Andy: You cannot just extend the wire and improve the range. The antenna
must resonate at the desired frequency, and changing the length will
change the resonance.
By combining the signal in-phase from multiple resonant elements (which
includes un-connected elements that increase the signal strength on
connected elements, as in a Yagi) you can increase the received power.
The trouble is that the multiple elements interfere with the local field
and hence with each other, so they will create a directional pattern -
stronger in some directions and weaker in others. In the case of a fixed
TV antenna where the direction to the transmitter is known, that's fine,
as long as you aim it right. If you go for a Yagi with large gain,
there'll be large nulls either side of the direction it's pointing. That
means that if you're flying at maximum range, and you fly into the null,
or point the antenna away a little, you lose signal. The higher the
gain, the narrower the central lobe.
You know those vertical rectangular antennae used for mobile phone cell
towers? They might have a horizontal spread of 45 degrees, but the
vertical spread is only 1.5 degrees... and that's perfect for mobile
phone use.
Summary: There's no free lunch. If you want gain, it has to be
directional. So if you can't point the antennae in the right direction,
you can't use a high gain antenna.
Clifford Heath.