David weote:
"How do you get an omni-directional pattern from this antenna?"

In a point to multipoint system, only the central station needs an omni
antenna.

One orderly radio data acquisition system operates half-duplex. Only one
station at a time transmits, and then only when called upon to do so.

A radio master interrogates remote stations within its reach, addressing
them by name, rhen listens for their response. Only a single radio
frequency is needed as remote stations don`t initiate transmissions
until callef upon. In this master-slave relationship, there is no
competition within the system for radio time.

The radio master can conveniently use an omnidirectional antenna as it
communicates with slaves on various azimuths. The slaves only
communicate with the master, even to communicate with each other. The
slaves each have a directional antenna aimed at the master.

A directional antenna improves signal to noise ratio when transmitting
and when receiving. Great gain and directionality, though desirable,
may be necessary only when very low transmitter power must be used..

The long-boom directional loop array may have a gain of 20 dB. But, a
3-element Yagi can give a 5 dBd gain which may be plenty. This gain is
almost equivalent to cutting the path length by half (6 dB).

The Yagi is close-spaced. With only 3 elements it is small and simple to
build.

Normal narrow-band receivers are very sensitive so that very weak
signals are sufficient if noise and interference are not severe. Higher
gain antennas can be used as needed at remote sites on a case by case
basis.

I built such a system decades ago and it is still in use.

Best regards, Richard Harrison, KB5WZI