Newtonian Aurora

[Yonder]

Not only would you want to hit, but you'd also want to have the most hits, though.  So if you had 1 shot, you'd take it down the center.  For 2, you'd split it fairly close to the center.  For three, four.... continue on.  But say you have 20? I'd still cluster my shots around the center, probably looking fairly bell-curve shaped. Putting 4 massive alloy rods through a ship is better than putting just one. Because, as the saying goes: "There is no overkill.  There's just 'Open Fire' and 'I need to reload'."

I'd rather a 100% chance of hitting them once than a 25% chance of hitting them four times. If you cluster all of your shots around the center you will only hit your target at all if he coasts or starts accelerating at 10% of his maximum or so. If he starts accelerating at full thrust in either direction (or just keeps accelerating if his engines are already on) you will miss him every time.

Take the Daring class again.  At 1,400,000 km away (current max beam), that 109m diameter equates to 0.016 arcseconds, roughly 1/2 the apparent size of Eris.  At that range, 21.83 mps² acceleration can result in a deviation of 237m diameter from projected location with no acceleration.  That equates to approx the same apparent size as Eris.

On a 1 dimension line, that's a target that's 45.86% of the area.  On a 2 dimensional area, that's a target that's 21.03% of the area. I don't know which is used for computing hit/miss chances, but since in current Aurora you can stop on a dime, I don't think it's taken into account.

Now, granted we're talking about a game about spaceships which does involve some handwavium, but that's awfully precise to hit at that range.  And even more so at greater ranges.  If you double the range, you halve the apparent size of the ship, but double the potential deviation.  If you quadruple the range (5.2m km), you have 0.004 arcseconds of target to hit in .130 arcseconds of potential, or approx 3%.  Going backwards, at 1m km you're aiming at a .022 arcsec target in a .025 arcsec field, so pretty good odds to hit.  And at 60k km, that target is .37 arcsecs big, or the approx apparent size of the asteroid Ceres.  And at 595km (same as Hubble) that ship would be the same apparent size as Jupiter, and visible to the naked eye.

Right, and while you are waiting for my spaceship to get close enough to you to look like the size of Jupiter, I'll start spraying the sky with flak at 30 light seconds out (because this isn't Aurora remember, it's Newtonian Aurora).

[Yonder]

I thought that I needed to put my claim that firing in a spread like this would greatly increase your effective range, so I wrote up the following script.
(This is C#, but it should be easy to port elsewhere if anyone else wants to fiddle with it)
Errr... Nevermind, it's actually quite too large to really post. PM me if you want it.

The basic purpose of the program, was that for the scenario of an enemy ship coasting right towards you, with a set evasion acceleration and diameter.

You have a settable number of weapons, with specific muzzle velocity, fire rate, etc, etc.

The program calculated the range at which the target couldn't dodge your bullets anymore. It then started "shooting" at that target as fast as possible until it reached that range. For each shot it calculated the expected number of hits, and then at the end it told you how many expected "extra hits" you had from the early spread shooting. This depended a huge amount on the different conditions. In each scenario I tweaked the initial separation so that you start shooting right around when you have .01 expected hits per shot. I figured a 1% chance was as good an arbitrary starting point as any.

My target ship was the Daring class, 21.83 m/s² acceleration, 109 meter diameter, approaching at 15k km/s.

My first example weapon system was a ship that had 8 railguns firing a 1kg projectile at 40 km/s (800 MJ) every 5 seconds.

Under these conditions you have a "can't miss range" of 33.6k km. That gives you time for a single shot 2.23 seconds before the target hits you. Albeit if you are still alive for that shot it will completely ruin your target. However if you start firing when you have a 1% hit chance that gives you an extra 60 seconds. That's 12 extra shots (of 8 slugs each), unfortunately odds are only one and a half extra slug impacts, and probably in that last ten seconds.

That didn't really help much, although the 164 million GJ of pain is nothing to sneeze at. (Keep in mind most of that kinetic energy would blow right out of the back of the ship though, Hmm, which really means you need more smaller slugs, if each of the slugs broke into 500 pieces 2-3 seconds before impact that would be a different ballgame)

Obviously we are going to need a less pathetically slow muzzle velocity to have more extra shots with the target approaching so fast. Lets jump straight to a laser. Or to be more precise, eight 800 MJ lasers.

At this point our "range" becomes approximately 2.23 light seconds, around 700k km. However we hit the 1% hit chance at 20 million kilometers, so we actually start firing at over a light minute away! Now at this point we may actually be leaving the bounds of a reasonably designed ship (we won't know until Steve give us more examples) because we are starting so early that we have 22 minutes of sustained shooting ahead of us. Who knows if that's reasonable. Anyways, all of this early shooting gives us 76 expected extra hits on the target, and starting at 2 million km we are guaranteed to hit every time. That's a total of 60.8 GJ of damage done. That's doesn't sound all that impressive considering that the example shield Steve has shown us was 72 GJ strong, but in a fight with numbers that would change things up. 10 ships on each side and focus firing would probably kill off 3-4 of the enemies before they got "in range".

I'd like to keep doing more examples, but it's super late here. Basically sometimes the early shooting helps a lot, sometimes it doesn't, but it's going to help a lot often enough (especially if you are doing things like fleeing from the enemy to keep them at range longer) that it's probably a good "most common" firing method.

Edit: One more example, since that 22 minutes of firing kept bothering me. If you wait until you have a 10% chance of a hit you starting shooting at 6.3 million km and only have 7 minutes of sustained shooting, but you'll still get 70 extra hits on them.

[bean]

I'm going to point out (again) that the expected range on a kinetic hit goes up significantly if you switch to guided projectiles, whatever you wish to call them.  They now have their own hit cross-section, which greatly increases the chances of a hit. 
But, yes, firing weapons will almost have to be in spreads.  Though there are two caveats here:
1. Projectiles might now have to deal with PD systems, which means that firing 1 is useless.
2. It would be helpful to be able to cluster your projectiles under various assumptions.  The most common are no thrust and current course.  I have equations for both in the spreadsheets I posted links to.

One other thing I question is the 100 kg/m3.  AV:T used 250.  I'm not saying Steve's wrong, but they did a lot of research, and that number is comparable to modern jets.

[chrislocke2000]

I guess laser tech could go one of two ways for improving hits: 1) A high number of small pulses every second with the spread of shots as discussed or 2) a single pulse that lasts for a longer perriod that follows a tracked path around the target.

I agree that it would make sense to have "guided" projectiles that improve individual to hit chances rather than lots of dunmb projectiles for when you are engaging and more distant ranges

[Yonder]

I'm going to point out (again) that the expected range on a kinetic hit goes up significantly if you switch to guided projectiles, whatever you wish to call them.

Those calculations are the next thing I'm adding to the script. 

[Steve Walmsley (OP)]

If targetting range is still limited to 5 lightseconds, then you don't really need this though.  You'd want to put as many points of damage as possible within the target window, and it's not going to change that much.

Using Steve's Daring Class from the first post, it's got a size of 6873 Tons.  That's 68730 m³, or approximately 109m diameter.

The most it can accelerate at 21.83 m/s².  Looking at a 1 dimensional line, at 5 seconds the center of the ship can be at most 117.15m off from where it would be with no acceleration.

I have been considering something along these lines, although it isn't final yet. My maths are slightly different so I'll post my thoughts here in case I am heading down the wrong track.

For a ship that can accelerate at 20m/s, there is more deviation than you might think. During the 1st second its speed increases by 20 m/s and it moves 20m further than without acceleration. During the 2nd second, it accelerates to 40 m/s faster but now it has moved 60m further than without acceleration. During the 3rd second, it increases to 60m/s faster and has now moved 120m more than without acceleration. By five seconds, it is now 300m from its projected non-acceleration point. It could also decelerate instead and be 300m behind where it would be without acceleration.

A ship of 68,730m3 is 50.8m in diameter (using the formula Radius = CubeRoot(3/4 Volume/Pi).

Using 1D only, before the five seconds starts, the ship occupies a line 50m long. After potential accel or decel, the entire width of the ship is contained within a line 650m long (the original 50m plus deviation of 300m either way). Assuming random accel/decel and a random shot, there is a 50/650 or 7.7% chance of a hit.

Using 2D and assuming the ship may modify its course left or right, there is an area within which the ship can be located. For ease of calculation, let's assume that is a circle with a 325m radius, whch has an area of 331,830m2. The ship itself occupies an area of 7853m2, so there is a 2.36% of the ship being hit randomly.

Of course, if this was really 2D then moving left or right on a course perpendicular to the firing ship doesn't matter because the shot would be in the same plane and just hit earlier or later. On a closing course, accel or decel wouldn't matter as the shot would hit earlier or later. However, in reality the ship would be maneuvering in 3 directions so using an area (instead of a volume) as a possible location is a reasonable compromise between reality and playability.

The other matter to consider is that the player may wish to apply some intelligence to his firing solution. For example, if the enemy ship has been under constant acceleration on the same bearing for an hour, he may wish to fire only at the exact predicted location based on current course and acceleration. Or he may wish to allow for speed changes but not course changes, or accel but not decel, or course changes without speed changes, or any combination of the above. He may also wish to apply different criteria to each fire control, or even each weapon, to bracket the target but still emphasise one option over the other (three weapons assume constant accel and one weapon assume random accel/decel and course changes for example).

So at the moment I am leaning toward the following:

1) Player specifies the parameters for the firing control using three checkboxes: Allow for possible Accel, Allow for possible decel, Allow for course change.
2) Aurora calculates the area in square meters, or line in meters if no course change is specified, or dot if no checkbox is checked, covered by that firing solution, and selects a random point within it (or along it).
3) The exact coordinates of that point are recorded, down to 0.1 meters.
4) Based on the speed of the projectile, the exact time of arrival (within 0.0001 seconds) at that point is recorded.
5) At the moment in time the projectile reaches the specified point, the location of the ship is checked to see if the location of the shot lies within the area of the ship.
6) Because the exact point in time will be partway through a sub-pulse and resolution of this will take place after movement, the location of the ship at the exact point in time will be calculated based on its heading and speed during the sub-pulse.

This means that a shot could actually miss even if the bearing would mean the shot would hit the target ship a fraction of a second later. However, because we are using an area rather than a volume, you have a higher chance to hit than you should have which compensates for this possibility. I haven't tested (or even coded) this yet but this is looking the most likely at the moment, unless someone comes up with a reason this won't work, which is entirely possible . This avoids tracking individual projectiles on the map but also excludes the chance of hitting something else. I could also check any other nearby ships to see if they are in the target location instead, although this is extremely unlikely and may not be worth it.

For shrapnel warheads, which may involves a lot of objects and may be an area denial weapon as much as a anti-ship weapon, I will probably use a debris cloud approach with a chance to hit something when you pass through the cloud (or the cloud passes a ship)

Steve

[Yonder]

Alright, I took a short lunch and added calculations for shooting missiles. I used Steve's latest example missiles and used them to build what I think is a missile that matches them in terms of tech. It's 1 kg, and .9 of that is the engine, the last bit is fuel. It has an acceleration of 216 m/s².

I then shot them out of that first example ship. 8 shots every five seconds, 40km/s muzzle velocity.

The real question for this situation is when you want to start firing your thrusters. Not because you will run out of fuel, not with the current setup if I've done my math right, but because if you turn on your thrusters too early your enemy may have time to shoot your missiles out of the sky. Too late and the missiles don't have time to correct much.

As with the target ships's acceleration, none of it is ever used to slow down or speed up with relation to the ship, just to match the target's motion perpendicular to the line of approach.

Burn Time (s)	1% Accuracy Range (m km)	Extra Volleys	Expected Hits
0	1	12	1.5
1	1.6	21	4.5
2	2.9	37	13.7
3	4.0	52	22.7
4	5.4	72	32.9
5	6.8	90	42.4
6	8.13	108	52.2
7	9.4	126	62.5
8	10.7	142	71.9
9	12.1	160	81.9

At 9 seconds of burn time we have surpassed 76 expected hits from the laser example. Not only that, but each of the laser hits were minor annoyances, while each of these hits would bore through a ship like swiss cheese.

[Steve Walmsley (OP)]

One other thing I question is the 100 kg/m3.  AV:T used 250.  I'm not saying Steve's wrong, but they did a lot of research, and that number is comparable to modern jets.

Traveller (at least for Fire Fusion and Steel) used 71 kg/m3 so there are other figures out there. It is admittedly an abstract figure, especially since a carrier or freighter is going to be lower than 100kg/m3 while a FAC or fighter is probably the other way. One fairly significant factor in that decision was also making ships larger and easier to hit. There is also a length figure for ships in Newtonian Aurora on the class summary. This is entirely for RP purposes (as sphere diameter is used for targeting and the number of armour columns is equal to the diameter in meters ) and is based on an assumed ovoid shape with a 2.5-1 ratio of length to width. This ratio gradually decreases for smaller ships, down to 1.25-1 for fighter sized. See below for some examples. Part of the rationale behind the 100 kg/m3 was to achieve ships that seemed to be about the right size, based on little else but gut feel . I could have assessed each component individually for mass vs volume but that would be a lot of work and I think the gameplay benefit would be minimal.

For example:

Atlas class Freighter    9,343 tons standard     34,843 tons full load      28 Crew     381.1 BP
Length 220m     Armour 1-88     Sensors 1/1/0/0     Damage Control Rating 1     PPV 0

Resolution class Destroyer    3,895 tons standard     4,895 tons full load      186 Crew     951.3 BP
Length 103.5m     Armour 6-46     Sensors 1/20/0/0     Damage Control Rating 1     PPV 16.92

Agincourt class Scout    4,612 tons standard     6,062 tons full load      204 Crew     692.9 BP
Length 120m     Armour 3-48     Sensors 18/24/0/0     Damage Control Rating 1     PPV 0

Steve

[Steve Walmsley (OP)]

Alright, I took a short lunch and added calculations for shooting missiles. I used Steve's latest example missiles and used them to build what I think is a missile that matches them in terms of tech. It's 1 kg, and .9 of that is the engine, the last bit is fuel. It has an acceleration of 216 m/s².

At the moment, missiles are a minimum size of 1 ton while unguided projectiles can be as small as 1 kg. I realise we have smaller real world missiles at the moment. This is partly based on the sensor model, which will allow the detection of missiles but not projectiles, and partly because of the firing rates of available energy weapons. If I allow lots of tiny missiles, I will need to change the sensor model and either allow lots of tiny energy weapons or extremely fast-firing energy weapons and I am not sure the added complexity will produce additional gameplay benefits. That doesn't mean I won't do it; just that I am not convinced about it yet.

Steve

[bean]

For a ship that can accelerate at 20m/s, there is more deviation than you might think. During the 1st second its speed increases by 20 m/s and it moves 20m further than without acceleration. During the 2nd second, it accelerates to 40 m/s faster but now it has moved 60m further than without acceleration. During the 3rd second, it increases to 60m/s faster and has now moved 120m more than without acceleration. By five seconds, it is now 300m from its projected non-acceleration point. It could also decelerate instead and be 300m behind where it would be without acceleration.

Your math is off.  The correct formula for displacement is x=.5at^2+vt.  So in the first second, it will move 10 m, then 40 m, then 90 m, and so on.

Of course, if this was really 2D then moving left or right on a course perpendicular to the firing ship doesn't matter because the shot would be in the same plane and just hit earlier or later. On a closing course, accel or decel wouldn't matter as the shot would hit earlier or later. However, in reality the ship would be maneuvering in 3 directions so using an area (instead of a volume) as a possible location is a reasonable compromise between reality and playability.

Given the sort of flight times and accelerations under discussion here, any counting of movement in line with the projectile is superfluous.

The other matter to consider is that the player may wish to apply some intelligence to his firing solution. For example, if the enemy ship has been under constant acceleration on the same bearing for an hour, he may wish to fire only at the exact predicted location based on current course and acceleration. Or he may wish to allow for speed changes but not course changes, or accel but not decel, or course changes without speed changes, or any combination of the above. He may also wish to apply different criteria to each fire control, or even each weapon, to bracket the target but still emphasise one option over the other (three weapons assume constant accel and one weapon assume random accel/decel and course changes for example).

That would be nice.  If it was me, and I knew there were enemy nearby, I'd probably go for semi-random course changes to throw pure unguided kinetics off.

I have a different means of tracking the target, which probably only works for guided munitions.  (I'm honestly not trying to get everyone to do that.  It's just how it works.  This is better for longer ranges, but I already had it available.)
In space flat space, an inertial object that is going to impact will appear to be closing on a course of constant bearing and decreasing range.  If the target is assumed to be inertial, then give each projectile a limited stock of delta-V, and keep track of the target's maneuvers.  If they run over the limit, then the projectile isn't going to hit.  (Or it won't hit if the target displaces out of its way.)  You can do the same if you assume the target to be constantly accelerating.  You just use a different baseline, using delta-V when the target doesn't burn in the expected direction.  It's not perfect, but do you really expect a tiny guidance system to be terribly optimized.
A worked version of this can be found in my spreadsheets.

[Sloshmonger]

I have been considering something along these lines, although it isn't final yet.

(snip)

Steve

My maths were mostly using long remembered formulas and wikipedia... probably should have stated that.

Related question: Will there be a difference between ship and fleet movements within this? Will "random maneuvers" be applied on a ship-by-ship basis, where Ship A and Ship B in the same fleet can have the same course and be considered part of the same entity, but have different dV with respect to targeting?  If this is the case, would accidental collisions be possible?

From what it looks like, shotgun type weapons are not yet planned aside from the area-burst missile/mine.  Would new weapons be created for such a role, or others adapted (plasma carronade, etc).

[Yonder]

At the moment, missiles are a minimum size of 1 ton while unguided projectiles can be as small as 1 kg. I realise we have smaller real world missiles at the moment. This is partly based on the sensor model, which will allow the detection of missiles but not projectiles, and partly because of the firing rates of available energy weapons. If I allow lots of tiny missiles, I will need to change the sensor model and either allow lots of tiny energy weapons or extremely fast-firing energy weapons and I am not sure the added complexity will produce additional gameplay benefits. That doesn't mean I won't do it; just that I am not convinced about it yet.

Steve

Hmm, good point. As far as the sensor portion of it goes, one way to do this would be to let Thermal Sensors give locks to the Fire Control. That way even very small missiles would probably be visible once their engines started.

Your math is off.  The correct formula for displacement is x=.5at^2+vt.  So in the first second, it will move 10 m, then 40 m, then 90 m, and so on.

And the reason your math was off was because it looks like you were using the acceleration to calculate the velocity at each second, and assuming that velocity stayed constant over the entire second.

[Steve Walmsley (OP)]

Your math is off.  The correct formula for displacement is x=.5at^2+vt.  So in the first second, it will move 10 m, then 40 m, then 90 m, and so on.

I should have mentioned that in Newtonian Aurora, course changes and accel changes take place before movement. The formula above relies on steady acceleration over the time period.

Steve

[Steve Walmsley (OP)]

And the reason your math was off was because it looks like you were using the acceleration to calculate the velocity at each second, and assuming that velocity stayed constant over the entire second.

That is how it works in the game, which I thought I had mentioned somewhere in the thread but I probably haven't . I could change it to a constant accel, rather than accel before movement, but it makes things harder to model, especially for interceptions, and for players to visualise. Overall velocity increase is the same either way.

Steve

[Steve Walmsley (OP)]

Related question: Will there be a difference between ship and fleet movements within this? Will "random maneuvers" be applied on a ship-by-ship basis, where Ship A and Ship B in the same fleet can have the same course and be considered part of the same entity, but have different dV with respect to targeting?  If this is the case, would accidental collisions be possible?

From what it looks like, shotgun type weapons are not yet planned aside from the area-burst missile/mine.  Would new weapons be created for such a role, or others adapted (plasma carronade, etc).

There are formations within Newtonian Aurora, as there are in standard Aurora, and it would be a good idea to use them if an opponent is using area effect weapons such as nukes. If ships are not in formation, they will essentially be in the same location and will use the same evasive manoeuvres. They will both be hit by nearby area effect weapons and they could be hit by separate beams from the same laser warhead but they will be hit individually by single shot weapons such as railguns and lasers. If you want to ships to follow independant evasive course then they need to be in formation or in separate task groups.

Ship launched shotgun weapons will be added at some point. I just haven't done them yet.

Steve