Actually, no.
Yes, 45 Colt has far more case capacity than 45 ACP or 45 AR. But that is because the cartridge was developed in 1873 for Black Powder. Black Powder is far less energetic than just about any modern Smokeless powder you can name. The case was that big so it could hold 40 grains of Black Powder. Black Powder must be compressed slightly. Any airspace left in a cartridge loaded with Black powder is a bad thing and can lead to unpredictable pressure spikes. So the 45 Colt cartridge case was designed to hold 40 grains of Black Powder, compressed slightly under a 250 grain bullet. 40 grains of Black Powder along with a 255 grain soft lead bullet made for a very powerful revolver cartridge for its day.
But in the Smokeless era, when you pour a stiff charge of modern powder inside the cavernous 45 Colt case, you wind up only filling the case slightly more than halfway. Same thing with 38 Special, another cartridge designed for Black Powder. Most 38 Special loads only fill the case up slightly more than halfway. So all that extra space in the old 45 Colt is wasted space. In fact, if you load it too lightly, you will start to get spotty ignition and incomplete burning of the powder. That's why you don't load 45 Colt below recommended minimums, the cartridge becomes inefficient and unreliable. By the way, that is why Trail Boss powder was invented. The donut shaped grains are very fluffy and take up lots of space in the big 45 Colt case, displacing much of the air, and allowing light loads to burn efficiently.
I don't load 45 Colt with Smokeless powder much these days, but when I did, my standard load was 7.5 grains of Unique under a 250 grain bullet. Not a barn stomper, a relatively mild load. That much powder did not take up much more than 1/2 of the case volume, but it was efficient enough that it burned consistently and velocity was consistent. Max load with a 250 grain bullet and Unique in my old Lyman Pistol and Revolver Handbook is 8.5 grains. The minimum load is 6.0 grains, and as I said it is not recommended to go below that. If I go over to the Thompson Center Contender only section, the Maximum load for 45 Colt with a 250 grain bullet is 11.5 grains of Unique. That will far exceed the industry standard SAAMI maximum pressure for 45 Colt of 14,000 PSI. We could argue all day about whether or not the Maximum pressure SAAMI standard for 45 Colt is pertinent for modern revolvers made of modern steel, but most of my 45 Colt revolvers are pretty old and will not take Thompson Center or "Ruger Only" loads without blowing up. So as far as being a 'far more flexible and capable cartridge than 45ACP/4AR', it is a moot point. If I load up 45 Colt to near 44 Mag pressures and fire it in any of my guns, they would probably blow up.
45 Auto Rim on the other hand has the exact same interior volume as 45 ACP. It can be loaded with the same dies, and more importantly, it can be loaded with the same data as 45 ACP. 45 ACP was developed in the Smokeless era and was designed around Smokeless powder. The interior capacity of the round is better suited to Smokeless powder, there is not as much empty airspace inside after the bullet has been seated. This means the cartridge can develop the same velocity and pressure for the same bullet with
less powder than 45 Colt can. I load 45AR relatively mild, with a 200 grain bullet and 5.5 grains of Unique. Even so with this mild load there are no unburnt powder grains and the cases come out quite clean. The same cannot be said for 45 Colt with a light load. The hottest Unique load for 45 AR in my Lyman book is 6.6 grains of Unique under a 230 grain bullet. When you get right down to it, 45 AR (and 45 ACP) is a much more efficient cartridge than 45 Colt is with Smokeless powder, unless you are going to load 45 Colt to 'Ruger Only' pressures in a very strong gun. But for an old gun such as this S&W Model 1917, made in 1918, it is a very efficient and useful cartridge.
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Just so we understand what we are talking about, the five cartridges in this photo, left to right, are 45 Colt, 45 Schofield, 45 Cowboy Special, 45 Auto Rim, and 45 ACP. Both 45 Colt and 45 Schofield are Black Powder era cartridges, and since they were stuffed full of powder, the comparative size of the two cases is a good indicator of their comparative power when loaded with Black Powder. 45 Cowboy Special is a cartridge developed for light Smokeless loads in 45 caliber revolvers in Cowboy Action Shooting. It shares the exact same rim configuration as 45 Colt, but it has the same interior capacity as 45 ACP or 45 AR. Since it shares the same rim configuration of 45 Colt, it can be fired in any 45 Colt revolver. And since it has the same interior capacity as 45 ACP and 45 AR it can be loaded with the same data as either of them. Since the internal volume is far less than 45 Colt, when loaded lightly, the powder will burn consistently without soot or unburnt powder grains. Lastly, you can see how much thicker the .090 thick rim is on the 45 AR cartridge than the .060 thick rim of 45 Colt, 45 Schofield and 45 CS.
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