This is not a problem and in fact potentially shows how you do not understand the topic involved.
This is a constant rate, constant level turn. This means that the plane will be experiencing a constant amount of radial acceleration. If I were to straighten the flight path before Columbia and after impact, then the plane would have to roll in order to change the lift vector. This rolling means that the plane would undergo
less radial acceleration while it is closer to horizontal.
What you seem to be misunderstanding is this, given the impact/flyover vector, and the Paik / NoC Columbia vector, there is a set number of degrees of turn required. By taking a circular flight path this results in the longest possible turn time, and therefore the
lowest possible bank angle.
Nobody reports a bank anywhere near the amount required, so either
- The plane was much slower
- The NoC flightplan is not consistent with witness accounts
I have biased this model against both possibilities by taking aircraft speed lower than the evidence shows, and an extremely optimistic flight path.
How does the plane execute this turn without banking to this angle?