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Moment of Inertia page 2

In figure 1 we have the horse at maximum extension of the foreleg. Note that the hoof lines up vertically under the nose which was a good point mentioned in the first article on length of rein. You will also notice there is a very slight lag of the cannon behind the forearm. Likewise the hoof itself lags behind the pastern. These lags in forward motion are due to the moments of inertia of those sections of the leg, the heavy hoof being the main influence because of its weight and also its distance from the main centre of rotation, the humerus/forearm joint.
It therefore stands to reason that to minimise the moment of inertia, it is essential to minimise the mass in the hoof region. This can be done by selecting as light as possible set of shoes.This accounts for some trainers opting for 3D printed titanium shoes. Very light but still strong. At around $5,000 a set, this cost would easily be offset by the prize money.

In figure 2 the forearm has now rotated in its backward motion. Because of the large moment of inertia of the hoof and cannon, they have been left behind because of the articulation of the knee joint. The whole limb takes on the appearance of “back at the knee”. This movement places undue pressure on the carpal bones which increases the danger of carpal chip or carpal slab fracture. A short cannon, a short pastern and a light hoof will seriously reduce the moment of inertia of these bodies at the knee joint.

In figure 3 the off fore hoof is firmly planted on the track while the rest of the horse rotates around the leg as mentioned in an earlier article. You will notice that there is still an angle between the forearm and the cannon. In this case the hoof is stationary on the ground while the forearm is still moving backwards. This will quickly change as the flexor apparatus takes charge and pulls the hoof back. You will also notice there is no sign of the hoof. As the hoof hits the ground the pastern deflects so that the fetlock is almost touching the ground in a shock absorber action. The track was a heavy 8 when these pictures were taken.

In summary, how does moment of inertia affect a horse’s performance? A large moment of inertia shortens the stride as the cannon and hoof are pulled back by the retreating forearm before they have reached their full extension. It also decreases the number of strides per minute as a heavy hoof is harder to get moving, for example a smaller horse can get more strides per minute, but shorter, as the leg has a smaller moment of inertia.
The way to limit the moment of inertia is to have a short cannon and pastern and a light hoof. However the hoof should be large enough to stand up to the pressures placed on it. By the same token a lightly boned horse will have a lower moment of inertia but may be subject to damage.

So we get back to balance mentioned in the previous Length of Rein article . Bone mass not too heavy but adequate for the job, leg length for a good stride but not too long to cause moment of inertia problems and a hoof large enough to spread the load but no larger..

For those who would like to examine Moment of Inertia as applied to horses in a more academic manner, may I suggest the paper from the Journal of Anatomy May 2011,  Inertial Properties of Equine Limb Segments.


fig 1

fig 2

fig 3