Ron wrote:

One more thing: Before thinking about all this, I always thought that
since a high gain antenna has a narrower beam than a lower gain antenna,
the high gain antenna "sees" a smaller part of the incoming field. I now
believe this is wrong. The higher gain antenna sees a larger field area.

Hopefully no one else was led to that belief by the exercise.

But as the antenna is rotated the sum of all the rays decreases faster
than if there were fewer of them. This is probably due to the rays from
the outer edge of the field causing a faster decrease in the coherent
summation of all rays than the closer in rays. Of course, as the
rotation is continued, many (but not as many) of the rays add coherently
again, giving rise to the side lobes.

Such a claim might be remotely plausible were it not for the fact that
rotating a directional antenna does not "coherently sum all the rays".
That's where the argument completely falls to the ground, as Monty
Python might say.

ac6xg

Ron, W4TQT

Ron wrote:

This was only a mental exercise to help me visualize the concept of
gain. No resemblance to a real antenna or RF field was intended.
Thinking about it has helped me understand what antenna gain is
(assuming my conclusions are correct). And that's all it was supposed
to do. I hope it has helped someone else to do the same.

Ron