7.62 or 5.56 will be much better choice than 12.7 as you will need direct hit anyway, and higher ROF and lower weight are huge advantage here. 20mm is also ok - but only with precise dalayed fusing. Such fusing will surery make whole system more expencive, but on the other hand will allow less precise aiming. So it is a good trade-off. Allthought in that case i would propose 30 or even 40mm shells - they have an order of magnitude stronger explosive effect.
This is pretty much on point. There are two ways to go about intercepting incoming missiles, and they are both covered here.
I'm going to expand a little and use the laymans explanation, so that other people who read this thread can pick it up, and also because I have little direct contact with these systems.
You can opt for the "wall of lead" approach, with smallish calibre and high rate of fire. The advantages are:
-It is cheaper than a fancy prox fuse system
-Easier to manufacture
-Can carry quite a number of projectiles
-High rate of fire
-The system itself is smaller, and has considerable weight savings and can slew quicker for a given size. (Weight savings possibly offset by large magazine)
-Supply lines would use existing boxed ammo, not requiring special resupply considerations to be made
The general idea being to throw so much at the incoming projectile that it simply has to run into something or other before it gets to you. Interception with a kinetic kill, requiring a direct hit, but upping your chances with a high number of attempts.
The other option is to go with a "smart" system and use large calibre, like your 20mm, then you have the advantages of:
-More flexibility as you can engage harder targets while slaved
-Better chance to hit with a given projectile
-Needs less ammo to intercept missiles, leaving more for engaging other targets.
Attempting to intercept the precise way requires some fancy calculations. Nothing a decent computer can't handle - you already have some pretty decent fire-control radar systems for the system already - but still means spending more money per unit.
Looking at the two lists, it's easier to pick the first way out, as any given defence force usually want the cheaper, smaller system that doesn't require anything special. Your advantages don't necessarily outweigh the 'smarter' system, but it's easier to manufacture, cheaper, smaller and uses the same ammunition as something or other out there.
I'd opt for the smaller projectile with the flattest trajectory, and then work up from there with testing. Flattest trajectory for each will depend on a few different things such as barrel length, twist, etc. The objective is to find a round that will positively go straight and direct and have minimal drop or drift, that way you don't have to track and adjust for wind and range constantly.
5.56mm FMJ rounds might not have quite enough mass to destroy the incoming weapon (although I am reasonably sure it would), and .50 calibre might be just that little too bulky to carry. It all depends on the system you come up with, and the proof is definitely in the testing.
Next you have to think about a couple of things:
1) Will your radar see only direct LOS weapons or will it be able to detect top-down missiles? Top down will defend against Javelin, and air-launched missiles, so you'll have to build a radar capable of looking up, and far. That'll make it pretty big.
2) Given the system is going to be active, how are you preventing EW from detecting and tracking you? Jamming? Radiation-seeking missiles? These are all things that need to be addressed, although not insurmountable.
3) How much lead do you want to throw? Are you using an automatic machine gun system? Chain or Gatling gun? Multiple gun system, with two or four linked together? Multiple-shot "Metal Storm" system?
I'd have to say, selling the concept is pretty much like selling the CIWS/Phalanx system for vehicles, and probably isn't new. I'd say there'd be patents existing that would cover the use of a system such as this for vehicles, so that's a hurdle there.
The concept sounds great, and I'm not trying to rain on your parade, even though I sound cynical. I'd think it's a decent idea, although I am not sure you'll be able to make it small enough to fit onto a tank or APC and not have it take up too much space that it would be deemed too big by the people you are trying to sell it to.
Your key points to try to sell the idea is: Low cost, compatibility of ammo, ease of maintenance and small size.