Recently, while volunteering for a race event with the Cal Poly Amateur Radio Club, I found myself (with the help of a friend luckily) carrying a 26 amp-hour sealed lead acid battery and mobile radio one mile down a trail. This was much less than ideal and while walking up a somewhat annoyingly tall hill, I came up with the notion that the lead acid battery I was carrying weighed so much (about 20lbs) that it would actually have more gravitational potential energy than chemical energy by the time I reached the top of the hill. In other words, does lead make for such crappy batteries that it's more effective to carry a rock up a hill and use the energy from it falling than from the energy stored in the battery?
This got me thinking, and after a few calculations, it turns out that this definitely isn't true. By a long shot. Even the relatively inefficient SLA would need to be lifted to over 12 kilometers (yes I'm using SI units) before it's gravitational potential energy exceeded the electrical energy it could produce. I tried the same calculation with a number of other batteries to compare them, and with no surprise lithium batteries prove to be about twice as energy dense as SLA's. On top of this, they have a better charge/discharge efficiency. I was, however, a bit surprised to find that high-end lithium 18650 cells as used in laptops and Tesla cars are more than twice as energy dense as the LiFeYPO4 cells in my car.
All in all, this may have been a somewhat useless exercise, but you have to appreciate the humor in measuring the energy density of batteries in kilometers from the ground.