Impulsion is the quality of energy in a horse's movement that comes from an active, engaged hindquarter driving the horse forward into a soft, receiving contact. It is distinct from speed — a horse can move very fast with very little impulsion if it is running on its forehand with a tight back and trailing hindquarters, and a horse can move slowly with significant impulsion if its hind legs are stepping well underneath its body and its back is swinging freely. Impulsion is the quality that makes a horse's movement feel alive, elastic, and powerful from the saddle, and it is the energy source from which collection, lateral work, and all more advanced training is developed. A horse without impulsion is flat, dull, and difficult to shape because there is no surplus energy to redirect into more demanding work. Developing impulsion begins with establishing genuine forward movement from a light leg aid and then encouraging the horse to step further underneath its body with its hind legs through transitions, hill work, and progressive demands on the hindquarter engagement. The rider's leg creates the energy and the rider's hand channels it forward rather than blocking it. A common error is confusing impulsion with speed — pushing the horse faster rather than deeper — which produces a horse that runs on its forehand with a quickening tempo rather than one that carries itself with genuine power from behind. A horse with correct impulsion feels like it could do more with less effort, and that quality of energy is what distinguishes a genuinely trained horse from one that simply moves around the arena.
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Watch: How to Develop Impulsion in a Young Horse and Why It Is Important

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Clinton Anderson: Getting Forward Movement — Developing Impulsion in a Young Horse
Downunder Horsemanship