Why did late WW2 American tank projects, such as the Pershing prototypes/modifications (e.g. the T25E1, T26E1 and E3, the T29E1, etc. etc.) have an "E" instead of the "A" which the military would later use in the future (such as the M60A1)? Did the "E" stand for anything? Was it an abbreviation? Why did they switch from it?
The letter E signifies an experimental modification of an existing project.
Since you brought up the Pershing, I can use that as an example. Development began with the Medium Tank T26. Even before that was built, a variant with a torque converter rather than an electric transmission was developed, designated Medium Tank (later Heavy Tank) T26E1. There were other experimental variants with the E suffix: T26E2 (howitzer variant accepted into service as the Medium Tank M45), E3 (improved E1, accepted into service as the Heavy Tank M26), E4 ("Super Pershing" with a longer gun, not accepted into service), E5 (uparmoured assault variant, not accepted into service).
Once the Pershing was standardized as the Heavy Tank M26, the name of the experimental variants "reset". The Medium Tank M26E1 was another variant of the Pershing with a longer 90 mm gun (also not accepted into service).
An E designation sometimes evolved into an A designation when standardized. For example, the Medium Tank M4E1 was a variant of the M4A4 Sherman with a D200A engine. The engine was mass produced as the RD1820, and similarly the M4E1 was standardized as the M4A6 (although not very many were produced and the tank was later downgraded to a limited standard).
E designations don't necessarily result in A designations. For example the Medium Tank M4E6 was an M4 Hybrid fitted with a T23 turret and a 76 mm M1A1 gun. This variant was standardized, but the resulting tank received the suffix (76). For example, a diesel Sherman with a 76 mm gun and wet ammo rack would be called Medium Tank M4A2(76)W.
Another famous example is the HVSS suspension. An M4A3 was used as the experimental tank, so it was designated M4A3E8. Once standardized, the tanks were given the suffix HVSS, so our diesel Sherman with a 76 mm gun and a new suspension would be called M4A2(76)W HVSS. However, the experimental designation and nickname "Easy Eight" stuck, so you very commonly see Canadians refer to their tanks as M4A2E8 and Americans refer to their tanks as M4A3E8 even though that is not the official designation and the suffix E8 only describes the suspension.
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