Help me understand wheel size impact on gear ratios. I'm researching 20" geared bikes for my kid, and they all seem geared really high for singletrack. My granny is like 28x42 because I'm a weenie, but most kids bikes are like 34 or 36 up front and 28 in the back. And because 90% of kids bikes come with bmx cranks, this isn't easy to adjust. Doesn't this seem really high for actual real trail riding?

Wheel size affects the final drive ratio when you look at it in terms of linear distance covered per crank revolution. Ignoring wheel size, you're only looking at a ratio of crank revs to wheel revs. One revolution of a 20" wheel will cover ~30% less distance than one rev of a 29" wheel. Therefore taller gear ratios are needed to keep a similar overall drive ratio.

How that relates to the anatomy of a smaller human in terms of available torque (relative to body weight), and ideal cadence and crank length is not completely clear to me. What is clear is that regardless of size (bike or human) there is a threshold minimum speed that needs to be maintained on a bike in order to stay upright. So the bottom gear final drive ratio (in terms of linear distance covered per crank revolution) can only go so low.

As an example:

A 34t front cog and 28t rear cog with a 20" tire will cover a similar amount of ground(75-76") per crank rev as a 28t front 34t rear with a 29" tire.

(Assuming effective rolling diameters of exactly 20" and 29" respectively)

I would expect higher gearing in bmx as you're going much faster, and usually start on a ramp. 

What got me thinking: my kid recently cleaned all the climbs at Purser on his 16" set up 28x16, but he was standing/cranking and it was obvious the gearing wasn't helping. With proper gearing on his next bike it could really open up trail options, but there's a vast difference in gearing setups between something like a basic Hotrock and some of the higher end options out there.