To push or not to push?

There is an ongoing controversy in the literature of whether Greek phalanx warfare routinely involved physical pushing against the enemy line or not (what is meant here is that not only the first ranks push against the enemy, but each rank braces against the shields of the ranks behind which in this way transmit force to the front). For the simulation this is of course important, since the question of what use a deep phalanx (many ranks, of which only the first two can reasonably attack) has hinges somewhat on whether pushing (where the deep phalanx offers a clear advantage) is done or not. And by extension - would other military formations have pushed against enemy lines if the need arose?

Of course a deep phalanx has other uses - it confers a measure of 'feeling safe' to the soldiers in the first ranks. It allows to rotate exhausted soldiers back and fresh forces to the fighting line. And it takes more time to destroy of course. But I feel that simply from a perspective of physics, the issue of pushing is important.

So for reasons to be outlined below, I belong rather firmly into the camp of people who believe that pushing the enemy line is an issue. But let's approach the question via a short detour.

Impact resistance

Imagine a soldier, with gear weighing perhaps 100 kg, standing stall and braced into the ground who is tackled by another soldier who comes at him at a slow walking speed. Chances are he manages to remain standing in the same spot - in more fancy words, an incoming momentum of some 100 kg m/s can be transferred into the ground via his legs.

If the attacker comes at a brisk walking speed or slow jogging speed (2-3 m/s) and tackles, the defender might stagger back a few steps, but has a reasonable chance to remain standing. So by staggering back and using several steps, a momentum of some 300 kg m/s can be dissipated. But if the attacker comes at him fully running (8 m/s), he will not be able to remain standing and be thrown.

Now, let's replace the attacker by a horse - which, with rider and gear may weigh some 800 kg and at full speed may do 12 m/s - this is what happens if a cavalry attack crashes into a sparse infantry line. The soldier will have no chance at all to dissipate 9600 kg m/s of momentum, be thrown backward and trampled while slowing the horse down to 10.6 m/s. This is independent of battle morale, training, gear or other factors - it is simple momentum conservation in an inelastic collision! So, to summarize, the horse will continue, the soldier will likely be dead.

Now imagine the same scenario with the horse crashing into a phalanx eight ranks deep, with the first ranks braced against the shields of the men behind them. The horse impacts into a 16 men strong column of twice the weight of the horse and alone by that its speed is reduced to 4 m/s. However - there's the momentum dissipation we have mentioned earlier (by bracing into the ground and/or staggering back). So now each soldier has to deal with 600 kg m/s - that's on the high end even for staggering back, true. So soldiers will fall, bones might break, shields might give - but it's not outrageously high. The net result will be that the horse is stopped.

For a cavalry charge that's pretty bad of course - if the rider remains in the saddle at all, he is now mired in a mass of other horses coming from the rear and angry infantry coming at him from the front. But the take-home message is - a single rank of soldiers can't physically stop a cavalry charge, but a braced phalanx eight ranks deep can (*). In fact, the Battle of the Hydaspes has demonstrated that a 16 rank Macedonian phalanx can withstand (albeit with significant losses) the 27000 kg m/s momentum of a charging war elefant.

The Greek commanders were well aware of this - when expecting a cavalry charge an ultra-dense formation with just 0.5 m distance between men called synaspismos was chosen to distribute the incoming momentum among as many soldiers as possible.

Pushing as tactics

It follows from the previous section that it pays off for an infantry unit to practice bracing the ranks against each other, because that offers a significant advantage against cavalry. But once soldiers know how to do it anyway - why would they not do that when moving forward, trying to break the enemy line?

Imagine Conan and his barbarian friends fighting a Greek phalanx. They can hammer their swords against a massive wall of shields without much avail - so they have to create a gap. But tackling the phalanx ends badly - they can hope to puch back perhaps two soldiers, but certainly not a full file of eight - in fact the phalanx just needs to advance and it will easily and without much efford push the barbarians back - who will have to fight moving backward all the time, and if they stumble, the phalanx just walks over them, spears stabbing downward and killing them.

Which is to say - using braced ranks to push forward is a winning tactics against anyone who doesn't do it. It is the obvious thing to do if the goal is to break through the enemy line. And most of the effect is physics rather than psychology or advanced weapons training, so it doesn't rely on certain conditions.

The Battle of Leuctra seems to show the principle in action - here a 50 man deep phalanx was used by the Thebans to break through the Spartan right wing.

Likely, bracing and pushing wasn't constantly used as it is a strenuous activity, but rather when needed, i.e. when the front ranks tried to charge or when it was necessary to resist a charge. Equally likely, it didn't always work as intended - at the Battle of Delium an eight rank Athenian phalanx held against a deeper Theban one (and there are other examples). But if pushing wasn't continuously done, its effectivity would depend on timing and, to a degree, on chance.

The upshot for the simulation is that density of soldiers inside a unit is used to determine impact resistance and ability to push other units, and for the initial collision of two units a comparison of momentum is factored into the determination of the results. To re-iterate - in my view these effects are a result of basic kinematics and hard to get rid off.

(*) Actually, a non-bracked stack of 8 soldiers in a row would be even more effective in stopping the horse - the downside of that strategy of course is that the momentum transfer to the first ranks wold be much higher, so the first few ranks of the non-braced soldiers would probably die - which makes the physically sound strategy much less attractive in practice.

Continue with Damage.

Back to main index Back to science Back to historical battle simulation

Created by Thorsten Renk 2022 - see the disclaimer, privacy statement and contact information.