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Saturday November 18, 2017
30
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Category: Hoof Mechanics and Physics
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The purpose of this paper is to discuss the basic mechanics of the horse’s foot and the horseshoe. A single, pilule major principle will be developed: The effect of the horseshoe on the movement or stance of the horse is completely determined at the moment of impact of the foot (and shoe) with the surface and at the moment of lift-off of the foot from the surface. When the foot is not moving relative to the surface, the horseshoe has no effect.

I shall not explicitly discuss various shoeing systems such as four point, Burgey’s, Duckett’s dot, etc. While these may be worthy of discussion, they do not directly relate to the present analysis. Some of these shoeing systems are said to be derived from study of the natural wearing of the unshod hoof. The nature of such wearing has been addressed by Rooney (1999).

In order to discuss the mechanics of the foot in definite, clear-cut terms we must define the forces which are acting on the foot. In mechanics there are two such forces to be defined: linear forces and moments. In what follows, a simplified and two-dimensional analysis is used. The real system is more complex and three dimensional, but for practical purposes this analysis suffices.

I realize from long experience that neither farriers nor veterinarians, on average, care to concern themselves with “mathematical stuff.” In order to have a clear understanding of how the foot works, however, that mathematical “stuff” is necessary. What follows is couched in mathematical terms but with immediate relationship to the physical situation. It is not difficult if the reader is willing to overcome fear and loathing and reread as necessary in order to understand.

The experienced farrier may say that all this is unnecessary, that experienced “rack of eye” is what is needed to properly shoe a horse. That is often the case. One hears and reads frequently, however, that if one thing doesn’t work, try something else, perhaps the exact opposite! That alone says that rack of eye is often guesswork without theoretical foundation. If the art of farriery is to become more science and less art, that theoretical basis must be understood and used. And if that is to happen, at least the simple mechanics and mathematics given here need to be thoroughly understood.

Linear Forces

mechanics_of_foot_and_shoe_1
Figure 1: The linear forces acting
on the hoof of the standing horse.

The linear forces acting on the foot of the standing horse are given in the following equations, and figure 1:

  • F-W=0
  • R-R=0
  • H-H=O

In the standing horse there must be equilibrium between the downward force of body weight and the upward force of the resistance of the surface upon which the horse is standing.

The force, H, is a frictional force between the hoof and the surface which prevents the foot from sliding forward under the influence of the force, -H. That frictional force is:
H=µF

That is, the amount of friction is a function of the vertical force, F, and the coefficient of friction, µ. The latter is an empirical measure of the roughness of the surface. Empirical means that µ is determined by experiment and cannot be calculated.

F is an upwardly directed force, the resistance of the surface, and -W the downwardly directed force of the body weight on the leg (downward forces are minus by convention). For equilibrium: F-W=0. Also, for equilibrium, H-H=0. The result of adding the vectors F and H and -W and -H are, respectively: R and -R. These latter are called resultant forces or simply resultants and are the actual physical forces going up and coming down through the digit.

The vertical force, F, is spread over the bearing surface of the hoof wall on a firm surface. It may also be spread over the frog and sole if the surface is soft and/or yielding. Stress, S, in mechanics is force per unit area; that is the amount of force experienced by some unit of the bearing surface such as pounds per square inch, kilograms per square centimeter, etc. Please note carefully that this is an exactly defined mechanical meaning of the word stress.

As noted the force F is exerted all over the bearing surfaces, those surfaces of the hoof in contact with the ground. In mechanics one considers that “spread-out” force to be concentrated at a single point called the center of pressure. That is done in order to simplify the calculations. It does not mean that “all” the force is concentrated at that point; it means that one can account for the mechanics of the foot if one considers that the dispersed forces are all concentrated at that one point.

mechanics_of_foot_and_shoe_2
Figure 2: The center of pressure
balancing the foot.

If a triangular support is placed precisely at the center of pressure, Figure 2, the horse could stand naturally and in balance. (I grant that is more easily said than done!)

No matter what type of shoe one puts on the horse’s foot, the stress S - force per unit area - on the bearing edge of the hoof wall remains constant so long as the bearing edge is the only part of the hoof in contact with the surface. Put another way, there is no way in which one can reduce the stress S acting on the bearing edge of the hoof wall by changes or modifications of shoe type unless one includes not only the bearing edge of the hoof wall but the frog and/or sole or parts thereof. One cannot change the value, the amount, of F by any method of shoeing.

To take an extreme case, nail a large snowshoe onto the hoof. The larger the snowshoe the less force there will be per unit area S experienced by the snowshoe, but the force per unit area experienced by the bearing edge of the hoof wall will not change. One can visualize this as the force “flowing” through the contact between the snowshoe and the bearing edge of the hoof wall.

Another example might be helpful. When you stand on a scale to weigh yourself, the area of the scale makes no difference. You weigh the same on a bathroom scale or on a platform scale for trucks.

To repeat: there is no type of horseshoe of whatever configuration that can reduce the linear force experienced by the bearing surface of the hoof. It is, however, possible to reduce the stress, the force per unit area, by the use of, for example, a bar shoe if the bar is in contact with the frog. If a wide-webbed, concave bottom shoe is in contact with sole and/or frog the stress will be reduced although, again, the total linear force remains constant. There are problems, of course, with the application of force to the frog and sole.

Moments

mechanics_of_foot_and_shoe_3
Figure 3: The moments acting on
the hoof of the standing horse.

Moments are turning forces such as one uses to unscrew a bottle cap or tighten or loosen a nut. The moments acting on the foot of the standing horse are shown in Figure 3, equation 2.

  • DFb-(Fa+CEc)=0

As there is equilibrium of linear forces, there is equilibrium of moments about the center of rotation in the distal end of the middle phalanx (syns.: short pastern bone, P2). The linear force, F, acting at right angles to the moment arm, a, generates a clockwise moment, -Fa. (By convention in mechanics counterclockwise moments are positive and clockwise moments are negative.) The common extensor and the extensor branches of the suspensory ligament also exert a moment, here lumped as -CEc. These moments are equilibrated (balanced) by the linear force, DF, of the deep flexor acting around the moment arm, b, the distance of the deep flexor tendon from the center of rotation, the moment being +DFb. Note that capital letters are used for the linear force and small letters are used for the moment arms - the perpendicular distances of the linear forces from the center of rotation.

It is important to emphasize that in the foot there is only one center of rotation . Once the shoe is nailed or otherwise fastened to the hoof, the shoe becomes mechanically a part of the hoof, and moments affecting the shoe operate around the center of rotation in the distal end of the middle phalanx.

mechanics_of_foot_and_shoe_4
Figure 4: The resultant R defining
the position of the force F.

It is necessary to locate the position of the reaction force (vector) F since its position determines the value of a and, thus, the value of the moment Fa. In order to determine the position of F we must know the position of the resultant R, Figs.1 and 4. Fortunately we can take R as identical to the anatomical axis of the pastern (proximal and middle phalanges), Figure 4. Remember that R is normally parallel to the horn tubules of the hoof wall and remains parallel no matter the position of the pastern during movement.(1) F for the normal digit is dorsal to (in front of) the center of rotation, so that the moment Fa is clockwise - negative.

The situation with moments is somewhat more complex than with linear forces. As discussed by Rooney (1984,1997), one can cause the pastern to become more upright(at a larger angle with the surface) if the hoof angle measured at the toe is decreased and more sloping if the angle is increased. One can accomplish that by trimming heels or toes or by the use of wedges or wedge-shaped shoes. While there has been disagreement in the past about this, I believe most now recognize that this is what happens. It is of interest that the change of pastern orientation with change in hoof angle was well know to Lungwitz among others in Europe at least as early as the 1880s.

The Egg Bar Shoe and “Support”

The bar shoe and, specifically, the egg bar shoe are frequently employed to provide “support.” In both conversation and the literature the nature of this “support” is at best vague and at worst completely undefined. In mechanical terms support must be force (or forces) which operates either as a linear force or a moment or both. One thing to be achieved in this paper is to erase the term “support” in favor of the more precise terms: linear force and moment.

As already noted the bar shoe, per se, can only decrease the value of S, the linear force per unit area of the bearing surface, if it is in contact with the frog. The egg bar shoe, on the other hand, extends behind the heels and is not usually in contact with the frog. What function, then, does the egg bar subserve?

mechanics_of_foot_and_shoe_5
Figure 5: The position of the foot when
the deep flexor tendon is severed
and in the “flaccid tendon” foal.

In order to answer that question I must go around the barn to a certain extent. If the deep flexor tendon is cut in half, the toe of the hoof will come off the ground, Figure 5. Examination of equation 2 and Figure3 will show why this happens. DF is no longer present, and there is only Fa and CEc both of which are clockwise. Obviously Fa cannot raise the toe from the ground, and this is done by CEc.

The foot is now in a position like that of Figure 6 with F, the point of contact of the hoof with the ground having moved toward the heels. In order to correct this an egg bar shoe is applied, so that F is in the position of Figure 7 and Fa is now counterclockwise and presses the toe back unto the surface.

An analogous situation pertains with the foal born with so-called flaccid tendons. The cause of that condition is not known but the tendons will shorten with time in many foals. The foot of a leg with flaccid tendons looks like Figure5 since a loose or flaccid deep flexor tendon is not unlike one with the tendon cut in half. Applying the egg bar to such a foot, then, would be expected to pull the foot unto the surface. Doing so tightens (increases the tension in) the common extensor tendon and the extensor branches of the suspensory ligament, both of which will tend to pull the pastern into a more upright configuration.(2)

mechanics_of_foot_and_shoe_6
Figure 6: F palmar to (behind) the
center of rotation, so that Fa
is counterclockwise.

In both of these situations, severed deep flexor tendon and flaccid flexor tendons, there has been loss of equilibrium of equation 2. There is insufficient DF (at least) in both cases. The egg bar places F in such a position, behind the center of rotation, that F acts as if it were DF.

  • DFb+Fa-CEc=0

The egg bar shoe has a place, then, in helping the foal with flaccid tendons achieve a more normal conformation until the tendons shorten appropriately.

The egg bar has been suggested and used for many other conditions such as bowed tendons and putative suspensory “strain”, among others. The mechanics strongly suggests that the egg bar can only function as discussed above, that is, when equation 2 is not in equilibrium. With a bowed tendon or strained (torn) suspensory there is no loss of equilibrium and the egg bar will accomplish nothing.

(A note for the exasperated reader: You can’t remember what equation 2 is all about. Go back and study it!)

Egg bar shoes, and the closely related shoes with trailers, do have an effect on the moving foot . Specifically, the trailer or egg bar will contact the surface first if the horse is moving fast enough for the normal heel-quarter-toe impact sequence. In the case of the trailer the foot will tend to yaw(3) around its axis (the axis of the pastern). It might appear that the trailer in contact with the surface is acting as a center of rotation. In fact, the center of rotation, as already emphasized, is always at the coffin joint in the distal end of the middle phalanx. At the point of contact of the trailer with the surface, the surface is exerting an upward linear force on the trailer which acts around the moment arm perpendicular to that force from the center of rotation, Figures 7 and 8.

mechanics_of_foot_and_shoe_7 mechanics_of_foot_and_shoe_8
Figures 7 and 8: The action of a trailer or egg bar shoe. The force F is acting at the end of the trailer which first comes into contact with the surface. The equation DFb+Fa-CEc=0 applies to Figure 8.

The bending of the trailer will absorb and dissipate energy (see egg bar, below). The trailer is usually on the outside (lateral) branch of the shoe as an aid to preventing or minimizing cross-firing by pacers. Since the trailer contacts the ground first, the foot will yaw laterally - the toe pointing more to the outside at impact. Pacers are predisposed to cross-firing by toed-in and/or toe-narrow conformation and turning the toe of the hoof outward at impact tends to counteract the toed-in, toe-narrow condition(4).

The egg bar, and, to a lesser extent the straight bar shoe, also contacts the surface first, bending the bar and so absorbing and dissipating energy with little tendency to yaw. The value of such a shoe is in reducing the energy of impact and thus reducing any pain being experienced by the foot as a result of impact.

Toe extensions are used for animals with so-called contracted tendon or tendons. The situation here is nearly a mirror image of that encountered with the egg bar and the flaccid tendon foal. Extending the toe of the shoe beyond the toe moves F and, so, increases a. The clockwise moment Fa is increased and tends to counter the increased counterclockwise moment of the flexor tendons. There are, of course, other measures to be taken to counteract shortening of the flexor tendon, Rooney (1999). Note that the value of the extended toe is dependent upon the continuing shortening of the flexor tendons. That is, the foot is continuously “trying” to rotate - move - as the tendons shorten. If this shortening ceased, there would be no effect of the toe extension. In other words equation 2 would be in equilibrium.

We can now restate the initial and major proposition of this paper: The effect of the horseshoe on the movement or stance of the horse is completely determined at the moment of impact of the foot (and shoe) with the surface and at the moment of lift-off of the foot from the surface. When the foot is still upon the surface, the horseshoe has no effect whatsoever. What this says can now be said more succinctly: the horseshoe has an effect only when the foot is moving, i.e., when the equilibrium of moments equation 2 is not in equilibrium.

Footnotes:

(1) As the vertical force F increases from impact of the foot with the surface to midsupport the force DF increases and, similarly from midsupport to lift-off both F and DF decrease. These two forces increase and decrease in phase with each other, so that the resultant, R, although increasing and decreasing in amount, does not change its direction of action. R, in other words, is a vector force and vectors have two characteristics: amount (scalar) and direction (vector). The scalar of R changes but its vector does not. It remains parallel to the horn tubules.

(2) The common extensor tendon is closely adhered to the periosteum on the front (dorsal) surfaces of the proximal and middle phalanges and, so, acts in a passive, check ligament-like fashion.

(3) The foot can move in three directions (Figure 7): 1. Tipping forward and backward is called pitching; 2. Rolling from side to side is rolling; 3. Spinning around an axis drawn through the long axis of the pastern, the movement being parallel to the surface, is called yaw.

(4)There is considerable variation in the literature about base narrow and base wide conformation. I don’t intend to become involved in the resulting confusion. In this paper base narrow and base wide refers to the space between the legs at the level of the chest and the thigh. Foot-narrow means the feet are closer together than usual when standing and foot-wide means they are farther apart than usual. Toed-in and toed-out have the usual meanings.

Bibliography

Butler, K.D. (1985) The Principles of Horseshoing. Doug Butler. Maryville, Missouri.

Rooney, J R (1984) The angulation of the forefoot and pastern of the horse. Journal of Equine Veterinary Science 4: 138-143.

Rooney, J R (1997) Plantigrade to digitigrade evolution of equids. Journal of Equine Veterinary Science 17: 340-345.

Rooney, J R (1999) Surfaces, friction, and the shape of the equine hoof, Online Journal of Veterinary Research 3:137-149.

Rooney, J R (1999) So-called clubfoot of horses. Anvil Magazine, In Press .

Lungwitz, M (1910) Leisering u. Hartmann, Der Fuss des Pferdes. 11th Ed., Schaper, Hannover.

Lungwitz, A (1913) Horseshoeing. Facsimile Edition. Oregon State University Press. Corvallis.

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