T o d d P a t t i s t wrote
A barrel roll is often described as: "imagine the wheels of
the aircraft rolling on the inside of a barrel." In
Dudley's description of the classic competition BR, the
track of those wheels is going perpendicular to the axis of
the barrel at the top, straight down the axis of the barrel
at the beginning and end, and the barrel is perfectly round.
In Dudley's expanded description of the BR (as any roll in
3D) the track might not be perpendicular at the top and the
barrel might not be perfectly round.

Todd, in your example, the wheels would "scuff" around the
inside of the barrel. In order to roll around the inside of
the barrel. The starting heading must be some number of degrees
off the axis of the barrel, 45 degrees in the classic example.

At the top of the barrel, the heading would have changed by 90
degrees, but would be 45 degrees off the axis of the barrel on
the other side.

Bob Moore