03-27-2014, 08:19 PM
One thought: if each infantryman carried 2 of the pilum muralis-type wooden stakes to form the protection to the earth bank, the length of the perimeter which can be fenced is proportional to the size of the force and the area is proportional to the square of the size of the force. A very small force cannot carry enough pila. I have had a go at the maths:
If three pila are lashed caltrop style, and each is 1.7m long, the lateral breadth of the "cube" Is 0.85m (1.7m x cos 45 deg x cos 45 deg), since the pila have 45 degrees of offset to both the vertical and horizontal).
(Pila placed vertically would have to be 30 cm apart - too wide - to get coverage of more than 0.85m per 3 pila, so caltrop-style seems more efficient.)
Simplistically, if a century of 80 men has 5 "non-pila-porters" (assuming centurion, optio, tessesarius, standard-bearer and musician are spared), then such a century would have75 x 2 pila = 150, enough to form 50 "caltrops". The lateral length of each is 0.85m, so this is enough to form a square (the 4-sided shape with the highest area for a given perimeter) of 10.6 x 10.6m (i.e. 50 caltrops x 0.85m x 1/4 for the four sides), an area of 112 square metres, or 1.4 square metres per person, i.e. not enough.
If we say 750 troops per hectare, the upper end of the above range for troop densities, we need c13 square metres per soldier (i.e. hectare = square of 100m x 100m).
Using the above assumptions, the relationship between area and number of troops when the are enclosing their camp only with pila they are carrying themselves is:
Area A = square of (Troops N x 75/80(to exclude officers) x 2(pila each man)/3(pila to make a caltrop) x 0.85m(caltrop length) x 1/4 (to divide caltrops into 4 sides of square)) = 0.0176 x N x N.
If we say that each man has 13 square metres, so that A = 13N, we can solve the equation to get the minimum number of men who can carry enough pila to complete a camp perimeter:
A = 0.0176 x N x N & A = 13N, therefore 13 = 0.0176N therefore N = 739.
This implies that anything smaller than a cohort & a half (especially when you consider cavalry, officers, etc) must have travelled with a few cartloads of pila if they really did put a continuous hedge of pila around the perimeter.
Thoughts anyone?
John
If three pila are lashed caltrop style, and each is 1.7m long, the lateral breadth of the "cube" Is 0.85m (1.7m x cos 45 deg x cos 45 deg), since the pila have 45 degrees of offset to both the vertical and horizontal).
(Pila placed vertically would have to be 30 cm apart - too wide - to get coverage of more than 0.85m per 3 pila, so caltrop-style seems more efficient.)
Simplistically, if a century of 80 men has 5 "non-pila-porters" (assuming centurion, optio, tessesarius, standard-bearer and musician are spared), then such a century would have75 x 2 pila = 150, enough to form 50 "caltrops". The lateral length of each is 0.85m, so this is enough to form a square (the 4-sided shape with the highest area for a given perimeter) of 10.6 x 10.6m (i.e. 50 caltrops x 0.85m x 1/4 for the four sides), an area of 112 square metres, or 1.4 square metres per person, i.e. not enough.
If we say 750 troops per hectare, the upper end of the above range for troop densities, we need c13 square metres per soldier (i.e. hectare = square of 100m x 100m).
Using the above assumptions, the relationship between area and number of troops when the are enclosing their camp only with pila they are carrying themselves is:
Area A = square of (Troops N x 75/80(to exclude officers) x 2(pila each man)/3(pila to make a caltrop) x 0.85m(caltrop length) x 1/4 (to divide caltrops into 4 sides of square)) = 0.0176 x N x N.
If we say that each man has 13 square metres, so that A = 13N, we can solve the equation to get the minimum number of men who can carry enough pila to complete a camp perimeter:
A = 0.0176 x N x N & A = 13N, therefore 13 = 0.0176N therefore N = 739.
This implies that anything smaller than a cohort & a half (especially when you consider cavalry, officers, etc) must have travelled with a few cartloads of pila if they really did put a continuous hedge of pila around the perimeter.
Thoughts anyone?
John
