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The Carro Armato M13/40 (whose designation meant "13-ton medium tank of 1940") was an Italian medium tank, that, along with its improved variants, was the mainstay of Italy's armoured forces during WWII.
The origins of this tank can be traced to the Spanish Civil War, when the L3/33 tankettes showed all their limits against Soviet-built tanks; a crash program to design and mass-produce a modern tank resulted in the M11/39, a transitional tank with a 37 mm gun in the hull, but in the end it wasn't successful. The M13/40 (which entered service in 1940) was basically an improved M11/39 with a better gun mounted in a turret; however, while its 47 mm gun was quite good (by 1940 standards) both against armored and soft targets, it suffered from an engine's lack of power, thin and mediocrely manufactured armour and various other shortcomings. These were gradually adressed, first with the M14/41 (in 1942, with a more powerful engine) and then with the M15/42 (in 1943, with better armament and armor), but by that time the design was all but obsolete.
While initially successful (except for the early period because of very poor training and tactics) against British cruiser tanks, as the British Army began to receive in 1942 American-built tanks like the M3 Lee and the M4 Sherman, the M13/40 proved to be decisively outclassed by such designs; the lack of more suitable tanks forced the Italian Army to keep using them, together with the few Semoventi da 75/18 (itself a derivative of this tank) and waiting for the Carro Armato P40.
In the anime
In the manga, Anzio Girls High School has several M13/40; serving as the backbone of Anzio's force, they took the brunt of its losses, but one of them managed to take down Duck Team's Type 89B (although the shot was meant to Ooarai's flag tank, the StuG III.
In the OVA, it seems that Anzio does not have any of these tanks; its force is instead composed of several CV.33s, supported by a few Semoventi and a single Carro Armato P40.
Additional material suggests that while Anzio does indeed posses a few M13/40 or M14/41s, they are inoperable, as the school lacks sufficient funds to restore them.
More details about the M13/40
|Light Tanks and Tankettes||7TP • AMR-35 • BT-42 • Crusader • CV.33 • FT-17 • Harry Hopkins • M22 Locust • M24 Chaffee • Mark VI • Panzer II • Panzer 38(t) • R35 • T-60 • T-70 • Tetrarch • TK Tankette • Type 95 Ha-Go • Type 97 Te-Ke|
|Medium Tanks||Centurion • Panzer III • Panzer IV • Panzer V "Panther" • M3 Lee • M4 Sherman • M13/40 • Matilda II • P26/40 • SOMUA S35 • T-34 • T-44 • Type 89B • Type 3 Chi-Nu • Type 97 Chi-Ha|
|Heavy Tanks||ARL 44 • B1 Bis • Black Prince • Churchill • IS-2 • KV-2 • M26 Pershing • Mark IV • Panzer VI "Tiger" • Panzer VI Ausf. B "Tiger II" • Panzer VIII "Maus" • VK45.01 Porsche Tiger|
|Tank Destroyers||Elefant • Hetzer • ISU-152 • Jagdpanzer IV • Jagdpanther • Jagdtiger • Semovente da 75/18 • StuG III • T28 Super-Heavy Tank|
|Self-Propelled Artillery||Karl-Gerät 040|
|Main Battle Tank||Type 10|