Tharkun said:

"This issue above concerning a squared velocity makes perfect sense so long as we follow the mechanics first and then apply the math to the mechanics."

I respectfully disagree. The reason his units come out wrong, is because Miles equation is wrong. Look at his definition for linear acceleration:

"acceleration is a squared velocity"

That's a false statement – it's simply not true. Linear acceleration is not the velocity squared. Acceleration is defined as a change in velocity, divided by a change in time (which is not the same thing as the velocity squared). And that's why his units end up mismatched – his definition for linear acceleration is wrong. And to compensate for this error, Miles has to illegally "dump" units.

--Richard Cage