# Why does the gravity of Earth appear in this formula estimating speed?

I'm currently reading the wonderful book The Dinosaurs Rediscovered by Michael J. Benton. It contains the formula

$$v = 0.25 * g^{0.5} * SL^{1.67} * h^{-1.17}$$

where $$v$$ denotes velocity, $$SL$$ is stride length in $$m$$, $$h$$ is hip height in $$m$$ and $$g$$ is the gravity of earth. Not being a biologist (in fact not being really familiar with any natural science), I don't quite understand why gravity appears in this formula. I can't imagine this would hold in any meaningful way in circumstances where gravity where different from earth's, so why not simply express the term $$0.25 * g^{0.5}$$ as $$0.78 m^{0.5}/s$$, which I assume stems from some fitting of terms to observed speeds given stride length and hip height.

• I know nothing about this, but this formula appears to be the work of one Robert Alexander. If you can find some of his papers, he likely explains how this formula was developed. Alternatively, this website seems to go into the derivation. – canadianer May 22 '20 at 13:30
• Reading a little bit about the derivation of the formula as well as the corresponding wikipedia article, I would assume the g stems from the origin of the equation in Froude's number. – Joseph Doob May 22 '20 at 18:46
• This question is about physics or engineering, not biology. The fact that the formula can be applied to biological movement is irrelevant. – David Jun 24 '20 at 18:20