The quantification and definition of a new hoof balance paradigm
An investigation into the current hoof balance parameters and the quantification and definition of a new hoof balance paradigm
The quantification and definition of a new hoof balance paradigm
U. Yxklinten1 and Y. Sharp2
1Bolestad Gård 4198, S-264 94 Klippan, Sweden, e-mail: firstname.lastname@example.org
2 Lion House, Lion Hill, Stone Cross, Pevensey, Bn245EG, UK, e-mail: email@example.com
A balancing point for the hoof at midstance is proposed with the aid of a qualitative analysis, using classical mechanics and measured data during the stance phase. The proposed balancing point is anterior of the centre of rotation (COR) of the distal interphalangeal joint, in between the extensor process of P3 and COR. For a normal unperturbed hoof capsule this is located ¼ of the length of the coronet from the dorsal aspect of the coronet. A definition of a balanced hoof is also made.
Studies have outlined the links between poor hoof balance, lameness, and catastrophic injury [1,2,3,4,5], with poor dorso-palmar balance having direct links to navicular syndrome [6,7,8,9] in the front limbs and higher pathologies in the hind limbs [10,11,12]. However, what constitutes correct balance of the hoof capsule and subsequent shoe placement remains debated within the industry.
As far back as Russel , creating proportions of the hoof has been recognized as important for reducing the risk of injury and maintaining healthy hooves. Russel suggested guidelines for the perfect placement of the shoe around the center of gravity.
Russel  suggested equality of opposite points around this center of gravity to secure a perfectly balanced foot. Ducket  recognized that to understand the balance of the foot, the internal anatomy had to be considered, over and above the external capsule. His work was the first to correlate external reference points with internal anatomy. Ducket established two main points of reference, Ducket’s dot and bridge.
Ducket  highlighted the importance of the dot, expressing its internal anatomy, its correlation with the extensor process of the distal phalanx, the action line of the extensor and flexor tendons and it being the “balance point of the distal phalanx” and center of pressure of the hoof (COP). However, when discussing the importance of hoof balance, it is the bridge that is used as a reference point for proportional balance. Ducket  suggested that the distance from the posterior of the heel bulb to the frog bridge equals that from the frog bridge to the point of toe, in the barefoot. This distance is also the same as the toe length in the wellbalanced foot . These proportions around the bridge were described as creating mechanical balance and it was suggested that an arc from the heel bulb to the toe in the sagittal plane, centered at the center of rotation (COR) of the distal interphalangeal joint pointed at the natural breakover point, optimum for balanced biomechanical function . The optimum balance when applying a shoe was suggested as also creating equal proportions around the bridge, with equal length from the heel of the shoe to the breakover point . Caldwell et al.  discussed Ducket’s theory stating that balance was theoretically achieved by way of proportional measurements. The external reference point center of rotation was found to relate to the position of the internal location of center of rotation of the distal interphalangeal joint  and creating proportional dimensions around this point has been supported as a good model for creating biomechanical efficiency . Much of the literature after Ducket  has expressed shoeing to place the COR in the middle of the base or shoe, as biomechanically optimal (and this practice is widely accepted as an ideal for farriery intervention).
Ferrie  discussed a method for establishing COR from the lateral view, this study also highlighted the importance of balance around this point. Berger  found these points to be accurate and discussed balance around the COR as a method that optimizes the biomechanics of the hoof. Moon  tested again the external reference points and their correlation to internal anatomy. Moon  outlined the recommendations of previous studies that 50% of the base of the hoof is palmar/plantar of the COR and 50% dorsal, however suggested this as impractical in daily practice with shoeing around the centre of articulation surface of the distal phalanx, as more practically achievable and that the position of the shoe relative to the centre of articulation surface of the distal phalanx and the distal border of the hoof is the most important consideration for functional mechanics. However, the study offers limited biomechanics or physics to quantify this statement, only stating that it is a more practically achievable parameter. All the studies above agree that proportions of the hoof are important for biomechanics and that hoof balance is achieved when specific proportions of the bearing border length are equivalent . However, none of the above studies discussing external reference points and balance around them, quantify their theories of proportional balance around these points or discuss the physics involved in creating optimal biomechanics of the hoof. While Ducket  suggested the dot as the balance point of the distal phalanx, any balance point of the hoof would have to consider the entirety of the capsule and the forces involved around that point. Ducket’s dot was also suggested as the COP, recent studies have questioned this, finding that COP did not relate to location of the extensor process of the distal phalanx (20) and many studies have identified it as a dynamic point [21,22,23].
The COP becomes an important mathematical point in the consideration of hoof balance as its position dictates the biomechanical forces experienced by the hoof and its internal structures. Modern research has used pressure mats to locate and trace the COP during the stance phase [21,22,23]. The COP was shown to move caudally over an 8-week shoeing cycle increasing load on the heels and increasing the moment around the DIPJ [21,22,23]. However, recent theoretical teachings  have suggested the dorsal migration of the point of force application, although agreeing that there is a resultant increase in flexor strain. These seemingly contrasting teachings have created confusion within the farriery industry. It could be suggested that the opposing theories are in fact measuring different point of action of the ground reaction force.
Dr Curtis expressed the lack of quantification of hoof balance,
“There is often a belief that foot balance and farriery in general are not scientific; that it is an art and cannot be quantified. This view suits most observers of farriery, not least the farriers themselves. Farriery may not have been defined by strict rules that can be applied universally, but this does not mean that it is not a science; it only means that it has yet to be defined. The forces (both natural and induced) that affect the equine foot are not divorced from those that govern the rest of the universe. We should view farriery as having almost infinite variations, all of which have recognisable patterns that can be predicted. In the same way, in tennis, no 2 shots are identical but they are still governed by the laws of physics.” .
The need for the definition of hoof balance indicates for the creation of a uniform language, with full understanding of the physical forces involved, both to quantify a balance point of the hoof based on physics and to clarify the effects of changes in balance.
List of abbreviations
COR – Center Of Rotation
COA – Center Of Articulation
POB – Point Of Balance (green dot)
PPSH – Pressure Point of Solar surface of the Hoof
COP – point of action or Center Of Pressure of the GRF
DIPJ – Distal Inter-Phalangeal Joint P3 – Coffin bone
GRF – Ground Reaction Force
FBD – Free-Body Diagram
ET – Extensor tendon
DDFT – Deep Digital Flexor Tendon
N.B. Forces and torques are vectors, meaning they have a point of action, direction, and size.
The model – a balanced hoof
In Fig 1 a graph over a horse in trot measured by a force-measuring plate is shown, the blue curve represents the measured horizontal force and the red is the measured vertical force . The stance phase is defined as when the hoof is in contact with the ground and consists of three parts: (1) initial stage involving first contact and a sliding phase, (2) the loading phase in which the hoof capsule is still, and (3) break-over which starts with heel-off and ends when the toe of the hoof leaves the ground. Midstance is indicated with a vertical line and as a function of time this is called t = tm and is equal to where the horizontal force is zero. In order to do the study of forces and equilibrium the system to be investigated must be determined. In this case, even if the horse is moving in trot on a hard surface, the hoof capsule is at rest during the loading in the stance phase. That means that the hoof capsule must be in force and moment equilibrium, i.e. statically determinate during the loading phase.
Fig 1. Ground reaction force data. The graph shows the horizontal (blue curve) and vertical force (red curve) during the stance phase, measured with a force-measuring plate . The interesting point is at midstance indicated in the graph as, t = tm, here the horizontal component is zero and the GRF is vertical.
The following analysis is done at midstance where the horizontal force is zero, t = tm, i.e. there is only a vertical force acting on the hoof from the ground (GRF is vertical). The term Free-Body Diagram, FBD, will be used which means that one part of interest will be studied. This technique is common standard in engineering when designing/constructing . The hoof capsule will be studied with all the forces acting on it.
Definition of GRF as a single vector and COP of the GRF
During the stance phase the horse’s hoof is in contact with the ground and the GRF is spread out over the whole contact surface, this is called a force-distribution, denoted (x) where x is a specific point on the solar surface of the hoof. In Fig 2 two different hoofs and their force distributions are shown, one even and one uneven distribution, the small arrows at the contact area between the hoof and ground represent the force-distribution, (x). In all the coming graphics the GRF is represented as a single force acting in a single point, the centre of pressure (COP), hence the following definitions must be made.
Fig 2. Force-distribution on the solar surface of the hoof. The force distribution, (x), on the solar surface of the hoof can be summed up, see Eq. (1), and act as one force in the centre of pressure (COP) yellow dot, Eq. (2). Here two different force-distributions are seen, one even, GRF(x), and one uneven, ’GRF(x). The large red arrow is the summed-up force-distribution, (x), giving a single vector, FGRF, acting at COP.
The force-distribution from GRF, (x), acts on the solar surface of the hoof, and the ground contact surface area of the hoof is called Asolar. The mathematical definition of GRF as a single force is
acting at COP, defined by the equation solving it for x0,
The large red arrow in Fig 2 represents the total GRF as a single force, FGRF, acting at the COP.
Free-Body Diagram of the hoof capsule
During the loading phase on a hard surface the hoof is statically determinate and the forces acting on it is then time dependent, Fig 3. When creating a FBD of the hoof all the forces acting on it must be identified and included. The forces acting on the hoof capsule during the loading phase comes from DDFT, 𝐹𝐷𝐹, extensor tendon (ET) acting in extensor process of P3, 𝐹𝐸𝑇, the force from the leg, 𝐹𝑙𝑒𝑔, going through COR and acting at COA of DIPJ, the gravitational force from the mass of the hoof, 𝑚 ∙ 𝑔, and GRF (Fig 3). At midstance where the vertical GRF is large compared with the gravitational force from the weight of the hoof, the contribution for equilibrium at midstance from the mass center of the hoof will be small and thus neglected. The same discussion can be made for the contribution from ET, 𝐹𝐸𝑇, during midstance and will also be taken out of the model.
Fig 3. Free-Body diagram of the hoof capsule. A FBD of the hoof with all forces acting on the hoof capsule (left). FGRF(tm) is the ground reaction force at midstance t=tm. FDF(tm) is the tensile force in the DDFT, Fleg(tm) is the collective force from the leg, FET(tm) is the force from the extensor tendon acting at the extensor process of P3 and finally mg is the gravitational force from the mass centrum of the hoof capsule. Using the assumptions in Eq. (3) above the FBD can be represented as in the right picture.
In Fig 4 the levers for DDFT, LDF, and the corresponding one for GRF, LGRF, is introduced. For the hoof capsule to be in equilibrium the sum of forces needs to be zero and the torque around any given point must also be zero. The COR of the DIPJ is chosen and there will only be one moment of force acting clockwise around COR (DDFT) and one counter-clockwise (GRF), Eq. (4). For the system to be in equilibrium the GRF must act along a vertical line anterior to the COR.
Fig 4. Graphical solution. A graphical solution at midstance for the three forces involved (to the right), the levers for the DDFT and GRF around COR are denoted, LDF and LGRF respectively.
Looking at the geometry of Fig 4, the length relations between the two levers, LGRF and LDF, can be measured. For the schematic hoof and choice of balancing point at midstance the lever for the GRF, LGRF, is 1/3 of the lever for the DDFT, LDF, meaning that the tensile force in DDFT at midstance is approximately 1/3 of the GRF. For individual horses the length of the two levers can be obtained from a lateral x-ray, LGRF is shorter than LDF and the quota, q, is
Which then gives the tensile force in DDFT at midstance with the direction drawn in Fig 4 as a constant multiplied with the GRF
A three-force FBD where the forces and torques around any given point add up to zero, can be drawn as a two-force body, Fig 5, putting the force from the FDF and Fleg into one force at a different interaction point. This point must be on the force line of the FGRF, so that the sum of forces and torques add up to zero.
Fig 5. A two-force body. Different representations of the forces acting on the hoof. Going from a three-force model to a two-force model which is equivalent to each other when discussing the effect of the GRF on the solar surface of the hoof.
Defining Point of Balance – POB
Using external mapping of internal structures [17,28], the balancing point is proposed to be anterior of COR of DIPJ, as is indicated by the above analysis, in between the COR and the extensor process of P3, see Fig 6.
Fig 6. External mapping. Using external mapping of internal structures [17,28], different parts of the coronet’s length will give the approximate position of the navicular bone, COR of the DIPJ, the extensor process of P3 and the proposed balancing point, POB.
The modelling made above shows that the three-force model of the hoof capsule can be viewed as a two-force object, Fig 5, where the combined force from the leg and DDFT act at the point of balance, POB, green dot at the coronet (Fig 7).
Fig 7. Point of balance. The symmetric hoof from in front and the symmetry line (dashed line) through the hoof and the point of action of the force from the leg (left), POB (green dot). In the middle and to the right the lateral views of the hoof (unshod and shod) are shown, and POB is again marked with a green dot (1/4 of the coronet’s length from the dorsal part of the hoof capsule).
Definition of the pressure point of the solar surface of the hoof (PPSH)
The pressure point of a surface area is the centroid of that area  and can be calculated exactly, see Eq. (7), and this is the ideal pressure point for the resulting normal force, an evenly distributed ground reaction force (GRF). In Fig 8 the pressure point for different geometries are shown, the most obvious is a circle and of course the pressure point is in the centre. The mathematical definition of the pressure point of the solar surface of the hoof (PPSH) is the centroid of the solar surface area Asolar,
and solving it to get x’0 which is the location of the pressure point.
Fig 8. Pressure point of a surface. The white dot in the circle, triangle and ground surface of the hoof marks the pressure points respectively. The pressure point can be calculated for any type of surface. A good approximation for the pressure point of the solar surface of the hoof (PPSH) is that the pressure point of the ground surface is 50/50 in dorso-palmar and medio-lateral direction.
Definition of hoof balance
A balanced hoof of a horse is one where the force distribution from the GRF on the solar surface of the hoof is uniformly, evenly, distributed over the solar area of the hoof and the COP from the GRF is aligned with the vertical line from POB and going through the pressure point of the solar surface of the hoof (PPSH), thus creating equilibrium at midstance.
With the definitions of the force centre from the leg to the hoof capsule and the pressure point of the solar surface of the hoof the balanced hoof is defined. In the unbalanced hoof the vertical force line from the leg will not pass through the pressure point of the solar view of the hoof, where the COP from the GRF acts, and hence the two sides will be loaded differently, see Fig 9. In the unbalanced hoof, the side where the force line from the leg goes beside the pressure point of the solar view of the hoof will have the largest pressure/force. On a soft surface it will be obvious, hence the side with largest force will sink more into the surface and the effect will be larger. The discussion is the same whether it is dorso-palmar/plantar or medio-lateral. In theory it is simple to achieve a balanced trim by ensuring the PPSH to coincide with the vertical line through the force centre from the leg, the point of balance (POB). In reality there are other variables to be considered, such as the position and shape of the sole, the thickness and strength of the hoof wall, these should be factored into the individual intervention to line up these datum points (Fig 9).
Fig 9. Hoof trim for balance. Three different hoofs out of balance (left in the figure), in each of the example hoofs the pressure point of the solar surface of the hoof (PPSH), white dot, is anterior to the POB (green dot). To balance the hoofs, the white dot (PPSH) must be aligned with the vertical line going through the POB, the right pictures. The dashed blue line in the top two left pictures indicate where the trim should be to balance the hoof capsule. In the example at the bottom the hoof is trimmed dorsally and shod to achieve balance.
When balancing the hoof, its relationship with the rest of the digit, the hoof pastern axis is another variable and must be considered. Poor digit alignment will affect the position of the PPSH, see Fig 10.
Fig 10. Trimming the hoof. To the left a hoof with broken back HPA and long toe is shown, the white dot is the PPSH, and it is not aligned with the vertical line going through the POB (green dot at the coronet). One could either shoe the hoof or trim it into balance, straight HPA, the grey area is what is trimmed away to achieve balance. Then the COP and PPSH of the ground surface are aligned vertically with the POB.
The current teachings on what constitutes hoof balance are based on geometry and the creation of proportions [13,14,15,17,18,19], but do not include the understanding of all the physics affecting the hoof capsule. This model suggests a new balance paradigm based on outlining these physical forces. While the COR is widely accepted as the datum for creating equal balance around, our model suggests the POB, a point in between the COR and extensor process as a theoretical point of balance according to our definition. This point can be easily used in practice to assess hoof balance and aid in farriery intervention decisions. By creating 50/50 proportions around a line dropped from ¼ of the hairline from the toe, the farrier will have lined up the PPSH with the POB and created an even distribution of the GRF across the solar surface (assuming a HPA within a working tolerance).
By introducing and defining the concepts of the center of pressure, COP, of the GRF, the pressure point of the solar surface of the hoof, PPSH, and a balancing point, POB, anterior to COR of the DIPJ some of the confusion in the farrier industry can be explained.
Previous studies [21,22,23] used pressure mats to generate the trajectory of the point of action of the GRF on a hard surface. The findings suggested the COP of the GRF moved away from the toe during the shoeing period. This can be explained with the above analysis, on a hard surface the GRF will be aligned with the vertical line from POB, the force from the leg acting at POB. Our analysis shows the PPSH moving forward of the POB thus it seems like the GRF is moving caudally, cf. left picture in Fig 10.
Theoretical studies  using vector diagrams suggested that the COP moves forward during the shoeing period and can be explained by the assumption that the COP of GRF follow the PPSH regardless of toe length, this implicates an increased tensile force from the DDFT for the GRF to move forward to act at PPSH. By defining the three main points in our model, clarity can be brought to the understanding of the physical changes occurring during a shoeing cycle. With these studies in mind our model suggests the perfect balance parameters at the point of shoeing. Balance of the hoof is time dependent and is a factor of the individual hoof’s conformation and growth. Our model can therefore suggest a “zone”, from the COR to the extensor process, that the base proportions would ideally remain proportional around from the beginning to the end of the shoeing cycle.
In this qualitative analysis we have shown that the balancing point must be anterior of the center of rotation of the distal inter-phalangeal joint, and in between this point and the extensor process of the distal phalanx, to achieve force and torque equilibrium at midstance. A balancing point in dorso-palmar direction is proposed. Using the proposed balancing point, a quantified and easily recognized balancing protocol, for farriers and veterinarians, is established to understand where the trim or shoeing must aim. Further studies will include different types of horseshoes and how the pressure point in dorso-palmar direction is changed when applying them. Unbalanced hoofs, long toe/low heel, orthopaedic shoeing, what structures will have increased load and which structures will be less loaded are also areas where the above model can give qualitative answers. The same analysis can be used for medio-lateral imbalance and further studies must be made, opening for simple understandable methods that can be used in the future.
Acknowledgments We would like to thank L. Lundin (Tech.D), G. Åkerström (DVM, FEI Veterinary Director) and M. Limbäck (MSc) for taking time to read and comment on the paper.
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