Scott, N0EDV wrote:
"O Now if I could only remember the math formula to figure the direction
of steering---."

All the simple options are bidirectional except the omni which results
from 90-degree phasing between the two dipoles.

You know that used separately, maximum radiation is broadside to the
energized dipole.

Fed in-phase or out-of-phase, the crossed dipoles have lobes at
45-degrees and 225-degrees, or at 135-degrees and 315-degrees. The
figure-8 pattern is the same as from a single dipole but shifted plus or
minus 45-degrees, depending on in-phase or out-of-phase feed of the two
dipoles.

Patterns of the crossed dipoles are similar to the oscilloscope display
of the same signal fed to both sets of defllection plates but with a
variable or selected phase angle between the plates.

Just by selecting one dipole or the other you could have a north-south
or east-west pattern.

By quadrature feed of the two dipoles you get a near circullar pattern
from the crossed dipoles.

From two dipoles and a 90-degree delay for a non-directional pattern,
and with some switching you get 5 radiation patterns. That`s pretty
versatile.

To get the 90-degree phase shift, a T-network with equal reactances in
all branches is often used. For a 90-degree lag, coils X1 and X2 are in
series with the load. Capacitor X3 connects between junction of the
coils and the other side of the line.

For a 90-degree lead, replace the coils with capacitors, and replace the
capacitor with a coil in the T-network.

It`s easy to remember the reactance values.

X1=X2=X3=Zo= sq rt (ZinZL)

The reactances may well be 50-ohms if we have a match to the usual load
impedance.

To adjust the phase lag of the T-network by as much as plus or minus
15-degrees without significantly affecting the magnitude of the
shifter`s output, X1 and X2 are often ganged variable inductors.

An imperfection in the phase shifter may result from uncertainty about
its input and output impedances. Nevertheless, many T-network phase
shifters are in use.

Best regards, Richard Harrison, KB5WZI