Three-stage vs. two stage multidrive missiles

Relax wrote:

SWM wrote:Let's try this one more time, Relax.

Attacker fires 2 missiles, a DDM (A) and an MDM (B). Let us say that each drive lasts 60 seconds.

At time T=60, drive 1 shuts down. Drive 2 on missile B ignites. At that moment, the enemy knows exactly where missile A will be at time T=120, what it's velocity will be, and what it's maneuvering options will be. But the enemy has no idea at all where missile B will be. They have a 60 second head-start on calculating how to defend against missile A!

Pause: You aren't saying said DDM goes in completely ballistic on final are you I certainly never was putting that forth. I was saying use, single drive, ballistic, final drive... Are you putting forth, drive, drive, ballistic for DDM??? I don't think you are, but if you are... then stop reading as we are talking apples, grape fruits, and space monkies.

The calculation for where each missile is and coordinates given to the missiles in question are identical. Velocity is immaterial to the calculation other than when to launch your CM's. The velocity portion should be the easiest to nail down. Especially with forward deployed RD as you know initial velocity and drive duration. It is a 2d problem. Accelerations are fixed for both CM and DDM/MDM. Both are predictive homing solutions. Velocity as a driving factor defining intercept becomes insignificant as CM launch time is on an integer scale measured in 8-10-12s for RMN ships, and who knows how long for the rest of the galaxy. An end point error of a second or more would not be uncommon and frankly would be immaterial as long as you do not launch the CM too soon. As soon as the CM is launched a 2d problem ensues. Straight up homing solution.

The "calculation" requires, 0.00000000000001s to compute even on a hand calculator. Ok, 0.0001s.

Now the error bars for the vector of a ballistic missile could be quite high compared to a constant burning MDM. So, the Ballistic missile will actually be harder to hit. Why? I would postulate the defenders guesstimated vector error of an incoming DDM/MDM at 30Mkm is far greater than that at 10Mkm. Of course it is actually useless information. Why? You know the flight profile for ALL missiles assuming they actually are going to fire on your ships. The defender knows their end point. Just throw out accumulated error possibilities that do not intercept the defending ship.

Anyways, way away from the original post of the thread.

Minutia

No, I'm not talking about having the ballistic phase at the end. I'm talking about boost, ballistic, boost.

And I'm not talking about the calculations the defenders make during the missile's final approach.

I'm talking about the predictive calculations that are made while the missile is further out. I.e. the missile has this position and vector at this moment in time; this is the probability cloud of the missile's position in 10 seconds, in 30 seconds, in 60 seconds when it is will be on final approach. If it comes in from this portion of the probability cloud, this is best allocation of counter-missiles and PDLCs, but if it comes in from that portion of the probability cloud, that is the best allocation of point defense.

This kind of predictive analysis based on probable future location of missiles takes a lot more calculation than you have assumed, especially if you are tracking tens of thousands of missiles. Being able to set up multiple options for point defense well in advance, based on predictions of future missile positions, makes it easier to select the best defense when you know the actual final approach vector. Having a ballistic phase from T=60 to T=120 gives the enemy 60 seconds to calculate the probability fields (and possible defensive strategies) based on where you KNOW the missile will be at T=120.

To start with, we said the same thing but with vastly different emphasis. Here is an additional emphasis that engineers deal with on a daily basis, but theoretical guys do not.

What is easier to track and meet with CM's at a greater probability; one missile or 100 missiles going ballistic?

Why?

Hint, has to do with the error portion of the vector.

SWM wrote:

This kind of predictive analysis based on probable future location of missiles takes a lot more calculation than you have assumed, especially if you are tracking tens of thousands of missiles.

Actually it doesn't. It is actually Less than normal tracking.

Enjoy the puzzle.

PS. I threw in several assumptions in there... Shocker, I know.

Relax wrote:Actually it doesn't. It is actually Less than normal tracking.

So I would expect that this is because lots of solutions are valid with a large number of targets, vs one and only one solution for a single target?

If you actually need to kill every target this seems to be only a pretty minimal help.

kzt wrote:

Relax wrote:Actually it doesn't. It is actually Less than normal tracking.

So I would expect that this is because lots of solutions are valid with a large number of targets, vs one and only one solution for a single target?

If you actually need to kill every target this seems to be only a pretty minimal help.

Nope. Normal tracking, one is running a continuous update and homing signal to the CM's in question. When ballistic, said missiles are essentially "stealthed". Prediction is easy. It is a singular calculation. What happens when there are multiple predictions all arriving at the same point? In this case multiple errors.

GIGANTIC HINT: Think statistics

But Relax, I'm not talking about how each counter-missile tracks it's target once it is fired. I am talking about deciding how many counter-missiles to fire here and how many to fire there, which incoming missiles have priority, which missiles are more likely to threaten vulnerable parts of your fleet, which missiles need greater attention from tracking.

I'm talking about deciding how to allocate your limited point defenses resources before the attack missiles get close enough for you to fire those counter-missiles.

By the time the attack missiles are close enough to fire counter-missiles, you had better have already figured out how many counter-missiles you are going to fire at each bunch of incoming missiles, and how much attention your analysis computers are going to pay to each bunch of missiles, and where you are most likely to need your PDLCs pointing when the counter-missiles are done. You need to make predictions on probable paths well in advance of the final approach. A ballistic phase makes it easier to get preliminary predictions earlier.

SWM wrote:But Relax, I'm not talking about how each counter-missile tracks it's target once it is fired. I am talking about deciding how many counter-missiles to fire here and how many to fire there, which incoming missiles have priority, which missiles are more likely to threaten vulnerable parts of your fleet, which missiles need greater attention from tracking.

I'm talking about deciding how to allocate your limited point defenses resources before the attack missiles get close enough for you to fire those counter-missiles.

We are talking the exact same thing.

A picture is worth 1000 words. Really need a graphical interface for this discussion.

Lets back up. You never answered my question. If you had, you would have obtained your answer for allocation.

The answer to: What is easier to track a single ballistic missile with its inherent positional errors when it goes ballistic or 100 such missiles? Is: the 100 missiles.

As soon as you get more than 3 of something you get to apply statistics. In this case, the vector error bands of all those missiles. Their positional error get to be root sum squared vastly decreasing the actual error. Why? You know their destination(your ships(position and @time) and you know their initial vector. Thus you know your allocation.

This RSS'ing of the errors obtains a far higher cone of probability. Most all of those cones of probability will overlap each other. Outliers can be ignored or given a high priority for late firing CM's or more care for PDLC. Of course here I have to note this assumes PDLC require more than 0.1s to change targets across a vast arc of space which honestly I do not believe they do. But, since it would appear you do, it could be a consideration. Anyways, back to cone of probability overlap. This will create a very simple 2d scatter density map. Fire your CM's to the targeted density and let them hunt. That is the only solution.

The defender against ballistic missiles do not have a homing solution as you cannot track those DDM/MDM at 10-50Mkm without active wedges! Thus you home in on density probability. You know how many are in the swarm, so allocation becomes very simple. Density/total = allocation per unit "hunt area". In fact, cannot get anything off of an DDM/MDM outside CM range when ballistic. Therefore there is no more need to even bother to calculate anything at all. Besides in a situation like this there never would be any calculation at all. It would be nothing but a pre-calculated lookup table just as it is in every other computer application. That is what R&D is for, creating said look-up tables to simplify final software coding, decrease time required, with the end result of offloading workload on the missile defense and obtaining better reliability. In this case higher hit percentage and fewer CM's going after same target.

The only thing that could change is if the DDM/MDM light off their drive early allowing you to individually designate CM's for individual DDM/MDM. Different look up table. Otherwise you simply have to rely on the onboard sensors of the CM outside of 1-3Mkm or so depending on several variables discussed below and in previous posts. Inside this range the DDM/MDM will have to go active to achieve its desired attack point.

You have to know A) before you can decide B). True for ballistic or continuous drive. Active all the way in you have no idea what aspect they are fired on. None. Why I did the very simple math that apparently you REFUSED TO CONTEMPLATE upthread(AGAIN).

It requires all of 11s for a missile to change its orthogonal plane if one is willing to give missiles a change of heading of 30 degrees and its last drive on sprint mode. Reality is much less than the need for a complete change from one broadside aspect to its orthogonal aspect as that 11s requires 90 degrees, instead of the reality of 30-60 degrees if one is willing to trade an angled shot at the sidewall instead of perpendicular. IE shoot your missiles at the 45 degree point between the broadside and the top of the wedge.

If a ship rolls you do not have to maneuver at all. If ship stays steady, all you have to do is move 45 degrees down for a perpendicular shot on the sidewall. If a missile can change heading by 30 degrees, this requires a delta of a mere 20,000km if attack distance is 30,000km! Or 40,000km at a 60,000km attack range. Or 9s if using sprint drive on DDM @30,000km or 13s @60,000km. This activates at a mere 80,000km/s(9) 700,000km from the SHIP! No CM's are fired at all assuming said ship does not accelerate onto a different heading.

Look at it this way. RMN CM's have a 75s duration. Thus, must be fired 75s before 3.5-3.75Mkm is reached. DDM/MDM is traveling anywhere from 80,000km/s from rest on a single drive activation, to 160kkm/s if dual drive. 75s@80,000km/s = 3.5Mkm + 6Mkm = ~10Mkm to 15Mkm out for dual stage MDM. Now add initial velocity to the mix and 10-15Mkm becomes around 20Mkm. Is there really a difference in error band at 10Mkm-15Mkm and say 50Mkm? No. Why? RD's are strategically placed for accurate data for vectors of incoming missiles.

The obvious RD placement points are roughly 1Mkm to obtain task force information, ~8Mkm from the enemy for best vector resolution and lowest error when the first stage of a DDM/MDM goes down and the opposition could choose to go balistic, and finally several layers out from your own ships for CM envelope data. These exact placements for CM envelope change with the closing velocity and range of the two opposing task forces.

Anyways, theory, meet reality. RSS the errors; basic statistics. Same way every single engineer has been designing systems for the last 100 years in this imperfect universe.

is there an "over the top of my head" smiley?

Relax wrote:We are talking the exact same thing.

A picture is worth 1000 words. Really need a graphical interface for this discussion.

Lets back up. You never answered my question. If you had, you would have obtained your answer for allocation.

The answer to: What is easier to track a single ballistic missile with its inherent positional errors when it goes ballistic or 100 such missiles? Is: the 100 missiles.

As soon as you get more than 3 of something you get to apply statistics. In this case, the vector error bands of all those missiles. Their positional error get to be root sum squared vastly decreasing the actual error. Why? You know their destination(your ships(position and @time) and you know their initial vector. Thus you know your allocation.

I didn't try to answer your question the first time because I was already assuming that you can get nearly perfect measurements of their current positions, through measurements and statistics. I agree that statistics will let you do that. That doesn't help you with prediction.

What I'm talking about is predicting at T=60 seconds where the missiles will be at T=105 seconds (when you can fire your counter-missiles). If the attack missile is an MDM, you can only make a guess where the missile will be 45 seconds later. You can make probability estimates only, and calculate contingency allocations based on several options. On the other hand, if the attack missile is a DDM, you know EXACTLY where the missile will be at T=105 seconds; the second drive won't be starting until at least T=120. You don't need several options--you can immediately start calculating the optimal allocation of point defense.

I guess what you are saying is that it doesn't matter if the enemy can exactly predict 45 seconds in advance where to aim the counter-missiles?

SWM wrote:What I'm talking about is predicting at T=60 seconds where the missiles will be at T=105 seconds (when you can fire your counter-missiles). If the attack missile is an MDM, you can only make a guess where the missile will be 45 seconds later. You can make probability estimates only, and calculate contingency allocations based on several options. On the other hand, if the attack missile is a DDM, you know EXACTLY where the missile will be at T=105 seconds; the second drive won't be starting until at least T=120. You don't need several options--you can immediately start calculating the optimal allocation of point defense.

I guess what you are saying is that it doesn't matter if the enemy can exactly predict 45 seconds in advance where to aim the counter-missiles?

On the one hand, the MDM is under power and can manouver, so it can actively run a somewhat evasive routing - so I agree you can't predict exactly where it will be 45 seconds later. On the other hand it's getting steadily closer and you're getting a solid and improving look at it's wedge, so you can track it better.

The missile coming in ballistic is moving on a predicable path (assuming it can't cheat a little with reaction thrusters of some kind), so if you had its vector nailed perfectly when the drive went down you could predict its future location virtually indefinitely far into the future (until it brings it's drive back up)
But there are two sources of error in that prediction; one I already touched on, you can't know exactly when it'll bring the drive back online - if it does so sooner than you expect then it won't be at the predicted intercept point for your CM (however it'll be trackable again). The other is that when the drive cut out it was probably quite far away from you - you likely had some error bars around your lock on its vector. So the longer it coasts the less accurately you know where it is (The 95% confidence zone volume keeps growing because it might have aimed been a a degree or two to the left, right, up, or down of where you though it was pointing, or a fraction of a percent faster or slower.)