Naval Gun Accuracy

It’s discouraging to see how many people believe that modern fire control systems guarantee unerring accuracy.  I’ve seen claims that the Oto Melara 76 mm only needs three rounds per engagement against anti-ship missiles.  That’s absurd!  When the head of Oto Melara, in a live fire test, agrees to stand on a target protected by one of his guns that has only three rounds in the magazine, I’ll begin to believe the claim.
 
So many people seem to think that modern guns can’t miss.  I guess this is an example of a little bit of knowledge being a dangerous thing.  People understand just enough about computers to know that we can write a program that predicts where a round should go to impact/intercept the target and they assume that the program can’t be wrong, therefore, the shot must hit with unfailing accuracy. 
 
Reality, however, is much different.  Yes, a program can make a prediction – that’s just simple mathematics and that’s child’s play.  What the program can’t do is account for the hundreds of factors that actually affect the accuracy of a naval gun.  Let’s briefly consider some of the more obvious factors:
 
Stabilization – One of the most blatantly incorrect beliefs among naval observers is the myth of stabilization.  People forget that both the firing platform and the target are continuously pitching and rolling, among other movements.  Yes, we have stabilization (of the firing platform, not the target!) but stabilization is not even remotely perfect.  The guns are large, heavy chunks of steel and have inertia.  Just because the stabilizer computer signals the gun to move doesn’t mean it can instantaneously accomplish that movement.  There is a lag and in the world of micro-deviations (we’ll address that shortly), which is what we’re discussing, that’s a problem.  Stabilization is a gross phenomenon, not a micro phenomenon and it does not, indeed cannot, assure accuracy – it just reduces gross inaccuracy.
 
Let’s consider some other common factors that impact accuracy:
 

• Barrel Wear – wear is a constantly changing phenomenon and is not uniform along the length of the barrel
• Barrel Temperature – changes on every shot and is not uniform along the length of the barrel
• Wind – constantly changing and changing throughout the length/time of the shell’s flight profile
• Barrel Movement – the barrel is moving (pitching, rolling, and attempting to stabilize) while the round is traveling through it!
• Shell Uniformity – every round has minute (and no so minute!) differences in weight, shape, smoothness, dents, etc. and each one affects accuracy
• Friction – this is a factor of the shape of the round, density of the air, humidity, wind, etc. and, of course, there’s always friction between the barrel and the shell
• Humidity – this is constantly changing on the micro scale as the shell encounters wind currents, spray, fog, rain, etc.
• Density – the density of the air is constantly changing due to temperature, humidity, altitude, etc. causing changes in friction and speed of the projectile
• Temperature – changes with elevation, wind currents, and wave behavior causing updrafts and downdrafts
• Target Movement – the target is constantly moving in all three dimensions while the intercepting shell is being fired and traveling through the barrel and the target continues to move during the entire travel time of intercepting shell;  some of the movement is due to physical factors (wind, friction, etc.) and some is due to intentional terminal maneuvering;  when we take a radar ‘fix’ on the target, the implicit assumption is that the target will continue on its path and that’s utterly false, as we just noted

 
What program has the slightest hope of accurately modeling those factors especially since we have no means of measuring most of them other than in the grossest sense?
 
 
Deviations
 
So, we’ve now acknowledged that there are too many factors that impact accuracy for us to account for all of them and we lack the sensors to do so even if we could program them into the fire control algorithm.  But, you say, the deviations are minor.  Well, let’s examine the magnitude of the effect of the cumulative ‘minor’ deviations.
 
Projecting a straight line from the shell in the barrel, waiting to be fired, to the predicted intercept point, gives us a travel path that we think/hope will meet the target.  Any deviation will cause an angular change from the predicted travel path.  That angular deviation can be considered in degrees.  If the shell perfectly follows the predicted path, that would be 0 degrees deviation.  If the shell were to, ridiculously, take an immediate right angle turn off the predicted path, that would be a 90 degree deviation.  Realistically, the deviation will be on the order of 0-10 degrees or so.  Let’s see what impact small degrees of deviation have on the difference between the actual intercept point as compared to the predicted point.
 
For this illustrative example, let’s consider a predicted intercept point at a distance of 1 mile (5,280 feet).  We’ll use the geometry of a right triangle to calculate the deviation.  Specifically, we’ll use the formula
 
     tan(deviation angle) = opposite/adjacent
 
rearranging,
 
     opposite = tan(deviation angle) * adjacent
 
where,
 
opposite = the deviation from theoretical intercept point, in feet
adjacent = 5,280 ft  (distance to theoretical intercept point)
deviation angle = the angular deviation from the predicted intercept path, in degrees
 
Using the above formula, we get the following results for various degrees of deviation.
 
10 deg = 931 ft
5 deg = 462 ft
1 deg = 92 ft
0.5 deg = 46 ft
0.1 deg = 9 ft
 
We see then that even a miniscule 0.5 deg deviation will result in a 46 ft miss.  We have to be down around 0.1 deg or less deviation to hit our predicted intercept point close enough to be effective.  Of course, that assumes the target perfectly followed its predicted travel path and didn’t change course, altitude, or speed!
 
Wow!  That is not much allowable deviation before we have a clean miss!  From observations of video of live fire gun exercises, my estimate is that deviations of 0.5-5 degrees are normal.  That’s not encouraging.  I’m beginning to think that hitting a target with a naval gun is almost impossible.
 
Before we throw up our hands and give up trying to hit an intercept point with a naval gun, let’s recall that there are a few things that can help improve our odds.
 
Number of Shells – It’s a given that every shot we fire will have a deviation to some extent.  However, if we fire enough shells toward the predicted intercept point, one or some of them will, statistically, wind up being close enough to be effective.  This argues for smaller caliber projectiles that can be fired quickly and in large numbers.
 
Rate of Fire – This is another way of saying, number of shells, but it goes beyond that.  There’s a time lag between every shot and the greater the time lag, the fewer shells we can put into the predicted intercept point.  To illustrate, if we could fire a thousand shells in one second, we’d saturate the intercept point and compensate for the individual inaccuracies with numbers.  On the other hand, if we can only fire one shell per minute, then we can only ever have one shell in the intercept area at a time before the intercept point changes significantly and odds are it will miss due to the various factors we’ve discussed.  This argues for extremely high rates of fire.
 
Stabilization – The quicker our gun can respond to stabilization commands, the more accurate we’ll be.  This is accomplished by decreasing the inertia of the gun which is accomplished by decreasing the weight of the gun and/or increasing the power of the train/elevation motors.  This argues for smaller, lighter weight guns.
 
We see, now, why a 5” gun is very unlikely to be effective at hitting a cruise missile.  In fact, modern 5” guns have been proven to be woefully inaccurate even against slow moving (relative to a missile) Boghammer boats (the Vincennes incident).
 
Fragmentation - Yet another compensating measure is fragmentation.  If we have to have a direct hit on the target to kill it, our odds are extremely poor.  However, if we can just be in the general vicinity of the target and kill it via shrapnel (fragmentation), our odds increase.  The larger the effective fragmentation area, the better our chances.  This suggests using large shells that can disperse large quantities of shrapnel.  However, there is a limit because the fragmentation pattern takes time to spread out after the shell explodes and if too much time is taken the target has flown past before the shrapnel can spread out.  So, there’s an effective limit on how big a pattern can be effectively used but I have no idea what that limit is.
 
Guidance – Guided projectiles offer another way to improve accuracy but at a significant, literal cost.  There are companies who offer, or are developing, small guided projectiles but, as far as I know, there is no test data under remotely realistic conditions that demonstrates that they are effective.  They may or may not be.
 
 
Conclusion
 
It is clear that naval guns are inherently inaccurate.  For the case of fixed land targets, we can compensate for inaccuracy with explosiveness.  If we’re firing 16” battleship shells, accuracy is a lesser concern as the giant 50 foot craters will compensate for a lot a inaccuracy.  We can also substitute multiple salvos for accuracy knowing that statistical odds will ensure that if we fire enough rounds, some will hit the target.  Besides, it’s not as if a fixed target is going anywhere.
 
However, if we’re trying to shoot down an anti-ship missile, we need small, light, very rapid fire guns which is the concept behind 20-30 mm CIWS guns.  It’s clear that larger guns (5”, 57/76 mm) are ineffective for the anti-air role, barring dumb luck.