Effective battle ranges

[Karl Heidenreich]

I have been wondering about all this fuss about Bismarck´s "inability" to defeat other BBs armour and, ironically, the capability of these ships to defeat Bismarck´s own.
Most of these arguments are born in the relation of gun size, shell weight, range and impact angle.
In the theoretical scenario forum the main arguments against Bismarck came from elements mentioned based, always, in the expected ranges the ships use to fight one against the other.
The first argument is that ships like Iowa or Nelson had a greater effective range (with their 16" guns) than those with 15" guns (Bismarck). But reading Naval History we didn´t find, in fact, that BBs did actually fought from the very beginning of engagements from extreme ranges but instead tend to close. The combats happened at ranges as close to 4K yards (May 27th, 1941) as to 16K yards (May 24th, 1941). As a matter of fact the long shots are the exception, not the rule, as the Schanhorst´s and Warspite´s firing shows.
This may be from the fact that even if a BB can shoot very long shots and can even straddle her enemy it´s more difficult for them to hit because at those ranges the shape of the target is so thin (at her relation with a near vertical plunging fire) that the hit/straddle ratio is very narrow. When a BB is firing against a closer target the angle of the incoming shell had two components, vertical and horizontal, which make it a little bit easier to hit with a not so narrow hit/straddle ratio (This affects the holy argument of the radar directed fire control that can guarantee the straddle but, at those ranges, can´t guarantee the hit).
This must be the reason for the likehood of the admirals and captains to close to the enemy instead of engaging at the extreme effective ranges.
But there is another interesting factor that come into play when the BBs close to one another: the "curves" of the ideal armour penetration for the "heavier" guns at longer ranges become surpassed by "lighter" guns at shorter ranges (and not so short but inside the effective ratio of the heavier gun, we can talk about intermediate ranges between 10K and 20K yards). In other words: the "lighter" guns are more likely to be effective because the actual combat range is, at the same time, their ideal range in which they could penetrate the enemy´s armour, not so the "heavier" guns which need more distance to achieve their ideal punch.
Given all these we have the scenario in which the radar directed "heavy" guns doesn´t have all the nominal advantage it´s expected from them, but the "lighter" guns do.

[Bgile]

The Denmarck Strait battle started at 25,000 yds. I think the British opened fire as soon as they could get a good firing solution on a recognized target. The reason the range closed is because the British wanted a decisive battle where they could concentrate fire on Bismarck and get lots of hits. The Germans couldn’t turn away because they needed to get past the British into the North Atlantic. In the event, the secondary batteries were completely ineffective, achieving no hits at all.

In the 2nd Battle of Guadalcanal, Washington’s secondary battery was effective because of radar fire control. It caused fires and did superstructure damage and had the possibility of destroying main battery fire control positions, so it could have been decisive in effecting the outcome of the battle if it had been between more equal opponents. As it was, the artillery duel was lopsided and Washington’s 16” shells penetrated armor and undoubtedly did terrible execution inside the Japanese ship.

I think an Iowa class ship would have attempted to keep the range long against Bismarck because that would take advantage of the heavy shells of the former. If both sides expend their ammunition and Iowa gets just a few hits on Bismarck, it might still be decisive.

Battle ranges were dictated to a great extent by the circumstances. I don’t think there was ever a situation where one side could maintain an advantage at long range and was also able to dictate the range.

[Karl Heidenreich]

Bgile:

Battle ranges were dictated to a great extent by the circumstances. I don’t think there was ever a situation where one side could maintain an advantage at long range and was also able to dictate the range.

That´s exactly my point: the extreme effective ranges are dangerous assumptions if you depend on them (and only on them). It takes just a bold and dynamic enemy to close to a range in which he could use his armament at his best.

[Bgile]

Bgile:

Battle ranges were dictated to a great extent by the circumstances. I don’t think there was ever a situation where one side could maintain an advantage at long range and was also able to dictate the range.

That´s exactly my point: the extreme effective ranges are dangerous assumptions if you depend on them (and only on them). It takes just a bold and dynamic enemy to close to a range in which he could use his armament at his best.

but how is your bold and dynamic Bismarck commander going to close on an Iowa in the North Atlantic? Hide behind an iceberg?

[Karl Heidenreich]

Bismarck, as any Battleship, could withstand punishment as it closes range. There is no need to hide. Bismarck, before her scuttling, was heavily punished while not having any steering and doing less than 7 knots.
At 29-30 knots and fully operational it could do it. That´s why they build battleship after all, to absorve damage and be able to deliver it.
But I was not thinking in a Iowa-Bismarck battle but in the concept in itself... and if considering a theoretical scenario then the Bismarck-Nelson combat is more likely.

[Dave Saxton]

.............This may be from the fact that even if a BB can shoot very long shots and can even straddle her enemy it´s more difficult for them to hit because at those ranges the shape of the target is so thin (at her relation with a near vertical plunging fire) that the hit/straddle ratio is very narrow. When a BB is firing against a closer target the angle of the incoming shell had two components, vertical and horizontal, which make it a little bit easier to hit with a not so narrow hit/straddle ratio .......This must be the reason for the likehood of the admirals and captains to close to the enemy instead of engaging at the extreme effective ranges.
.............In other words: the "lighter" guns are more likely to be effective because the actual combat range is, at the same time, their ideal range in which they could penetrate the enemy´s armour, not so the "heavier" guns which need more distance to achieve their ideal punch.
Given all these we have the scenario in which the radar directed "heavy" guns doesn´t have all the nominal advantage it´s expected from them, but the "lighter" guns do.

That's an astute observation that the percentage of hits scored from straddles is more a function of ballistic characteristics, than in aquiring targeting data. The ability to straddle may not result in a higher percentage of hits. Of course one must have sufficiant targeting data to obtain a straddle in the first place, or you have virtually zero chance. In cases of poor visability, usable radar is a big plus. The example of the Battle of North Cape comes to mind. Nonetheless, the range at where a higher percentage of hits might be obtained, may be greater with a lower flying projectile, radar or not.

This may seem counter intuitive, but a higher velocity gun of the same caliber may have a greater effective range, as defined as the limit were hits are more likely. As range increases for any gun, the probability of scoring hits goes down, and there seems to be a strong relationship of the probability of scoring hit's, with the angle of departure, and the angle of fall. As these angles increase with range, the probability of scoring hits goes down.

A low trajectory gun, extends the range were these angles are still optimal. For example, the angle of departure of the German 38cm is less than 15* all the way out to 25km. Wow, that's out there! Additionally, at ranges of less than 25km, the Bismarck projectile will still have a great striking velocity, but because it's relatively light for it's caliber, it will have a steeper angle of fall at ranges greater than 25km, than a heavier shell of the same caliber of similar muzzle velocity. This will aid deck penetration at the ranges were deck hits are more likely.

As originally designed, the Nelson class 16-inch utilized similar principles as described above. However, they had to reduce the muzzle velocity of the gun, because of bore wear problems. The Nelson class 16" was probably better suited to shorter ranges as it was used.

As long as the beginning velocity is equally, or nearly equally high, a heavier shell will maintain greater velocities at increasing range. This may help extend the range to were it may obtain a higher percentage of hits, by reducing the angle of fall, but it would also increase the range of where it begins to present a great danger to decks.

If we define effective range as the ranges where hits are more likely, it will probably be to the limit of the optimal angles of departure and fall. Other factors, such as scatter, may also reduce the effective range were hits are more likely. Does the armour scheme of a given BB match up well at such ranges?

[tommy303]

Dave and Karl have some interesting points and I agree. Discussions of range often overlook the ranges at which hits can be predictably achieved, and these are always much shorter than a gun's maximum range.

Major factors determining maximum range of a gun (not to be confused with the maximum range allowed by a gun's mounting, but instead at optimum elevation) are velocity, angle of elevation, weight of the shell, and the aerodynamic efficiency of the shell design. As an example of the latter, the absolute maximum range for the German 38cm was actually longer than the USN 16-in 50 cal by several thousand yards. This was due to the higher muzzle velocity of the German gun, although if all things had been equal the heavier 2700-lbs shell should have ranged farther; however, the calibre radius head of the German shell was larger, giving it a more efficient low drag nose compared to the US shell. In this instance, a combination of less drag and higher initial velocity translated into greater range.

Presuming all other factors being equal--ie namely that the gun/shell/velocity combination provide for a reasonable amount of accuracy with minimal dispersion--most naval guns begin to achieve a reasonble expectation of scoring a hit with a straddle on a battleship at about 50%, or slightly more, of their absolute maximum range with the standard shell and service charge. For the 38cm, whose absolute maximum range with a 1764-lbs APC shell, was approximately 44,000 yards, this works out to about 22,000 yards before mathimatical hit probability makes it really worth while to begin shooting in earnest. One could, and many commanders did, open fire at longer ranges in hopes of aquiring the target and registering straddles sooner, but the rule of thumb was not to expect too many hits until range was down to half of maximum.

If one looks at the Denmark Straits battle as an example, Bismarck's most effective gunnery ranges started at about 22,000 yards, while Prinz Eugen's started at about 18,000; likewise, PoW's and Hood's optimum ranges started at about 20,000. While Holland opened fire at slightly over 25,000, somewhat beyond optimum, Luetjens, instead of being indecisive, may have been biding his time until the range fell to within the best range for his flagship's guns. The hits scored by PoW fell within the expected range of 50% or less, as did Bismarck's, and only Prinz Eugen acheived a notable success at greater than her 50% when she hit Hood with her second salvo; all the rest of her hits (all on PoW) were achieved at or only slightly under her 50% figure.

Just to clarify, at ranges much over 50% of maximum, hit probability is never 0; if you consistently straddle the target, you will eventually hit it, but the ammunition expenditure would be very high. It might also be wise to state that the 50% figure applies to battleship sized targets manouvering normally. Larger or smaller targets would tend to increase or decrease the figure respectively.

[Bgile]

Tommy,

What you seem to be saying is the USN handicapped themselves by going to the heavy projectiles and they should have stayed with the lighter, higher velocity shells.

You have to wonder what their thinking was. I have always assumed it was to achieve better deck penetration, but at the ranges you are hypothesizing there wouldn't be much chance of any deck penetration at all.

[tommy303]

Hi Begile,

Well I am not quite saying the US handicapped themselves. Perhaps to a slight degree with the 16-in 50s they did, but the lower velocity 16-in 45s of the two preceeding classes would definitely have benifited from the steeper trajectories, at least as far as deck penetration went. While one of the benefits of the 2700 lbs projectile was certainly better performance against deck armour, at a slight trade off against side armour, the 2700-lbs shell was more optimized tor surviving a wide variety of impact angles. That this included impacts against horizontal armour might have been more coincidental, however desirable.

The higher velocity guns of the Iowas naturally had slightly lower trajectories and would have suffered some in regards to horizontal penetration, but with a slight increase in danger space--ie better chances of hitting.

It is also possible, at the time the 2700-lbs shell was adopted as service standard, that there were hopes of greater possible gun ranges due to advancements in rangekeepers and stable vertical elements of fire control.

One also has to remember that in the US navy, battleships usually carried mostly AP ammunition prior to the war and for a time during it until calls for shore bombardment turned the emphisis to HC or HE type shells. If one has only AP ammunition, one can afford to open fire at longer ranges in a battleship duel and possibly expend a large number of shells for a relatively small number of hits, particularly since at long range you might only need one. Holland's two capital ships were armed in the same fashion, with mainly APC shells, and so it behoved Holland to fire when he felt he had a chance of aquiring the target; Bismarck on the other hand had only 1/3 AP in her outfit of shells because of the nature of her mission, so Luetjens could not afford to be extravagent.

[Tiornu]

At what angle of descent does danger space cease to be relevant?

[Bill Jurens]

For what it is worth, the USN considered 'long range' to be where the angle of fall exceeded 30 degrees, and/or less than one hit could be assumed per salvo. This, incidentally, was one reason why the 12-gun BBs were seen to have a longer effective range than the 8-gun BBs...

Bill Jurens.

[Dave Saxton]

As I recall, some of the people at Dahlgren figured it was when the angle of depature exceeded approximately 15*. Looking at the German 38cm this would equate with angles of fall, to about 23*, and ranges to about 27,000 yards. If we figure that an angle of depature, up to say 18*, is only marginally more, then the angle of fall limit would be around 27*. A 30* angle of fall would occur with angle of depature slighlty exceeding 20*. In the case of the German 38cm, this is also the range of angle of departure (15-20*), with the least possibility of scatter.

Using Thomas's general rule of it being 50% of the absolute maximum range, this would be 21km for the German 38cm. We would find the angle of departure to be about 13*, and the angle of fall to be around 18*, so this rule of thumb would not follow with all guns. At 22,000 yards, the angle of fall would be around 16-17*. This point of 16* Angle of fall, would come at about 20,000 yards for most 45 caliber length guns.

As to Steve's question about the USN handicapping themselves, a comparison of the angle of fall of the three American 16-inch combonations, is an interesting study.

The West Virginia 16"/45 using a 2240 lb projectile reaches a 23* angle of fall at about 24,000 yards. It's point of 16* Aof is reached at about 20, ooo yards. It would reach 30* angle of fall at about 29,000 yards.

Going to the 2,700lb projectile in the 16"/45 shifts everything to a slightly lower range, by reducing the MV. The 16* AoF point, comes at only 17,000 yards (about the same as the KGV 14"). 23* AoF is reached at about 23,000 yards, but the 30* AoF point is reached at about 28,000 yards.

By restoring the MV when using the 50 caliber length 16" gun, these dynamics are changed quite a bit. 16* Aof comes at about 21,000 yards, 23* at 26,000 yards, and 30* AoF at about 31,000 yards.

As long as the muzzle velocities are more or less the same, a heavier projectile extends these ranges. It's interesting that the USN 16"/50 and the German 38cm have similar danger space, and the range were 30* AoF is reached. The German 16" danger space extends to farther ranges.

[Karl Heidenreich]

Still, there is something that bothers me and cames from another thread (which I can´t find now ). It cames from Bill Jurens, I believe, and was very clear: the American Mark VII 16" gun can penetrate Bismarck´s armour at any range. Bismarck´s amour was vulnerable whatever range and angle due to the enemy shell dynamics.
Did we all agree with that? Or not...?

[Brad Fischer]

This is an interesting discussion. I think that there is perhaps too much focus placed on dangers space – which is obviously a function of angle of fall, which in turn is related mostly to IV – but when talking about straddles and hitting efficiency in general dispersion arguably plays a much larger role. A point of comparison is the USN 16/45 and 16/50 guns with the Mark 8 2,700lb projectiles. As noted the angle of fall at any given range is lower for the higher velocity gun and hence the danger space will be larger. Seemingly this would indicate that the larger gun will have a longer effective range but in fact the 16/45 has better dispersion – not by much – but enough to compensate for the differences in danger space (actually the 16/45 has a small advantage in hit probability).

There seems to be a perception that over a certain range even consistent straddles will only produce occasional hits. Certainly this would be true if TMD was excessively large but as a general rule TMD has a (more or less) linear relationship with range and it’s unlikely that one would find any marked drop off in hit probabilities from this effect alone. Of course one must of course factor in other variables such as MPI errors (which in turn have a relationship with dispersion) and target size (which also varies with range). Leaving MPI errors aside for a moment, if one looks simply at the increase in TMD and decrease in hitting space, this ‘raw’ hit probability curve is much more shallow than when one factors in MPI errors. With even average TMD figures, if one were to consistently straddle a target at even very long ranges, one could expect to get fairly consistent hitting.

The key here is MPI errors, which is actually a indication of control. Control is how well the guns are aimed to hit the target (i.e. your computer ‘solution’) and dispersion is how well the guns are aimed collectively to that point. When I say “aim” for control that is a gross simplification as it goes far beyond simple battery alignment. To get consistent straddles you need accurate range/deflection observational data, accurate computations and accurate observation of the fall of shot. Again a simplification but still generally valid. More often than not gunnery engagements historically failed in the 1st and 3rd criteria.

Until the advent of fire control radar, MPI errors in combat could only judged in general terms which is why obtaining a straddle was the common metric by which to assess weather your ship had found the hitting range. This makes it very difficult to even guess at the mean and standard deviation of MPI errors, BUT one should be able to tell if one is straddling, particularly at short ranges. What I’m eventually getting at is even in such cases, where one is straddling consistently, even at long ranges were the patterns are large the MPI errors are good enough to score fairly consistent hitting.

Where I think folks become confused is when they see in the action reports that X ship straddled Y ship a couple of times (or mentions straddles in passing) they tend to think “OK see here X ship is straddling but only score 1 hit…”. For instance if you read POW gunnery report from Denmark Strait, you see the troubles they had that day in establishing and keeping the hitting range and deflection and indeed they crisscrossed Bismarck several times. You see this type of MPI behavior in prewar battle practices as well.

I am quite skeptical of the 15° angle of departure “rule”. I have not see this anywhere in any official documents nor has any of my correspondents. I have seen this in a couple of internet forums but they all seem to point back to one source from which I have yet to see a plausible or official citation. I think these rules of thumb tend to emanate from urban legends and sea stories than any sort of systematic analysis. The only rule of thumb that I’ve seen – a second hand source admittedly – is from the RN, where a time of flight of 50 seconds is considered to be the maximum for effective fire control.

This makes much more sense as fire control is a position-motion-time problem. This is of course one viewpoint; certainly the pacific naval powers had another. You can see this reflected in battle practice shoots. For example I have a report discussing the accuracy of the RN 14-inch Mark VII covering all KGV class exercises from 1942-1944 and the max range was about 24,000yds. This compares to the USN of about 35,000 yards and the Japanese out to 37,000yards (prewar). This doesn’t imply that one viewpoint is correct, just a reflection of doctrine and training. The latter be the most vital component to any weapon system.

Brad Fischer

[Tiornu]

I have to agree that the 15° "rule" is probably nonsense. Almost the entirety of Empress Augusta Bay was conducted at higher elevations (at least as far as the US CLs were concerned), and the Japanese were explicit in assessing the incoming as disturbingly tight and accurate.