Equine Physics -- When a horse gets stuck going up a steep slope

[Vasi]

TL;DR

gravitational forces involved when a horse gets stuck going up a steep slope

I rode Tigger down a steep slope. He had no problems, until he arrived at the bottom of the slope and he saw a creek with flowing water. He made a quick decision to go the other direction, which was up the steep slope. I felt his front feet come off the ground. My thought was to use my body weight to shift his center of gravity. This worked and his front feet came down.

a horse weighs about 1000 to 1200 lbs. what I would like to calculate is the angle of the slope that would make it recovery impossible. not that I want to attempt this, I want know where the limit is. In that situation, could the horse flip over or could he recover on his own at that extreme angle?

I know this is not a typical physics question and if you think I am an idiot for asking, please don't vent on me, just ignore the question.

 

[Ibix]

It's not a stupid question, but it's probably an intractable problem.

It's fairly straightforward to solve a toy problem like "if a wooden mannequin is sitting on a wooden horse, how steep a slope can it be placed on" and "if the mannequin hinges at the waist and now lies flat against the wooden horse's neck how steep can it go now". Unfortunately, that's a completely unrealistic model of a falling horse and rider. There are a lot of moving parts in a horse and rider, and in a dynamic situation like a fall it doesn't just matter where each one is but also how fast it's moving, which means an awful lot of variables, many of which will vary from horse to horse and rider to rider. The maths would end up being a set of coupled differential equations that you could only explore numerically, filled with parameters ("weight of horse's left foreleg below the knee" etc) that you probably can't measure accurately. So the answer (even if you do all the work to find it) will almost certainly be "it depends on things you don't know".

Analysing biomechanical systems is very difficult, I'm afraid.

 

[Baluncore]

I want know where the limit is. In that situation, could the horse flip over or could he recover on his own at that extreme angle?

The fundamental limit will be the security of the footholds, or the shoes and coefficient of friction. Then comes the experience of the rider and the training of the horse.

When climbing a steep hill the back legs will be stretched out backwards and down, as they carry almost all the weight of the horse and rider. The front legs will be bent and as far back as possible, with the front legs folded, almost kneeling. There is very little weight carried on the front legs. The horse's neck and chin will be stretched uphill and close to the ground. The centre of mass of the horse and rider need to be forward of the back legs contact with the ground. The rider should be seated on the shoulders, body hugging or next to the neck, with short stirrups.

To advance up the hill, the back legs will take a couple of short steps, making sure the CofM is ahead of the foothold. The horse will then straighten the back legs and body, lifting and pushing both front legs up the hill, still kneeling, without straightening the front legs.

Now you need the geometry of the horse and rider, to work out the maximum possible slope.

We are assuming the horse climbs straight up the hill. A goat will stand sideways on the slope, then walk forwards and upwards, leaning into the hill, with the outer legs straight and the inner legs bent.

 

[Vasi]

It's not a stupid question, but it's probably an intractable problem.

It's fairly straightforward to solve a toy problem like "if a wooden mannequin is sitting on a wooden horse, how steep a slope can it be placed on" and "if the mannequin hinges at the waist and now lies flat against the wooden horse's neck how steep can it go now". Unfortunately, that's a completely unrealistic model of a falling horse and rider. There are a lot of moving parts in a horse and rider, and in a dynamic situation like a fall it doesn't just matter where each one is but also how fast it's moving, which means an awful lot of variables, many of which will vary from horse to horse and rider to rider. The maths would end up being a set of coupled differential equations that you could only explore numerically, filled with parameters ("weight of horse's left foreleg below the knee" etc) that you probably can't measure accurately. So the answer (even if you do all the work to find it) will almost certainly be "it depends on things you don't know".

Analysing biomechanical systems is very difficult, I'm afraid.

things I don't know: the force the horse produces. Yes, i see what you mean.

 

[Herman Trivilino]

I would guess that the determining factor would be the traction of the hooves, which of course depends on the soil conditions. I doubt the rider's position would make a significant difference but I would experiment with different positions. Of course the horse's motivation is a dominant factor which is hard if not impossible to replicate as you try to experiment with different riding positions. Horses are smart. Trigger will wonder why this rider wants me to repeatedly climb the hill. Maybe try one climb per day, at the same time each day, with the horse's meal waiting at the top.

 

[Vasi]

there are several forces at work at the same time, which as has been pointed out, renders a solution near to impossible, when considering the variables, and horse motivation is significant variable, as someone mentioned. So, if I am allowed, I would like shift the solution from a specific angle to a generalized reaction. Leaving out the biomechanics of the horse and assuming the horse is not producing any force and has no motion. Then gravity is the only force acting on the horse, is that correct? The Center of Mass on a horse is in the shoulder / chest area. For him to flip over, the force of gravity would have to create a moment arm at the C of M. It seems to me that since the force of gravity is vertical down, the slope would need to near vertical for the horse to rotate over. Based on experience with horses going up steep grades, I had the sense that a flip over is possible at an angle less than vertical, so it seems that the concept I proposed in in error. any thoughts on this?

 

[Baluncore]

Google pictures of horses climbing and descending steep hills.
It is a problem of anatomical geometry.

 

[Lnewqban]

Leaving out the biomechanics of the horse and assuming the horse is not producing any force and has no motion. Then gravity is the only force acting on the horse, is that correct? ...

Correct.

Based on experience with horses going up steep grades, I had the sense that a flip over is possible at an angle less than vertical, so it seems that the concept I proposed in in error. any thoughts on this?

Correct.

Let's assume the horse-rider assembly shown in the attached diagram is in static balance while the horse is rearing (not falling forward or rearward for an instant).

For that to happen, the horse-rider's combined center of mass must be located along the represented vertical line starting at the point of contact of the legs with the ground.

That position should be the limit, beyond which the horse-rider will fall backwards.
The balance sense of the horse should be clearly indicating that fact to its brain.

The represented slant line running between the front and rear legs indicates the maximum slope of the hill, which is far from vertical.

 

[Baluncore]

Then gravity is the only force acting on the horse, is that correct?

No. The back legs oppose most of the weight, the front legs counter the torque of the line through the CofM and the back hoofs.

The represented slant line running between the front and rear legs indicates the maximum slope of the hill, which is far from vertical.

The horses head and the rider are both leaning backwards to maintain balance on the rear legs. The slope can be significantly greater than you show.

 

[Lnewqban]