... if it calls for an 84 foot length, do I cut the wire exactly 84 feet or do I add some length to allow for strain relief on the 9:1 Unun and for installing the insulator on the far end?...
First of all, the length isn't all that critical in this case.
Basically, you want a non-resonant length. There are
lots of tables that use the standard formulas to calculate
such lengths, and the values they publish are often the
center of a range of lengths that will work.
Of course, one issue is that the "standard formulas"
aren't necessarily correct - they are just estimates.
The actual resonant lengths depend on the wire diameter
and the insulation type and thickness, as well as whether
the wire is straight or bent. Without running some tests
on the specific type of wire you are using, you probably
can't calculate any of the resonant lengths exactly.
Besides, the UNUNs often described for using with such
antennas aren't perfect transformers anyway, so the
resulting impedance won't be what you would predict.
The best thing you can do is to put up the antenna,
measure the feedpoint impedance on each band, and
then calculate the impedance at the tuner (and the loss
in the coax) based on that impedance.
Now, with an EFHW, where you are trying to make it
work without a tuner, you may need to adjust the wire
length for minimum SWR at your favorite frequency,
or pick a reasonable compromise for a usable SWR on
all the bands of interest. In that case, the length may
be more critical.
Regarding allowing some extra length for strain relief
and connections: there are two different scenarios.
Bare wire shorts to itself, so loops or knots count less
towards the overall length (they are just a bit of added
capacitance due to the thicker wire). For insulated
wire, that isn't the case, and the full wire length needs
to be considered, although bending the wire does
increase the length of wire required for the same
resonant frequency compared to a straight wire.
In that case, a knot needs to be thought of as a form
of linear loading, and the effect on the resonant length
depends on where it is placed along the wire.
I had a case where I had tied a loop in the end of a
dipole wire and was trimming the free end to set the
resonant frequency. Turned out I pruned off all the
excess without quite getting to my target frequency,
so I tied the same knot another couple feet down
the wire to continue the process. But now the wire
was too short. I ended up moving the knot until the
wire was resonant where I wanted it. But the point
is, moving the knot shifted the resonant frequency,
for the same wire length.
So the question is far more complex that a simple
answer can account for. So my general approach is
to cut the wire a bit long, put it up in the final
configuration, then prune (or fold back) the end of
the wire to raise the resonant frequency if needed.
So in your case, I'd say cut the wire a bit long,
perhaps 85', and see how it matches on each band.
If you have problems on some band(s), try folding
back an extra foot or so and see if that helps.
If you have a problem at the bottom of a band,
then try adding some wire. If it is at the top of
a band, try shortening the wire to move that
inconvenient impedance up above the band.
But don't get too worried about hitting an exact
length.
So consider that number to be
about 84', and it
may be that anywhere between 80' and 90' is close
enough to make it work.
