Dogs (Canis familiaris) were run up and down 7.4, 11.8, and 20.4% grades as well as on the horizontal at speeds of 3 and 6 km/h while their steady-state oxygen comsumption was measured.
On positive grades the metabolism was directly dependent on both grade and speed.
On the negative grades the metabolic rates were dependent only on speed and for each dog were depressed about the same amount below the metabolism needed for horizontal running at each speed.
The clustering of the metabolic rates for the downhill slopes means that to cover a given distance gorizontally and downhill the dog will use the minimum energy if it descends via the gentlest grade.
This is so because such a route allows the animal to maintain the lowest metabolism for the longest time.
There is no best uphill route.
The grade metabolism of the dogs was an almost exact duplicate of that found for humans running on grades which implies similarity of mechanical and biochemical aspects of running.
J. L. Raab, P. Eng, R. A. Waschler