My question is, if we go direct from point A to point C, bypassing point B, as compared to point A to Point C with abeam point of point B inserted into the FMC, will the distance travelled by the a/c be different?
My logic being the FMC will calculate the great circle track from point A to ABEAM point B then another great circle track from ABEAM point B to point C. Will the recalculation differs from a direct great circle track from point A to C ?
99% of the time we navigate using great circle tracks i.e. we follow either straight lines on something like a conformal lambert's conic projection chart or we follow radio signals which of course always follow the great circle track.
Based on the question posed it is clear that A, B and C are not on a great circle track - in simple terms, they would not be on the centerline of an airway defined by a VOR for example. If they were then changing the route from A-B-C to A-C would still cause the aircraft to overfly B.
Since there is a change in routing overhead B then the following applies-
The FMS will calculate a great circle route between A and C - just like if you tracked outbound from a VOR at A on a radial towards C. At some place on this great circle the aircraft will be abeam B and this point on the great circle between A and C is marked at the point abeam B.
If this was not the case, how would the FMS decide where to locate the "abeam B" waypoint?
One will find that the abeam point is a point on the surface of the earth where a great circle passing through A and C intersects a great circle passing through B at an angle of 90 degrees.