# Would a horse be sufficient buffer to prevent injury when falling from a great height?

I'm writing a sci-fi story with some fantasy elements, and I'm trying to keep even the most outrageous moments grounded in the laws of our universe. This is one of those moments.

## The Situation

A man on horseback (Tarn) is at the top of a small cliff. There's a medieval-style battle raging on all around him, including in the field below. In that field, the commander of the opposing force has just decapitated Tarn's commander.

This is his chance. If he avenges his commander, Tarn will be sure to advance in the ranks. But he needs to get down there right now. He's not afraid of death.

With no easy way down, Tarn spurs his horse into a gallop towards the edge of the cliff. Before it can consider stopping, he drives his sword into its head and holds on tight as momentum carries them over the edge.

They hit the ground. The horse splashes, but Tarn bounces and lands on his feet with a stumble. He pulls his sword out of what's left of his horse's head and charges forward on foot.

## The Question

Could a horse plausibly break your fall in any significant way? If so, what's the greatest height this could be done from?

The horse and rider would be landing on grass and potentially soldiers in the middle of combat. If there are factors that would make this more likely to succeed I'd be interested in hearing them!

Bonus: if there are other elements of this that are implausible I'd be interested in hearing alternatives, especially regarding the whole "killing the horse you're riding with a sword" bit... but that's not necessary!

## My Research

Googling hasn't turned up much on this specific scenario. I don't really have a science background, but maybe this will help:

Average Horse Stats

• Weight: 500kg
• Length: 2.44m
• Width: 0.76m (don't judge my sources too hard)
• Height: 1.58m (from where the neck meets the back)

Based on a comment from Halfthawed, let's sayyy the height from stomach to spine is 0.67m. Source: I eyeballed photos of horses.

## Edit: Thank you all so much!

Okay, we've been beating this dead horse long enough. It became pretty clear right off the bat that the answer is a resounding NO: horses don't make good airbags.

I am honestly blown away by this community. Y'all are amazing, and if I could collectively accept all of your answers I would, as they've all had some affect on how this scene will end up playing out. Speaking of, here's a roughly revised sequence of events...

This is his chance. If he avenges his commander, Tarn will be sure to advance in the ranks. But he needs to get down there right now.

In the direction of his target, Tarn spots a cluster of trees whose branches reach up nearly as high as the cliff is tall. Perfect.

He spurs his horse into a gallop towards the edge of the cliff. It's a well trained horse, normally extremely trusting, but something has been off about Tarn lately and perhaps the creature senses it. Metres from the edge, the horse slams its hooves into the ground and sends Tarn flying.

The horse slides half over the edge of the cliff, barely holding on with its front legs as its rear ones kick fruitlessly at loose rocks and soil.

Tarn just nearly misses the trees, but through some combination of luck and skill, he hooks his battle axe onto a branch and is jerked into the path of several more. They break and bend under his weight as Tarn stumbles downward in a barely controlled manner before slamming into the ground below.

He crawls up onto his hands and knees, and his trusty battleaxe punches into the ground head-first, directly in front of him. Barely phased, he uses it as leverage to help him stand up.

Behind him, the sounds of clanking swords cease. Tarn turns, exhausted, and locks eyes with an enemy soldier who stands over the corpse of one of his own.

The soldier runs at him, sword raised. Tarn tugs on his axe, but it's stuck in the ground good. Tarn starts yanking at it with both hands, the screaming enemy only a few second away.

The axe comes out and Tarn raises it up high over his head in both hands-

His horse slams into the ground, flattening the soldier in an instant and erupting into a geyser of blood. Tarn is bathed in it.

He turns to face the commander. That seems to have gotten her attention.

• Comments are not for extended discussion; this conversation has been moved to chat. – L.Dutch - Reinstate Monica Sep 25 at 14:05
• relevant – Paralyzoid Sep 26 at 3:53
• The trees are more likely to kill him than a good landing on flat land. Trying to slow your fall with your axe would look like this: what-if.xkcd.com/133, and any fall that would explode your horse on flat ground would rip you limb from limb in a tree. – Nosajimiki - Reinstate Monica Sep 26 at 16:41
• @Nosajimiki. The cliff doesn't have to be 240m high. – Mad Physicist Sep 26 at 17:40
• Nice followup. I am always interested to know what the authors will do with the information provided here, especially when its this good. – Mad Physicist Sep 26 at 17:43

While I have no actual evidence, I have a good bit of practical horse-riding experience. There are several possible scenarios.

1. If you're doing a normal jump on a live horse (not from so great a height as to injure it), the horse's legs will flex, absorbing some of the shock. Then your legs in the stirrups absorb some more, and your crotch does not painfully contact the saddle. If you do this wrong, it hurts. Heck, even a trot hurts until you learn how to ride it.

If you or the horse happen to be rather uncoordinated, or just a bit off balance, you can easily fall off the horse when it lands, or the horse can fall, either throwing you clear or landing on top of you. This generally hurts, if you're lucky. If you're not, the fall kills you.

2. Now you're falling from a considerable height with a dead horse. You have the same problems as in #1, but the horse is probably in its death throes from your cruel & treacherous stab. That gives you four basic possibilities, but you don't get to pick which.

1. The horse stays upright, and you stay in the saddle, and the horse lands feet first. But it's dead, so there is no shock-absorbing from the leg muscles. Hurts worse than the same thing on a live horse.

2. The horse twists in mid-air, and you come out of the saddle and land on top of the dead horse. But horses aren't a whole lot softer than dirt, so there's little shock absorbing. Not good.

3. You miss the horse and land on the ground. Bad.

4. The horse - all 500 kg or so of it - lands on top of you. Really bad.

Bottom line, this is a really bad idea, requiring near-miracle level luck to survive.

• Honestly, I think I'd rather hit the ground than land on a horse from 20m. Broken horse bones don't sound like a lot of fun to be perforated by. – Arkenstein XII Sep 24 at 4:14
• agreed the horse does not help in anyway whatsoever. The horse's bones are stronger than human bones by a wide margin so when you hit it, your bones are more likely to give way than the horses, thus the shock absorption is minimal. – John Sep 24 at 4:39
• This would be the perfect answer if you expanded on point 1. With the right size cliff the horse's legs could buckle and absorb the fall, while injuring the horse but preserving Tarn. Literally using the horse legs as a crumple zone. Without the horse it would've been Tarn's legs, but he had the horse so everyone's happy! (Except the horse.) – Grimm The Opiner Sep 25 at 14:51
• @Grimm The Opiner: Except that it's going to be a short cliff, and a live horse is probably going to panic. FWIW, my experience is that while horses are ok jumping over things (at least when trained), they are very reluctant to jump down. They really don't have a lot of depth perception. – jamesqf Sep 25 at 17:23
• @jamesqf Except that it's going to be a short cliff, it would have to be a well chosen cliff. But this is a story, so, that's easy. : ) – Grimm The Opiner Sep 26 at 7:06

A well trained horse can slide down a rather steep slope:

My suggestion would be making it less of a cliff and more of a very steep slope - or, even yet, it is a cliff but there is a section of it that eroded into a steep slope or something of the sort, and have your rider slide down that thing on horseback.

It would be more credible and make your main character look rather skilled instead of a reckless madman.

• If the horse has armor covering its belly, I would imagine it should be able to do even steeper/rockier cliffers safely. But if the armor interferes too much with the horses form than the horse would just be using the armor as a sled. – Tezra Sep 24 at 12:25
• Anywhere with scree would suit, though ymmv if you would call it a cliff. alamy.com/… comes to mind, which is about as steep as it'll get, but I'd call the rocky areas around it (beyond it in this photo) at a similar gradient a cliff still, so I think it is valid. – Baldrickk Sep 24 at 13:44
• That picture looks... 'photoshopped'. The horse is digging in with its feet, but the rider isn't so much as leaning backwards? No bracing with his arms or legs? Just casually sitting there? It would look more like this, but that horse might not have even lived. – JPhi1618 Sep 24 at 21:00
• Found another source with two horse pics. Looks like these are real but the framing makes the drop look higher. – JPhi1618 Sep 24 at 21:09
• @JPhi1618, who says the rider made it down the slope seated? This might be the guy's first try and landed before the horse. Also, the arms look like they are braced at the base of the horses neck. Also, I'm not sure the credibility of the site, but it's also located klubfedotova.ru/en/sportpit/… as well as several places on Pinterest, as per Google Image search. – computercarguy Sep 24 at 21:24

Your scenario has a historical precedent... for some values of "historical" at least.

Fact: Vysehrad is a fort dating back to the 10th century AD, situated right against the Vltava river. Now part of Prague, Czechia. It features a 42m cliff straight into the river.

Fact: Neumětely is a small village about 35km (straight line distance) or 50km (road distance) from Vysehrad, existing since at least 1331 AD. Current population: 577 as of 2019-01-01. The kind of place that would, at the time that minor nobles tended to govern such places, plausibly be governed by a minor noble.

Claim: Šemík (Schemig) is a horse owned by a minor noble named Horymir. Said noble also owned a village named Neumětely. Fact: there is a Šemík's grave in Neumětely, in the shape of a horse head.

Fact: Schemig is a horse mount available in Kingdom Come Deliverance, an RPG set in medieval Bohemia and praised for its historical accuracy. The horse's name is a direct reference to the real-life version of Šemík, mentioned above.

Claim: Horymir visits multiple gold and silver mines across Bohemia, systematically vandalizing its equipment; gets sentenced to death in Prague; flees the execution by jumping the aforementioned 42m tall cliff and rides all the way to Neumětely; After having ridden through 50km of Bohemian landscape, Šemík dies of 42m-tall-jump-related injuries while Horymír is forgiven all of his crimes and lives on.

Whether there is a historical ocurrence of an unusually fit horse jumping off a 42m cliff, carrying a minor noble 50km and then dying as a consequence of the jump, I cannot attest. Whether there is a historical record published in 1541 describing such incident - there definitely is.

Conclusions:
First, don't kill the horse, it doesn't help you in any way (and killing it mid-air - that is, without the assistance of gravity - might prove difficult anyways).
Second, if you, as a fiction author, ride a horse off a 42m cliff and have it survive, your audience will gladly accept your version of the events.
Third, if you're still worried about the believability of your story, put a river right below the cliff for the horse to jump into, and then simply don't mention the river in the jumping off a cliff part.

• +1 for "don't kill the horse". Trick it, give it LSD to make it think it's Pegasus or whatever, but if it hits the ground conscious, it will try to land, absorbing as much as possible of the shock in its legs. It will probably die, and you don't want to get caught underneath it. Also a bog might be more effective than a river – Chris H Sep 24 at 12:57
• @ChrisH A bog might be more effective than a river in killing you. The river is just water, so you and your faithful (stupid?) horse can swim in it. The bog acts exactly like water on impact, but you can't swim in it. Once your legs are caught in the bog, there's is only one direction you go: down. – cmaster Sep 26 at 10:36
• @cmaster that depends how deep it is, even assuming a worst case consistency – Chris H Sep 26 at 12:17

Something that a lot of answers are missing is that in a collision, there is an entire set of impacts that people forget about.

In EMT school many years ago, I learned that organs do not always respond to sudden deceleration very well. This applies to any case of sudden deceleration as in a car crash or fall onto solid ground, or even into water. Your organs are suspended in what is basically a big bag of water with a mostly rigid area around the top and several squishy tubes in the bottom. Even so, a sudden impact can do all kinds of nasty things even when there are no nasty external damage. Nasty things include:

Fractured solid organs like the liver and kidneys. If they fracture this can lead to a lot of internal bleeding in addition to the filtration aspects shutting down and letting nasty substances into the bloodstream.

Damage to the Heart and Aorta. Your Aorta is about the size of your thumb and if it gets damaged you will bleed out in a matter of seconds. That said there is a bit of tissue that joins the aorta and the Pulmonary artery that is a leftover from being a fetus. It shrivels up after birth. Here is problem. Certain kinds of lateral impacts can jerk that bit of tissue loose. Turn the wrong way and it's like a cork popping out of a champagne bottle, and the victim bleeds out very quickly.

Now the obvious one, Concussion. Your brain is in a sealed box. land even slightly wrong and your brain will slam into the bone walls of your skull.

Keep in mind that your organs are moving at the same speed you were at the time of impact. They stop a fraction of a second after you do.

This is of course secondary to the problems of things like bone fragments jamming you from the horse below you, your own bones fracturing, your joints giving way, and the possibility of things like internal decapitation (the skull moves enough in relation to the spine that the spinal cord gets severed). If you are going to fall far enough for the horse to splash, I don't give you high odds of survival, much less combat readiness.

• Thigh bone fractures are also a great way to bleed out very quickly, and are often found on people who fell from a great height. The problem with your answer is that it doesn't account for the horse at all, which was the main question. We all know falling from great heights is almost always fatal. But we also know that there's many things about it that are almost survivable. The acceleration on your body (and organs) is going to be significantly smaller thanks to the extra height of the horse, and the terminal velocity is lower too. You didn't address that at all. – Luaan Sep 25 at 11:27
• @Luaan the OP didn't give enough information to calculate whether or not the cliff was high enough to even reach terminal velocity. Only that the horse might "splash". A fall from a height great enough to cause a "splash" (in my mind the complete collapse of the ribcage) would be high enough to cause tons of trauma and take him out of the fight even if he did survive. And you are absolutely right about femoral trauma. The extra height of the horse does help, but no where near enough. – Paul TIKI Sep 25 at 13:27
• This question rather seems to be addressing the fallacy of a suit of armour protecting you from a fall (cough cough Tony Stark cough). In the actual scenario described we potentially have the crumpling of the long legs of the horse to gradually (ish) decelerate the rider in order to protect them. – Grimm The Opiner Sep 25 at 14:43
• @GrimmTheOpiner Tony Stark....Everytime I watch those movies the EMT in me just shudders knowing the damage that would be done to body inside the suit. – Paul TIKI Oct 1 at 15:07

This is one of those times that the square cube law should have been invoked and no one does it?

The Horse splashes and with good reason. It's surface area goes up slower than it's volume, meaning it has a lower air resistance which causes it to accelerate faster and have a higher terminal velocity than a human.

Since your Tarn is falling with the horse he'll accelerate with it. While the horse will definitely help absorb the impact it'll also increase the speed at which the impact occurs.

Since the horse is dead it's legs will flail about but be generally air resistance will push them into a lying-down position for the horse, meaning the bones within the legs are barely in a position to really absorb the impact. You are basically going to have to rely on the absorbtion ability of the horse's torso... Which as your source already says will splash. So consider this: If you are falling with the same velocity of the horse, which will splash upon impact, then you have to be falling with the same speed and also splash. The horse's body will splash on the ground with you on top, which might help cussion you a little bit but is unlikely to really help you survive especially since your legs are level with the horses body and will happily splash with it. The flesh of the horse will splash but it's bones will create shards that will be pushed into a lot of directions, including through Tarn who is still decellerating using the horses body.

Other answers have focussed on the impact. The question does have one questionable part though, and that's the "kill the horse" part. You say

Before it can consider stopping

Horses are trained specifically so that they will trust their rider and obey the rider's commands over their own instincts. Given a choice, a horse would never jump any obstacle the height of a steeplechase obstacle, especially on obstacles where it cannot see the other side. Of course horses do "refuse", but that's considered a failure on the part of the trainer or the rider. This goes in spades for warhorses, which also have to learn to ignore the noises of battle around them, and other horses and people running towards them at high speed. So no, he doesn't need to kill the horse before the jump - he just needs to command the horse, and it'll do what he tells it to do.

Now let's think about surviving the impact...

Armies aren't just men with weapons - they also include a baggage train. The baggage train may include covered wagons, which are large springy hoops covered with tough fabric. Landing on one of those could give your hero enough bounce to survive the impact - but only without the horse. If the horse hits the wagon first, your hero will be landing on a wagon-sized collection of splintery wood. And a horse.

The book and film First Blood both include a scene where John Rambo jumps off a cliff into trees. The book has him doing this in a controlled way; the film version is more of a "survivable splat". If you'd like to include trees at the bottom of the cliff, not just grass, then this could work. Again though, you'll have to leave the horse out of it.

• The movie has it as a survivable splat, because that is what really happened — Stallone did one of the stunts and survived with a broken rib. – jmoreno Sep 27 at 0:35
• @jmoreno Fair enough - I respect actors doing their own stunts. In the book though, that jump is Rambo doing something familiar that he trained for, not a last- ditch escape, and he executes it near-perfectly. (By the way, David Morell did turn out a lot of rubbish later, but First Blood is a really good bit of writing. Much better than the film, as much as I love Stallone and Dennehy as actors.) – Graham Sep 27 at 1:07

There actually is a historical example of something similar to that allegedly happening in addition to the one John Dvorak mentioned in his answer.

Mehmet Ali Pasha was the Ottoman governor of Egypt from 1805 to 1848, making his family hereditary rulers of an almost independent Egypt. His many changes including breaking the power of the Mamluk class in Egypt.

A famous story tells how Mehmet Ali invited a bunch of high ranking Mamluks to a feast at the Citadel of Cairo. As the Mamluks left the feast and passed through a narrow ally, gates were closed ahead and behind them and soldiers in the buildings shot down at them. All of the Mamluks were massacred except for one who rode his horse to the top of a wall and over the wall. The horse was killed by the fall but apparently the Mamluk was uninjured enough to make his escape.

So you now know of two stories - possibly true ones - of men jumping their horses off of heights and surviving.

However, there are also stories of persons doing the same and not surviving, such as Leo Sgouros, besieged in the Acropolis of Corinth since 1205, who eventually despaired and committed suicide by riding his horse off the walls in 1208.

So perhaps you should try to find out the heights of those three alleged jumps, and other such jumps, and make certain that your character jumps a shorter distance than someone known to have survived.

There have been horse diving acts where horses, often with riders, dive into pools of water. So if there is a deep enough river or pond beneath a low enough cliff, a horse and rider could jump off the cliff into the water and both be uninjured.

In winter my younger brothers used to ride sleds down a steep slope at our place, which was so steep I nicknamed it "suicide hill". That part of the property was later sold to a developer who build a house on it next door to the barn where our office was.

The first family living in that house had preteen children who had vehicles looking sort of like motorized tricycles which they rode around their house so much they wore a path in the lawn. There was also a path going down the slope I called "suicide hill" and I sometimes saw the kids riding their vehicles straight up and straight down the "suicide hill" path.

So I can imagine that a daring horse and rider might ride down a steep but not vertical slope that nobody else would dare to, much as T. Sar suggested. Or maybe Tarn can jump his horse off the edge, land father down and jump again, over and over until they reach the bottom. Possibly the slope has a series of almost vertical slopes and flat strips of land, like a series of steps in a giant stair case.

And if Tarn is surrounded by a dozen bloodthirsty enemies atop the cliff when he sees an opportunity to become a hero, his leap of faith can be motivated by certain death if he stays as well as a chance to become a hero if he can reach the bottom and kill the enemy commander.

And if Tarn has a close relationship with his commander and thus a strong personal desire to avenge his death, he will have a third motivation to jump off the cliff.

And if Tarn's soldiers below on the plain start to waver and fall back when they see their commander slain, it will seem likely they will be defeated. But if the enemy commander is also slain, that will discourage the enemy and perhaps turn the tide of battle, giving Tarn a fourth motive to jump.

If you don't want Tarn to seem incredibly, reckless and suicidal, you should establish as many and as strong potential reasons for his action as you can think of, so the readers will more or less accept that he might jump off a cliff.

The problem with falling and hitting the ground, is that you experience a great deal of force applied to your body, or to part of your body. This force causes damage to the bodily tissues to which is is applied.

Force is mass times acceleration. Your mass. And your acceleration. When you hit the ground. If you hit the ground "hard", then you experience a very great deal of acceleration (from the velocity of your fall, down to 0) over a very short period of time. This great deal of acceleration equates to a great deal of force. I'm not sure how fast one accelerates when hitting the solid ground, but we can compute how fast one accelerates if one had a cushion underneath.

Specifically, let's assume the best possible cushion. If your cushion is $$h$$ meters high, and we'd like to minimize the acceleration at any point in time over those $$h$$ meters. The best way to do that will be to decelerate at a constant rate the whole way down. Plugging constant acceleration into some physics equations, we have:

$$h = \frac{1}{2} a t^2 + v_0 t$$

Where $$v_0$$ is the velocity at which you hit the cushion, $$a$$ is your acceleration, and $$t$$ is the time it takes for your cushion to slow you down to 0. $$t$$ is an unfortunate variable that we need to know, but don't care about. We know that we want to eventually have velocity 0, so we can also employ:

$$0 = a t + v_0$$

Doing a little algebra gives:

$$a = \frac{3v_0^2}{2h}$$

So, if we double the height of our cushion, $$h$$, then we half our acceleration $$a$$, and if we double the velocity at which we hit the cushion, $$v_0$$, then our acceleration is quadrupled.

In any case, here are some example situations:

You hit an $$0.67m$$ high cushion (your numbers) at terminal human free-fall velocity, $$\approx 200kph$$ (you and your horse jumped out of an airplane). Your acceleration is $$\approx 124m/s^2$$, which is about $$13g$$ of acceleration for about half of a second. That's well within human tolerance, although it might be quite a shock.

However imperfect your horse cushion is, this would increase your acceleration at impact. For example if your horse was only a quarter as efficient as a perfect cushion, you would need to have a truly remarkable constitution in order to withstand the impact.

OTOH, if you fall from a not totally incredible height, then that would decrease your acceleration at impact. One reaches about half of terminal velocity in about 3 seconds of falling, which would happen from a height of about $$40m$$ (the equations above) or so. $$40m$$ is about the height of a 12 story building. As mentioned above, if we half the velocity, we quarter our acceleration upon hitting the ground.

SO, putting these results together, if your horse is only a quarter as good as a perfect cushion (e.g. it slows us down at a constant rate, but only compresses to $$3/4$$ size), but we only fall from 12 stories in height, then we get back to about $$13g$$ of acceleration which we've already decided was endurable.

• Perhaps it would be better to model the horse as an ideal spring, i.e., a cushion with linearly increasing force. – Vaelus Sep 25 at 16:58
• @Vaelus could be. Linearly increasing force means linearly increasing acceleration. Since we need to get to 0 velocity, and velocity is the integral of acceleration, it is instructive to note that a linearly increasing acceleration from 0 with an equal area under the curve to a constant acceleration has double the maximum acceleration (by just some geometric maneuvering). So, if you want a spring instead of an ideal cushion, the maximum attained acceleration is double all of the accelerations in my analysis. – Scott Sep 25 at 17:36
• I'm thoroughly disappointed by the severe lack of spherical horse assumptions in this proof. – vinchenso Oct 2 at 13:50
• @vinchenso, spheres would make the problem much harder. This only works when both the person and the horse are point masses. :) – Scott Oct 2 at 15:12
• @Scott actually I think spherical assumptions just require you to take the integral of your displacement equation with radius initial conditions. Harder is when you model the energy transfer as a second order system of springs, viscous dampeners and inertial masses! But I guess that would just a case of flogging a dead horse! XD – vinchenso Oct 3 at 5:53

I'm going to focus on a list of factors you can use to help.

• When falling at terminal velocity, you're going to need to decelerate to a safe speed without passing out. This means you can only only shed up to ~50m/s per second (roughly 5 Gs). Note that this is purely vertical, as in ending your fall in a roll only helps so far in that it extends the time you decelerate vertically when you hit the ground. So you will want 1+ things that give to help slow your descent (the horse makes this part harder, as you have to also slow the horse)
• Deep snow
• Tree branches
• water at lower speeds
• Ideally you want to also limit your terminal velocity.
• Be a lower weight
• More surface area (wingsuits aren't available. Use that belly!)
• Use friction (avoid a true freefall)

It would be worth considering that instead of jumping (especially since you are already at the cliff edge to observe what is happening below), to try and 'sled' down the side of the mountain. As Sar mentioned, a good horse can go down very steep cliffs without aid, though this works much better for a dirt hill than a rocky mountain. With a more extreme cliff side, it will probably be more believable to armor/shield surf your way down the side. A horse with metal belly armor would probably be better at this thanks to momentum, but most horse armor didn't have belly armor [citation needed].

Of course, in your scenario, technically you don't even need to reach the ground. As long as your sword gets down there in time, and flys true, you can take your time getting down.

Horses contain a skeleton. They are not bean bags. A skeleton is hard, and prone to having bones break under the kind of forces involved here. Your hero may end up with broken horse bones perforating his body.

• I've seen autopsies of fall victims. Half of the bones are broken, yes - but it's rather rare for the fractures to protrude outside of the body. Keep in mind that you're sitting on the horse's back - the fractures generally want to expand outwards, rather than up towards you. Definitely harder landing than on a cushion, but pincushion goes in the opposite extreme :) – Luaan Sep 25 at 11:34

Yes, if you use your horse as a platform instead of as a mount.

If instead of riding like one would usually do you get up on the horse's back and jump using it as a platform after accelerating enough that your jump would not reduce your speed to 0, you'll be slowing your fall. If you don't wait enough the maneuver would be less effective and you could even make things worse, if you end up higher than where you jumped from. Since horses are much heavier than people, it will be almost as effective as jumping from the ground. However, that is still not too effective. The formulae are quite complicated and depend on quite some factors (height, weight, jump height) but, as a simple approximation, you'll be substracting 0.5 seconds of your fall (meaning, if you are falling 1.5 seconds your speed when you hit the ground would just be 9.8 m/s, not 14.9). Again, this isn't a lot. Still, and especially if you practice beforehand or are an athlete specialized in jumping (maybe if your character is a martial artist you can say he is coordinated enough) you may do a bit better. You could even employ the now leg-broken-if-not-dead horse that fell instants under yourself as a platform to cushion your fall further, for example by rolling over it as you hit it, though I really don't know how to calculate how much force you could mitigate from that or how much the horse would help compared to rolling in the ground.

In the end, you are unlikely to make an obviously lethal fall easily ignored by employing your horse-trampoline, but if your cliff is 5 meters tall (usually this would mean a hard fall, sprained ankle or serious damage if you don't fall too well, though some parkour artists can regularly drop this height without problem) you might touch down ready to fight instead of breaking a leg. And if you are a parkour artist and high-jumper, you might do quite better, but how much would depend on too many factors that are not easily measurable. If you want to avoid breaking the suspension of disbelief and your character is especially athletic and not too heavy (maybe likes jumping across roofs in the city, or climbing and dropping down from trees) I'd say ten meters is roughly the most you could drop using this trick and still hit the floor ready to murder an enemy commander.

• a Horse hits the ground with about 22m/s. Looking over some charts it looks like the maximum m/s a man can jump is around 5m/s for the best of athletes, which the armored Tarn isn't going to manage. Even so that would be 17m/s that he hits the ground with or 61km/h. Using a graph from here: ec.europa.eu/transport/road_safety/specialist/knowledge/speed/… It looks like 60km/h crashes into pedestrians has about a 70% chance of death for the pedestrian. Even if you survive you'll not fight anymore – Demigan Sep 24 at 6:37
• @Demigan I guess you are talking about the 10 meters fall. I agree that it's not perfect, but remember that getting hit by a car moving at 17m/s is very different from hitting the ground at 17 m/s. When you hit the ground you can roll to cushion your fall, and get prepared for a good landing. Plus, you could fall on top of the horse, and horse flesh does have a better elasticity than the ground or a car. Thus, if you knew how, you could cushion your fall further. Learning how to roll over a dead horse to cushion your fall is something else entirely, and I'm not opening that can of worms. – LordHieros Sep 24 at 6:50
• between hitting the car with 17m/s and the ground at 17m/s I think the car is the better thing to get hit with. Usually you'll be driven under (you roll over the car) and will get accelerated over a longer period of time compared to falling from a height when you roll. And to roll you have to first create a turning momentum which means you would have to stand on the horse as you fall. – Demigan Sep 24 at 7:53
• For reference, the a typical round parachute decent rate is 7 m/s. – Keeta - reinstate Monica Sep 24 at 12:47

You're missing a critical piece of information--how high the cliff is. The higher the cliff the faster you are going when you hit.

Fundamentally, this comes down to whether the horse provides enough distance to reduce the acceleration to safe levels. For any substantial drop I do not believe this is possible. For a high drop consider something approximately similar: Parachute drops gone horribly wrong. The deceleration distance is about 6 feet--more than you get in the horse scenario. Assuming a reasonably soft landing this is just barely survivable--a jumper who does everything just right ends up with a myriad of broken bones. Your horse jumper has no ability to do this, he simply lands vertically (anything else is far worse because of the horse.) The distance he has to decelerate before taking serious injury is from his feet to the bottom of the horse--and that's not much at all. Remember that any appreciable injury even to the feet means he has little mobility and thus almost no combat capability. (And you can't avoid this by lifting the feet--the deceleration forces will be far beyond your strength.)

I also doubt it's going to work at all. Killing the horse before it decides to balk will almost certainly leave you still up on the cliff.

After reading the other answers regarding the unlikelihood of surviving such a fall, you could consider an option slightly less unlikely. There is a scene in the movie The Revenant where a horse and rider plunge off a cliff, but their fall is slowed by trees on the way down.

You could potentially contrive a situation where the cliff had enough "fluffy" trees or other foliage that could be combined with a slight slope to the cliff to slow their fall enough for Tarn to survive. This method could also involve the horse not surviving, as it's being used as a buffer. A little less brutal than Tarn murdering it, too!

Deceleration in g's is Height of fall / distance of deceleration.
Linear deceleration helps.
Trying to get your mount to collapse linearly may be beating a dead horse.
A 10m fall (impressive - but small for a "cliff") and a 1m effective linear deceleration distance gives you 10/1 = 10g. You probably live.
You MAY not break anything significant.
May not.

To add to the historical stories, a man at point of being killed (a general who had fallen out of favour with his ruler) horse-leaped off the 'Red Fort' front wall in Agra India. Reportedly he lived and escaped and the horse died. There is a mote, now dry. May this wet and or boggy and the tale gains (a little) more credibility.
I'd estimate the height at about 10 metres. There will be web data thereon.

Forget the horse: tuck-and-roll.

Various sources say that a strong, well-trained athlete with a good tuck-and-roll can routinely do falls from 15-20 feet without any injury. I once knew a slightly overweight, middle aged, retired Navy Seal who fell from a 36 foot rooftop with nothing worse than a sore back the next day because he followed his training, so with a little bit of luck and a lot of training, I'd suspect a younger healthier person to be able to come out of 40-50 fall unscathed. With a lot of luck your hero could pull a Vesna Vulovic, and jump off of mount Everest with only a broken leg. It is also not uncommon for certain people to break a bone in a fight and not even notice it until latter; so, your hero might get injured from the fall, but be in too much shock to stop fighting.

All these factors combined, I'd say you have an upper limit of "however high you darn please" just depending on how much you want your Hero's skill, strength, luck, and grit to play into the scene.

The more limiting factor here is, "why are you killing the horse?" The horse will trust that the rider knows what he is doing and make the jump before it knows it will fall to its death. This means that the more likely situation here is not that the rider needs to kill it before the jump, but that the rider is doing a mercy killing because he knows the horse may survive the fall but be crippled. For your scene to make since, this will help you limit your fall to a range of somewhere between what would cripple your horse, and where you would expect it to die on impact.

The exact figures on a horse's ability to survive a fall are much harder to find than for people, but based on how humans perform when not doing a tuck and roll (a manuivour a horse can not do), and the fact the inverse square rule is working against their size factor we can make some general approximations. A person who does not "fall well" can sustain significant injuries in the 4-10 foot range or severe injuries with minor risk of death starting at about 15ft. The chance of maiming and death goes up reaching nearly guaranteed death on impact at about 150ft.

For a horses size and weight, I'd expect the problem of the inverse square law to reduce these heights by about 50% because the horse weighs a lot more than a person with only slightly better bone and muscle cross sections.

This means that your fall should be at least 8 ft before your rider even begins to worry that his horse will probably be crippled by the fall, and 75 ft should be high enough that the rider has no hope of his horse surviving the impact to begin with. Your rider also needs enough time to kill and dismount his horse mid-air to be able to jump clear for a tuck-and-roll (meaning higher is in some ways better). You can calculate if you have enough time to do this with a tool like this.

My best guess is that 40-50 ft is probably best for your story.

It gives you 1.5-1.7 seconds to kill and clear your horse. It is short enough for a well trained and rather lucky human to possibly walk away from with none-to-minor injuries, and it is long enough to guarantee crippling the horse with no guarantee of a quick death.

However, if you care more that the horse splatters in a gory fashion than the rider killing of the horse part, then ~60-80ft would be better (people need 80ft to splatter under ideal/worst-case conditions, again hard to find facts on horses), but when your Hero is done killing the bad guy, and his adrenaline wears off, he'll probably discover he's torn major ligaments and/or shattered a few bones.