Ah yes, quite right about the loading inductor - thanks for the correction.
.
.
However, the 9:1 impedance ratio unun shown above (3:1 turns ratio) is probably not the unit that's in the commercial end-fed box.
The commercial unit likely contains a 64:1 or 81:1
impedance ratio transformer or unun (8:1 or 9:1
turns ratio). A 64:1 or 81:1 impedance ratio, or thereabouts, turns out to be a decent transformation ratio for hi-Z end fed operation.
There's always endless confusion and hilarity when talking about transformer ratios - half of us are talking
turns ratio, the other half of us are talking
impedance ratio !#%&!*%#!!!!
Both are popular - the 9:1 impedance ratio is GREAT for wideband use with a tuner (and is part of the BMU (Base Matching Unit) recommended for verts and L's and EARCHI types), but likely the end-fed unit is used WITHOUT a tuner and is more like these 64:1 or 81:1 impedance ratio transformer units:
.... and transform impedance to be a fairly close match to the impedance seen at the end of a half-wave and it's harmonics - like this:
The 9:1 turns (81:1 impedance) ratio unit is good, the 8:1 turns (64:1 impedance) ratio unit is probably a bit better.
The graph also shows that the system is pretty INsensitive to counterpoise length, which is kinda cool.
I'm not quite sure why anyone would want to put up a 250 ft antenna to get 160M coverage, when 1/2 that, or 1/3 that would likely be a better DX antenna in a base-fed vertical, slopper, or inv-L configuration.... (assuming one can install some sort of ground radial or counterpoise system). And, if DX work is your goal, hanging this half-wave antenna any lower that around 180 ft is going to be pretty disappointing - 160M is not an easy band!!! DX work is almost exclusively done with vertical polarization.
However, if NVIS is your goal, then you'll be just fine.
So, if end-fed is your cup of tea, remember that as stated above, a very good feedline choke should be used to knock down the common mode current on the coax shield. RF in the shack is one potential problem, but the other
SNEAKY problem that coax shield current causes is noise pickup from the coax, which often runs right next to every noise producing item in your house.