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Design for wire trap antenna to fit inside a flag pole to operate on 15-20-40-80 meters?"
You need the ARRL Antenna Handbook
The inductances and capacitances must be in line with the radiator which is a requirement that will be difficult if not impossible to achieve with a tubular metal flag pole.
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"I want to use a PVC Pipe for the floagpole............."
That might be satisfactory. PVC pipe size & length (heighth) considerations for strength and wind load. Also consideration as to trap coil sizes.
Determine coil and trap dimensions, then select pipe to accommodate coils. Don't forget that a radial grounding system may be required depending on where antenna is mounted.
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Do Nothing Simply When a Way Can be Found to Make it Complex and Wonderful
Note that the lower half is a metal tower. Total height is 53 feet. There is a link on the above page where you can download a 36 page Instruction Manual in .pdf format. study this manual to get an idea of what you what you proposed doing.
A horizontal dipole would probably be a better choice if ground space is available.
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Do Nothing Simply When a Way Can be Found to Make it Complex and Wonderful