Electronic – How do power adapters automatically detect the output voltage

I agree with others that switchers are a better choice in terms of efficiency, but they can be somewhat complicated to deal with if you're inexperienced, and there can be lots of weird effects that aren't immediately obvious (precharge sinking, beat frequencies, etc.) that can make life difficult. Assuming you've figured out your power dissipation and know how much current each rail can deliver, if the linears will work for you, stick with them (at least for the first pass).

If you're trying to achieve a variable-amplitude square wave output on your adjustable rail, the chopping may introduce noise into the main 24V rail, which could show up on the other rails. You may want to have an LC filter between the main 24V rail and the regulator input to provide high-frequency isolation, and will probably need extra capacitance on the adjustable regulator output (bulk electrolytic as well as low-impedance ceramic) if you expect the square wave edges to be sharp.

1, 5) There are some dangers with your scheme.

Power dissipation in the linear regulators will be

\$(V_{out} - V_{in}) \cdot I_{out} \$

which is significant, especially for the lower output rails. 78xx-type regulators have built-in thermal protection around 125°C, and (without heatsinking) a junction-to-air thermal resistance of 65°C/W. Your thermal management will be challenging.

Another potential problem - if the series-pass element in any of your low-voltage regulators fails or gets bypassed (shorted), you'll present the full 24V input to the output. This could be catastrophic to low-voltage logic. You should protect your low-voltage rails with SCR crowbars that can sink enough current to put the DC/DC brick into current limit and collapse the 24V rail (they'll need big heatsinks too). Fuses are unlikely to be good protection since the 24V brick likely isn't stiff enough to generate the \$I^2 \cdot t\$ needed to blow a fuse.

2) Whatever floats your boat.

4) Meters aren't huge loads. Just use one of your rails.

3) Correct - all regulators have headroom requirements. If you want the maximum 24V out, you'll need a direct connection, and will have to rely on whatever intrinsic protections the brick will provide you.

I am fairly new to this stuff as well but I will do my best to answer your question.

I do not believe that four 1.2v batteries will be sufficient on their own (at least not for too long) because of the inevitable voltage drop that will occur over time.

Most NiMH batteries I have come across have between 1800 and 2500mAh and four of these will be able to run your board for a while before they lose the ability to source 750+mA, but when they do it will cause the supply voltage to drop below 4.8v.

I see that the typical max current supplied by the USB ports on the board is 1500mA, and assuming outbound USB current was not factored into the typical average current draw of the board, it could mean that as much 2250mA could be needed at any given time. (maybe even a bit more, I don't know enough about the beagleboards to say). At that level of current draw it wouldn't take very much time for a voltage drop to occur.

I would instead use a switching regulator to power your board. I looked briefly but didn't find many prefabricated "boost" converters that would supply sufficient amperage, but I did find a lot of "buck" type converters that would take a higher input voltage (say 7.2v, from six batteries) and convert it to 5v 2A+ at the output.

You can also do a little research and build your own buck or boost converter instead of buying one, or take a simpler approach and build a linear regulator, but these are not as efficient and you wont get as much run time out of your batteries.

The max current draw may(MAYBE, not sure) also be something that is only approached infrequently in quick spikes. If this is the case then it may not be necessary for your regulator to source the max current, but it would mean that you should put some extra capacitors in your regulator's output stage to handle instances of increased current draw.

I hope this helps. :)