The figure eight is arguably the single most useful training tool for developing flying lead changes, and its effectiveness comes from a combination of geometric logic, natural balance assistance, and the progressive way it can be structured to move from simple changes through to confirmed flying changes without creating the tension and confusion that direct approaches to flying change training often produce. Trainers across disciplines — dressage, western performance, jumping, reining — use the figure eight as the foundation of their flying change programs for good reason. The geometric logic of the figure eight is what makes it so valuable. When a horse canters a circle on the right lead and crosses through the center of the figure toward the left circle, his body's natural tendency is to shift balance toward the left as he begins moving in the new direction. At the center crossing point, the horse's momentum is carrying him from one circle to the other, and his balance is naturally transitioning from being organized for the right lead to wanting to organize for the left lead. This natural balance shift means the horse is already partially prepared for the change at the exact moment the aid is applied — the geometry is working with the training rather than against it. A flying change asked straight down a long side requires the horse to reorganize his balance without any directional assistance; the figure eight provides that assistance naturally. The progressive training sequence on the figure eight begins with clean, prompt simple changes through trot at the center crossing. The horse canters one circle, trots at the center crossing, and departs promptly on the new lead for the second circle. This simple change confirms that the horse understands the departure aid on both leads, is balanced enough to reorganize his lead at the center, and will not lose his forward thinking or become tense during the transition. Many sessions should be spent developing this simple change until it is completely reliable, prompt, and relaxed before any reduction in trot strides is attempted. The next stage reduces the simple change from three or four trot strides to two — a barely perceptible trot before the new departure. This requires better timing from both horse and rider: the downward and upward aids must be applied more precisely and in closer succession, and the horse must remain balanced and forward through a transition that allows very little time for reorganization. Two-stride simple changes that are clean and balanced represent significant progress and should be consolidated over multiple sessions before further reduction. Reducing to a single trot stride places the horse at the threshold of the flying change — one footfall of trot between the two canter leads. At this point, the rider begins to feel what the flying change will be like, and some horses offer the flying change spontaneously when the single trot stride is asked, reorganizing in the air rather than touching down. When this happens, it should be recognized immediately and rewarded generously — the horse has offered the correct answer without being specifically asked, which is among the most valuable training moments available. Asking for the flying change directly builds from this point. The rider approaches the center crossing with the horse balanced and forward in the canter, and as the current leading foreleg lands — the stride before the crossing — applies the new outside leg behind the girth, shifts the new inside flexion, and allows the horse to reorganize in the suspension that follows. The circle geometry provides the balance assistance at the crossing point, so the horse has the physical conditions that favor the change at the exact moment the aid arrives. After the first flying changes are confirmed on the figure eight, the training progresses to asking for changes on a serpentine, which introduces the change from a curve in one direction to a curve in the other but without the specific center crossing reference point. From the serpentine, the progression moves to a diagonal line across the arena — which provides some directional assistance but less than the figure eight — and finally to a straight line down the center or long side, where the horse must perform the change from the aids alone without any geometric assistance. Each step of this progression should be consolidated before the next is introduced, and returning to the figure eight whenever quality deteriorates is always productive rather than a step backward.
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Watch: How to Use a Figure Eight to Train Flying Lead Changes

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Larry Trocha: Flying Lead Changes — How to Use a Figure Eight to Train Flying Lead Changes
Larry Trocha Horse Training