Last week I had some time to spare and spent a lot of midnight oil trying to read up on shell balloting phenomenon. Its not like only OFB shells and India Army guns have this problem. Except since we don't understand it we whine to half baked reporters.
Many of the reports I read are quite mathematical but I will keep it qualitative and at high level to make the points. I will refer to reports available online to make the points for further reading.Background:
Over past five years Indian press has reported numerous instance of 155mm shell burst and muzzle strikes in barrels. Many of these are documented in this thread on earlier pages and can be searched for details. Number of occurrences per press reports is Bofors (40 times), upgraded M-46 130mm guns, Dhanush (3 times), and now M777 (1 time).These incidents have happened in Bofors 39 calibers, Soltam 45 caliber, Dhanush 45 caliber and M777 BAE guns. And have happened with imported NASCHEM and OFB made shells. The only data we have is the shells have burst after many rounds have been fired. We know for the M777 incidents the shells were ERFB/BB and BT units. We don't know about the other shells as the sources were not forthcoming. However in most likelihood it could be the ERFB types of shell as the IA wants maximum range for the artillery.Discussion:
Shell burst in barrel and muzzle strike are all phenomenon related to internal ballistics of the gun. They relate to interaction of shell and gun barrel after the charge is ignited. We can ignore all other types of ballistics as not being germane to this topic.
Lets talk about the barrel. The barrel is designated as 155mm x 39, 155mmx45 from breech end to muzzle exit. This means the barrel is 39 x 155 equals 6045mm and 45x 155 equals 6975 mm. The muzzle is not rifled.
The barrel can be considered as a long thick wall pressure vessel and has a muzzle brake at one end to reduce forces of recoil. After the charge ignition, the barrel develops circumferential tensile stresses (hoop stress) which are prominent. Hence the barrels are made of high strength steel and are heat treated and a compressive pre-stress by auto-frettage to overcome the high tensile stresses. There could be micro cracks developed in the manufacturing process and occasional high charge ignition. Repeated firings induce fatigue and could cause barrel to fail. Part of development testing is to find the fatigue life and change barrels before barrel failure.
Another phenomenon is barrel wear. The shell is a tight fit in the barrel at the driving band and the bourrelet. The charge ignition causes the shell to move forward and the rifling of the barrel imparts spin to the shell. Usually the rifling is 1 in 20 for the 155mm gun. That means the rifling twist is 1 in 20*155mm i.e. 3100 mm. This means the shell makes one revolution in a travel of 3100 mm.
(note the barrel length including muzzle is about 6045mm. In other words the shell hardly makes less than 2 turns inside the barrel!)This causes friction wear. In addition due to the high temperature gases and chemical compounds in the shell propellant there is erosion wear. Studies have shown the erosion wear is higher than the friction wear as the shell driving band is made of copper or other softer metal than the steel used for the barrel. Part of development testing is to find out the barrel wear life and determine when the barrels need to be changed. Gun barrel wear is measured after numerous firings and the population divided into four quartile. 1st quartile would be like zero to little wear and 4th quartile would be maximum wear and near to replacement.
Comparing the barrel fatigue life to the barrel erosion life the latter is found to be more predominant for determining gun barrel life. In other words a barrel will wear out before It burst unless there is an accident.
Lets talk about the shell. The shell at macro level is a long cylinder with an ogive nose for aerodynamic shape. In order to resist the firing pressure the base of the shell is thicker and hence the cg is closer to the base. The center of pressure is forward of the cg and will lead to static instability, like a top will rest on its side when not spinning.
The ogive portion has the fuze cavity and houses the fuze. Early 155mm shells like the M107 were made from low carbon steel and were stubbier. The search for longer range and for fragmentation effects led to developing the ERFB/BB shells which are long and made from manganese steel which can fragment easily. Then to sum up these two type of shells are shaped differently and made from different materials but both are fired from same gun barrel with constant 1 in 20 rifling which imparts same spin. The charge determines how quickly the shell gets spun. Now both shells are manufactured by forging from steel blanks and are machined on lathes, driving band shrunk fit and explosives filled. This process ensures the shells are quite defect free as the forging process subjects them to large forces and machining ensures they are concentric. However there could be manufacturing tolerances that are inherent in the process. The driving band could be installed slightly closer to the base or farther from the base. The center of gravity could be offset from the axis of the shell and at an angle due to manufacturing and assembly. Analysis:
Earlier I had proposed looking at the shell as a spinning top from our childhood. Usually there are short and squat tops (SQT) or long, thin tops (LTT). A SQT needs less spin and is more stable in the sense it wont be disturbed when it gets a side load. The LTT needs more spin and is less stable as it gets disturbed easily when it gets a side load. And both tops spin true when they are axisymmetric. If you recall there is a brass nail that's driven into the top of the wooden top to give more mass to the large end. This makes it more balanced and stable during spinning. When the top is slowing down the cg point moves in a rosette pattern called nutation. This shows up as wobble. Balloting is the shell wobble in the gun barrel.
During World War I it was noticed that shells when they emerge from the barrel would hit it at exit and sometimes catastrophically. This was called 'side slap'. Not much was understood. During WWII, British mathematicians studied this and described the forces due to slide slap could be around 20,000 gs and sometime break off the fuze while the shell still travels as a dud to its full range. After WWII, US army started studying this phenomenon and produced numerous papers. During Vietnam war it was noted that 175mm barrels were bursting way before their 4th Quartile life. Analysis showed that due to cg offset (only 0.1") and barrel wear the shell was hitting the barrel sides and exploding in it. During the recent decades the phenomenon was called balloting and more studies have been undertaken as the shell fuzes are upgraded to electronic components which are fragile. Now with PGK fuzes there is a need to study the forces and not have failures.
Of these one relevant study for our purposes is "Characterization of the Parameters That Affect Projectile Balloting using FEA" Phd Thesis by Kelly Laughlin in 2008 (Ref 2). Laughlin modeled the 155mm barrel and shell and calibrated it to test data prior to changing different parameters that affect balloting. He looked at barrel wear by running two models to represent 1st and 4th quartile and at zero and 70 degree elevation. Next he varied the location of the driving band with respect to the base of the shell. He also moved the CG axially forward and aft of its theoretical location and offset it from the shell axis by a set number. He also varied the distance between the rear and forward bourrelet (wheel base), and finally the total shell length within the drawing tolerances.
The barrel 1st and 4th quartile and the two elevations did not produce any differences in axial accelerations. The higher elevation had slightly less balloting but both had some degree of balloting and prominent as shell moves closer to the muzzle exit. As the CG moves forward, balloting at muzzle exit increases to almost double of the nominal case. As CG moves closer to base it reduces the balloting effect. The wheel base (distance between the bourrelets) variation effect of the balloting is similar to the CG variation as it increases with increase from the base and decreases with reducing the distance. The driving band location is also similar to the CG and wheel base variation. He found that installing the driving band towards the base reduces balloting. The body length variation is similar in that a short body has reduced balloting while a longer body has more balloting (ERFB note is long body)
The most interesting thing happens when the CG is offset at a distance (0.148") from the shell axis. The balloting frequency is higher than all other variations and very high magnitude of up to 5,000gs and up. This trend is same for all four gun tube variations. i.e. 1st and 4th quartile and zero and 70 degree.Analysis Discussion.
Analysis shows that CG offset from centerline causes extreme radial accelerations due to the unbalance nature of the shell even in nominal barrels. The magnitudes show it could result in muzzle strike while emerging from the barrel.
We know from various reports that Dhanush development trials had barrel burst due to shell wobble.
And this gun fired 3000 rounds before the barrel burst.
The Dhanush prototype suffered a barrel burst during firing trials at Pokhran in August last year, which has since been resolved.
An official with knowledge of the matter said. “It's true that the trial at Pokhran didn't go well. There was a barrel burst. However, it was later confirmed that the burst was not due to a defective barrel, rather the ammunition wobbled out-of-axis to exert additional pressure on the barrel, causing the accident”.
The M777 gun had a shell break up at the 1164th roundviewtopic.php?p=2230473#p2230473
I don't know the barrel life for these at max charge. I suspect its close to 1100 rounds.
On page 57, the forward shift from the base of the CG gives 5K gs for even nominal barrel.
Further on page 115, 4th quartile with CG offset shows the large radial accelerations at muzzle exit.
IA Board of Inquiry should look at barrel dimensions as part of the investigation.
Most likely firing the guns at max charge quickly puts them in the 4th quartile.
It would definitely show the muzzle strike severity.Conclusion:
Muzzle strike happens with CG offset. And will worsen with barrel wear.
Most of the IA field trials having barrel burst are likely after barrel wear which makes even small CG offset into a big problem.
Also IA should consider going to eight gun batteries is they desire a high volume of fire and not subject the guns to beyond normal usage which causes barrel wear that in turn magnifies any shell imbalances even within tolerance.Reference:
1) Hindu : Dinaker Peri No Dhanush for Army
3) Characterization of the Parameters that Affect Projectile Balloting using Finite Element Analysis: PhD thesis