The unicorns would be used to charge a line of infantry with their horn. They are as big as a horse and the horn is similar to this image:
The infantry is a standard medieval army made mostly of soldiers wearing longsword, wooden shield and chainmail.
If I use my unicorns to charge the enemy’s infantry, are they more likely to die in the attempt or will they cause massive damage?
That depends on a tactic.
If you just have two swarms of different meatbags charging at each other, then the one with more speed and durability wins. You didn't provide any numbers, but assuming 1-1 ratio, even normal horses should be able to defeat the humans, longswords or not.
Horses are big, powerful beasts:
https://www.youtube.com/watch?v=-srzT2olJ2Q
https://www.youtube.com/watch?v=J95LsygVMaQ
They can kick, bite, or just run you over.
And when it's charging, and you stab it with your tiny long sword it'll have enough momentum to run you over, most likely killing you and the guy behind you.
And now let's add a horn to that scenario. With them, you may never even have a chance to use that sword - you'll be a dead long before the beast is in range.
Now, there are ways to defeat them, even with such weak weapons like swords.
One of them is preparing the battlefield to your advantage (for example by digging trenches). Given the title I assume that we are talking about an open field, so we can cross out this option.
Second tactic would be scaring the beasts off with noises they don't like, fire, commotion, etc. I don't know if it's possible in your setting.
Third way I can think about is simply outnumbering them in overwhelming odds - but expect HEAVY losses, because it will take lives of several men to kill one horse (and even more with a unicorn).
But if your question was about only about the first impact in an open field, then my answer is that there will be no line of infantry after the two forces meet.
[EDIT] To address a good point made by @Monica Cellio in a comment:
I'd say that killing a horse (or a unicorn) with a long sword is a no small task.
For starters, let's assume, that we have one man trying to kill a unicorn, which cannot fight back. The only restriction is that he has too attack beast's front. What are his options?
He can try to attack the head. Good luck with that. Here is how a typical horse looks from the inside:
http://www.infovisual.info/02/072_en.html
You'll notice, that it's pretty much nothing but a skull. You may have some luck with a hammer or a pick, but a long sword is most likely the worst weapon to use for such attack - it will scratch the skin and bounce off the bone. A horn provides even more protection.
Next on the line is the chest. In this case it is a matter of luck, but even if you somehow manage to stab right through the heart, it will take a couple of seconds before the brain runs out of oxygen, so even with best of luck, you have no chance of an instant kill.
But that is not a likely scenario. In most cases the horse would look like this:
Please notice, that there is not much of the chest visible to hit, mostly it's protected by the head.
If you get the chance to stab the beast, you'll most likely hit hard and dense muscle tissue - not exactly an armour, but you need some effort to go through it to juicy internal organs.
I'd say that your best chest option is slash it several times and wait till it bleeds out.
Last but not least - legs. Hard bones, surrounded by muscles designed to move a heavy body with a great speed. This, however, is your best option - you won't kill the beast, but if you damage the muscles enough, you'll incapacitate it for good. Long sword is best used for slashing, and that's exactly the kind of damage you need for this task.
And now apply the story scenario: the unicorns are charging, the attack, fight back, there is a lot of kicking, screaming, nobody really knows what's going on. Complete, utter chaos. Some soldiers will get lucky and damage the legs, some unicorns may bleed out afterwards, but I don't think that swords will be much of a use in this case.
Not enough time to use them properly, not enough space and the targets fight back to well.
So to rephrase the original question:
Charging unicorns WOULD survive an impact with a line of infantry.
As the "real" unicorn horns (in our world) were scavenged from Narwhals, I guess we can just take this as base:
A unicorn is a huge, strong horse with magical powers and the tusk of a Narwhal
Else we couldn't do any kind of reality check on that.
The tusk itself is 1,50 - 3,10m (60 - 120 inches) long Source: Wikipedia. As elephants and rhinos have tusks as well, we can assume that it's pretty durable as it's used in battle and during charges on rivals.
You can read in the book Mammoths, Mastodonts, and Elephants: Biology, Behavior and the Fossil Record by Gary Haynes, that the densest tusks (or "dentinal tubules") are those of Mammoths and Mastodonts - both old species. What makes them interesting for us is that they had tusks which "[...] grow spirally in tight curves[...]" like the ones of Narwhals. Due to their high density they could grow larger and were much more elastic. Something that might be important for a horse that has a minimum 1,50m long horn sitting on his fore head. Different sources have a wide range of densities for tusks. They go from 3,00 g/cm³ up to 5,00 g/cm³ for Mammoth. I think we can safely assume that a Unicorns would range at the upper end of that scale.
Default horn/tusk/keratin has a pressure resistance of 30 kN/cm² (which is 3 tons per square centimeter). The horn of an Unicorn is assumed to have 25cm² (5x5cm; guess based of images of Viking spears forged out of Narwhal tusks) and a much higher density. The lowest quality horns have an elasticity of 3% (3cm moment per meter). That means that a stiff tusk of low density would with that surface at least withstand 750 tons pressure before it starts bending.
As base, taking the length and weight of the tusk into account, I'd go for an unusually large horse. The largest breeds are Shire horses with a height of 1,70+ meters or 68 inches. I'd assume it to have a shoulder height of at least 2,00m or 80-85 inches.
When you look at breeds with a good duration and good jumping and racing abilities like the Akhal-Teke Source: horse-breeds.findthebest.com (or similar), then they have a weight between 800 up to 1.1k pounds (360-500kg) at a height of 15 to 16 hands (60-65 inches/1,50-1,70m). When interpolated up to a unicorn, this would be around +25%, so we end up at ~450-625kg (or ~1k-1350 pounds).
Top running horses (you will have to look up different sources for confirmation) can go around 55mph (85 km/h): "Quarter horses, bred and raced for short distances at speed". I'd assume a magical horse-like species who is larger to go even faster than that and take their charging speed (or the impact speed) up to 100 km/h (60mph).
All above tears down to the following data
impactor density: 5 g/m³
human body av. density: 1,05 g/m²
impactor diameter: 0,0001 m² (5cm x 5cm impactor size)
velocity: 27,78 m/s (100 km/h)
distance from impact: 100 m
impact angle: 90°
The needed formula is pretty much the same that we would need to calculate the impact force during a car crash:
$$\frac{-\frac12 m v²}{d}$$
For the sake of a shorter answer, I'm not doing the math now, but the resistance the unicorns horn would have would be equal to sticking a spoon into a glass of jar.
The unicorns weight at this speed hitting a human body with such a small surface would be more than just a few tons and worse than getting knocked over by an average sized car at the same speed - impactor surface matters. In other words: The soldier would be torn apart.
Depending on formation (I would imagine it to be triangular), the soldiers would not stand a single chance. A long sword (and even a rapier) are shorter than the shortest horn. The density of the horn wouldn't be a problem (for the unicorn) and just knock the chains apart (which already has been a problem to this kind of armor when crossbows were invented).
1:0 for unicorns
I switch between Metric and English units. The English separator [used in this answer] is a ., while the Metric is a ,. I tried to avoid the thousands separator whenever possible. Still, 1.1k pounds equals 1100 pounds.
The height of a horse is measured in hands, which you might want to refer to in your story. I think it adds a nice touch. A hand equals 10 cm or 4 inches.
Depends on your unicorn.
An Elasmotherium was twice the height of a human and weighed 4 tons (other sources say 6 tons). It (probably) had a 2m armoured horn with substantial muscle to control it. Probably a vegetarian but likely fierce if threatened.
Legends and names referring to a special type of unicorn or mysterious beast with one horn, as opposed to the delicate imaginary unicorns of Europe based on narwhal horns, are scattered across the former range of Elasmotherium from China to Eastern Europe. They have been noted there since the first known literature of the Middle Ages. ...
In the northeast of the range, in 1866 Vasily Radlov reported a legend among the Yakuts of Siberia of a "huge black bull" killed by spear, who had "a single horn" so large it required a sledge for transportation. In 1878 A. F. Brandt suggested the beast was an Elasmotherium.[58] In Yakut mythology is known also the one horned Bull of Winter with pale blue fur. It symbolises winter and frost. In 1921 Gavril Ksenofontov collected some Sakha legends about huge, one horned bulls, usually with pale blue or dun, long, wool-like fur. The big bull with a single, long horn is mentioned also in yakut epics Olonkho.
So if you want your unicorns to win then choose this type of Asian unicorn over the namby-pamby European 'magic horse with a horn' type. Unknown psychological factors aside, it's hard to imagine the humans being victorious armed with any weapons less substantial than a main battle tank.
This type of unicorn has the advantage of actually having existed and being real. Also you don't need to worry about possible enemy deployment of tactical virgins.
Longswords? Sure. Many unicorns will fall to the longswords, but there is a reason the cavalry charge was a standard military tactic. It it not fun to try to stop several tons of horse with a mere pointy piece of metal.
However, add pikes into the mix and the story is different. Pikes were designed to stop the horses (violently) out of range of the infantry. After that, calvalry charges were used as a flanking attack, attacking unprotected sides rather than front on charges.
A lot of unicorns would die in the immediate crash, or by getting stabbed to death on the ground by infantrymen.
I will elaborate on the mechanics after giving a short military history background on the subject of cavalry vs. infantry, which has been more or less completely neglected here. I am puzzled as to why Oldcat's answer was downvoted, but except for Dronz and vsz, he is the only one focusing on the most important part of a battle: psychology.
The main objective of a cavalry charge was not to ram into a wall of humans, but to intimidate the enemies before contact - making them turn around and flee, which means that the battle line is dissolved and individual soldiers can be cut in the back by the riders.
The main objective of an infantry line holding ground against a cavalry charge would be just that: to hold the ground long enough for the charge to be broken up. With horses, especially ridden horses, it is as simple as that - they won't go through something they perceive as a solid wall. But holding ground when hundreds of animals are galloping against you, sounding worse than thunder, and with armed warriors in the saddles, is probably easier said than done.
There are very few occasions when a close formation of infantry soldiers held ground and a horse actually galloped right into it. Extremely few, I might add. It did happen once though, during the battle of Garcia-Hernandez in 1812:
On this occasion one of the leading cavalrymen, a Heavy Dragoon of the King's German Legions, was killed close to the French square. Both horse and rider were shot and killed in mid-stride, but momentum and a nervous reaction kept the horse moving, so that it finally toppled over on top of the French infantry, dragging men down with it. This dead horse had done what no living animal and rider could have done, and actually struck the face of the enemy square, creating a gap and allowing the rest of the unit to enter. (Goldsworthy, A. K., 1996, The Roman Army at War, p. 230)
The problem with reasoning along the lines that a cavalry unit could use its momentum to break up a solid line of long sword equipped infantry men (it is actually not that relevant what kind of weapon they are carrying, unless it is pikes or long spears which are excellent against cavalry, what matters most is the tightness of the formation), is that the same momentum would be devastating for the horses and riders alike. That would in most cases be true for one horse versus one man on an open field. But different factors weigh in when we are talking about formations. A skewered infantry man does not vanish the second he is killed, nor is the path behind him cleared. A fraction after being speared to death by the unicorn, the unicorn would crash into the man. It could power through until the next man, with a soldier hanging on its spear. But inevitably, it would topple over and drag down several soldiers with it in the fall. A split second later, the next wave of horses would crash into the heap of soldiers and jerking unicorn legs, or they would leap over the heap - only to crash into the following lines of soldiers. Then comes the next way, and the next, until it is all a bloody mass of fractured legs, skewered torsos, long sword-impaled unicorns, and so on and so forth. Clashes of cavalry and infantry lines can be seen in literature and movies, but they did not took place on a regular basis in any war the military historians know of. And for them to take place when unicorns have replaced horses as animals in a cavalry unit - well, it would presume that the unicorns in question all entirely lack self preservation, and that is entirely up to the OP to decide upon.
Summary: If the unicorn psychology was very different to that of a horse, then it would suffer the same consequences of crashing into a mass of bodies as a horse would - resembling a violent accident much more than a battlefield maneuver.
Its best chance of survival when facing an infantry line that won't break up would be - just as it would for a horse - to hold the charge before impact. The main force of a cavalry charge has - despite Hollywood depictions - never been physical but rather moral. (Goldsworthy, A. K., 1996, The Roman Army at War, p. 230f.)
It would mainly depend on the morale and training of each side. Some human armies of the appropriate culture might panic and run away if attacked by a charge of unicorns, because it would seem to be a supernatural event to them.
As another writer mentioned, the opposite could be equally true: the unicorns may be the ones who are likely not to go through with the charge, or to break early.
Of course, if one side does run, unicorns will be very good at running away from men with swords, while humans trying to run from unicorns will have a very hard time.
Apart from one side breaking and running, the fighting skill, discipline, coordination and tactics will also be a big deal. Either side might be superior, depending on the details of how they fight, and how well.
You could try using Dominions 4 to run simulations with various attributes for both sides, to get results for various situations, and to give you a basis for choosing what attributes you want your unicorns to have to be consistent with the results.
Unicorns are magical! Of course they can survive it.
A unicorn is a huge, strong horse with magical powers and the tusk of a Narwhale
It seems clear that if you have magical powers and a horn, that one of the magical powers is going to be the ability to skewer things with the horn without taking massive head damage.
Presumably, also, as with any magical weapon, it is incredibly tough and achingly sharp, so it will pierce any feeble medieval armour.
Also, the unicorn is magically strong (and just look at the neck muscles in the picture!), and can fling the impalement victim(s) off it's horn through the air, without noticeable effort.
If you have a magical mythical beast on your side, what hope does a mere medieval footsoldier have?
It would be just like a regular old cavalry charge, but at least slightly less effective. Mounted knights carried lances which had a much longer reach than unicorn horns, and a human rider can also carry a wide variety of weaponry. Once in a melee, a unicorn cannot do much with its horn, while a human rider can chop at his enemies from above.
So, if the unicorns had riders on them, then it's no big difference from any historical cavalry, and if the unicorns didn't have humans riding on them, they would be less effective.
(Assuming that unicorn biology is similar to the horse except for the horn)
One single factor, however, could put unicorns into an advantage: if they would be much less fearful than horses, or even humans. Battles were not decided mechanically by a fight which lasts to the last man: armies almost always broke into a rout when losing 20-25% of their men, sometimes even much less.
If the unicorns are intelligent, their horns are tough enough to take multiple sword blows, and their horns are approximately as long or longer than the infantry's effective reach (sword + arm, extended to a length where the weapon is a real threat), then the infantry is toast.
The battle goes like this: unicorns charge in tight formation. For each unicorn, if the infantryman in front of them swings, they block it with their horn and stomp the guy with their hooves. If not, they skewer them with the horn (which, unless shockingly dull, would easily penetrate chainmail). The formation then turns and gallops away. Since unicorns are presumably fast and have considerable endurance (like horses), they can attack any part of the formation that sticks out, where the escape part is easiest. If the infantry is exceedingly good at starting with a tight formation, unicorns could choose to go on a semi-suicide charge to break the formation (was done on occasion with warhorses), after which the following unicorns could attack the vulnerable infantry.
If, on the other hand, the infantry has considerably better reach or can cleave through the unicorn's horns, and also has a numerical advantage, then the infantry has a winning strategy: pack warriors in tight formation so that at least two of them can strike any incoming unicorn. Both aim for the neck, one high and one low. Most of the time, the unicorn may kill one of the soldiers, but the other one will kill the unicorn. (This is why pikemen rendered cavalry almost obsolete except for chasing down fleeing soldiers; any well-organized unit would present a forest of sharp metal points to any incoming cavalry.
Either way, if one side outnumbers the other hugely, the larger army will win; the question is really by how much you need to outnumber the other. If you're going for some sort of heroic fantasy setting, probably ten-to-one men to unicorns would be a tense battle, assuming nerves held on both sides and neither had a big tactical advantage (of the sort described above).
For ideas about how the two sides should try to maximize their chances, you can read about infantry and cavalry battles and tactics. (The Greeks, esp. under Alexander the Great, had very effective wedge-shaped formations of cavalry.)
Horses are not rutting Elk. Their necks are not evolved for impacts. Of course a unicorn may be designed to impale things with its horn. That's a world-builder decision.
If you want them to take out footsoldiers, then they can. Use magic to handwave away any difficulties.
Cavalry charges with horses do not work against formed infantry in lines because the horses will not run into something that looks like a wall of their own volition. They will instead stop, and turn aside. Even without horns, a 'kamikaze' horse will break into a line or square. I recall a story of a horse being shot and killed in a charge and the body crushed in the square and disordered it, allowing it to be broken
So if a unicorn reacts like a horse, it would stop to 'fence' with its horn when faced with formed infantry and its momentum would not matter at all, unless the line broke. Only if a unicorn would allow itself to charge that solid seeming wall would they be any better than horsemen, and then the horns don't matter as the mass of the body would be sufficient.
One thing to remember, horses and therefore unicorns do not have front facing eyes like us primates... this makes aiming and slashing a real difficulty.
That's why (among many other reasons) things like elk and deer have great big horns that splay out.
If your unicorns are mounted and directed then that will significantly improve the odds in their favor.
I would however point you to the wikipedia article on charging as below.
The shock value of a charge attack has been especially exploited in cavalry tactics, both of armored knights and lighter mounted troops of both earlier and later eras. Historians... have shown that when correctly prepared... by standing firm in face of the onslaught, cavalry charges often failed against infantry, with horses refusing to gallop into the dense mass of enemies, or the charging unit itself breaking up.
However, when cavalry charges succeeded, it was usually due to the defending formation breaking up... and scattering, to be hunted down by the enemy. It must be noted... that while it was not recommended for a cavalry charge to continue against unbroken infantry, charges were still a viable danger to heavy infantry.
Parthian lancers were noted to require significantly dense formations of Roman legionaries to stop... However, only highly trained horses would voluntarily charge dense, unbroken enemy formations directly, and in order to be effective, a strong formation would have to be kept – such strong formations being the result of efficient training.
Heavy cavalry lacking even a single part of this combination – composed of high morale, excellent training, quality equipment, individual prowess, and collective discipline of both the warrior and the mount – would suffer in a charge against unbroken heavy infantry, and only the very best heavy cavalrymen throughout history would own these in regards to their era and terrain.
Longswords and chainmail? The unicorns would massacre them easily.
I'll make the assumption that these are military bred unicorns who are trained to charge and have necks and skulls designed for impact, as well as a magically tough as strong as a rhino. So something like soldier ant vs worker any range.
First, cavalry were feared because they had the advantage of strength. The horses added a lot of momentum - mass and power. Imagine a motorcycle colliding with a pedestrian. The engine gives it more power and the combined weight of the driver and bike gives it more power. Cavalry, without the horn had enough power to knock someone down and badly injure them.
Second, height. It's easy for a mounted person to strike an infantryman's neck as opposed to the infantryman striking a horse's neck. Assuming these are war unicorns, they likely evolved necks and skulls designed for impact. They would be much harder to kill with a blow to the neck, compared to normal horses.
Third, reach. A longsword would never reach past that horn. Even a spear has trouble against a typical cavalry charge. A longer polearm like a pike might be needed.
Fourth, chainmail doesn't protect against piercing attacks. You can look up how chain fares against spears and arrows. Chain is designed to protect against blades like swords and axes, to keep soldiers from losing a limb. Maybe if they had something like lamellar armor, they would fare much better. Even hardened leather might do better than chain.
Finally, intelligence. Unicorns may be sentient or at least more intelligent than war horses. Even the dumb ones have natural control of their feet and weapon. They can fight naturally, easily jumping back, dodging with animal instinct, and then spearing through rows of infantry.
So I'd say that the infantry would have a devastating defeat in such gear. If they wore non-chain armor and had pikes, they might have a chance.
But let's look at it this way: Mike Tyson would lose against a gorilla. And a trained unicorn is a scarier opponent than a gorilla.
As stated above, an army of sword-wielders might not fare well against cavalry, especially one with pointy horns.
But why would anyone attack horse-like creatures with swords only? There are proper tools for killing cavalry, for example halberds: https://en.wikipedia.org/wiki/Halberd
Imagine a spear with the end thrusted into the ground, the pointy front pointing upwards and forward to the charging cavalry: When a horse meets the tip, the tip will stab the horse but go through resulting in mutal destruction as the dying horse still tramples the soldier. Now, with some sort of bar on the spear, it will go partly into the horse but then stop, instead lifting the horse like deadly pole vaulting.
With the unicorns horns, the pole vaulting part might not work as the halberds might have to be longer to protect the soldiers from the horns, meaning that they may have to hold the longer halberds at a too shallow angle. But they might just use stronger shafts that can instead bear the onslaught and transfer the kinetic energy into the ground? This way, the next wave of unicorns would first have get through a wall of their friends that did not make it.
A lot of people saying Pikes/halberds beat horse/horn but riders can use lances/pikes etc themselves. In a world in which unicorns exist there will effective tactics on both sides for different situations/geography in attack & defence.
Horn can be boosted with metal encasement and/or horse helmet. Unicorn can be armoured to protect head & chest. Mithril TM, the half as heavy but twice as strong metal perfect for this LOL.
In this scenario unicorns are not just a horse with a horn but a horselike creature that has evolved to have a horn. Means it's either a very aggressive herbivore (territorial/mating fights within own species) or it's an aggressive predator, maybe carnivorous but probably an omnivore. It's horn is strong yet flexible, it's skull & neck is adapted to bear the horn. In addition existence of unicorn in a military body means training, breeding for directed aggro, strength, horn length. Unicorns if not herbivore prey animals but somewhat predatory themselves (therefore likely at least a bit smarter than the horse) more likely to not baulk at formations of soldiers. In a world where they existed they would have advantage over horse through horn alone adding that extra bit of spice. Force of impact/weight of unicorn/s trength of neck could mean horn getting stuck no more a problem than sword or axe occasionally getting stuck. Even if gets stuck, the rider can assist. In my world Elves tamed & utilised the unicorn long before man, and man started riding horses in emulation of the Elves, not having access to the unicorns. If the unicorn is sentient or semi-sentient that could be a choice the unicorn makes. It will serve just about every Elf ...but only a few humans are found worthy enough (not virgins necessarily, but spiritually pure/pure at heart LOL). If unicorn chooses the rider and a mindmeld bond is necessary/is formed the unicorn & rider will be way more effective than a horse and rider.
Now Unicorns vs Centaurs is what I want to see.
The unicorn charge would fail. Unicorns might be strong and brave, but once a unicorn has impaled a soldier in the front rank it would have a 300 lb weight stuck to its horn. That weight would drive the horn of the unicorn into the ground allowing the soldiers to kill the unicorn while it was trying to scrape off the corpse.
Why you would have the infantry line, but no charge:
The combination of mail, shield, and longswords were only owned by knights and similarly well equipped men-at-arms, meaning that this equipment was not generally used by your normal rank-and-file infantrymen, but rather men who also owned war-horses.
So what your unicorns are actually facing are not "infantry" per say so much as dismounted knights. Contrary to popular videogame mechanics knights are not actually glued to the top a horse. They in fact often fought on foot when the need arose; so, they would strap their shields to their backs, leave their lances and horses behind, and then go off to fight where their horses could not go: typically in difficult terrain, urban, or castle environments.
These leads to a very interesting conundrum. If the knights abandoned their horses and lances, but have the rest of their gear, it means that they have gone somewhere that horses, and by extension, the unicorns can not go. So for them to have put themselves in this situation implies that they deliberately took to foot to get onto some castle wall, or steep ridgeline, or bog, or something of the sort to seek safety from the unicorn threat.
So, wherever they are, they are somewhere that the unicorns can not charge, and probably can not even reach if they tried; so, the idea of a unicorns being able to charge this infantry formation is VERY likely a moot point, because knights would only be thusly equipped against a unicorn threat if they 100% believed they not be charged.
But let's pretend you have a situation where the unicorns can charge the knights...
Let's pretend that your knights have abandoned their horses and lances to climb up onto a steep ridge to get away from the unicorns only to find out that there was another way up and the Unicorns are now charging them from behind. How would your knights react?
For this scenario to happen, there are two pretty safe assumptions you can make: One, the knights perceive the unicorn army to be too big of a threat to risk engaging in an open field battle on horseback, and two, by leaving behind their lances and horses, your knights have scarified the two biggest advantages they would have for dealing with a charge that they already perceived as an overwhelming threat, but now they are getting charged anyway.
This is such a horribly terrible situation to be in that I can not even begin to express how bad this is for moral. Normally military training is good for maintaining discipline, but in this case all that training is really doing is telling the knights just how screwed they are. Without any long-spears to counter, their imperative will not be to assume a battle formation, but to try to scramble to get out of the way of the charge. Some knights might try to assume a formation, but in the chaos, many others will be trying to run back to their horse to retrieve their lances, others will be running for the nearest trees or rivers just trying not to die. Some will try to join the formation, see everyone else scrambling away, then change their mind and run... the result will almost certainly be a very thin and poorly formed battle line, if not a total route,
So... even if your charging unicorns could be stopped by a thick block of well formed longswordsman with good moral, this is just not a likely scenario... the panic would assure that you probably would not have enough depth or resolve in your formation to stop the charge.
The one possible exception...
When you remove shields from the equations all together, there was one warrior culture who at least preferred mail and longsword on foot: the gallowglasses of Ireland. These were fanatical warriors who sought heroic deaths for entry into valhalla; so, in battle they either prevailed or they got horribly slaughtered... either way, one could expect the battle to be over quickly. The thing about gallowglasses is that they were actually quite bad in a head to head open field battle. The space needed to swing a longsword is greater than you need to fight with a spear; so, each longswordsman would be having to simultaneously protect himself from many spears without having a shield to help in this endeavor.
Instead, gallowglasses would normally be allocated to ambush or flanking maneuvers where the flexibility of the loser formation could be used to your advantage.
What does this have to do with a unicorn charge? Well as it turns out, loose infantry formations have a long history of getting slaughtered by cavalry charges. The space between the gallowglasses mean that the horses (or in this case unicorns) can recover some of their momentum between trampling soldiers; so, if the unicorns maintain a tight charging formation against the gallowglasses, then they will simply trample their way in on one side of the army and out through the other without ever being slowed down enough to give the infantry much opportunity to fight back.
