I was hoping there would be a better discussion of the technical reasoning behind using a header tank.
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The header tank is a choice some designs use, but not all. It may simplify a fuel system on a FI aircraft that requires engine return fuel. On carbureted engines, its used to prevent fuel starvation if a wing tank is un-ported for a period of time. Many taildraggers with little or no wing dihedral and a wing fuel tank with only one fuel pick were manufactured. Even a crowned runway with 1/4 tank can un-port the fuel pick up and starve the engine so the header tank was installed.
Fuel flows into a header tank via gravity at the rate that an engine consumes fuel. It is vented, and so it always remains full until the main tanks are empty. The fuel port out of the header tank to the engine is alway is covered with fuel. The header tank is a good place to plumb excess engine return fuel to.
Cessna 310R, C-185, and Beech Bonanza's use Continental's Fi system which returns excess fuel from the engine back to a tank. The 310 always returns the fuel back to the respective main tank, even when the Aux tank is selected. So the C-310 main tanks fill back up when burning off the Aux tank. The Bonanza returns fuel back to the selected tank via a duplex valve. The C-185 has a header tank that is labeled a "Fuel Accumulator Tank".
The Continental FI system design requires a fuel return because that system pumps excess fuel, like SDS. Having a header tank simplifies the fuel system.
-The header tank is a destination for the engine return fuel and the tank supply fuel,
-The Header tank is always full even if one tank is run dry,
-A simple ON-OFF fuel valve may be used to control engine supply to the engine.
-It allows for a L-BOTH-R fuel selector.
-Multiple return fuel lines do not have to be plumbed back to the wings all the way back to the wings,
-A duplex fuel valve is not required.
The original Super Cub fuel system is gravity fed with a header tank located aft of the baggage area. Each wing tank in a Cub had one fuel line supplying fuel to the header tank. (Bob's design has two, one near the front, one near the rear to allow fuel supply with near empty tanks in a nose low or nose high attitude)
The header tank allowed take-off with 1/4 tanks without worry of unsporting a tank. The C-140 did not have a header tank, but had a placard "Do not take off with less than 1/4 tanks." (I un-ported a C-140 tank on takeoff once and momentarily loss power even though we honored the placard.) A Super Cub STC does away with the header tank if the system is modified to what the Bob Barrows original design is.
So, the technical reason for having a header tank is to maintain a positive supply of fuel to the engine in all normal aircraft states, to simplify fuel system plumbing, and in some cases to have a place for fuel to cool after traveling through an engine compartment.