Quote Originally Posted by Ken White View Post

Four of every maneuver element is better than three, enables better bounding overwatch and rotation off line. Also allows for mix of 2 Tk Co and 2 Mech Inf Co at Bn. Allows one element for Assault and three for breakthrough and follow up. Four Firing Batteries allow two to be ready to fire no matter how much you move. All sorts of advantages. The triangular setup was a German invention to force unbalanced formations and defense -- same thing can be achieved by better training.
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Far be it for me to resurrect a thread (I am no necromancer) but it appears E. S. Johnston in his “Field Service Regulations of the Future” published in 1936 would agree with the desirability of four manoeuvre elements. His view and that of others (such as Leslie McNair) is discussed in Major Glenn M. Harned, The Principles of Tactical Organisation and their Impact upon Force Design In the US Army originally published as a monograph for the US Army Command and General Staff College (1985). The monograph is rather good at getting to the nuts and bolts of unit organisation (“force design”) through the analytical lenses of two principles of war (Unity of Effort and Economy of Force) and seems to me at least to be as relevant today as it was in 1985 or, for that matter, in 1936;
(According to E. S. Johnston...) Two subdivisions provide one to fix and one to manoeuvre, while three also provide a reserve. "Four subdivisions provide an organization yet more flexible, there being sufficient elements to manoeuvre around both flanks as well as for fixing and for the reserve. This organization is also useful in penetrations, in which case the entire unit may be used in a deep narrow column, in a square or similar figure, or in a T-shaped formation. A unit of four subdivisions in particularly flexible [because] the "four subunits may be combined into three or two, according to the situation and the ability of the commander." A unit with four subdivisions is also more economical, requiring little more overhead than a unit with only three.(p.6)
The paper also has a rather interesting “take” on the principle of Unity of Command which, according to Johnston, should actually be Unity of Effort or (Co-operation as per The Principles of War in UK JDP 0-01 British Defence Doctrine p.2-6);
According to Johnston, "Organization is the mechanism of control. Its purpose, therefore, is unity of effort". Thus, tactical organization is a mechanism of control, which produces unity of effort, which results in the economic expenditure of combat power. In the 1923 Field Service Regulations, as in FM 100-5 today, the US Army recognized Unity of Command as a principle of war, but Johnston argued that the principle should be Unity of Effort, not Unity of Command. He wrote, “Wellington and Blucher [at Waterloo] succeeded by reason of cooperation; they had no unified command ... Unity of command, then is merely a method of obtaining unity of effort ; cooperation is another method ... The real problem is where to provide for unity of command and where to depend on cooperation”.(p.3)
Furthermore, in terms of Economy of Force the monograph quotes LtGen. Jacob L. Devers (in a letter to Gen. Marshall c.1941) who criticised McNair’s economising/pooling of resources efforts (i.e., attaching CS and CSS units as and where needed rather than having them organic to the subunit in question);
Economy of force is not gained by having a lot of units in a reserve pool where they train individually, knowing little or nothing of the units they are going to fight with. It is much better to make them part of a division or corps, even to the wearing of the same shoulder patch., If they are needed elsewhere in an emergency, they can be withdrawn easily from the division or corps and attached where they are needed. Economy of force and unity of command go together. You get little of either if you get a lot of attached units at the last moment. Team play comes only with practice.(p.9)