Here is how I'd approach it.
Given that you have a Lycoming O-540
and it is gravity fed I looked in the
and found a chart showing that maximum power is
at 28” Hg of manifold pressure will yield a fuel burn of
approximately 25.25 gal/hr.
Looking in the Federal Aviation
Regulations (FAR) 23.955(b)
we see that certificated aircraft (not your experimental) must ensure
that a gravity system is capable of delivering 150 percent of the
takeoff fuel consumption of the engine. FAR 23 gives good, safe,
numbers if you want a starting point. So, if we assume you will want
to use all of your engine's horsepower at takeoff we multiply 25.25
by 1.5 and get 37.875 gal/hr that the fuel system should be capable
of delivering to the engine.
If it were my plane, I'd mount the fuel
tank in the airframe and run the smallest lines and fitting that you
think you want to use, 3/8” in your case. Ideally, you should tilt
the airframe to the most adverse angle for the flow but that will
likely be very difficult. Cap the end of the line and fill the tanks,
then uncap the line let it run for 10 minutes and measure how much
fluid passed through the system in gallons (or use pounds and convert
to gallons). If the number is less than 38 gallons, you need bigger
fittings and/or lines. Note that you can run this test with any line,
it doesn't have to be aircraft quality since this is just a test. If
you are not able to determine the most detrimental angle for fuel
flow or you can't get the airframe into that position, I'd add a
significant safety margin to compensate, perhaps use 200 percent
instead of 150 percent and then confirm that all is well during the
initial flight testing?
If you don't want to rig the test
lines, there are ways to mathematically calculate the flow rate based
on gravity but that can't take all the variables into account. As I
said, I'd go with testing it on the airframe.
Based on the information you've
provided and some quick calculations, I think you are going to have a
problem with the 1/4” fittings being too restrictive. If you
increase the size of those, I think you might find that you actually
need 1/2” through the whole system, but I'll leave that for you to
make the final determination.
Hope this helps. I'm not an engineer,
so confirm everything I've said for yourself.