Lateral extensions their effect on the centre of pressure of the foot and loading of the horny wall

By R. V. Mackie AWCF ©

Farriers sometimes shoe horses with shoes that extend outside the profile of the foot. The reason that is usually given is, 'to give support to the foot or limb' or 'equalise pressure within the foot or limb'. In farriery textbooks there are few explanations as to how this support and change in loading is achieved mechanically. We are generally told it just does.
Although the perceived wisdom appears plausible, when investigated the theory does not make sense. To explain the true effect that a shoe has on a foot you need to apply some basic maths.
These laws and equations are a good place to start:-
A. Sir Isaac Newton’s Three Laws of Motion
1. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.
2. The relationship between an object's mass m, its acceleration a, and the applied force is
FORCE = MASS x ACCELERATION
3. For every action there is an equal and opposite reaction.
B. 2. PRESSURE = FORCE÷AREA
Scientists in other fields of study use two dimensional free body diagrams to explain and explore the workings of more complex three dimensional structures. When the study involves organic structures this method is called biomechanics.
In the example shown below, to simplify the calculations I have used the figures of 10m/s2 for acceleration and the area at z = 2m (load bearing surface area of the foot) and u = 5m (load bearing surface area of the shoe). The figures used are not important at the moment. They are used purely to explain the principle.

The example clearly shows although the pressure at the shoe/ground surface has reduced (due to a greater contact area), the pressure at the points of contact of the foot are unchanged (because the surface area of the foot is unchanged). In both the shod and unshod foot the amount of pressure felt by the foot is the same (pressure at surface z = 2500N/m2). It would appear that a lateral extension does not change the force or pressure that the foot feels. So how does the 'support' or the 'equalisation of the pressure' occur? Does it occur?
But of course the foot is not a simple two dimensional rigid structure. So let us take this theory one stage further and look at a more sophisticated model. First we must be clear on where the force acting on the hoof capsule comes from and how it arrives.
The weight and direction of travel of the horses’ body produce a force that has direction and magnitude. This force is transferred to the foot by the linkage of bones and joints. It finally arrives into the pedal joint as a joint force applied by the distal articular surface of the middle phalanx. This force will have a constantly changing magnitude and direction as the horse moves. To make this force easier to work with we are able to break it down into three force vectors. One lateral horizontal, one vertical and one horizontal cranio-caudal force. Because the models that are used here are in the frontal plane, we will only use the horizontal lateral and vertical forces.
This diagram shows a force being broken down into a vertical and horizontal forces

By applying Newton’s three laws of motion to a standard model of a foot, with a standard joint force (broken down into a horizontal and vertical force) you can compare the effect a horse shoe has on the forces affecting the horny walls and centre of pressure of the foot (see page 10). The model used here is an asymmetric foot. The joint force (Fzcoffin & Fycoffin) centre of pressure is offset to the lateral side of the foot, and the force values and dimensions of the foot, more realistic. To describe the actual mathematical calculations involved may bore you. If you truly are interested or are having trouble sleeping, I am more than happy to provide the full mathematical procedure I followed to get the results.
Standard models used – unshod, shod no extension, shod with extension

Applying the principles of Newton’s laws of motion to these standard models we are able to calculate the force applied to the shoe by the horny wall, the lateral forces at the foot-bearing surface of the shoe and the location of the centre of pressure of the foot. We can then compare the results to see if the shoe has an effect.
Forces experienced by the hoof walls of the asymmetrical foot (FcopHWl & FcopHWm)
Lateral force experienced by the solar surface of the foot

Location of the centre of pressure

The results show that if the foot is weight bearing on an unyielding surface, then the shoe has no effect on the loading of the horny wall. Once again, the lateral extension is shown to neither 'support' nor 'equalise pressure' in the foot. Could it really be true that shoes with length and width do not change the loading or forces within the foot?
Remember Newton’s third law. 'For every action there is an equal and opposite reaction'. The shoe is producing an equal and opposite reaction to the forces applied to it by the foot. The shoe can neither enhance the force nor reduce the force during weight bearing. It is purely a platform on which the foot is stood. The horizontal force experienced at the distal extremities of the foot and the location of the centre of pressure are also unaffected. Interestingly, the foot’s centre of pressure is located directly below the joint force of the pedal joint. This should come as no surprise. We are often informed that we should shoe around the centre of rotation of the pedal point or 'Duckett's dot', because experience has shown that it benefits the horse. The maths explains why this is the case. The centre of pressure of the foot lies directly below the centre of pressure of the pedal joint, which, by definition, will be in the joint and close to centre of rotation of the joint.
There are many arguments against using such a simplistic mathematical exercise to determine the forces that affect a complex dynamic structure such as a horse’s foot. Many will question their viability and accuracy. The foot is complex and has many shock absorbing structures. Their functions are to absorb or dissipate energy. These structures change the shape of the hoof as they soften the transference of force from the pedal joint force to the weight bearing structures of the hoof. They may reduce the energy but the remaining forces generated by the horse are applied at points of contact at the foot/ground or foot/shoe interface (no matter what shape the foot has been forced into by the shock absorbing properties). So it does not matter about the dynamic effects the axial skeletal column produces, the conformation of the horse, soft tissue elastic effects, hoof capsule shearing forces or any other manifestation that the equine limb can do to alter the direction and magnitude of the force. All these alterations culminate in the force and pressure acting through the points of contact the foot has with the shoe. This force and pressure when the foot is weight bearing, is not affected by the shoe on an unyielding surface.
The use of the two dimensional model will also be questioned. However, if you take a three dimensional object (such as a hoof) and sliced it into an infinite number of cross sections you are left with an infinite number of two dimensional structures. Applying the method of calculating the location and size of force to each of the two dimensional slices will have the same results as the two dimensional model used in this example. The shoe would still have no influence on the pressure/force affecting the wall or the location of the centre of pressure at that specific slice of the foot. The argument that this simplistic approach does not take into account the differences between the front or hind foot are also null and void. The starting point for the force entering the foot is the pedal joint force. The pedal joint force is the result of the skeletal linkages, body mass and motion. All these forces culminate in the force being applied to the pedal bone by the distal articular surface of the middle phalanx. This pedal joint force will constantly be changing in magnitude and direction, but is the starting force that culminates in the force and pressure generated at the ground/shoe bearing surfaces of the foot. Any soft tissue forces and elasticity that alter the forces magnitude and direction within the foot will only be links in a chain that produces the resultant force and pressure at the shoe bearing surface of the foot. It is this force and pressure that acts on the shoe. For the shoe to affect the force and pressures in the foot and leg, it must first have to change the forces experienced at the points of contact between the foot and shoe.
So the question must now be asked, how can a shoe influence the force and pressure experienced by the foot during the weight bearing phase of stride?
The shoe must either:-
1. Increase the surface area of supporting structures of the foot in contact with the shoe thus reducing the pressure experienced. The centre of pressure of the foot will still remain below the location of the centre of pressure of the pedal joint force.
2. Change the angle at which the foot weight bears. (The raised portion of the foot experiencing a reduced loading and the lower portion a greater loading). The centre of pressure experienced by the foot will still remain below the centre of pressure of the pedal joint. It is arguable that if the angle that the joint comes to rest at is within its natural range of joint movement, then the forces and pressures experienced proximal to the pedal joint will not be altered. A lateral extension beyond the symmetry of the centre of pressure of the foot may cause the foot to come to rest at an angle in soft going. Having an unlevel foot will alter the forces experienced at the horny wall. This may be the beauty of a lateral extension and how it has benefited some horses. It alters the forces and pressures when the horse is worked in soft going yet allows the joint to rest in its natural position when stood on an unyielding surface.

Conclusion
Having explained the simple static scenario we must now explore the differences that will occur when the horse is moving. We know that by increasing or decreasing the distance from the breakover point at the toe of a shoe to the pedal joint we will increase or decrease the torque and forces applied to the structures involved during breakover.
A shoe that grips or slips will also have an effect on the force applied to the foot of the moving limb as it comes to rest during locomotion. The shoe outside the profile of the foot will present a greater surface area of resistance to the ground therefore increasing the deceleration of the foot as it comes to rest in soft going. A shoe that is asymmetrical around the centre of pressure of the foot will come to rest and start weight bearing on an angle determined by the severity of asymmetry, joint ligaments and ground resistance. This will also affect the forces experienced.
The shoe that interferes with the natural placement of the horses’ foot (such as a trailer) will cause the horse to place its foot for the weight bearing phase of stride in an unnatural position. This in turn will cause the force and direction of the pedal joint force to alter. The altering of the magnitude and direction of the joint force entering the foot will have an effect on the force experienced at the points of contact between the foot and shoe.
Once the foot enters the weight bearing phase of stride, what effect does the shoe have on the forces that are generated by the horse at the points of contact with the foot? We know during the dynamic situation of locomotion, the magnitude and direction of the forces within the foot will be very different and constantly changing to those experienced by the horse at rest. However, if Sir Isaac Newton is to be believed the shoe will only present an equal and opposite reaction to the one applied to it by the foot at its points of contact with the shoe. This argument, supported by the static calculations, would indicate that the shoe is a passive component in the interaction of force at the foot/shoe interface during the weight bearing phase of stride.
As farriers we should (quite rightly) be suspicious of theories based on two dimensional models with supporting mathematical equations. Farriers generally need to see to believe. To demonstrate to yourselves the physics involved in this argument you need two coins (one larger than the other in circumference) some gum and an index finger. If you imagine the tip of your index finger to be the distal extremity of the middle phalanx, the smaller coin to be the foot and the larger coin the shoe. Place the smaller coin on a table. Initially push your finger down on the table. Remember how it feels. Then push down on the small coin with your finger. It does not feel any different. Now place the smaller coin on top of the larger with the gum between them (fixing your lateral extension shoe to the foot). Now push down on the smaller coin that is now resting on the larger. Once again you will not feel any difference to the forces experienced by your finger. Why? Because your finger is feeling the equal and opposite force that it is applying to the small coin, which in turn is experiencing the equal and opposite force to the one it has generated on top of the larger coin.
If the shoes are not altering the forces felt by the horse then the horse will not change its natural gait and foot placement. If the foot placement of the horse is unaffected, do shoes such as egg bars and lateral extensions alter the loading of the foot during the weight bearing phase of stride or enhance the 'support' of the horny wall? I would like to think I have demonstrated that they do not. For a shoe to change the forces felt by the foot during the weight bearing phase of stride it must change either the angle at which the foot weight bears, or the weight bearing surface area of the foot.

"My aim in writing this is to open some debate on what we teach our apprentices about the mechanical interaction between the foot and shoe. Am I saying that you should stop putting lateral extensions on or shoeing with length and width? No, as long as it can be justified to be of benefit to the horse, ie, the shoe is providing symmetry around the centre of pressure, thus allowing the foot to come to rest level during the weight bearing phase of stride in soft going. What I would advise is, to be careful about the claims made when explaining the function of the shoe and its influence on the loading of the foot and limb. The shoe can only present an 'equal and opposite' force to the one place on it by the foot.
I hope I have done enough to demonstrate that a shoe outside the profile of the basal surface of the foot does nothing to change the forces and pressures experienced by the foot or limb during weight bearing. If the shoe alters the angle at which the foot weight bears, causes the horse to place its foot in a position different to the one it would naturally choose, or changes the rate of retardation of the foot placement, then the forces experienced by the foot will be different. Once the foot enters the weight bearing phase of stride the shoe only replicates the force exerted on it by the foot. The shoe offers only an equal and opposite reaction to action applied to it by the foot. I would hope by understanding the facts on the interaction of the foot and shoe readers may review how they shoe some horses and the function and application of certain shoes.
Ross Mackie"

 

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