On 11 Jul 2016 at 19:26, Jonathan Clark wrote:

> It depends partially on the target. If this is something which can't
> change course "quickly" (see below) (e.g. a capital ship), then a
> computer can handle the targeting just fine. Of course, the target is
> likely to have defensive armour, and so on. OTOH, if the target (e.g.
> a missile) can "jink", (change course, direction, and acceleration)
> then it is likely to be doing so throughout its trajectory, and it
> won't have a lot of defensive armour. From now on I'm going to refer
> to such a target as a 'missile', but you can generalize the concept
> easily enough.

Alas, physics doesn't work that way.

In space, you have to use thrust to change course. No steeering by
aerodynamic forces like missiles in atmosphere.

The vector movement rules do a semi-reasonable simulation of that.

A few things to remember, direction of movement and orientation of
the ship/missile have *zero* connection.

My classic example is a ship moving at X due "north". It took Y
minutes at Z thrust to do get that vector. It wants to wind up moving
at X due "east".

Two ways to do it. Point the ship due "south" and thrust at Z for Y
minutes. That brings it to a stop. Then point due east and thrust at
Z for another Y minutes.

Second way. Point SE and thrust at Z for 1.4 time Y minutes.

Now consider that all motion is measured relative to some frame of
reference, and all non-accelerated frames of reference are equal.

This means that if you are tracking a target you can take the latest
vector you have for it, and figure things from a frame where it is at
rest.

This simplifies the problem *amazingly*.

Sensors work at lightspeed.  Let's use active radar or lidar as an
example. And a laser or other ligtspeed weapon.

So, if they cut thrust and coast. their position will be the same
(remember, our frame of reference their current vector).

If they accelerate in any direction at full thrust, their new
position will vbe on the surface of a sphere defined by the thrust
and twice the speed of light lag.

Say they are one light second away. and thrusting at 100 m/s^2. ( bit
over 10 gees)

It took one second for the radar pulse to get from them to you. It'll
take another second for the laser beam to get from you to them. For a
total of two seconds of lag.

D = 0.5 * A * T^2.

D = 0.5 * 100 * 2^2

D = 50 * 4

D = 200

So the target can have moved a *maximum* of 200 meters from the
position it would have had if it had coasted by the time the beam
gets there.

If it made multiple course changes during those 2 seconds it'll
actually be *closer* to the predicted position.

If the target was only half a light second away, it will be a max of
12.5 meters from the predicted position.

For slower weapons like missiles or guns, you've got the
speed-of-light time from the target to you, plus the travel time of
your weapon to the target. Which gives it a lot more time to dodge
and thus a *much* larger sphere of possible positions by the time
your weapon gets there.

The bottom line is that it's hard to *miss* with light speed weapons
at any sort reasonable range. Remember, a light second is 300,000 km.

It's also hard to *hit* with missiles at longer ranges, and darn near
impossible with "passive" kinetic kill weapons.

Missiles also have some fun issues for guidance. Since they have to
point in those "odd" to us directions to change course, you can't
have the tracking sensors in the nose. They have to be able to be
aimed at the target regardless of the direction the missile is
pointing.

Two over-simplifications in the above. First, I ignored the time
it'll take the target to rotate so the main drive points in the right
direction for the course change. That reduces the distance it can
move from the predicted position during the lag time.

Second, I ignored the time it takes from reception of the radar pulse
to firing the laser. Part of that will be lag time in computing the
predicted position of the target, and part of it will be the time it
takes to physically *aim* the laser. That increases the lag time, and
thus the possible distance the target could move from the predicted
(coasting) position.

> Such jinks would be driven by random-number generators, so the best
> that a computerized weapon could do would be to put 'a lot of ammo
> down-range', that is, to put a large amount of ammo through the
> target's "trajectory cone" (to coin a phrase) - the places that the
> target is likely to be when the ammo actually arrives.

Except, as noted, by picking the "right" frame, it's a sphere.

Believe me, it makes the problem *much* simpler to calculate.

> This can be
> done, but uses up a lot of ammo, and is, the way I play it, not likely
> to be successful. BTW this is basically how a point defence weapon
> works, even today. (Side note: if the missile is using a pseudo-random
> number generator and someone can steal or predict the number sequence,
> then you have a different situation. Yes, in RL this would be a lot
> harder, and I'm not getting into it here.)

Lasers as point defence are *nasty, because of the way the possible
location sphere shrinks so drasticaly as range decreases.

> "Quickly" of course depends on how far the source and target are away
> from each other, and their relative velocity vectors. If it takes ten
> light-seconds for the missile's position to reach the target, then by
> the time a laser pulse can arrive in response, the missile has had
> twenty seconds to jink, and it's probably doing this (again, IMTU),
> every second or so. That's a lot of potential variation in the
> missile's trajectory.

Except that 10 light seconds is *way* outside of combat range. That's
3 *million* kilometers.

> So how does Gunnery skill help? I hand-wave it as either a Luck-based
> skill, or perhaps a Psionic one. It gives someone with the skill a
> chance to sub-consciously predict *how* the missile will jink, that
> is, exactly what course changes will be triggered by the missile's
> random-number generator, over the next few iterations of this. The
> closer the missile is, the fewer iterations would be necessary to
> predict its co-ordinates, and vice versa. So the more skill levels in
> Gunnery you have, the more course changes you can 'predict' and/or the
> better you can predict them (again, this is all sub-conscious), so you
> end up with a higher probability of hitting that incoming missile, and
> being very popular with your ship-mates for doing so.

There's a sequnce in Heinlein's "Citizen of the Galaxy" that goes
into that quite well.

>      But not for Thorby -- not for those assigned to fire-control
>      computers. Sweating into their straps, for the next minutes or
>      hours the life of Sisu is in their hands. The fire-control computer
>      machines, chewing with millisecond meditation data from the analog,
>      decide whether or not torpedoes can reach the target, then offer
>      four answers: ballistic "possible" or "impossible" for projected
>      condition, yes or no for condition changed by one ship, or the
>      other, or both, through cutting power. These answers automatic
>      circuits could handle alone, but machines do not think. Half of
>      each computer is designed to allow the operator to ask what the
>      situation might be in the far future of five minutes or so from now
>      if variables change . . . and whether the target might be reached
>      under such changes.
>
>       Any variable can be shaded by human judgment; an intuitive
>       projection by a human operator can save his ship -- or lose it. A
>       paralysis beam travels at speed-of-light; torpedoes never have
>       time to get up to more than a few hundred kilometers per second --
>       yet it is possible for a raider to come within beaming range, have
>       his pencil of paralyzing radiation on its way, and the trader to
>       launch a target-seeker before the beam strikes . . . and still be
>       saved when the outlaw flames into atomic mist a little later.
>
>       But if the operator is too eager by a few seconds, or overly
>       cautious by the same, he can lose his ship. Too eager, the missile
>       will fail to reach target; too cautious, it will never be
>       launched.

Yes, the computers are *woefully* limited by our standards. But the
principle remains.

--
Leonard Erickson (aka shadow)
shadow at shadowgard dot com