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Are ship based ballistic weapons practical?

MR TEK

SOC-12
How impractical would ballistic weapons mounted on a star ship be?

Using DU or even heaver, denser material would work very well, and a 10 cm round could contain a DU nose and frame and a nuke package, (TDX, Thermal explosive, a high tech napalm for anti-personnel, Probably twice the diameter could fit a plasma bottle or other equally nasty surprises.) If I recall my military armaments correctly, the US has field rounds for tactical use that contain enough uranium to reach critical mass in a standard 105 mm round

Advantages: no maintenance at all of delicate guidance systems, propulsion systems or the elaborate fusing and slave tracking systems to transfer a weapons lock from the ship to the on board guidance system.

Few defenses would affect them. they would be too dark and too fast for any point defense systems. Sand casters MIGHT slow their velocity enough to make them pass behind the ship. Meson screens would only bother radioactive payloads, and a totally new defense, that hand waving would set at any effect from none at all to rendering the weapon useless. ANY changes in course or speed during the flight time would cause the weapon the be wasted. Depending on how hard it is to detect the heat bloom of the explosion that drives the round, you would know when they fired, and where not to let you ship reach. If they are a bright flash, easily detected by the computer, they are worthless. On the other hand, a combination of flash suppressors, a flash shield with a hole to let the round pass a few meters out, and positioning them against large emitters of waste heat, and the target will never know you fired until the round hits.

Erratic maneuvering would instantly defeat cannon, though it has costs that make it troublesome. Then the only course corrections left are dictated by the tactical situation, and the flight time of the projectile.

I have not worked out a velocity yet, but is should be massively higher that a ground based weapon. I am guessing a couple of minuets of flight time at effective ranges.

Effective range is set by the accuracy of the sensors to determine velocity relive between the ships, course, acceleration of the target and exact relative position. I don't have guestimates yet, but I'll bet any number of artillery folks can rough them out is short order.

Between the mass of the ship, and gravitics, no energy will be lost to recoil of the firing tube. all energy goes forward with the shell. Same thing, there is NO shock wave, compression wave, or any other aerodynamic fluid effects. Third, because the open end is a vacuum, the is no static column of air to push out the tube before the bullet comes out. All off those effects drastically reduce the muzzle velocity of a gun fired in atmosphere on a platform that has recoil. There is also no drop in speed from the muzzle velocity, and the trajectory is absolutely flat as long as no gravity fields are encountered.

They would be at the bare minimum as effective as their missile counterparts, except that they can pack all projectile and payload into their mass, having no fuel, guidance or other systems sharing space.

A hit would pass through the outer bulkhead, and only lose velocity when passing through a structural bulkhead or heavy equipment, drive core and containment vessels only. It WILL hole any thing else in its path, and will expose every compartment it enters to hard vacuum. And the most deadly effect of DU rounds is the heat they generate passing through metal. they flash the air inside the compartment, incinerating everything. Finally, when the payload detonates it will be DEEP inside the ship, taking crew, control electronics, piping, computer links and other delicate systems that are shielded from missile attack.

the weapon uses zero energy except for the loading mechanism, and swiveling the mount. Not much computer draw either. A gun would hardly use a ton plus storage for the ammo.

not real downsides in the firing cannot be detected.

Chemical explosives require no special handling precautions compared to rocket fuel, solid, liquid or gas. and being really industrial grade products as opposed to mill spec, amazingly cheap per round. DU is a higher tech product, but is available for the cost of processing spent fuel rods, which have to be processed somehow, and reactors would be common. Fusion might be a better source of power, but the radiation, heat and mix of exotic compounds needed to make most of the high tech materials that the Traveller universe requires to make all the wonderful toys come from controlled transmutation in either the cooling blanket or the core of a Fission power station.

In short the best transfer of kinetic energy and delivery of a payload at rock bottom prices, removing several delicate systems, with troublesome maintenance overhead, simplified and reduced power, comp and fire control and tracking, and storage and inventory control of spare parts.

The ONLY thing you lose is nail biting for a few moments that the target does not change course. Missile flight times are never dealt with, but the muzzle velocity would be many times the initial launch velocity of any missile, and the missile would only gain the same velocity near the end of its flight. So transit time for a shell could conceivably be LESS than a missile flight. And unless you are under erratic maneuvers, how often is a course change really needed.

Range would be reduced drastically on a fighter. The nature of a fighter is to high gee acceleration, uber high agility, and constant changes in vector though out an engagement. You would be back to the recoil of a conventional aircraft, but in vacuum there is never any danger of the round slowing enough due to drag that you run over your own rounds. Again you would have to know the range that fighter combat occurs, and flight time would have to be less then ten seconds for certain, and likely less than 1 second.

If these are practical, I can pull out the physics books and generate some real numbers.
 
Massy unguided weapons are really only efficient at Star Wars ranges. Beyond the ranges where your opponent's colors are visible to the naked eye, the amount of ammo you need to toss out to achieve statistically viable hits is just sick. Meanwhile, you're also changing your own vector in non-trivial ways, and quite possibly causing the whole ship to shake at frequencies that will render your own sensors near-sighted in a hurry.

Mass weapons are best in orbital or closer fights, and as bombardment tools.
 
would depend on engagement distance. if a shell were moving at ten miles per second it would need five hours to cross one light second.
 
Mass weapons, great for a first strike, really quite poor for an interactive fight.

I'm not quite sure what the ranges are like in other editions, but in T20 effective sensor range is only arround 600,000km, with engagement much past 1 gigametre being only for long range missile volleys and particle accelerator spinals.

This range is in the order of a light second or two (where a light second is approximately 300,000 km), however firing a physical projectile at near-light-speed is a poor choice for a couple of reasons, leaving you with needing to pre-plan the targets position significantly in advance. A half light speed projectile at 0.6gm takes 4 seconds to collision point, meaning that you will need to predict a full 6+ seconds in advance, vs a laser at 4 seconds. If the projectile is moving at a more reasonable speed (such as 0.1C) then quite quickly there are enormous delays in transit.

There is on place where they would come into their own. At really short range (in metres, rather then kilometres). So a gatling weapon on a fighter could be an interesting solution.

That said I quite like railguns as space weaponry, especially in combination with repulsors to guide the projectile in flight.
 
They are only truly effective if the ship you have can get really close and go really fast at the opposing ships. Think Torpedo Bomber or Dive Bomber, you point your OWN ship at the enemy, drive fast, release weapons, and let inertia do the rest. For a good torpedo bomber, get a fighter (or one of my own HiG fighters from the Civilian Contract topic on Fleet Strategies) and a 1-3 ton super missle.
 
Now rail guns get to reach .1c or better.

You can predict future location as many years in to the future as you chose to consider, as long as no course or velocity changes occur.

The only question is realistically how often does a ship change course. I am thinking a couple of maneuvers and then stable for 10-12 minutes to analyze the new tactical situation.

Erratic manuvers are likely small course corrections every two to three minuets, so a tracking system has to realign to your new course and heading. Every few seconds seems excessive, as no jink would last long enough to materially change your position, if you are at all maintaining a heading.

So a projectile would have to cover the distance in maybe half that time to be effective.

Again, a rail gun would be effective even under constant jinking, because 6 gs for 4 seconds is not going to move you position more than a couple of hundred meters or so, maybe the length of a subsidized merchant.

4 minuets of sustained 6g acceleration is good for 1728KM displacement in position. If I recall dim dark memory massive behemoths produced in Trillion credit squadrons topped out around 1 KM. that means in 4 minuets of acceleration at 6 gS is going top move you 2000 times further than you need to to miss the projectile, if you CHANGE acceleration with or with out course change within a few seconds of the other ship firing.

It is not velocity changes, but acceleration changes that matter. If you are at a constant 4G acceleration, on a constant heading for 4 minuets. As long as I know your position at a specific time and your Relative heading and relative velocity. I KNOW where you will be in 4 minuets are accurately as my measurements allow. I know what your position will be as accurately as I know it now. If you keep that burn and that heading and do not encounter a gravity well, I know were you will be in 4 WEEKS when you exhaust your fuel, and in 200 years when you are still traveling at the velocity you where when your fuel ran out. And let me correct. Since I know all local gravity sources, If I have enough data to know all the perturbation of the orbits, I know where you will be within the same accuracy in 200 years ACCOUNTING for the gravity wells. The ONLY reason I cannot know your exact position at any given time is if your ACCELERATION changes, either in direction or value, and As I id above, I can plot an EXACT ring of space that it possible for you to reach, given only one more value, your max acceleration.

NASA does it with accuracy to the SECOND 4 years out with the acceleration constantly changing as the mass of the space craft decreases by the amount of fuel expended. That is with current computer tech, only 50 years after we started space flight and 200 years since the first ballistic course were hand tabulated.

Traveller is 50 CENTURIES into the future with mind-boggling advances in sensors, computers, and orbital mechanics. Not to mention the wholly new science of behavioral analysis and prediction.

So it all comes down to How often WOULD a target change acceleration, you would need to guess a statistical mean and maybe 1 standard deviation from the mean. Subtract, the deviation from the mean and you have a nice safe assumption as to haw long you have at a given acceleration, before you can COUNT on a an acceleration change. I would say half of that time is how long you would want your projectile to be in flight for a reasonable chance for the target to still be where you predicted it would be. Reduce to the time it would take the target to change its course by half the length of the ship and you guarantee a hit. So a Rail Gun is going to be as effective as a laser at the max sensor range.

By the way, is that max range to detect or max range to determine course speed and acceleration? Again I think it is a safe bet that the range at which fire is exchanged for effect is significantly less than detection range. At detection range you are only a few seconds from opening the range enough to evade. If one side is significantly stronger that the other, then the weaker side will attempt to open the range and the stronger side will attempt to close.

If they are evenly mathed the only sensible tactic would be to close to a distance the normal movement during battle would not carry you out of detection range.

If the rules where sophisticated enough fire control would increase with decreasing range as you can increase the accuracy of your measurements as range decreases.
 
There's no reason you can't combine things: have a railgun fire a round that has its own terminal guidance and a basic rocket engine for last-second homing. This allows you to have the projectile sneaking up but still follow evasive maneuvers.

And don't bother with a warhead. At any decent velocities the kinetic energy alone will be enough to do all the damage you could want.
 
Thanks, I thought KE might be high enough especially knowing how hot the surfase gets at penitration at hypersonic speeds, but, had not worked up enough numbers to really know. The prolem with terminal gudence is you bring back rocket fuel, a drive system, and storage and maintenance issues. Much smaller of course, but part of the bonus was eliminating them in the first place.
 
Just to add my Cr.02. At ranges that normal space combat occurrs in Traveller a Balistic weapon is virtually useless. First they are relatively slow. You can only impart so much initial velocity. (For example muzzle velocity for even the fastest bullets today is less than 1250m/s.) Second they are fairly easy for point defense to pick off. (Unlike spacecraft and missiles they do fly straight and level.)(Patriots hit balistic weapons 13 years ago.) For a point defense laser system it would be a joke. The weapon described in the initial comments has no guidance or warhead, which means it actually has to hit. In space combat you are not going to travel straight and level for any length of time. (In the Battle of Britain pilots were instructed not to fly straight and level for 5 or more seconds.) Any course correction, no matter how minor will generate a miss at normal ranges unless you are using a Phalanx/Seawiz style weapon and all your mass savings just went out the window with ammo capacity for one shot and even then you are firing into a fairly limited window.

Radar being a light speed sensor at any range would provide returns on the weapon long before the weapon reached the target. At 45,000KM a bullet, travelling at 150Km/sec (or more than 10 times what the fastest bullet today travels)is going to take 5 minutes to reach its target area. (Light travels the same distance in less than 7 seconds.) In T20 that is space craft, short range.

1 second of angle at 100m is about 2.54cm. So 1 second of angle at 45,000Km is 11.43Km. Talk about a miss as good as a mile. (You just missed by over 7 miles.) The area covered by one second of angle from your initial target prediction is approximately 410 Square Kilometers. A Free Trader is 200Dtons or 2700 cubic meters. A Sphere of that size has a radius of 9.5M. So to guarantee 1 hit with an error of just 1 second of a degree you would need to fire 41,000 rounds. (That approximately puts one round every 10 meters in that circle at 45,000Km) (And if your prediction is that accurate you will hit your target once.) Point defense only has to hit the one that actually is going to hit, because they know where they will be when the bullet arrives.

The second problem you find with a purely ballistic weapon is damage. A hit by a bullet will cause some spalling, and possibly, explosive decompression, in the compartments along the path of the bullet, and then pass through the other side. You may have lots of kinetic energy but the problem is passing that kinetic energy on to the target. Unless you actually hit something vital all you are going to do is some fragmentation damage to a localized area. I have been inside a tank that has been hit by a Sabot round, (though not while it was actually hit, only after the fact.) actually the tank was hit twice. There was spalling evidence at both the entrance point and the exit point. (Both of them.) I am sure the seat cushions were replaced and I know it was cleaned out and painted before I got inside but the damage to most of the internal components were minimal. (The rounds passed through the turret front to back.) THe main gun didn't appear to be significantly damaged, and the blast doors that protected the ammo storage were not penetrated by the fragments. So aside from the personell causualties in the turret (And probably the radio, I don't recall.) the tank was still combat effective with a new crew. (If they didn't mind the holes in the turret.
) And it certainly could have driven away because the Driver's compartment, fuel and engine were untouched. The turret still rotated, even on the hand crank. (They wouldn't let us fire it up or fuel it but we did tend to have the main gun pointed at the Bn Commander's Office window.
)
 
If you want a good set of rules for use of ballistic weapons, you need to look at ATTACK VECTOR:TACTICAL from Ad Astra Games, where "coilguns" are a major weapon. Of course, space combat in their game happens at a much closer range than in TRAVELLER.
 
In Scott Westerfield's book The Risen Empire, the naval forces use "sand" and "sandcasters", as weapons. Diamond sand is deployed in large clouds at high speed (1% c, or so, IIRC). Enemy vessels that enter the cloud can suffer severe damage.
 
Originally posted by The Oz:
If you want a good set of rules for use of ballistic weapons, you need to look at ATTACK VECTOR:TACTICAL from Ad Astra Games, where "coilguns" are a major weapon. Of course, space combat in their game happens at a much closer range than in TRAVELLER.
And, while it's largely hidden by the rules, coilgun rounds in AV:T have terminal guidance (it was more obvious in the original rules, where it was clear that a CG round only needed a vector that carried it within the same 20 km hex as its target).

There's a substantial amount of cherrypicking of numbers in AV:T, designed to produce an interesting mix of different weapons and tactics.
 
Fastest infantry calibre bullet is probably the one belonging to the IWS2000 at a little under 1500 m/s.

Naval railguns get up to arround 5000 m/s.

Note that to get much past 6km/s requires something other then a railgun. Mass drivers might be able to project at faster then that velocity, but the very design of a Mass Driver would limit the weapon to being a spinal mount only. Chemical projectors at this point are well out of the equation.

Oddly enough talking about Mass Drivers, they have a near identical design to most particle accelerators. The only real difference is size of projectile. Mass drivers use a secondary coil as the projectile impeller, Partical Accelerators use the charge on the particles.

Getting on to TravellerTech(tm) the logical conclusion would be a Mass Driver like device using pulsed grav devices rather then magnetics. Depending on how fast a grav device could cycle would be the limit on this type of projectile device, if it was fast enough significant percentages of the speed of light could be acheived.

Lastly you wouldn't want an explosive head, you would want something dense but as fragile as possible (frozen mercury perhaps) so that as much of that wonderful KE would be transferred. This changes if you ever intend to fire the weapon in an atmosphere, but in the near vacuum of space it would be more efficient.

A 1kg blob of frozen mercury, travelling at 0.5C has in the order of 0.5*1.15*1.5*1.5*10^16 Joules or about 2.6*10^16 Joules, for reference this is the equivalent of a 3 MegaTon Nuclear device. Note that the 1kg (at rest) blob of mercury actually has a mass of 1.15 kg at this velocity, this becomes far more noticeable the closer you get to C.

1kg at
0.1C = 0.11 MegaTon = 1 kg projectile
0.8C = 12 MegaTon = 1.7 kg projectile
0.99C = 80 MegaTon = 7 kg projectile

The energy involved is linear with initial mass.

An exposive head could have one big advantage. 1 gram of matter at 0.8C has a yeild of 12 KiloTon. If you could accurately time the explosion to spread the warhead into a radial sphere of fragments, suddenly the possibility of hitting an area rather then a point becomes available.

The only question is how to pump the spinal weapon.
 
OK, the IWS is 1500m/s and a Rail gun is 5000m/s. Still way too slow for space combat. I mentioned 150KM/sec. (Instead of 1.5km/s or 5Km/sec.) My math was off when I said more than 10 times as fast as a bullet, it is more than 100 times as fast as a bullet, and more than 30 times as fast as a rail gun. Accellerating a large particle to a significant percentage of light speed gets into relativity where mass increases. (Which is why PAs are so power hungry and they are dealing with sub atomic particles.)

The initial question was to get a low power, low mass weapon firing slugs. At .1c you are still dealing with a weapon that can be avoided and/or intercepted. At 45,000KM you know about it at 7 seconds (speed of light) and it hits, if you are still there, at 70 seconds. Your computer knows about it, informs you, you have 3 seconds to react (Or the computer automatically reacts.) and you still have a minute to get out of the way. Just 1G accelleration for one minute moves a ship, if I remember my math correctly, about 35Km (9.8m/s/s) from where it was predicted to be. You would still need an absolutely silly number of rounds to generate one hit. Slower weapons, Longer ranges or higher agility targets are significantly worse.

Which means it won't be a low mass low energy weapon.

Now since a nice spherical 200T target has a radius of 9.5m or a Diameter of 19m, to generate one hit with all the possible positions within a 35Km radius circle at a range of 45,000Km, you would need to fire 202,550,052.7 rounds. (And you are only getting one hit.
) That assumes 2D maneuvering of your target and a nice spherical target, other shapes are a real bitch to hit and the 3D math is way too complicated.

If using something like mercury you are going to do more damage than a simple lead bullet, however micro meteorites hit a ship at fairly high velocity and kinetic energy and don't penetrate the ship's hull, so if you do generate a hit you have to figure out how good the particle shielding of a ship actually is.


Originally posted by veltyen:
Fastest infantry calibre bullet is probably the one belonging to the IWS2000 at a little under 1500 m/s.

Naval railguns get up to arround 5000 m/s.

Note that to get much past 6km/s requires something other then a railgun. Mass drivers might be able to project at faster then that velocity, but the very design of a Mass Driver would limit the weapon to being a spinal mount only. Chemical projectors at this point are well out of the equation.

Oddly enough talking about Mass Drivers, they have a near identical design to most particle accelerators. The only real difference is size of projectile. Mass drivers use a secondary coil as the projectile impeller, Partical Accelerators use the charge on the particles.

Getting on to TravellerTech(tm) the logical conclusion would be a Mass Driver like device using pulsed grav devices rather then magnetics. Depending on how fast a grav device could cycle would be the limit on this type of projectile device, if it was fast enough significant percentages of the speed of light could be acheived.

Lastly you wouldn't want an explosive head, you would want something dense but as fragile as possible (frozen mercury perhaps) so that as much of that wonderful KE would be transferred. This changes if you ever intend to fire the weapon in an atmosphere, but in the near vacuum of space it would be more efficient.

A 1kg blob of frozen mercury, travelling at 0.5C has in the order of 0.5*1.15*1.5*1.5*10^16 Joules or about 2.6*10^16 Joules, for reference this is the equivalent of a 3 MegaTon Nuclear device. Note that the 1kg (at rest) blob of mercury actually has a mass of 1.15 kg at this velocity, this becomes far more noticeable the closer you get to C.

1kg at
0.1C = 0.11 MegaTon = 1 kg projectile
0.8C = 12 MegaTon = 1.7 kg projectile
0.99C = 80 MegaTon = 7 kg projectile

The energy involved is linear with initial mass.

An exposive head could have one big advantage. 1 gram of matter at 0.8C has a yeild of 12 KiloTon. If you could accurately time the explosion to spread the warhead into a radial sphere of fragments, suddenly the possibility of hitting an area rather then a point becomes available.

The only question is how to pump the spinal weapon.
 
Um, Bhoins, the speed of light is 300,000,000 m/s.

I agree with your arguement, but that puts the 45,000 km mark as 0.15 lightseconds, or at 0.1C 1.5 seconds travel time. Or in other words you are firing at the ship 0.3 seconds in the past with a laser and 1.65 seconds in the past with a 0.1C projectile.

At the maximum range for the longest range weapon (PA spinal at just over 1.5 million kms) you are talking 5 lightseconds distance. From the known traveller weaponry it is known that 10+ second firing solutions can be used. At 0.1C a similar firing solution would be 1 light second (300,000 km) which is well within the useful set of weapon ranges in Traveller.

These facts still make a mass based weapon less then optimal compared to projecting photons or other paticulate matter, where near C velocities can be attained.

*********AAAAAARRRRRRRRRGGGGGGGHHHHHHH************

I have just realised that this discussion is daft.
Traveller already has Mass based weapons. The ship based fusion and plasma guns are projecting matter as weaponry.

So to answer the initial question, yes ballistic weapons are realistic, and are already described. Why you would want the material non-fusing, or non-plasmarised is another question, the projectile is so much more effective when it is doing so.

An epiphany. I am even more impressed.
 
A gravitic mass driver need not be pulsed...

A 20G acceleration tube, 20m long, accelerates RAPIDLY... but if I instead use a 1km tube at 50G, that is a whopper of a speed... but last time I did the math, not fast enough for reasonable starship combats. The problem becomes keeping it inside the tube. Additionally, since traveller does have repulsors...

as for plasma and fusion... yup those are mass projectors of some form... perhaps the gravitically propelled kind.
 
I have some very basic disagreements with a number of the previous posts about shortcomings.

First of all, if your detection gear in accurate enough for energy weapons to hit, it is accurate enough for kinetic weapons to hit.

Same with accuracy of the actual aiming mechanism. If something as delicate has laser focusing coils, a particle accelerator or similar systems can be aimed and fired with the massive amounts of waste heat generated in microseconds, and those delicate components do not deform enough to decrease the accuracy then a gun tube with the luxury of materials of almost miraculous rigidity, strength and thermal properties would fare just as well.

Second, no, I had not thought about radar. Thinking now, first the energy of returns from a MASSIVE target are going to be barely above background radiation level. So I cannot accept radar as at all effective at tactical ranges, and there are other more effective detection systems. (if radar was such a useful solution, why do we even TALK about the possibility of dark silent ships being able to hide?)

Second, you would have to know the reflectivity and reemitting properties of Depleted Uranium at radar frequencies to have any hope of knowing how detectable the round is.

Same with heat transfer properties to know how much the round was heated by the method providing the initial impulse. This will tell you if the shell reaches a high enough temp to be particularly detectable to IR and other such detectors.

Also remember, unless you detect the firing you have that expanding expanse of space that proved a round could not hit its target is the same amount of space you have to detect on object that you don't even suspect is there. And this is for a cold, dark mass at its MOST MASSIVE SIZE would be little bigger than an apple crate.

Muzzle velocity. To the best of my knowledge, (I am NOT an expert on the latest technologies.) virtually all modern guns use a low-density explosive to fire. Nothing exotic for our time like shaped charges of C4 or other even more powerful explosives. They would rip ANY current gun systems to shreds for anything portable, and research in larger scale systems has been minimal. For anything over the range of the horizon, active systems have been preferred in the high tech arena. (at least in part, because wiz bang exotic system get the research money in ALL fields, but this is true in SPADES in weapon systems.)

Also, muzzle velocities in ATMOSPHERE are severely limited by aerodynamic issues. Air is only slightly compressible at anything beyond hypersonic velocities, and at the speed of light, even something nearly mass less, such as a laser has to deal with heat and compressibility issues.( as the Air ionizes, its transparency, refractivity and other optical properties degrade. Fail to account for these issues and there have been some pretty light shows as thermal shock has bled of the entire energy of the beam.

So, the muzzle velocity of a projectile in an atmosphere is severely degraded by the column of still air that can only be shoved out of the way so fast.

This brings us to the effectiveness of the round at imparting energy. At hypersonic velocities, DU does not deform at all when striking an enemy target. At a higher velocity, the Round should still penetrate. Since the round dose not need to travel through air, it can be any shape you want. A flat or maybe a slightly concave face would give max shock at the surface impact. A more ballistic shape would penetrate much deeper, and if you reached enough heat to actually ignite the round or explode it, the results word be hundreds of times the yield of a lighter element.

So, I think that you would get massively higher energy transfer than conventional projectiles that we are experienced with. Even Traveller high energy weapons are not real efficient.
 
The issue is NOT "Can we hit a static target", but "Can we get rounds on target before the target is able to dodge or intercept"

The basic calculations are
Target Cross-Sectional Area (Atcs): Which, for a ship with unknown angle at potential intercept, must be reduced to the shortest two dimensional shillouette; for practicality, though, use lowest 2 dimensions of the rough shape.
Time of Sensing Return (Tsr) the time it takes to sense a target given an active pulse, from time of arrival of the pulse at target until it is returned to the sensor
Time on Target (Tt) the time for the fire to reach the target. Equals distance/speed of round
Time of Reaction (Tr) the time it takes to act upon the sensor return
Acceleration of target (At) in m/s, for Traveller, that's a convinient 10m/s

Shots required (Sr) is the number of simultaneous shots to assure a single hit.
Sr=Pi*(0.5(At*(Tt+Tsr+Tr)^2))^2/Atcs
With non relatavistic speeds, at the ranges Traveller engages in use of, projectiles which can not reduce Tsr and Tt by on-round guidance will require large numbers of shots...

Note, tat gunnery by this method is saturation fire, and assures 1 hit, and depending upon configuration, might secure up to 10 shots or so... what you are doing is tiling the cross section of the possible final position with the cross section minima of the target, and then putting a round in each place. This works GREAT for beams, provided pulse length, in m, is greater than the diameter of the saturation oval. Speed, even relative speed, is only a factor when figuring Tt, really, and so is ignored.

But, for kinetic weapons, we need a 3-D intercept to assure a hit... so the fomula needs another variable:
Length of Round (Lr) the length of the round fired, in m. For lasers, take beam length in S and multiply by 300,000,000m; 1 milisecond pulses are thus 300Km long... in the OTU. 310Km in the Real World, For physical weapons, take the length of the physical round.
Effective Volume (Ve) the max of the target's volume or the Atcs*Lr

Formula morphs to
Sr'=4*Pi*(0.5*(At*(Tt+Tsr+Tr)^2))^3 /3*Ve

Again, this ONLY assures 1 hit, but may result in many more. Unlike the above, they need not be simlutaneous, but the rounds per volley are a function of filling the volume of a sphere with rounds spaced such that they will guarantee no space big enough for the target exists without encountering a round.

This also fails to account for
1) point defense
2) systemic accuracy.

Now, why is nasa able to set this to 1 shot required? because At is 0, and thus 0/Atcs is 0. Actually, At is replaced with Emao (Error of Measurement Accuracy of Orbit), which is pretty small....
 
The only practical uses I can see for kinetic weapons are planetary/station bombardment and point defence.

Unless, of course, the range of ship combat is reduced ;)

I can't see gravitic powered projectile weapons as feasable due to the low G ratings of Traveller gravitic tech. You need hundreds, or even thousands of G to approach electromagnetically propelled rounds (unless you make your grav accelerator tunnel quite a length - but then you can make your rail gun just as long and get a greater acceleration).
 
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