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You might want to re read the post before you start inserting words that are not there.


 I never said it would not work, I did say that the reflector and director would have to be 5% higher and lower in resonance to get any hope of having a pattern like a yagi.


 Now if the builder wanted to have three (3) gain masters, with the reflector 5% lower in frequency for resonance, and the director 5% higher in frequency for resonance than it might develop a yagi type of pattern. Maybe, but would it be worth the time and expense? The weight and the wind load?


 Would it be better than a half wave yagi? You would never be able to tell the difference on the receive end.


 Just because an electrical length of a conductor is resonant be it wire, tubing, copper, or aluminum foil, pick your poison all will have a different length when made resonant at the same frequency. With the reflector and director there would also have to be a matching network, when dealing with something beside a 1/2 wl doublet or full wave length quad any type of antenna will have to have a matching network. the full wave loop even needs a matching network to lower the impedance.


 Also you have to take into consideration  mutual coupling between elements.


 Since you brought the ARRL antenna hand book into the conversation why don't you provide a link to a yagi made up of 5/8 wl driven elements. I will be very interested in reading that link.