Flying Poodles

Physics of jump heights…

The debate is endless: should dogs jump at the highest allowable height or the lowest… AKC has the “Championship” program and the “Preferred” program, and the Championship program is pretty much preferred as more meaningful by most competitors. Ditto USDAA’s Championship program and Performance program. And NADAC’s Proficient and Skilled programs. CPE has Regular, Enthusiast, and something else entirely that I’ve forgotten. But in all cases, the competitors see the lower height program as the place NOT to be.

Should dogs be jumped at lower heights for long-term soundness?

I used to teach high school physics, which is where mechanics (Newton’s three laws) is taught. I would like to suggest that simple high school level physics explains why it may be better to jump lower rather than higher.

Two physics equations apply to the jumping question. The first is:

** Force = mass multiplied by acceleration (F=ma)

The second is:

** Kinetic energy = 1/2 mass multipled by velocity multiplied by velocity (KE=.5mvv) (or KE=.5mv**2) (since I don’t have a symbol for squared, I’m using old FORTRAN notation in the second equation)

In jumping, the dog will have a constant force in the direction of the ground while it is in the air. That is, the dog’s mass and the acceleration of gravity do not change while the dog is in the air.

However, the higher the dog is in the air, the more time it will spend accelerating toward the ground, and the more velocity the dog will have toward the ground when it reaches the ground. Note that the downward velocity is unchanged whether the dog is jumping collected or extended; it is purely a function of the height of the apex of the jump. Thus, more height leads to more velocity when reaching the ground which increses the kinetic energy GEOMETRICALLY (it’s a squared function). An increase of 10% in velocity (about what you’d get with one jump height increase) would lead to an increase of about 20% in kinetic energy that needs to be absorbed when the dog reaches the ground.

Note as well that forward speed does not matter in this analysis; only the speed toward the ground creates kinetic energy that must be absorbed by landing.

Now, dogs are beautifully built for jumping, and in fact, their tendons, ligaments, and muscles in the legs act as springs to absorb some of that kinetic energy. A biophysicist could calculate the force that a dog can safely absorb, and it would vary with breed and structure (things like shoulder angles and hip flexion matter). That lies beyond my knowledge base.