If you delve deeper, you will read that each time you add directors - you have to recalculate the spacing between each director.
The length of each director and the spacing is very important.
Wood is a poor choice for anything more then a experiment - it is heavy, and not very strong.

If you are serious about building that antenna, you would want to look for a old UHF / VHF television antenna such as the Radio Shack VU 190.
Rob the elements off the antenna, cut them to length and mount your gamma match to it with a appropriate sized reflector.

There was a channel master VHF antenna that was made back in the 1970's that was about 24 feet long which also made a excellent donor antenna / platform for a home brew beam antenna.