Why do gun's barrel length and caliber matter? and how?

[kambiz]

As title suggests I need to know why it is important for guns to have longer barrels and larger caliber (approximate internal diameter of the barrel) or better say why for example great powers espcially during WWII were in race to acquire guns (or tank guns) with big caliber & longer barrel??? I've heard somewhere that longer barrel helps the gas to propel trajectory for longer period of time thus giving it higher velocity when it exits from the end of the gun barrel, is it true? Also I know bigger caliber might contribute to explosive in at least HE shells but have no idea how it can contribute to anti-tank aspect of the shots?

[Condottiere 40K]

Material science determines viability of bigger guns, and their capability of containing more explosive propulsive force.

[neep]

A longer barrel allows for longer acceleration of the bullet/shell, although I would assume it's not a linear effect. So at some point the effort to make a longer barrel becomes not worth it in terms of the extra muzzle velocity that is achieved. Plus the logistical problems of moving around a very long barreled gun can be too much.

A larger caliber = the diameter of the bullet/shell means that there's more mass being fired at the target. But it also means you need more oomph to get the thing up to speed, so potentially more energy is needed to drive the shell. Simple Newton's law of motion; getting a larger mass to hit a target over there with a lot of speed requires that more energy has to be applied.
Even relatively small changes in caliber can have a large effect since you're increasing the total volume of the shell (diameter x length)
On a smaller scale, I've read a fair amount of discussion on 9mm bullets vs 10mm bullets and the corresponding increase in effective damage that is done to a ... um, er ... target.
Also note that there is a corresponding increase in recoil which has to be handled.
(Very interesting topic that you can rat-hole down into for days

I think ( but I'm likely wrong since I'm not an expert) that WWII tank armour was basically dumb plates of steel/alloy so the requirement for an anti- tank gun was raw punching ability.
High speed and/or a large caliber shell to just punch through the plates of armour.

HEAT was a different trick of getting a shaped charge to impact the tank and inject a narrow, very fast, VERY hot stream of liquid metal into the interior of the tank.

[kambiz]

Thanks neep This is what I kind of assumed as well but needed someone with knowledge over the matter to confirm it. Afterall as you mentioned these are all based of basic physics

However the question that comes to mind is if all apparently all nations (or at least all great powers) of WWII already knew about these simple facts why they still having problem making the most powerful effective gun (AT-gun) possible ? why not make tanks such as tiger or Tiger II or IS-2 from the very beginning? where the technical problem was?

the I reached is maybe because bigger guns with longer barrels need bigger turret (especially due to balancing) and as bigger turret means more ,thus it means there needs to be more powerful engine to run the beast ! so the actual technological advancement must come from engineering a better engine ,right?

[Condottiere 40K]

Doctrine and money.

Most tanks had relatively thin armour, so that a twenty millimetre bullet shot from an oversized elephant gun was considered sufficient to take one out.

Adaptions could be taken from existing anti aircraft guns, which already required a high velocity shell for their role, the most famous example being the German eighty eight.

[empr guy]

the I reached is maybe because bigger guns with longer barrels need bigger turret (especially due to balancing) and as bigger turret means more ,thus it means there needs to be more powerful engine to run the beast ! so the actual technological advancement must come from engineering a better engine ,right?

Engines are part of it, there's a lot of technology that goes into a tank, for example there was a better armored version of the tiger called the Tiger P. They could never get the drive system to work reliably, so it was never mass produced.

And afaik tank on tank battles as doctrine weren't a thing until much later in the war, so there wasn't a reason to mount big guns on every vehicle (as opposed to specific anti armor vehicles like the Marder II) and there was never a point where a tank was immune from all enemy guns.

[neep]

Indeed, there's no breakthrough in physics needed.
It's just (!) engineering and economics - it's possible to have a heavy armoured tank with a BFG on top - but it costs a lot of money.
And there are matters of supply, maintenance and reliability in the field. Failing to get that right means your forces just get bogged down and become ineffective.

Actually if you play a simulation/strategy game of WWII you'll see that it's not feasible to just crank out battalions of heavy armour and artillery since the economics and availability of raw materials won't really support that.
I think that Germany had the better individual tank with the Tiger + 88mm - but the allies superior production ability allowed them to grind down and defeat the German forces.
Do you build 1 super tank, or several lighter tanks that don't break down so much - always a tough choice

[empr guy]

Yes, that actually reminded me of something, the PzIV, the german work horse that was their most effective tank and chassis which was used as the basis for like 5 other combat vehicles and served the entirety of the war, was actually first produced in 1936. It's main strength was that it went through tons and tons of upgrades as the war evolved and could face off against soviet KV-1's (which were fantastically armored for the time) and T-34's, but production was continuously cut for other vehicles so Germans produced about 8500 PzIV's (+ maybe 5,000 derivative vehicles) in ~9 years, Soviets produced over 35,000 T-34's in ~5 years including their factory relocations, and tens of thousands more of upgrade variants.

"better" tanks as the Tiger and Panther took a ton of resources to build and maintain, and then broke down constantly anyway, especially the Panther at Kursk where it was introduced. Something like 7,000 of both were produced and, logistically speaking, were a horrific investment.

[Condottiere 40K]

For a brief period of time, the Germans discovered only their Sturmpanzers had an effective gun against the T-34, which was basically a howitzer, one of the impetus that made them build the Panthers and the Tigers.

[Adar]

Just to build upon what have already been said with some physics.

Newtons second law state that acceleration is the force divided by the mass (a = F/m). This mean that if you want to double the acceleration of a projectile you need to double the force exerted on it if you wish to maintain the same weight of the projectile. An alternative to that is to increase the amount of time spent accelerating an object, this can be accomplished by a longer barrel as the blast of propellant can accelerate the projectile as long as the blast is contained inside the barrel (the final velocity of an object subject to a constant acceleration can be calculated as v = a * t where t is the time).

This mean that there are two ways to increase the velocity of a projectile:
1) Using more propellant to increase the force.
2) Use a longer barrel to provide more time for acceleration.

Given the first formula (a = F/m) you can also use both these two methods to instead fire a larger (heavier) projectile with the same acceleration.

The big problem with both methods is that they involve containing a high pressure inside a constrained space throughout a period of time. Increasing the force mean that you need a sturdier gun and that is usually complicated to achieve. If you look at WW2 then it is very interesting to follow how, just as empr guy said, a continuous improvement in engineering allowed bigger and heavier equipment to be produced.

A major issue for Germany was however that their ambitious designs often exceeded their capacity to produce equipment that performed reliably when exposed to the forces created by operating them. The most famous examples being related to failures of the power transmission of their tanks which often struggled to keep up with the force generated as a massive engine would propel over 40 tonnes of tank at speeds over 40 km/h.

This is for example how the power transmission of a Panther tank looked. To move the Panther tank that complex machinery needs to withstand a force equivalent to 690 horses pulling it.


Regarding the German design issues I also found this quote by Albert Speer on Wikipedia when looking up the speed of the Panther tank.

Since the Tiger had originally been designed to weigh fifty tons but as a result of Hitler's demands had gone up to fifty seven tons, we decided to develop a new thirty ton tank whose very name, Panther, was to signify greater agility. Though light in weight, its motor was to be the same as the Tiger's, which meant it could develop superior speed. But in the course of a year Hitler once again insisted on clapping so much armor on it, as well as larger guns, that it ultimately reached forty eight tons, the original weight of the Tiger.[17]

[kambiz]

Thank you so much guys for your very informative answers

So based on what you gentlemen said ,It can be said that in order to actually advance in tank technology great/involving powers needed to research on making better engines in order to run their beasts as well as advancements in metallurgy to let them build better and sturdier gun , armour plates ,ammunation and etc (?)

One more question regarding the ammunition type(s). When I first saw a scheme of an AP round it was not sharp (I forgot the actual word ,but the head of the shot was semi-spherical) while I was expected it to be sharp ! why is it so? interestingly modern AP rounds that are actually APFSDS (an evolution over early APDS) do have sharp nose and have resemblance of arrow !

[Adar]

I am glad you like it and this is also a great opportunity for me to rehearse some knowledge that I have not been using for a few years.

The reason that AP rounds and APFSDS look different is that they use completely different methods to damage their target. In general there are three common ways to damage an armored target.

AP ammunition: AP ammunition relies on penetrating the armor and then blowing up. If the armor is to thick or hard the AP round will fail to penetrate and make very little damage as most of the force takt the path of least resistance and just create a shock wave in the surrounding air. The big weakness of this design is that the round must impact with huge force to penetrate but still remain intact enough to detonate properly. Towards the end of WW2 it was possible to build so large and well armored tanks that AP rounds would either be to heavy to fire over a distance or to weak to survive the impact against the armor. The shape of such a round is based on the need of providing good aerodynamics while carrying an armor penetrating cap and the explosives that must explode reliably after impact.

Sabot ammunition (APFSDS etc): Sabot ammunition relies completely on kinetic energy to cause damage. This mean that the missile consists of a solid and heavy material such as tungsten that impact with the armor at a high velocity. The shape of such a round is decided by providing as good aerodynamics as possible which mean a narrow shape of a high density material.

High Explosive Anti Tank (HEAT): HEAT weapons also consist of an explosive charge but does not rely on the kinetic energy of the round to penetrate the armor. Instead it consists of a shaped charge that detonates upon impact with the armor and creates a stream of high velocity particles penetrating into the armor of the target. This is based on the Munroe effect which is a bit complicated to explain (I stole a picture that you can look at below). The easiest way to visualize it is that with an AP round it is the armor of the target that prevent the blast from dissipating in the air, in a HEAT weapon the explosion happens outside the armor but the shape of the explosive makes the blast collide with itself and push a dense material located in the front of the round into the target.

Spoiler Alert, click show to read: 

So the reason old fashioned AP weapons have fallen out of fashion is that it is impossible to resolve the conflict behind the need for a forceful impact with the ability to explode reliably after the impact without making the round huge. The Sabot removes this conflict and instead relies on the weight and velocity of the projectile (ie a better gun allows you to use simpler ammunition) while the HEAT round removes the need for the explosive to be robust enough to survive the initial impact.

In modern warfare all three kinds of ammunition are used for different applications. AP ammunition is still being used but mainly for stationary targets which can have thick but low density protection such as concrete or natural rock which allows the AP round to penetrate and explode inside it. The Sabot got excellent long range precision due to its high speed and good aerodynamic shape but requires a powerful gun to fire it which means it must be mounted on a suitable vehicle such as a tank. HEAT based weapons generally have a lower muzzle velocity which makes them less useful over large distances (unless mounted on an expensive guided missile) but can be fired from relatively small and cheap platforms.

Edit: It is also worth mentioning that lubricants, manufacturing techniques and electronics got a huge impact on the development of weapons as well. I have recently been engaged in some discussions about the potential danger of new Russian weapons due to this. Basically they promise excellent performance of new platforms but lack the people and technology to produce the components of the platform. So even in the modern world the development of weapons remain reliant on access to continuous development in engineering.

[Condottiere 40K]

Let's not forget that besides armour getting thicker, which requires more pony power, they also started sloping it, which at the angle of impact by the AP round, means relatively more kinetic power was needed for penetration.

As for the round, you resolved that by concentrating that force in the smallest possible area, around the hardest possible material.

[kambiz]

Thanks Adar ,But I'm still having problem to grasp how HEAT shells actually work :p

Anyways ,based on F=m.a one may think why not just focus on F by making charges as powerful as possible thus giving projectiles the fastest speed they can get? for example germans ultimately used 128mm gun which due to bigger caliber compared to 75mm needed more powerful charge ! the question is why use that more powerful charge to propel 75mm rounds? theoretically it looks plausible but what was the actual issue behind this solution?

[Condottiere 40K]

Weight; you needed a more powerful platform to move it around, and after the experience with the Elefant, a well protected one as well.

[neep]

Hi Kambiz,
as always it comes down to practical economics and engineering

If you want to fire a 75mm shell with a more powerful charge, you will need a MUCH stronger barrel. What does that mean ?
Basically a gun firing a shell is an enclosed space that has an explosion inside it. The shell works like a movable obstruction where the explosion pushes the shell up the barrel.
As this is happening the barrel has to contain the explosion so that the least path of resistance is to push the movable shell up the barrel.
For the sake of getting your head around this, imagine the barrel was made of chocolate (my favourite building material). In that case, it wouldn't be able to contain the explosion and the barrel would fail catastrophically before the shell leaves the barrel.

So, to apply a larger charge to get more oomph the barrel has to withstand higher forces to contain the larger explosion.
A thicker barrel, or a different type of metal alloy perhaps, will allow this to happen.

AND your gun platform has to handle the extra recoil of the more powerful blast. That's going to be extra, upgraded hardware as well.

Now it's getting expensive since you need to buy more raw materials.
And you need to build a bigger turret to handle the larger barrel and recoil system; and a larger body to handle the extra mechanics of rotating a larger weight turret; and a more powerful engine to move the whole thing around.
And some extra power just to move the extra weight of the more powerful engine
There's a whole cascade of upgrades and extra hardware just to get back to the original performance you had with the smaller gun.

Before you know it, you've built a monster that trundles around at a top speed of 5MPH and guzzles fuel faster than you can supply.

[Condottiere 40K]

A seventy five millimetre is perfectly adequate for nine out of ten situations, since it can fire an AP round that can take out medium tanks, and a HE round that will take out infantry.

In that sense, the Sherman was probably the best good enough tank of the Great Patriotic War.

[kambiz]

@neep
Well I knid of knew that more powerful charge needs sturdier gun to withstand the blast. However as I mentioned in my post Germans already began using 128mm gun late in the war. as this new gun used more powerful charge compared to 75mm gun ,My question was what is the technical problem and issues in using 128mm gun that already have much powerful charges to fire 75mm caliber rounds instead? (note that you talked about practicallity of design ,whoever in this example germans already employed the bigger and stronger 128mm gun)

A seventy five millimetre is perfectly adequate for nine out of ten situations, since it can fire an AP round that can take out medium tanks, and a HE round that will take out infantry.

In that sense, the Sherman was probably the best good enough tank of the Great Patriotic War.

I used to think US tanks were a bit (not much though) inferior to their germans and even Soviet counterparts but now I'm realized US actually made the best weapon for that time when considering all aspects of the fighting vehicle.

[Adar]

@neep
Well I knid of knew that more powerful charge needs sturdier gun to withstand the blast. However as I mentioned in my post Germans already began using 128mm gun late in the war. as this new gun used more powerful charge compared to 75mm gun ,My question was what is the technical problem and issues in using 128mm gun that already have much powerful charges to fire 75mm caliber rounds instead? (note that you talked about practicallity of design ,whoever in this example germans already employed the bigger and stronger 128mm gun)


I used to think US tanks were a bit (not much though) inferior to their germans and even Soviet counterparts but now I'm realized US actually made the best weapon for that time when considering all aspects of the fighting vehicle.

A light bullet with high speed will lose its velocity very quickly so even if you get a good muzzle velocity the velocity would be much lower when actually reaching the target. When travelling at a high speed the aerodynamic drag becomes very important and the drag is proportional to v^2 as well as 1/m. This mean that when increasing the speed of a projectile the drag increases exponentially which require you to make the projectile much heavier.

Spoiler Alert, click show to read: 

The drag formula used above:

For example lets say that your projectile travels at 600m/s and weight 3 kg. If you double the velocity of the projectile to 1 200 m/s, then the drag can be expected to be approximately 4 times higher for the projectile than before (this is very simplified as the aerodynamics around the bullet change when you increase the velocity). To counter act this you could increase the weight of the bullet which mean that you need to make the projectile 4 times heavier to maintain the same drag. This does however mean that you need 4 times as much force to accelerate the projectile to the same speed as before... Which mean that you now need to make both the projectile and propellant 4 times larger if you use the same materials as before. As you increase the size this mean that both the internal dynamics of the gun and the aerodynamic profile of the projectile are completely different than before and that makes things too complex for me to work with .

And this complexity is why weapons development tend to be so incremental. Better metallurgy may for example allow a producer to increase the pressure of the gun which increases the muzzle velocity. This in turn makes it more attractive to fire larger shells which are heavier and may therefore need a longer barrel to produce more time for acceleration. This in turn makes the gun heavier which requires the turret to become larger which mean that engineers need to produce stronger engines and suspension equipment to carry the weight of the turret...


So when managing weapon development the military planners constantly look at the development in different sectors. Prior to D-day for example the British recognized that the next generation of German tanks would have far heavier armor than the current generation. This encouraged some officers in the British army to make plans on how to mount a British 17 pounder gun into the turret of the American Sherman tank. The 17 pounder was much more powerful than the 75 and 76 mm cannons developed for the Sherman tank but it was also much larger and had a huge recoil that made the normal Sherman tank turret incapable of carrying it.

This ment that the British had to make a lot of modifications to make the Sherman tank capable of carrying the gun.

https://en.wikipedia.org/wiki/Sherman_Firefly#Design
It was W.G.K. Kilbourn, a Vickers engineer working for the Department of Tank Design at the time, who transformed their idea into the reality of the prototype of the tank that would serve the British forces from D-day onwards. The first thing Kilbourn had to fix was the lack of a workable recoil system for the 17-pounder. The 17-pounder travelled 40 in (1.0 m) back as it absorbed the recoil of the blast. This was too long for the Sherman turret.^[6] Kilbourn solved this problem by redesigning the recoil system completely rather than modifying it. The recoil cylinders were shortened to allow the turret to take the gun and its recoil, and the new cylinders were placed on both sides of the gun to take advantage of the width of the Sherman's turret rather than be hindered by its height.
The gun breech itself was also rotated 90 degrees to allow loading from the left^{[note 1]} rather than from on top.^[7] The radio normally mounted in the back of the turret in British tanks had to be moved; an armoured box (a "bustle") was attached to the back of the turret to house it, with access through a large hole cut through the back of the turret.
The next problem encountered by Kilbourn was that the gun cradle, the metal block the gun sat on, had to be shortened to allow the gun to fit into the Firefly, and thus the gun itself was not very stable. Kilbourn had a new barrel designed for the 17-pounder that had a longer untapered section at the base, which helped solve the stability problem. A new mantlet was designed to house the new gun and accept the modified cradle. The modifications were extensive enough that 17-pounders intended for the Firefly had to be factory-built specifically for it.^[3][7]
Kilbourn had to deal with other problems. On the standard Sherman tank there was a single hatch in the turret through which the tank commander, gunner and loader entered and left the tank. However the 17-pounder's larger breech and recoil system significantly reduced the ability of the loader to quickly exit if the tank was hit; a new hatch was cut into the top of the turret over the gunner's position to resolve this.^[8] The final major change was the elimination of the hull gunner in favour of space for more 17-pounder ammunition, which was significantly longer than the original 75 mm shell and took up more room.
The Firefly had no armour or mobility advantages over the normal Sherman tank, although the gun mantlet was some 13mm thicker.
By October and November 1943, enthusiasm began to grow for the project. The 21st Army Group was informed of the new tank in October 1943.^{[citation needed]} Even before final testing had taken place in February 1944, an order for 2,100 Sherman tanks armed with 17-pounder guns was placed, as the Challenger program was suffering constant delays and it was realised that few would be ready for Normandy. Even worse, it was discovered that the Cromwell tank did not have a turret ring wide enough to take the new High Velocity 75mm gun (50 calibres long), so the Cromwell would have to be armed with the general purpose Ordnance QF 75 mm, leaving the Sherman Firefly as the only tank available with firepower superior to the QF 75 mm gun in the British Army's arsenal. Not surprisingly, it was given the 'highest priority' by Winston Churchill himself.^[2]

So the Sherman Firefly was designed almost entirely around carrying the strongest cannon available. This did however come with several important trade offs as shown below from the same Wikipedia article.

The main armament of the Sherman Firefly was the Ordnance Quick-Firing 17-pounder. Designed as the successor to the British QF 6-pounder, the 17-pounder was the most powerful British tank gun of the war, and one of the most powerful of any nationality, being able to penetrate more armour than the 8.8 cm KwK 36 fitted to the German Tiger I or the Panther tank's 7.5 cm KwK 42^{[citation needed]}. The Firefly 17-pounder was able to penetrate some 163 mm of armour at 500 m (550 yd) and 150 mm at 1,000 m (1,100 yd) using standard Armour Piercing, Capped, Ballistic Capped (APCBC) ammunition. Armour Piercing, Discarding Sabot (APDS) ammunition (shown here) could penetrate some 256 mm of armour at 500 m and 233 mm at 1,000 m, which on paper could defeat the armour of almost every German armoured fighting vehicle at any likely range.^[10]However, war production APDS rounds lacked accuracy, and the 50 mm penetrator was less destructive after it had penetrated enemy tank armour than the 76.2 mm APCBC shell. In any case, APDS ammunition was rare until the post-war.
While the 17-pounder had superior anti-tank capabilities, it was inferior to the regular Sherman 75mm gun against soft targets such as enemy infantry, buildings and lightly armoured vehicles due to its lack of an effective HE round. As the war in Europe neared its close, the Allies found themselves encountering these more often than heavy German tanks. Allied tank units therefore typically refused to completely switch to Fireflies. A good HE shell for the gun only became available in late 1944, and even then was not as potent as the standard Sherman 75 mm HE shell.^[2] Another problem was that the powerful blast from the 17-pounder gun kicked up large amounts of dirt as well as smoke, making it difficult for the gunner to observe the fall of shot and forcing him to rely on the commander to observe it and to order corrections. Dirt and dust revealed the position of the tank, so Sherman Fireflies would have to move every few shots. The recoil and muzzle blast could be severely jarring to Firefly crews and the muzzle blast frequently caused night blindness as well. This was a common problem of any tank armed with a high velocity gun, including the Panther and Tiger. The cramped nature of the turret meant that loading the large 17-pounder shell was difficult, so Fireflies had a lower rate of fire than regular M4 Shermans.^[7] Since the Firefly was a stopgap, these problems were never eliminated, as the Firefly was to be retired with the introduction of the new British tank designs.

With rockets attached to the turret

The Firefly's secondary armament was the standard .30 inch (7.62 mm) coaxial machine gun in the turret; the hull-mounted machine gun was removed to increase ammunition storage for the main gun. A top-mounted .50-inch (12.7 mm) machine gun was also attached, though many crews removed it due to its awkward mounting and position near the commander, which limited a full 360-degree view when unbuttoned in battle

Alternative solutions to the problems described above was to build a vehicle with completely different specifications than a medium tank and this was also done with projects such as the Achilles and Challenger tanks. This mean that three different main platforms were capable of carrying the 17 pdr gun for the British in WW2.

The Sherman Firefly which was heavily armored, reasonably shaped, reasonably fast and had poor crew ergonomics.


The Cruiser Mk VIII Challenger which was fast, poorly armored and had a horrible silhouette.


The 17pdr Achilles which look like a tank but is actually a self propelled gun. This mean that it have very little armor and the turret could only be slowly moved using manual power. The Achilles would have no chance in a normal battle but was instead used to support the infantry to help them deal with enemy tank attacks.


Later addition by Jagdpanzer: Archer tank destroyer, a turret less design with the gun facing towards the back and mounted on an obsolete Valentine chassi. The low profile and rearward facing gun made it a good tank for setting ambushes and then rapidly leaving the area.


What I want to show with this example is that if military planners decide to focus on one thing such as the capability of destroying enemy tanks. Then they have to look into what technology they have available in other areas and find a suitable compromise. So in WW2 the 17 pound cannon was the most powerful cannon widely available to Allied forces to mount on a tank. But doing so forced them to either make a tank that was very specialized and poorly suited for other tasks (the Sherman Firefly), poorly armored and shaped (the cruiser) or settle for a self propelled gun (the Achilles).

Towards the end of the war the first true Main battle tank was developed in the form of the Churchill. This design combined all the experience of different British tanks and could carry the 17 pounder gun (soon upgraded to an even more powerful 18 pounder) with good crew ergonomics and at higher speeds than the Sherman.

[Condottiere 40K]

Currently playing HOI4, though while planning a war economy wasn't unknown to me, planning out what you will produce and when, tends to put a new complexion on tank design and production, amongst others.

Wartime tends to be an exceptional pressure cooker to speed this up, but usually you want to decide in advance what your troops are going to be equipped with, in sufficient numbers to be effective.