I don't know if what I'm about to say is specifically true for 377's reserve rides, but it is a possibility. There was a fair period of time, a transition period, when sport skydivers moved away from using military surplus 'gutter gear' (back mains and front reserves), and started using 'piggyback' rigs (main and reserve both on the back) designed and built specifically for sport jumping. This started before square chutes were used at all, and continued for some years as squares were used for mains but rounds were still used for reserves. 26' navy conicals were popular reserves through that period, then sport gear manufacturers were designing round reserves, and eventually square reserves took over. So 377's 26' conical may have been in a sport piggyback rig. My first reserve ride was also on a 26' navy conical packed in a sport piggyback rig.
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Actually it is. All the gear in the Cooper case were reserves, with the possible exception of one of Cossey's rigs, IF in fact any of his were taken. Pilot emergency bailout rigs ARE reserves. The harnesses, containers, and canopies are designed and built as such, are tested to FAA TSO standards, and are required to be packed by FAA licensed riggers. Such requirements do not apply to sport mains. (For sport skydiving gear, the TSO standards apply to the harness, reserve container, and reserve canopy, but not the main container or canopy.)