A question about a cavalry charge

There are things I am wondering about...

Should not cavalry charge always be as equally powerful, when the soldier does carry a spear/lance?

It is depended upon the speed of the horse, when it does run, regardless of that whether it is light cavalry or heavy cavalry?
(the armor does not affect the cavalry charge).

It must of course be used a spear, or a lance, rather than a short weapon like sword.

The length of the lance does determine the reach of the weapon, so that a two-handed lance will hit the enemy sooner,
but is the blow more powerful?

Could not any light cavalry have charged the enemy infantry, then retreated, and repeated it again?
(If the enemy infantry had already depleted all its javelins and would be unable to shoot down the light cavalry).

It is simple physics, but also common experience. Your conclusions as implied by your questions are all wrong. Except that light cavalry can repeat its charges. Speed, mass, equipment, horse breed, military training, even morale, all determine the impact.

Well, I do not know the difference between the impact of a racing horse or a normal horse... km per hour.
Like if it would matter if somebody got blown up by a cannon-fire or a missile? the extra explosion superfluous, death still guaranteed.
This is why I was wondering whether any non-encumbered horse could be just as lethal...

What about one-handed lance vs two-handed lance? Was it only for the extra reach, or could it also make the charge more powerful?
(like by going through the first target, and then to the person next from behind).

Mass x Speed= Force. bigger horses, bigger weapons make bigger crush. The question of morale and training of cavalry is also vital. A regular horse will, understandably, shy away from a large group of men, let alone armed and violent ones. Larger horses are also scarier for the infantry they face. As a reenactor myself, and having been at the receiving end of a charging horse (scripted mind you), I can tell you it's bloody terrifying. As for light cavalry, being without armour and with breeds designed for speed and stamina, will not want to engage in melee. Neither will their riders, if they have any sense.
To use your cannon vs missile analogy, the damage of the cannon is a simple high-speed impact, whereas the missile's explosives will affect a wide area. Bear in mind that "racing" horses are not bred for combat, there are few breeds today that are.
The two handed lance is not for extra reach, but extra power, it puts more momentum of horse and rider into the tip than a one handed lance. Late Medieval lances were one handed, but a world away in terms of design. As for going through multiple targets, unlikely but possible, probably more for piercing thick shields and armour. The impact of a charging horse and rider will be deadly to an open or disorganised formation, as people will be thrown to the floor and trampled. A strong, tight formation, even without pikes or spears, will fare much better. With a long lance and a big mount, you can turn that formation into a terrified and open one but, again, few horses will charge in this case. After a successful charge reorganising your cavalry, calming the horses and stopping your men from running down fleeing enemies is not easy so even a well trained unit couldn't do that repeatedly.
Light cavalry, being without armour and with breeds designed for speed and stamina, will not want to engage in melee. Neither will their riders, if they have any sense.
In the end it's so hard to figure out how battles were actually fought. We are forced to infer things from the designs of equipment/contemporary artwork/knowledge of physics.

armour counts alot as it as been said massXspeed

the impact probably counted more on killing people then the spear itself an heavy set horse+armour could do 10 times more damage then a nimble horse at half the speed

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Originally Posted by Bodeni

Mass x Speed= Force.

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That is actually wrong... but the rest is good.

@Bodeni: when considering a horse charge, you do not need the mass of the horse itself when figuring out the strength of a blow from a lance (couched or not). you need only the velocity of the horse, plus the mass of the soldier and what he wears. the reason is because the trooper and lance act as one unit: the horse is another: the horseman is not glued to the horse, and is thus like a passenger in a car, or a kleenex box that just sits on the dash: he's going at the same speed as the horse, but he isn't actually part of the horse.

thus at impact, only the horseman (and his lance) is affected, not the horse (in fact, you can see any example of a guy jousting at the tilts to see what I'm talking about: the man recoils, but the horse isn't slowed down). It's like the kleenex box that flies forward and smacks your head when you slam the breaks: if the mass of the car mattered, you'd be dead. And in case you're wondering: saddles don't make much of a difference here: the same result occurs with or without it (the best thing I can compare its function to here is like a seat-belt, but even then it isn't all that accurate, since it isn't really necessary--it just makes it easier).

that is why people didn't use drought horses for cavalry: they didn't need the mass, but the velocity. Drought horses just aren't fast enough. Heavy warhorses were heavy (not as much as Droughts though), mostly to carry the guy on top, plus all the equipment he wears. it also looks quite formidable. the only time the horse's mass matters is when it stops before a line, and is used to go through it "by its breast", but even then, it's at most at the trot (yes, you can train a horse to do that: no, it isn't easy, and it really just works with Stallions: there's a documentary by Mike Loades about shield-walls (weapons that made Britain Episode 4,) that shows him doing that). however horses will (usually--there are exceptions) not just gallop or canter into a line of soldiers.

Sorry I'm a BA not a BSc student. Force= Mass x Acceleration. Speed doesn't matter, after all we're all travelling thousands of kph around the sun at all times...
And I agree completely with Ibrahim's description, sorry I didn't explain the horse part fully.

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Originally Posted by Bodeni

Sorry I'm a BA not a BSc student. Force= Mass x Acceleration. Speed doesn't matter, after all we're all travelling thousands of kph around the sun at all times...
And I agree completely with Ibrahim's description, sorry I didn't explain the horse part fully.

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??????

velocity* does actually matter in this situation (the cavalry charge): in fact it's pretty much the only reason there is a force imparted when the lance hits the target (think about it: the horse is pretty much at constant velocity just before impact, as is the the rider). This is because it imparts kinetic energy and momentum to the lance charge**. the kinetic energy is transferred into the target on impact (at least ideally), which is where force comes in (force in this case is kE/s***, where s is displacement--basically the distance the person theoretically recoils back from the blow.

This of course is ideal: we are not accounting for friction here, between the lance and the hand and/or armpit, and between the rider and the horse. nor are we accounting for the person flexing his back, or a host of other factors.


* srsly people: Speed=/= velocity in physics. velocity is a vector quantity.

**kE=0.5mv^2 (v is squared, so matters more than mass). p=mv (p is momentum).

***W=Fscos(theta), where W is work (measured in Joules, as is kinetic energy: they're basically two forms of the same thing), and since the impact is more or less head on, we can ifnore cos(theta), since the cos(0) is 1. so W=Fs, and so F=W/s. substituting W for kE (again, yes, this is fine), we get F=kE/s.

The first questions have received adequate answers, so I will move to the next ones...

When the foremost cavalry does charge and kills enemies then it can head further into the enemy line/ranks...
Would it then involve a chain reaction where the cavalry from behind gets enough space to charge, and then the cavalry further back, until most of them have charged on the move?

Or is it like that a significant numbers of cavalrymen need to wait idly from behind, having been unable to get enough space to charge the enemy on the move?

So it does all come down to: Did the cavalrymen to the front get in the way of those further back?

Perhaps in context with wedge-formation, when the best troops where positioned in the middle and needed to 'drill' through the enemy line.

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Originally Posted by Ibrahim

??????

velocity* does actually matter in this situation (the cavalry charge): in fact it's pretty much the only reason there is a force imparted when the lance hits the target (think about it: the horse is pretty much at constant velocity just before impact, as is the the rider). This is because it imparts kinetic energy and momentum to the lance charge**. the kinetic energy is transferred into the target on impact (at least ideally), which is where force comes in (force in this case is kE/s***, where s is displacement--basically the distance the person theoretically recoils back from the blow.

This of course is ideal: we are not accounting for friction here, between the lance and the hand and/or armpit, and between the rider and the horse. nor are we accounting for the person flexing his back, or a host of other factors.


* srsly people: Speed=/= velocity in physics. velocity is a vector quantity.

**kE=0.5mv^2 (v is squared, so matters more than mass). p=mv (p is momentum).

***W=Fscos(theta), where W is work (measured in Joules, as is kinetic energy: they're basically two forms of the same thing), and since the impact is more or less head on, we can ifnore cos(theta), since the cos(0) is 1. so W=Fs, and so F=W/s. substituting W for kE (again, yes, this is fine), we get F=kE/s.

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Ah ha. You've proven me right. I don't have a clue what you're on about now... ;p
The way I understand it is that speed=how fast you're moving, acceleration=change in velocity etc. So the force that the cavalry's impact imparts on its target is the effect of the cavalry's mass, multiplied by the difference between the velocities of the cavalry/target. Which I think is what you've written, only in a more accurate (???) way.

As for the cavalry questions.
A cavalry formation is unlikely to be more than a few beasts thick. Going by the number of horse compared to numbers of infantry in classical descriptions of battles, there really isn't that many. Especially when you consider that most of the cavalry (in western-European armies at least) were likely scouts, messengers and skirmishers.
If, and I stress, if, the cavalry have actually charged, and not been driven off, the ranks behind the initial one would be mopping up a broken line, no need for mass or impetus if the infantry are breaking. Wedge formations are more effective for the same reason blades are wedge shaped. It puts a lot of pressure on a small area, making the line easier to break. once among the infantry the sides of the wedge can cause far more damage as there is no longer the surface tension to hold it back. The cavalry in the middle of a wedge are, like the rear ranks of infantry, there to replace the dead, wounded or tired and add greater mass to the unit, not so much in physical terms for cavalry, but psychological.

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Originally Posted by Bodeni

Ah ha. You've proven me right. I don't have a clue what you're on about now... ;p
The way I understand it is that speed=how fast you're moving, acceleration=change in velocity etc. So the force that the cavalry's impact imparts on its target is the effect of the cavalry's mass, multiplied by the difference between the velocities of the cavalry/target. Which I think is what you've written, only in a more accurate (???) way.

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no, not even close.

let's go over this:

let's start with your understanding of Force:

Spoiler Alert, click show to read: 

yes, F= ma, where F is force, m is mass, and a is acceleration.

m (mass) in this case would be the mass of the horseman and whatever he wears (including his weapon): this you got right. you do not factor in the mass of the target, the horse, or anything else: just the man, and his weapon.

However, the acceleration is not the difference between the velocity of the cavalryman and the target--that's just wrong. The acceleration here would be the change in velocity of the cavalrymanonly.

now to explain why this equation is inadequate for a person looking at a cavalry charge's impact, and how to get around it.

Spoiler Alert, click show to read: 

as the horse and man are going at a constant velocity prior to impact, no force is being imparted on anything (since a is now 0). However, Force is being imparted on impact by the cavalryman. How does this happen?

first, remember that by cantering or galloping, the horse is imparting kinetic energy to the whol esystem. kinetic energy is kE=0.5mv^s. m here is still the mass of the man and what he wears, velocity I think you can figure out.

when the man's lance hits the target, both the cavalryman and target will recoil back away from one another (again assuming ideal conditions). that is because kinetic energy is converted to work (so now, kE becomes W).

Now, Work is as follows: W=Fs, where F is force, s is the displacement of the worked on object. Put another way, at the moment of impact, the kinetic energy on conversion to work, imparts a force on target (and an equal and opposite force on the cavalryman).

at this point, you have two options: you can use the displacement/recoil of the cavalryman, or that of the target to calculate the force generated by the impact: Only here does it make no difference who you use (though in this case, it's easier to use the displacement of the target). in that event, F=W/s.

seriously, this is not hard to understand, or figure out--we're dealing with entry-level physics: I've known this since I was an 8th grader. It isn't some sort of black magic.

The reason it doesn't slow a horse down (much) is that at 20 times plus the weight of a person the change in momentum is insignificant.

But you can count some of the mass of a horse in a charge. It does depend on stirrups, saddles (to a lesser degree but some do provide a better join) and the type of weapon. A lance in line as much as possible with the center of mass of a charging horse is going to be more stable (pun intended) and more deadly then one further away. The stirrups can transfer energy and work as a fulcrum too... So if you stood up and held the lance at eye level you would pivot backwards on your rump on contact.

The lance piercing a target is one thing. Surely enough a rider's xyston or kontos will do the trick. The solid mass of a heavy armored and disciplined cavalry element in tight formation should have another effect altogether. Even without the piercing, the impact will disrupt infantry formations and cause casualties, just like a car crash where no spears are involved. Just a lot of blunt hard surfaces and a significant amount of energy accumulated during the charge and discharged on impact. For the physics of it, what we should be looking at is the equation that defines momentum. And that is:
m*v=F*Δt (mass times velocity equals Force multiplied by the time interval during which the force is applied). Assuming that the time interval is more or less the same (the duration of the impact) for most charges, you can clearly see that the Force applied within the Cavalry-Infantry system increases as either Mass or Velocity increase.
Now this force can have two effects. It can increase the target's kinetic energy through acceleration (elastic impact) or it can have a more lasting effect on the target, i.e. part of the kinetic energy that was stored in the cavalry does not become the infantry's kinetic energy (in order to send them flying) but crashes bones, compresses air pockets in the human body, causes internal hemorrhage and all sorts of damage.

Does it really take equations to see how this would work? If it does then I've been posting on the wrong forum!

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Originally Posted by kdrakak

The lance piercing a target is one thing. Surely enough a rider's xyston or kontos will do the trick.

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already explained, and you're right about that.

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Originally Posted by kdrakak

The solid mass of a heavy armored and disciplined cavalry element in tight formation should have another effect altogether. Even without the piercing, the impact will disrupt infantry formations and cause casualties, just like a car crash where no spears are involved. Just a lot of blunt hard surfaces and a significant amount of energy accumulated during the charge and discharged on impact. For the physics of it, what we should be looking at is the equation that defines momentum. And that is:
m*v=F*Δt (mass times velocity equals Force multiplied by the time interval during which the force is applied). Assuming that the time interval is more or less the same (the duration of the impact) for most charges, you can clearly see that the Force applied within the Cavalry-Infantry system increases as either Mass or Velocity increase.
Now this force can have two effects. It can increase the target's kinetic energy through acceleration (elastic impact) or it can have a more lasting effect on the target, i.e. part of the kinetic energy that was stored in the cavalry does not become the infantry's kinetic energy (in order to send them flying) but crashes bones, compresses air pockets in the human body, causes internal hemorrhage and all sorts of damage.

Does it really take equations to see how this would work? If it does then I've been posting on the wrong forum!

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If I understand you right (please correct me if I didn't): that's another way of looking at the problem, and it is also valid--if you assume the horses are directly crashing into the line relying on mass of horse alone (so breast to face I guess :clown:): they did not necessarily do that at full tilt (at a trot, maybe). you are certainly correct to say that in practice a good deal of any kinetic energy imparted would not go into force that pushes the target back: this applies both to the crushing angle, or to the lance itself (I've thus far been describing things in an idealized manner--for simplicity: mentioned it in my first post).

You do bring up a point (which I only incidentally mentioned): Momentum is important here--not just for the horse itself, but the lance.

to answer your question: It's good we bring this up. beats the hell out a boring lecture. :wink:


@Papewaio as to the first part of what you said: not really: remember, even factoring in friction, that's not why the horse is hardly affected: the horse and the rider are two separate entities, so the horseman is the one taking the hit at its worst, not the horse itself (if anything, the friction between the two will affect the displacement of the rider more than the horse, specifically by reducing the amount of displacement along the back of the horse).

secondly:

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But you can count some of the mass of a horse in a charge.

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well, not really. see above: I've been saying this repeatedly: the horse and the rider are separate in this case. even taking into account friction, the role of a horses' mass is negligible. To give you an idea of how dramatically unimportant the horses' mass itself is, here's an in-depth look at the matter--from a jouster:

http://www.classicalfencing.com/articles/shock.php

he treats the whole unit (horse, man, lance) slightly differently (and slightly inaccurately: he conflates the mass of the horse with that of the rider at times, and mass with weight, so his explanation seems contradictory: not the most precise language for sure), but his conclusions are generally the same--and best yet, based on years of observation: the size of rider himself is the main factor in determining the force and energy of impact of a lance, not that of the horse. Otherwise he wouldn't be worried about the Big guy on the little horse more than the Little guy on the big horse.

in fact, we can put what he observes into context pretty easily:

1-man's size: the force itself (as well as kE)
2-the man's strength/technique: efficiency of delivery, direction of delivery, etc.


finally:

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A lance in line as much as possible with the center of mass of a charging horse is going to be more stable (pun intended) and more deadly then one further away.

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if the horse were the one wielding the lance, sure :clown: (seriously though, you're not the first to figure this out: IIRC one Sassanid knight was described as lashing his lance to his mount directly). This would be extremely powerful, but lacks precision--for somewhat obvious reasons.

again, it must be emphasized that it's the rider who matters here in the end in most cases (since he's the one holding the lance). further, due to the way the lance is held (and the fact that he isn't standing up, but seated on his horse), his center of mass is going to be higher up than where it would normally be (where exactly depends on his posture). Not that any of this really matters when determining what the kE or F is (or p), but only on how efficiently it is transferred.

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The stirrups can transfer energy and work as a fulcrum too... So if you stood up and held the lance at eye level you would pivot backwards on your rump on contact.

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no, saddles and stirrups don't work the way you described in this context (and are not required--though they make life easier: I recommend the above link): And doing it the way you describe would make the man get knocked off his horse, not into his seat (the force affecting him pushes him directly back, or back and slight to one side: usually in context of jousting, it means the feet are removed from stirrups). Also, There's no practical way the stirrup can act as an effective fulcrum here: it even comes across as dangerous, even if we ignore the whole "knocked off your horse" problem.

Finally, No one did that historically: we have many depictions of European, Saracen, and Turkish riders--even Mongols and Mughals, and none use the method--quite the opposite: the soldier is firmly planted in the saddle, with the stirrup playing a support role (it really shines in melee, or in horse archery: the soldier can rear up on the stirrup to deliver a more powerful mace or sword strike from above, or deliver specific types of shot).

@Ibrahim
Yes it is another approach. The math proves that both equations are equivalent. However, your approach implies no effect when there is no displacement. Which does not reflect what would happen when the heavy infantry front lines are packed and cannot be displaced. No effect? I don't think so...

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Originally Posted by kdrakak

@Ibrahim
Yes it is another approach. The math proves that both equations are equivalent. However, your approach implies no effect when there is no displacement. Which does not reflect what would happen when the heavy infantry front lines are packed and cannot be displaced. No effect? I don't think so...

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I agree with you. What I provided is admittedly a simplified view of the matter--to demonstrate that the force, kinetic energy, and momentum of the lance thrust doesn't rely on the horse's mass itself. it definitely doesn't take into account that a good deal of the force and energy imparted goes into penetrating the target (so that there need not be a displacement for there to be an effect). yours doesn't rely on there being a displacement.

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Originally Posted by Ibrahim

Finally, No one did that historically: we have many depictions of European, Saracen, and Turkish riders--even Mongols and Mughals, and none use the method--quite the opposite: the soldier is firmly planted in the saddle, with the stirrup playing a support role (it really shines in melee, or in horse archery: the soldier can rear up on the stirrup to deliver a more powerful mace or sword strike from above, or deliver specific types of shot).

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It also improves side-to-side stability in that same melee.