As tech progreses and programambe and even guided rounds are becoming a norm the gun is far more versatile than ever

I particularly like how Italians chose to have 2x 76/62 mm Super Rapid guns on their STOVL carrier .

Russian AU220 naval munt with 'stealth garage' , 5T total weight

Thought this might be relevant.

L3 / DARPA have developed and plan to field a guided 57mm shell. This would be employed on the new FGGX Frigate and LCS.

https://www.navalnews.com/naval-news/2019/07/video-darpa-mad-fires-anti-ship-missile-self-defense-for-lcs-ffgx/

https://www.upi.com/Defense-News/2019/05/28/L3-awarded-92M-to-support-Navys-57mm-HE-4G-ammunition/3631559049733/

https://www.youtube.com/watch?v=vY9rJBL1S2Y

This would give the 57mm potential capability against UAS and missiles, and a very good capability against rapidly moving small boats.

If effective, this would prove a very useful Naval Gun indeed. 

Then add in work on 76 and 127mm rounds of similar capabilities, and we'll have naval artillery for a long, long time.

I taught the BAE Orca is already a thing?

file:///C:/Documents%20and%20Settings/CDSS/My%20Documents/Downloads/baes_ds_Mk295%20ORKA_redesign_digital.pdf

https://www.google.com/url?sa=i&url=https%3A%2F%2Fwww.baesystems.com%2Fen%2Fdownload-en%2F20170726161933%2F1434555371520.pdf&psig=AOvVaw10ElLzoMImSNcNjkpw5_F6&ust=1599590983661000&source=images&cd=vfe&ved=2ahUKEwiDupr02tfrAhWG-qQKHboEByIQr4kDegUIARCfAQ

From what I could see, ORKA was first (and more similar to what DARPA envisioned - a sort of cannon fired 'glide missile'). This would probably be a better option for highly maneuverable targets like missiles.

L3's H4 is a simpler, likely cheaper option. It appears from the video to be a shell, with some sort of internal rotor that helps course correct the shell / counter the natural dispersion of the gun on a moving ship. 

Both options - and the future ability to scale for 76mm and 5" guns - point to a continuing utility for Naval guns. Especially as a last line of defense against incoming anti-ship missile threats. 

Also makes me wonder about the potential for a 57mm armed Tank/IFV that could provide both ground attack and air defense capability...

It seems the Naval Gun is about to get a lot more useful:

https://breakingdefense.com/2018/01/86000-5600-mph-hyper-velocity-missile-defense/

BAE's HVP projectile is $86k for a guided, Hypervelocity projectile capable of shooting down missiles.

A 155mm version of the HVP was recently fired from an Army Howitzer to shoot down a Cruise Missile in training:

https://www.forbes.com/sites/davidaxe/2020/09/06/sci-fi-awesome-a-us-army-howitzer-just-shot-down-a-cruise-missile/#61c7268f209e

Given the cost of Patriot Missile or Standard 6 missile interceptor is $3 million, 35 HVP's could be fired for the same cost. And a ship can carry far more HVP shells then it can carry Missile Interceptors, making it a very compelling last line of defense.

These shells have already been fired from Naval 5" guns.

There are three 57mm guided rounds that were being offered for the USN.

ORKA from BAE has an IR seeker and pop-out fin steering.  It seems fairly conventional but with a flexible seeker that combines autonomous imaging IR and a semi-active laser receiver in one unit.

ALaMO from L3 had some unspecified guidance mode (something RF to judge by the lack of a glass seeker nose) and a fairly unusual mass counterweight course correction system.  It apparently has 4 "bolts" that can be ejected laterally to redirect the round, like the side thrusters in PAC-3.

These two are primarily anti-surface rounds for small boat targets, though both are said to have some anti-air capacity against UAVs and helicopters. ALaMO won a USN competition and is on the way to being type classified and deployed.

MAD-FIRES from Raytheon is a different beast.  It's primarily intended for antiship cruise missile raid defense.  Again, they're being cadgey about guidance, but it seems to be some sort of semi-active radar.  Big selling point seems to be the ability to redirect following rounds in flight to reengage targets that survive a first intercept attempt.  The technology may also have application to Army guns in either 50mm or 30mm.

gatnerd said:

A 155mm version of the HVP was recently fired from an Army Howitzer to shoot down a Cruise Missile in training:

In the same tests, they also fired HVP from a Navy 127mm deck gun and something that looks like a 155mm Advanced Gun System test rig.  

It's been intriguing to watch the pivot; when HVP was announced a few years ago, it was sold as an extended range anti-surface round, but this test shows the transition to air and missile defense has been fairly complete.

taschoene said:

It's been intriguing to watch the pivot; when HVP was announced a few years ago, it was sold as an extended range anti-surface round, but this test shows the transition to air and missile defense has been fairly complete.

Thats a welcome change in my book. It shows that the US is finally waking up to the threat posed by Chinas fireworks factory of anti-ship missiles. Of course, if they were really waking up to the threat, they'd be putting more emphasis on Cruise Missile Submarines rather then trying to overcome anti-ship missiles with their current plan of more ships. 

Along those lines, I hope MAD-FIRES comes to fruition, as that does seem the most promising cannon candidate for stopping missiles. 

Anti Missile use presents an interesting tradeoff for 'optimum' cannon size.

57mm MK3: 220rpm, 120rd magazine, ~10km range

76mm Super Rapid: 120rpm, 80rd magazine; ~20km range 

5": 20rpm, 20rd magazine, ~50km range

Smaller guns offer higher rate of fire and magazine capacity, but less range for interception, and lower probability of destroying / deflecting the missile. 

Larger provide a further interception range, and higher stopping power, but offer a substantial reduction in magazine capacity and rate of fire.