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ATC would momentarily see the size of your primary target triple in size as the radar reflects off of the aluminum gum wrappers.

I've always wondered about Center and Approach radar capabilities. My ground school instructor told the class the other day something that was quite shocking to me. He said that Center and Approach radar has very little ability to see aircraft without a transponder and that if you fly with your transponder off, you are more or less invisible to them because their radar is not the sophisticated type that the military uses to detect bad guys. . . . does this sound true ?