My Baby Ace has copper fuel primmer lines and so does this picture.
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I have seen plastic,copper, alumimun and steel fuel primer lines in home-built aircraft.
My military experience I have worked on fuel systems with rigid aluminum, stainless steel, titanium and nickle fuel lines. These installations are rigid, have compatible flared fittings and are bonded to structure. Most fuel lines have a wall thickness of 0.035 -0.050 thickness. Standard practice is to remove rigid lines with dents or nicks of 10% wall thickness.
In the picture supplied by Tim Brown the plastic fuel line could have been better secured and as pointed out, this line has been snagged a few times and is on it's way to failing. Plastic lines can not be bonded and often are secured with clips/ lockwire over stepped fittings. Not the best in my opinion.
My preference is aluminum tubing. Proper AN fittings, flared ends, overall rigid installation for fuel primer lines.