# Why do horses have several gaits?

Éric Herbert, Christophe Goupil

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Éric Herbert, Christophe Goupil. Why do horses have several gaits?. Multidisciplinary Biomechanics Journal, 2025, 50th congress of the.., 10.46298/mbj.16231. hal-05191785v2

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Submitted on 23 Oct 2025

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<figure><img src="image_1.png" /></figure>
# Why do horses have several gaits?

Éric Herbert*, Christophe Goupil

Laboratoire LIED, Université Paris Cité, France

* Corresponding author: eric.herbert@u-paris.fr

Received date: 06/04/2025

Accepted date: 27/06/2025

Publication date: 27/10/2025

Keywords: energy conversion, optimal dissipation, entropy production

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Vertebrate terrestrial locomotion is based on the synchronicity of locomotor organs (tendons, muscles, leg bones, etc.), which can be used to define several gaits. For bipeds, beyond the stride frequency, it's the flight phases that distinguish running from walking. Some bipeds (e.g. birds) walk at high speeds, due to anatomical constraint, see Bijlert (2024). In the case of humans, the ability to maintain a running pace at low speed seems to have played a major evolutionary role, see Bramble (2004).

For quadrupeds, gaits are distinguished by the time series of ground contact and their synchronization. For example, the well-known gaits of walk (3 simultaneous contacts with the ground), trot (2 simultaneous contacts) and gallop, which includes a flight phase. It is possible to train or observe animals in their natural environment showing only some of these gaits or, on the contrary, different gaits (canter, pace, amble...). For example, horses use these 3 gaits to move at very different speeds. In its natural environment, a horse chooses its gait according to the speed at which it moves. Naturally, the biomechanics of the various organs involved in locomotion are crucial. In this summary, we introduce the energy conversion mechanism as a constraint on the power available, via feedback on the boundary conditions. From this point of view, the question that then arises is to understand why different gaits exist and what criteria determine the transition from one gait to another.

## 2. Methods

Experimentally, the Cost of Oxygen Transport $COT = \dot{V}_{O_2}/v$, is widely used to quantify energy dissipation per unit length travelled. $\dot{V}_{O_2}$ corresponds to respiration and $v$ to translation speed. COT minimum, $COT^*$, is obtained for a specific value of the velocity, $v^*$. $COT^*$ represents an energy optimum, which is different from the maximum efficiency and maximum power. In Herbert (2020), we proposed an expression for $COT$ based on Onsager's force/flow formalism, widely applied to engineered power generation systems (eg thermoelectric devices). We introduced the possibility of recruiting an arbitrary number of $N$ muscle units at each gait. All these muscle units are identical, do not depend on gait and work in parallel. We assume, the operating intensity of a muscular unit is related to the translation speed by the proportionality factor $k$. This allows us to derive an expression of the $COT$ based solely on thermodynamically-based parameters

$$COT = \frac{N}{N_0} \left( \frac{B}{v} + a_0 k + R k^2 v \right)$$

$B = Nb$ is the energy consumption at rest ($v = 0$), $a_0$ is a constant related to the conversion feedback, $R = r/N$ is the viscous dissipation, $r$ and $b$ are the corresponding values for a single muscle unit. $N_0$ is the number of muscle units involved in the reference gait. Muscle units, as defined here, are not biological entities (as muscle fibers
are) in the sense that it would be possible to count them by dissection, but rather as systems integrating control.

It is interesting to note that COT* does not depend on the number of fibers N, allowing us to test the assumption of identical fiber behavior. More specifically, the following predictions can be made, i/COT* and ii/the product RB do not depend on animal's gait, and iii/the only parameter of the number of muscle fibers allows to distinguish the different gaits. To test this model, following Herbert (2020), we use horse respirometry data from Hoyt (1981).

<table><caption>**Table 1.** COT thermodynamic characteristics from respirometry fit procedure.</caption><thead><tr><th></th><th>Rk<sup>2</sup><br>[1/s]</th><th>B<br>[W/kg]</th><th>u*<br>[m/s]</th><th>COT*<br>[N/kg]</th></tr></thead><tbody><tr><td>Walk</td><td>1.1</td><td>1.60</td><td>1.21</td><td>2.27</td></tr><tr><td>Trot</td><td>0.42</td><td>4.11</td><td>3.14</td><td>2.16</td></tr><tr><td>Gallop</td><td>0.24</td><td>9.01</td><td>5.99</td><td>2.20</td></tr></tbody></table>

10% error must be taken into account.

### 3. Results and discussion

Table shows that *B* increases with speed, while $Rk^2$ decreases in to same proportion, leading to an identical COT* prediction for each speed. This can be clearly seen in Fig. 1, which shows COT as a function of speed. This suggests that muscle units behave identically at all speeds. Normalizing each COT by N, we find a master curve for the typical muscle unit (see Fig. 1 inset). This means that dissipation per unit length travelled remains constant as the speed of translation increases. This is made possible by mobilizing a greater number of N fibers, which are worked at lower intensities. We find that the number of muscle units involved in locomotion for the trot is $N/N_0 = 2.59 \pm 0.04$ and resp. for the gallop $4.95 \pm 0.06$ compared to the walk.

COT represents the energy dissipated per unit length covered. At low speeds, it is therefore clearly advantageous to use pitch to reduce the number of muscle fibers employed and thus the basal $B = Nb$. At higher speeds, it is the dissipative part that dominates, and it becomes advantageous to increase the number of fibers and change gait. Figure 1 clearly shows the speeds at which a given shape is more dissipative. For example, below 4.5 m/s the trot dissipates less than the gallop, and above this value the trot dissipates more than the gallop.

Unlike an engineered system, which is designed to satisfy the highest power requirement, the gaits are designed to adapt to demand, as if the number of cylinders in an internal combustion engine could adapt depending on the requested speed (eg in town or on the freeway). The described locomotor process demonstrates a dissipation allocation that is both minimised and optimised. Dissipation is minimised by organising motor output through a set of recritable fibres, activated according to the required speed. It is optimised insofar as the reduced dissipation lowers the organism's metabolic intensity, thereby reducing fatigue and mechanical wear. Optimisation also arises from incorporating feedback from the operating point into the global response of the locomotor apparatus.

A machine inspired by these principles would comprise a collection of articulated actuators governed by feedback control, designed to deliver a predictable and adjustable effective power. Adaptation to varying demands would be achieved by modulating the number of active actuators, rather than altering the operating intensity of each individual unit.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** per unit mass in function of speed for walk (red) trot (blue), gallop (green). Inset: Same COT vs speed normalized by $u^*$.</figcaption></figure>

Credit: Éric Herbert.

### 4. Conclusions

We show in this abstract that consideration of energy conversion is crucial to understanding the gaits and methods employed by vertebrates for locomotion. The number of muscle fibers recruited is the crucial
parameter for understanding how gaits are chosen and
how locomotion is kept optimal despite a wide range
of speeds. Walking allows a low basal thanks to a small
N, while trotting and then galloping compensate low
viscosity by increasing N.

Conflict of Interest Statement

None.

Contributor Roles

Éric Herbert and Christophe Goupil contributed equally
to this work.

References

van Bijlert, P. A., van Soest, A. J., Schulp, A. S., & Bates,
K. T. (2024). Muscle-controlled physics simulations
of bird locomotion resolve the grounded running
paradox. *Science Advances*, *10*(39), eado0936. https://
doi.org/10.1126/sciadv.ado0936

Bramble, D. M., & Lieberman, D. E. (2004). Endurance running and the evolution of Homo. *Nature*, *432*(7015), 345–352. https://doi.org/10.1038/nature03052

Hoyt, D. F., & Taylor, C. R. (1981). Gait and the ener-
getics of locomotion in horses. *Nature*, *292*(5820),
239–240. https://doi.org/10.1038/292239a0

Herbert, E., Ouerdane, H., Lecoeur, Ph., Bels, V., & Goupil, Ch. (2020). Thermodynamics of animal locomotion. *Physical Review Letters*, *125*(22), 228102. https://doi.org/10.1103/PhysRevLett.125.228102