One night, Eric had a conversation with his fiancé, Kat, about the force on a horse’s hoof.  Normally, it’s not clear how this topic could even come up in a conversation.  But Eric is a structural engineer, and his fiancé is a veterinarian.  So that partially explains why they talked about it. 

After they spoke, Eric was curious and he surfed the net.  He found a website, “Understanding the Horse”.  It was a website for readers who wanted to understand the horse.  The site had a series of entries about calculating force and stress on a horse’s hoof.  The subject was also related to a somewhat controversial topic of whether or not it is desirable to apply shoes on horses’ hooves.  We’ll get to why this might be controversial in a moment. 

When calculating stress at the bottom of a horse’s foot, an appropriate formula would be: 

f = P/A 

where f is the stress, P is the applied force, and A is the cross sectional area of the hoof. 

The value of P would include the weight of the horse, appropriately spread among the legs in some fashion.  It would be not be conservative to divide the weight by four, since the distribution of self-weight would be more concentrated on rear or front legs as the horse moved.  The value, P, would also include the weight of the rider, the saddle, and other loads carried by the horse.  Dynamic impact should be considered.  The force, P, would be larger for a gallop than a trot.   

When calculating stress, one could use the full cross sectional area for A, but it would not be conservative to do so.  This is because not all of the bottom of the hoof can be expected to make contact with the ground.  The website presented an analogy to concrete behavior to illustrate this point.  In regular concrete, loading leads to cracking and downward deflection.  But for prestressed concrete, which is precompressed, a beam bows up slightly, only to level off under applied loading.  Likewise, the author notes that a horse’s hoof is naturally bowed up slightly, just like a prestressed beam.  Under applied loading, the hoof flattens out a bit. 

If a horse’s hoof under loading acts like a prestressed beam, then the area of contact would tend to be greater under applied load, and thus the stress less.  In that case, installing a shoe on the horse’s hoof may not be such a good idea.  This is because, in part, the shoe would reduce the natural area of contact due to flattening out and thus increase stress.

This behavior, therefore, calls into question the need for a manmade shoe on the hoof, since apparently the horse has a foot surface naturally adapted to handle loading.  But additional factors include the added weight of a rider the horse must carry, and sharp surfaces such as rocks that the hoof would encounter.  Many people would argue that it makes sense to shoe the hoof for these reasons.

Overall, Eric enjoyed the discussion with Kat.  He was pleased to learn that the horse world and the engineering world really aren't that far apart.