Overhand spear

[lankylars]

@ El Muerte:
A phalanx is not a big, rigid body in the sense you're thinking. Sure, it moves as a cohesive unit, but it is composed of freely moving soldiers within its ranks that do not necessarily keep perfectly in line with others in the ranks, nor do they share a common momentum, weight, or force. Your calculations of momentum only work if the men are somehow joined into one unit that is not free to move apart in any way.
Otherwise, to find the force that will be absorbed in a collision, you need only look at what one soldier must endure, which at most might be one or two men head-on, not an entire 8 man row.
Also, a human running into another is not a perfectly inelastic collision as you're thinking of it; both men will not continue onward in one direction with a certain velocity and 100% of the original momentum.
You're also forgetting that the human body doesn't have to absorb all of the force of another soldier charging straight into it. With a shield held away from the body, a soldier could cushion the impact much as you would cushion your fall by extending your arms. Thus, some of the force would be absorbed as the soldier with the outstretched arm slows down the other. If both men do this, there will likely be a significant reduction in overall force. After this, it is extremely likely that the human body could endure, rather well, the remaining impact.

[Archbaker]

If two men weighing 135 kg run into each other at any speed, they survive.

If they decelerate along the way*, and wear helmets, and use shields to absorb the force of the impact, they are likely to not even be hurt.

The fact that there are men behind them and to the sides have no impact on that calculation.

The men to the side have absolutely no impact, whether they have interlocking shields or not, they are not one body.

The supposed eight men behind each man in the first line only add to his weight if they are actively pushing the man in front, which nobody says they did.
And even if they do push on the man in front, the force is not increased by such a neat calculation, which is why it is harder for two people standing behind each other to force open a door than for two people standing side by side.

Your ideas about absorbing force are also not entirely correct. If a phalanx is pushed back, then some of the force must be transmitted through the line (or it wouldn't move) and so we can safely conclude that not all of the force goes into the front rank.

Above, I have tried to explain why I think it makes sense to form a shield wall and to use it to push against the enemy. I welcome comments on that.

[El Muerte]

If two men weighing 135 kg run into each other at any speed, they survive.

Really???
Mass of 270kg moving at 20 kmh will break you if you try to hold it (if you try to stop someone on motorbike moving 20km/h with hands resting on wall.....will you get out withouth a scratch??) .....imagine if speed is 30 kmh or 40km ?????
At ANY SPEED they will survive???

@lankylars
You are right...i made calculation for piling up to mass while speed is constant ....if you want to see those calculations i will post it...but only if you'll read it becouse it,s long.
anyway...when body (m1) hits another one(m2) of same mass...speed of (m2) will be hlafed....and again and again....anyway.....(having in mind that soldiers pile up,reducing impact as soldiers form behind will be hitting "piled up mass")total force per phalanx on first rows still will be enought to breaks hands, shoulders and ribs...and it can kill human...and in phalanx battle if you break your arm or shoulder in first rank....you are dead.
anyway...if we continue this way we'll be off subject but fact remains - that ammount of force breaks human body no matter how you try to absorb it.

[Archbaker]

Really???
Mass of 270kg moving at 20 kmh will break you if you try to hold it (if you try to stop someone on motorbike moving 20km/h with hands resting on wall.....will you get out withouth a scratch??) .....imagine if speed is 30 kmh or 40km ?????
At ANY SPEED they will survive???

Generally, yes. I must admit I was not considering sprinters going at 40 km/h or above when I wrote that, but unless they run into each other head first, even at that speed, their bodies should not be exposed to so much trauma as to kill them; they are much more likely to fall over backwards.

The example that uses a motorcycle and a a wall is a straw man argument and an insult to my intelligence. We are comparing two hoplites who eac have (using your numbers) one metre to fall back before they hit another elastic body which has another metre to fall back.

And you did not explain to me how the phalanx could be pushed backwards if all the energy was absorbed by the front line.

anyway...when body (m1) hits another one(m2) of same mass...speed of (m2) will be hlafed....and again and again....anyway.....(having in mind that soldiers pile up,reducing impact as soldiers form behind will be hitting "piled up mass")total force per phalanx on first rows still will be enought to breaks hands, shoulders and ribs...and it can kill human...and in phalanx battle if you break your arm or shoulder in first rank....you are dead.
anyway...if we continue this way we'll be off subject but fact remains - that ammount of force breaks human body no matter how you try to absorb it.

If we continue to pursue the foundation of your calculations we will be off topic? I am sure you did not mean that.
At any rate, it is not true that any amount of force breaks the human body unless it is the human body which absorbs it. If some of it is absorbed by the shield, and some of it is transferred into the air and ground because the hoplite moves backwards on impact, and some of it is absorbed by the man behind him if he steps that far back, then we are no longer dealing with the same amount of force.

[DimeBagHo]

El Muerte: I think you are just confused over two very different senses of the word 'rigid'. A phalanx is a rigid formation compared to other infantry formations of the time - meaning that it could not bend or turn as easily as other types of formation - but that has little to do with the engineering or physics sense of the word. In physics a body is rigid if it doesn't change shape when a force is applied to it. The human body does change shape (the arm holding the shield can bend and flex for example) and the men in a phalanx are hardly welded together with steel rods, so the formation itself will change shape under an applied force. Because it is not a rigid body you can't treat it as a single mass, with a single velocity and momentum - not even approximately. You can't even treat a single hoplite that way - each man is more like two masses (man and shield) connected by a spring (the arm) - and that is still an over-simplification.

It's been a while since I studied physics as an undergrad in college, but I can assure you that your calculations don't work.

[chazap]

Mass of 270kg moving at 20 kmh will break you if you try to hold it (if you try to stop someone on motorbike moving 20km/h with

errr:hmmm:.....270kg x 2.2lbs = 594 pounds!!!! a 594 pound man moving at 20km/hr????? . a 600 pound motorcycle (being a single cohesive unit) of course! but we're talking men, not machines!! even 2 men at 135kg each = 297 pounds!! its pretty hard for a man weighing that much to maintain a 10km/hr speed and to expect a whole phalanx unit to do it seems a little ridiculous....

and for the record....i'm not disputing that Newton's formulas don't work!!! as i've stated before i'm merely pointing out that you're applying bad mathematics (i.e. you're using the formula wrong to suit your purpose)....from the comments i have read thus far.....everyone else seems to be telling you, in one way or another, the same thing.

[El Muerte]

a 594 pound man moving at 20km/hr?????

Equivalent of 20 km/hr let me ilustrete it for you phalanx 1 = 10kmh ----> <------phalanx 2 = 10km/hr
10 = -10 geti it now???
And how many of them are familiar with those formulas?????
im not saying am expear...not at all......but does anyone here have a clue what im talking about?
Anyway....it is not ridiculous for hoplite to charge 10km/h ....but oly in last 20-30 meters thats more than enough.
here is a hint : Have you ever been squashed by a crowd on concert to a fence??? Thats just couple people standing behind you moving couple inches in direction towards you .....imagine if they RUN!!
And now imagin heavy infantry of 8 strong men !!!
The problem is...you people think that such force can be absorbed without any consequences.
I have seen many serious injuries in American Footbal...with all that absorbing armour and composite hi-tech materials........and still....player get hurt very badly , and some player even loose an eye from such impacts.Dislocated shoulder is also very common...now compare precent of thoose injuries and then compare bunsc of soldiers covered in bronze charging towards enemy wearing that same broze....in same formation formation with prupose to kill and crush the enemy!
How can you possibly tell me that no one will get killed in such collision?!?!?!?!?

You say i calculated it wrong...i say : PROVE IT!