Author: M Santarini
Editor: W. Jurens
Warship International 2020 December 57/4
In this piece Santarini systematically investigated dispersion in the Italian 381/50. This was done with respect to single gun dispersion; battery dispersion was not considered, so things like alignment of turret planes and shell interference effects are left out. There is a certain inconsistency of terminology (so angle of incidence, yaw angle and angle of attack appear to be used for the same thing) and of mathematical notation (often subscripts to factors are shown as such, but other times not so that the reader might think there are two factors multiplied together). But, on the whole it is well written and presented.
Adm. Iachino claimed the large dispersion seen in many Italian guns in the time after 1912 was due to manufacturing tolerances in shells and charges. As far as proving ground dispersion was concerned this could not have been the case. Santarini says that this was not the case as so called 'al peso' ammunition was used. Here only shells were used with carefully controlled geometry and weight, while the weight of the charges was also almost exact. [However, on the battlefield some dispersion from this source might have occurred. ] In the mid-1940s Adm. Marcelo Pellegrini developed a theory that held that excessive muzzle blast was the cause of this dispersion. As a shell passes through the shock wave front, forces act on it. Santarini provides a table showing muzzle blast pressures for various Italian guns. There is no relation between blast pressure and dispersion. [The 203/53 was the most accurate Italian heavy gun. But the dispersion of its practice rounds fired with a 200 m/s lower MV had a higher dispersion than the normal rounds.] Next, Santarini considers another two causes of dispersion: loading density and the inverse expansion factor. Loading density is the density of the charge in relation to the density of water, and the inverse expansion ratio is the ratio of the chamber volume to the volume of the interior of the gun barrel. Again, he finds no reason to think the 381/50 was exceptional in either of these respects. Then he moves on to the effect of barrel vibration. Barrel vibration is sometimes a factor in short range dispersion. He gives a table showing a modest amount of dispersion due to barrel vibration that is fairly constant with range. Barrel vibration was not the cause of excessive vibration in this weapon either.
Figure 3 shows curves of dispersion versus range for various guns, mainly of 15 in calibre. The uppermost curve is that for the Italian 15/50 SAP. The next higher the krupp SKC 34, then the 15/50 with APC. The curve for the British 15 in with 4 crh shells is a good bit lower. At the bottom in descending order are the British 15 in with 6 crh shells, the British 14 in and the US 16 in. Sources are given for the data in the curves. [5 AKB 1861a and 3 AKB 2721 are given as sources for the later German 15in. However, as far as I can see the first reference gives a value for dispersion of less than a third of what Santarini has in the curve in Fig. 3. For example, the curve in 5 AKB 1861 has a 50% longitudinal dispersion at 10000 m of about 9.5 x 50 decimetres = 48 m (similar to the dispersion of the US 16 in), while Santarini has a value of about 190 m at this range. The dispersion values of the earlier German 15 in was lower still below 15000 m (see gkdos100, vol. a). Some of the British data were revised data published in 1948 and 1951. I prefer that in comparisons data is all for about a given year, say 1940 or so].
Finally Santarini comes to ballistic data. As a shell is accelerated out of the gun barrel and moves through the air forces act on it. These he works out by solving the appropriate differential equations numerically. In the battleship era this could not be done. Gravity acts on the shell at its centre of mass, while a resistance force and uplift act on the centre of pressure. Both centres are on the axial centreline of the shell with the centre of pressure being about half a metre in front of the centre of mass. Consequently, the resultant of the resistance and the uplift apply a torque about the centre of mass. Unless the shell is spun sufficiently this torque will eventually cause the shell to tumble. The ratio of the actual spin to the critical spin required to prevent tumbling is called the stability factor. However, if the spin much exceeds this critical value the shell will tend to remain pointing in the same absolute direction so that, as the shell follows its curved trajectory, the yaw angle increases. [Much earlier Tressider published a paper in which he IIRC assumed that shells remain pointing in the same direction due to their spin. This caused the aforementioned progressive increase in yaw. Tressider suggested this was the reason for the inferior penetration values found on the battlefield compared with proving ground data. However, it was obvious that this progressive increase in yaw did not in general happen to the extent he suggested.] The shell traces out a helix with a further circular motion superimposed on the precession orbit. There is an interesting diagram showing the motion of the shell, viewed from the front, with its combination of precession and nutation. Yaw increases resistance and there is a relationship between yaw amplitude and dispersion. As a shell slows down, its spin rate slows down too, but by less than the velocity. Consequently, as a shell moves downrange its stability factor increases. This means that yaw and yaw dispersion increase more or less inevitably with range. Yaw is also the origin of drift: if there is drift there is yaw.
To test this idea Santarini compares the stability factors at the muzzle for the British and Italian 15 in guns. Unfortunately he found similar values and seemed to have found a null result again. But then he realised he should have compared the stability factors at given velocities. When he did this he found the answer he was expecting. Two figures, copyrighted to W Jurens, show curves of, respectively, stability factor and axial angular momentum, plotted against velocity for the British and Italian guns. The uppermost curve is for the 15/50 SAP, closely followed by the 15/50 APC, then a bit lower the British 15 in 4 crh, the 15 in 6crh and at the bottom the British 14 in.
To recapitulate, the large downrange dispersion of the Italian 15/50 found in the range tables was mainly caused by excessive spin stabilization that caused progressive increase in yaw amplitude with increasing range. Santarini says various things could have been done to ameliorate this problem, had its cause been known. Most basically the guns could have been relined with modified rifling to give lower spin rates. More simply, lower muzzle velocities would have improved the situation. Such a solution would have likely been unwelcome though because the high velocity of the 15 in was chosen because it gave similar vertical penetration values to most 16 in guns.
However, Santarini says the main problem was not technical it was tactical. Italian admirals knew that many of their guns had very large dispersions at long ranges. They should have countered this by using their speed advantage to close the range to where dispersion was smaller. They should have also fired faster than was the case to increase the number of hits. At the action of Pantelleria in June 1942 two Italian cruisers did close the range. And they scored many 6 in hits on two British destroyers, an old cruiser, and two merchantmen. The 6 in guns in question were not very accurate at long range. The Italians were the superior force and should have done well, but there were many other times in the war where they did not take advantage of such situations.
[The increasing yaw of the 15/50 with increasing range would have reduced its ability to penetrate both vertical and horizontal armor. None of the usual penetration formulas would have applied to it downrange. Tressider was probably right in this case.]
Neil Robertson
Editor: W. Jurens
Warship International 2020 December 57/4
In this piece Santarini systematically investigated dispersion in the Italian 381/50. This was done with respect to single gun dispersion; battery dispersion was not considered, so things like alignment of turret planes and shell interference effects are left out. There is a certain inconsistency of terminology (so angle of incidence, yaw angle and angle of attack appear to be used for the same thing) and of mathematical notation (often subscripts to factors are shown as such, but other times not so that the reader might think there are two factors multiplied together). But, on the whole it is well written and presented.
Adm. Iachino claimed the large dispersion seen in many Italian guns in the time after 1912 was due to manufacturing tolerances in shells and charges. As far as proving ground dispersion was concerned this could not have been the case. Santarini says that this was not the case as so called 'al peso' ammunition was used. Here only shells were used with carefully controlled geometry and weight, while the weight of the charges was also almost exact. [However, on the battlefield some dispersion from this source might have occurred. ] In the mid-1940s Adm. Marcelo Pellegrini developed a theory that held that excessive muzzle blast was the cause of this dispersion. As a shell passes through the shock wave front, forces act on it. Santarini provides a table showing muzzle blast pressures for various Italian guns. There is no relation between blast pressure and dispersion. [The 203/53 was the most accurate Italian heavy gun. But the dispersion of its practice rounds fired with a 200 m/s lower MV had a higher dispersion than the normal rounds.] Next, Santarini considers another two causes of dispersion: loading density and the inverse expansion factor. Loading density is the density of the charge in relation to the density of water, and the inverse expansion ratio is the ratio of the chamber volume to the volume of the interior of the gun barrel. Again, he finds no reason to think the 381/50 was exceptional in either of these respects. Then he moves on to the effect of barrel vibration. Barrel vibration is sometimes a factor in short range dispersion. He gives a table showing a modest amount of dispersion due to barrel vibration that is fairly constant with range. Barrel vibration was not the cause of excessive vibration in this weapon either.
Figure 3 shows curves of dispersion versus range for various guns, mainly of 15 in calibre. The uppermost curve is that for the Italian 15/50 SAP. The next higher the krupp SKC 34, then the 15/50 with APC. The curve for the British 15 in with 4 crh shells is a good bit lower. At the bottom in descending order are the British 15 in with 6 crh shells, the British 14 in and the US 16 in. Sources are given for the data in the curves. [5 AKB 1861a and 3 AKB 2721 are given as sources for the later German 15in. However, as far as I can see the first reference gives a value for dispersion of less than a third of what Santarini has in the curve in Fig. 3. For example, the curve in 5 AKB 1861 has a 50% longitudinal dispersion at 10000 m of about 9.5 x 50 decimetres = 48 m (similar to the dispersion of the US 16 in), while Santarini has a value of about 190 m at this range. The dispersion values of the earlier German 15 in was lower still below 15000 m (see gkdos100, vol. a). Some of the British data were revised data published in 1948 and 1951. I prefer that in comparisons data is all for about a given year, say 1940 or so].
Finally Santarini comes to ballistic data. As a shell is accelerated out of the gun barrel and moves through the air forces act on it. These he works out by solving the appropriate differential equations numerically. In the battleship era this could not be done. Gravity acts on the shell at its centre of mass, while a resistance force and uplift act on the centre of pressure. Both centres are on the axial centreline of the shell with the centre of pressure being about half a metre in front of the centre of mass. Consequently, the resultant of the resistance and the uplift apply a torque about the centre of mass. Unless the shell is spun sufficiently this torque will eventually cause the shell to tumble. The ratio of the actual spin to the critical spin required to prevent tumbling is called the stability factor. However, if the spin much exceeds this critical value the shell will tend to remain pointing in the same absolute direction so that, as the shell follows its curved trajectory, the yaw angle increases. [Much earlier Tressider published a paper in which he IIRC assumed that shells remain pointing in the same direction due to their spin. This caused the aforementioned progressive increase in yaw. Tressider suggested this was the reason for the inferior penetration values found on the battlefield compared with proving ground data. However, it was obvious that this progressive increase in yaw did not in general happen to the extent he suggested.] The shell traces out a helix with a further circular motion superimposed on the precession orbit. There is an interesting diagram showing the motion of the shell, viewed from the front, with its combination of precession and nutation. Yaw increases resistance and there is a relationship between yaw amplitude and dispersion. As a shell slows down, its spin rate slows down too, but by less than the velocity. Consequently, as a shell moves downrange its stability factor increases. This means that yaw and yaw dispersion increase more or less inevitably with range. Yaw is also the origin of drift: if there is drift there is yaw.
To test this idea Santarini compares the stability factors at the muzzle for the British and Italian 15 in guns. Unfortunately he found similar values and seemed to have found a null result again. But then he realised he should have compared the stability factors at given velocities. When he did this he found the answer he was expecting. Two figures, copyrighted to W Jurens, show curves of, respectively, stability factor and axial angular momentum, plotted against velocity for the British and Italian guns. The uppermost curve is for the 15/50 SAP, closely followed by the 15/50 APC, then a bit lower the British 15 in 4 crh, the 15 in 6crh and at the bottom the British 14 in.
To recapitulate, the large downrange dispersion of the Italian 15/50 found in the range tables was mainly caused by excessive spin stabilization that caused progressive increase in yaw amplitude with increasing range. Santarini says various things could have been done to ameliorate this problem, had its cause been known. Most basically the guns could have been relined with modified rifling to give lower spin rates. More simply, lower muzzle velocities would have improved the situation. Such a solution would have likely been unwelcome though because the high velocity of the 15 in was chosen because it gave similar vertical penetration values to most 16 in guns.
However, Santarini says the main problem was not technical it was tactical. Italian admirals knew that many of their guns had very large dispersions at long ranges. They should have countered this by using their speed advantage to close the range to where dispersion was smaller. They should have also fired faster than was the case to increase the number of hits. At the action of Pantelleria in June 1942 two Italian cruisers did close the range. And they scored many 6 in hits on two British destroyers, an old cruiser, and two merchantmen. The 6 in guns in question were not very accurate at long range. The Italians were the superior force and should have done well, but there were many other times in the war where they did not take advantage of such situations.
[The increasing yaw of the 15/50 with increasing range would have reduced its ability to penetrate both vertical and horizontal armor. None of the usual penetration formulas would have applied to it downrange. Tressider was probably right in this case.]
Neil Robertson
statistics: Posted by neilrobertson1 — 2:06 PM - Today — Replies 4 — Views 141