eli5 why didn’t they but .50 caliber instead of the 7.62mm in the coaxial and hull gun in the m4 sherman
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It’s an anti-personnel weapon. The 7.62mm is almost as effective as 50 cal against un-armoured targets. The 7.62mm cartridge is smaller and lighter allowing more to be carried on board at one time. Combine this with the 7.62mm being cheaper and more readily available (both machine gun and cartridge) you’ve got lots of reasons to not use a 50 cal gun.
.30 cal took up less space, both gun and ammo. More rounds could be carried for the same amount of limited storage. Also resupply as the supporting infantry’s standard mg was also a .30 cal. But mainly the number of machine gun rounds per sq. foot of storage
.30 cal is smaller and more nimble, with more compact ammo. The .50 cal would have been harder to fit in the hull mount especially. The larger caliber does give you a bit more punch and range, so it made sense for the top-mounted gun that might see antiaircraft use, but there wasn’t much need for extra anti-infantry power alongside the 75mm gun’s generous high explosive round, which pre- combat studies suggested was more effective than a machine gun against infantry.
Why would they? A M1 today has a 7.62mm coaxial, the majority of the tank has the caliber today.
Take a [look at the two catridges](https://i.imgur.com/F8p3lqm.jpeg) and consider the size, it is a 7.62×51mm not a WWII .30-06 but the result is the same. .50 takes a lot more space. So for the same number of projectiles .50 requires more storage space and that is a major limitation in a tank. 7.62mm it is commonly used in tanks because you can fit more ammunition. You would need to remove the main gun ammunition to have the same amount of .50 as .30. We talk about 4-6x times the ammunition for a smaller caliber for the same space.
It is not just the ammunition the machinegun themself have a different sizer and there is not a lot of it in a tank.
The machine guns are there for use against unarmoured targets and a human gets killed the same way with both, so having more ammunition is an advantage.
The .50 machine gun on top was there for air defense where it has a clear advantage. It was also quite useful against lightly armored targets and used in that way. That is why a M1 has a .50 on the turret today. If you look at typical ammunition load-outs an M1 carries 11,400 7.62 versus 1,000 .50.
The hull and coaxial machineguns were .30-06 caliber, which would be 7.62x62mm in a metric designation but that was not what the US army called them. It is the less powerful development to 7.62×51mm NATO that have a metric designation. I you change the name why not call .50 for 12.7mm?
A 7.62 AP round will do just fine and is far smaller
Tanks, especially early in the war, were designed to be infantry support. They’d travel with the infantry, fight infantry, take out bunkers and pillboxes for the infantry. You don’t need a 12.7mm round for infantry, even against light vehicles a 7.62mm round is plenty
Sticking with M1919 machine guns for the bow and coaxial guns resulted in more space inside for the crew, more ammo for those guns, and no loss of effectiveness. They carried about 6000 rounds for those guns but only up to 600 for the 12.7mm on the roof for the commander
Having the heavier roof gun is beneficial though. A 12.7mm round is more likely to take down a dive bomber before it gets to you than a 7.62mm so it’s worth the extra weight
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