that for whatever reason (and keeping the math simple for author and readers isn't an insignificant possible reason) wedges seem to ignore the mass increase and consequent reduction in acceleration caused by approaching the speed of light).
[snip]
Which actually gives you the insane answer than the new 4 drive system defense MDMs, with their CM derived final drive, have a top speed in excess of light.

Which is why I prefer the 'unreliable narrator hypothesis'.

Fourth stage, Kaid, would really only be good for use during terminal maneuvers. Not endurance. With no forces acting against the missile, once it was up to near relativistic speeds it would continue to coast along at them.

kaid wrote:Fourth stage would be more for endurance than speed as its already going about as fast as it can.

And for maneuverability. Ballistic components give ships a chance for evasive maneuvers -- by happenstance or design.

cthia wrote:

kaid wrote:Fourth stage would be more for endurance than speed as its already going about as fast as it can.

And for maneuverability. Ballistic components give ships a chance for evasive maneuvers -- by happenstance or design.

Though the first missiles this really matters for are the 4-drive Apollo + Mycroft controlled system defense missiles.

Without Mycroft relays you just can't control a useful number of missiles at long enough range that the enemy can get out of the 7.3 million km lateral range of the 3rd drive if you do a dual drive burn + coast.

We're told that 8 lm (~ 144 million km) is beyond the range of (non-relayed) Apollo FTL fire control - and way beyond the effective range of lightspeed fire control.

A 3 drive MDM can get to 144 million km in 17.1 minutes . In that time even at 600 gees a ship can only alter it's trajectory by a maximum of 3 million km. So at ranges within the control limits of pre-Mycroft missiles ships weren't able to outrun the target basket of even the 3rd stage.

But with the system spanning ranges possibly once Mycroft can relay your FLT control links you can have much, much, longer flight times. For those having that 4th stage for terminal maneuvering helps a lot. I'm assuming the CM derived drive has the same 75 second endurance of the Mk31/Viper in which case it has 2.5 million km of lateral range. Even ignoring the 4th drive just being able to use the 3rd drive to add base velocity before your coast would cut the time to 144 million km by almost 3 minutes.
Or for much longer flights you could potenitally boost with the first 2 and use the final 2 drives for terminal maneuvering. You'd only be coasting across the system at only 2/3rds the speed, but your lateral engagement range at end of run would go up from 2.5 million to 15.9 million km!

With Mycroft factored in, and a system wide deployment of system defense pods, you're really looking at an impossible engagement for attackers.

Mycroft spins up the moment you enter the system, then fires from well outside your sensor envelope. Say from the other side of the system even. Missiles accelerate on their first two stages then go ballistic. The whole time Mycroft is using the FTL system to keep an updated plot running and updating the missiles.

These missiles are coming in ballistic on the attacking force. Even if the enemy is running hot, with all defenses constantly running, they're sitting ducks. Missiles without wedges up are very hard to track. These missiles are coming in very quickly and you never even knew they were on their way. At the last possible moment your defenses might pick them up, but at the same time their third or fourth stage is going active, providing final maneuvers and terminal run power.

Fireflair wrote:With Mycroft factored in, and a system wide deployment of system defense pods, you're really looking at an impossible engagement for attackers.

Mycroft spins up the moment you enter the system, then fires from well outside your sensor envelope. Say from the other side of the system even. Missiles accelerate on their first two stages then go ballistic. The whole time Mycroft is using the FTL system to keep an updated plot running and updating the missiles.

These missiles are coming in ballistic on the attacking force. Even if the enemy is running hot, with all defenses constantly running, they're sitting ducks. Missiles without wedges up are very hard to track. These missiles are coming in very quickly and you never even knew they were on their way. At the last possible moment your defenses might pick them up, but at the same time their third or fourth stage is going active, providing final maneuvers and terminal run power.

You can spot a missile wedge way the hell out. It's a huge beacon. And even Apollo has a maximum effective range.