Saddle Points and Limit Cycles

A comment on my FB group when we were looking at images of Square Horses at the trot got me thinking about how horseman learn to see patterns of movement intuitively. Sometime back I found an article where a member of one of the North American Horse tribes explained the markings they painted on their horses. The spiral painted on their horse’s shoulders and thighs was intended to insure that they stayed sound and returned healthy from long journeys.

Explaining those spirals according to the western scientific model takes a few more words and a whole lot of research. We have that research thanks to DR. James R. Rooney DVM, Professor Emeritus, the grandfather of equine bio-mechanics. Dr. Rooney devoted his working life to coming up with an over-arching theory of lameness in horses. Most of his research was funded by the Thoroughbred racing industry.

But he made sure that he put his life-work out in a format that was accessible to non-veterinarians in the hopes that educating trainers, competitors, breeders and owners would reduce the frequency of injuries in horses. His books are out of print and rarely show up used. When a used copy does appear, the price is in the triple digits. So I only own The Lame Horse and I am waiting for a copy of The Bio-mechanics of Lameness.

In my FB group, we were discussing the combination of soundness, smoothness and speed at the trot. Square Horses have a tremendous length of stride with minimal elevation. Yet they rarely interfere even when moving at remarkable speeds. A normal trot ranges from 8-12 MPH, but the horse in question was clocked at 17 MPH and was still moving smoothly and easily under their rider.

Dr. Rooney defined two essential aspects of sound movement in horses. You can find the hardcore physics explained in the Biomechanics of Lameness. For now, it is important to understand that there are two primary aspects to consider when looking for functional soundness.

  • Saddle Points mark the position where the horse’s mass is balanced. They depend on how the horse’s bones are put together.
  • Zero points mark the moment when the incoming and outgoing energies balance each other. They depend on how the horse is moving.

Bio-mechanics studies how those two aspects interact. The limit cycles of the front and hind limbs of a sound horse in movement must not intersect. Instead the limbs move towards and away from their zero points.

  • Limit cycle stability means that the energy coming into a system is equaled by the energy leaving a system.

Ideally, a horse’s saddle point and the trajectories of their limit cycle stability coincide. Then, when a rider is seated at the saddle point, their presence disturbs the horse’s zero points the least and they move within their cycle stability limits. Dr. Rooney concludes:

  • ‘For any given lameness condition
  • we know that there is an instability, an unstable state,
  • and we can , knowing the nature of the lesion
  • and the normal anatomy of the area,
  • determine the specific necessary conditions
  • for the development of that specific lesion,’

However, all too often the addition of a rider and their demands de-stabilizes the horse. When a horse’s hoof impacts the ground, the horse’s connective tissue absorbs the impact of landing. Then the limb moves smoothly into the weight-bearing phase of the stride while the horse’s mass moves forward. Finally, the limb releases that energy as the hoof pushes off the ground. The limit cycle is completed by the limb flexing as the leg comes forward through the air.

Instability in the system is the cause of injuries. Tracking saddle point instabilities in moving horses demands tracking several factors. In simplest terms, the model needs to track:

  • velocity or how fast the horse’s limbs are moving,
  • force or how hard their hooves hit the ground and
  • frequency or how long it takes to move through a full stride.

Saddle point instabilities occur when waves of incoming energy from velocity, force and frequency repeatedly build up to a certain point, then decrease once more. When patterns of velocity, force and frequency are within the limits of cycle stability, the risk of injuries is minimized. If the velocity, force and frequency of the stride exceeds cycle limit stability, something has to give and the horse’s connective tissue begins to break down.

The most informative visual for tracking saddle point patterns is a spiral with the center as the zero point and a spiraling curve or ‘phase plane’ tracking the changes in velocity, force and frequency. When the spiral of the phase plane expands and contracts smoothly and evenly around the zero point, all three factors of the stride are safely within the limits of cycle stability. As the Horse Tribes have long understood, a regular spiraling pattern is essential to a horse’s safe sound return from a long arduous journey.

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