There seems to be an assumption by some posters here that
a mobile antenna must be electrically 90 degrees in length.
Here's a simple transmission line example to illustrate why
that is not true in the case of a loading coil used with straight
sections of antenna. In the following example, all transmission
lines are lossless.

We want to build a stub that is electrically 90 degrees long,
i.e. a 1/4WL open-circuited stub. The impedance at the
mouth of the 1/4WL open-circuited stub will be 0-j0 ohms,
a short circuit. The first stage of the stub is made from
Z0=450 ohm transmission line and is 30 degrees long.

0-j0 ----30 deg of 450 ohm line----+----50 ohm line---open-circuit

The question is: How many degrees of 50 ohm line do we need
to add to get 1/4WL in all. Sounds simple, huh? Just add 60
degrees and we will have our stub. But that is NOT what happens.

The impedance at '+' is -j259 ohms. That is -j.0575 on the 450 ohm
Smith Chart but is -j5.175 on the 50 ohm Smith Chart. So it takes
only 11 degrees of 50 ohm line to replace the function of 60
degrees of 450 ohm line. Want to stuff 90 degrees of function into
a 41 degree long stub? Make it a two-stage stub as above and
take advantage of the impedance discontinuity.

There is 60 degrees between -j0.575 and infinity on a Smith Chart.

There is 11 degrees between -j5.175 and infinity on a Smith Chart.

The Z01/Z02 impedance discontinuity has provided the "missing"
49 degrees of the stub.

The stub is only 41 degrees in physical length yet it functions
just like a 90 degree stub.

The same thing holds true for mobile antennas with loading coils.
The difference between the Z0 of the straight section and the Z0
of the loading coil provides the "missing" degrees of the antenna.
There is no requirement that the antenna be physically 90 degrees
long. There is no requirement that the delay through the coil plus
the delay through the straight sections add up to 90 degrees.
The impedance discontinuity provides the "missing" number of
degrees.
--
73, Cecil, W5DXP