06-13-2014, 11:30 AM
It's worth bearing in mind the engineering mechanics involved when an arrow hits the lorica hamata. I am calling on distant recollections of school physics and university aeronautical engineering from a couple of decades ago, so if anyone spots any errors in my statements, by all means correct me and I won't be offended!
Penetration occurs when the metal in the ring reaches fracture point. Metal under strain tends to behave linearly initially (it stretches like elastic) under lower strain, then it deforms (it stretches like modelling clay) as the strain increases, then it reaches fracture point. So the question is, how does the metal reach fracture point? (Strain is measured in Newtons per square milimetre.)
Firstly consider what the armour must do to stop the arrow. All kinetic energy must be absorbed by the ring pushing against the arrow head in the opposite direction of the path of the arrow.
The kinetic energy of the arrow which must be absorbed by the armour Energy = 0.5 x Mass x Velocity squared), i.e. a heavier or faster arrow has more energy.
The equation for the work done by the armour (the "energy absorbed") = Force x Distance over which the force is exerted.
Therefore, the longer the distance over which the force is exerted, the LOWER the average force required.
So, a lorica hamata with some room to yield (i.e. one which is not stretched tightly over the wearer's body) is able to move backwards for a very short distance to exert force over a longer distance in comparison to one when the rings have less freedom to move. Clearly this movement of the ring (and arrow head) must not allow the arrow to injure the wearer, hence the use of padded undergarments with flexible armour, but the key mechanical feature here is that if the length of the trajectory of the ring can be doubled, the force halves.
The halving of the force means that the indiviudal ring is less likley to reach fracture point.
If fracture were to occur, it would be at the point where strain were highest. Given that the hoop force would be constant through the ring if the arrow were pointing through the centre of the ring (i.e. the force running at right angles to the radius of the ring which is acting against teh movement of the arrow), the hoop strain would be higher at the thinnest point and any fracture would occur there first. Conventionally, a weld is slightly thicker than the surrounding surfaces so a well-done weld (mine were always pretty awful - "like birdshit", one instructor once told me!) should be a stronger rather than a weaker point.
So, for a person shot by an arrow who is wearing padding and whose armour can yield a little, penetration is much less likley than for a person whose hamata is worn in a way where the arrow hits it and the ring cannot continue to move for any meaningful distance. A very small difference in the amount of distance which the ring can move could have drastic effect on whether the ring breaks or not, a matter of a few millimetres.
Of course, all other factors like skill of archer, quality of metal, weight of arrow, shape of arrowhead, windspead also have an impact. However, consideration of the mechanics shows that the penetration outcome can be drastically affceted by the path length of the ring at the point of impact. If the padded undergarment were a little thin, then one can envisage that the length of the path of movement of the armour would be longer, for example, over the belly area versus (soft) the upper rib-cage (hard).
The ancent and medorn evidence shows that arrows could penetrate this kind of armour, but in the contest between mail and arrowhead, there are a lot of factors affecting the outcome, and correct "fitting" could have had a signifiicant effect on this.
This sounds like a title in the Osprey "Duel" series - "Parthian composite bow vs. Roman Lorica Hamata"!
Regards, John
Penetration occurs when the metal in the ring reaches fracture point. Metal under strain tends to behave linearly initially (it stretches like elastic) under lower strain, then it deforms (it stretches like modelling clay) as the strain increases, then it reaches fracture point. So the question is, how does the metal reach fracture point? (Strain is measured in Newtons per square milimetre.)
Firstly consider what the armour must do to stop the arrow. All kinetic energy must be absorbed by the ring pushing against the arrow head in the opposite direction of the path of the arrow.
The kinetic energy of the arrow which must be absorbed by the armour Energy = 0.5 x Mass x Velocity squared), i.e. a heavier or faster arrow has more energy.
The equation for the work done by the armour (the "energy absorbed") = Force x Distance over which the force is exerted.
Therefore, the longer the distance over which the force is exerted, the LOWER the average force required.
So, a lorica hamata with some room to yield (i.e. one which is not stretched tightly over the wearer's body) is able to move backwards for a very short distance to exert force over a longer distance in comparison to one when the rings have less freedom to move. Clearly this movement of the ring (and arrow head) must not allow the arrow to injure the wearer, hence the use of padded undergarments with flexible armour, but the key mechanical feature here is that if the length of the trajectory of the ring can be doubled, the force halves.
The halving of the force means that the indiviudal ring is less likley to reach fracture point.
If fracture were to occur, it would be at the point where strain were highest. Given that the hoop force would be constant through the ring if the arrow were pointing through the centre of the ring (i.e. the force running at right angles to the radius of the ring which is acting against teh movement of the arrow), the hoop strain would be higher at the thinnest point and any fracture would occur there first. Conventionally, a weld is slightly thicker than the surrounding surfaces so a well-done weld (mine were always pretty awful - "like birdshit", one instructor once told me!) should be a stronger rather than a weaker point.
So, for a person shot by an arrow who is wearing padding and whose armour can yield a little, penetration is much less likley than for a person whose hamata is worn in a way where the arrow hits it and the ring cannot continue to move for any meaningful distance. A very small difference in the amount of distance which the ring can move could have drastic effect on whether the ring breaks or not, a matter of a few millimetres.
Of course, all other factors like skill of archer, quality of metal, weight of arrow, shape of arrowhead, windspead also have an impact. However, consideration of the mechanics shows that the penetration outcome can be drastically affceted by the path length of the ring at the point of impact. If the padded undergarment were a little thin, then one can envisage that the length of the path of movement of the armour would be longer, for example, over the belly area versus (soft) the upper rib-cage (hard).
The ancent and medorn evidence shows that arrows could penetrate this kind of armour, but in the contest between mail and arrowhead, there are a lot of factors affecting the outcome, and correct "fitting" could have had a signifiicant effect on this.
This sounds like a title in the Osprey "Duel" series - "Parthian composite bow vs. Roman Lorica Hamata"!
Regards, John
