How much smaller and better?
Well, the batteries I use are fairly medium-sized ones, with 3000 milliamp-hours of charge, meaning that they can put out 3000 milliamps for an hour, or 6000 mA (6 amps) for 20 minutes, and so on. There's an upper limit to how fast they can be safely discharged, but let's ignore that and just look at the total power available.
If we know the voltage the battery provides, which the label tells us (and a meter confirms) is 11.1 volts, we can convert that to watt hours: 3 amp-hours times 11.1 volts is 33.3 watt-hours. One watt-second is a joule, so 33.3 watt-hours times 3600 seconds in an hour is 119880 joules. Let's round that off a bit and say 120 kJ.
Now, something to compare it to:
One gram of TNT is, Google conveniently informs me, 4184 joules. It's a bit harder to find the TNT-equivalent of modern grenades, but Wikipedia says that the stereotypical "pineapple" grenade seen in a thousand world war II movies contained 57 grams of TNT (the real ones, I mean, not the ones in the movies. Those were fake, I hope). That means a grenade in the '40s would put a total of 4184 joules-per-gram times 57 grams, or 238488 joules of energy into the Nazi tank of your choice.
So again, let's round that off for convenience and say 240 kJ. What that means is, the little blue battery pack on top of my quadcopter is the energy equivalent of half a hand grenade.
For a fun exercise, look up the specs on your smartphone. It's probably got a LiPo battery, just like my quadcopter. How much TNT do you carry in your pocket?
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