Mind you some would say I only squeaked by my engineering physic classes            , but I THINK this is how it works.  All objects ACCELERATE toward the earth at the same constant rate.  Objects do not DROP at a constant rate, but rather ACCELERATE in a perfectly downward direction at a constant rate through the time of fall/flight.  The longer the arrow is in flight the faster it is going toward the earth.  The resultant velocity/force however(the sum of both horizontal and vertical aspects of the velocity/force respectively) will be less than the original velocity as well as determine it's flight path.  This of course is within reasonable velocities.

A higher FOC is generally associated with a heavier arrow so it moves slower and therefore stays in flight longer prior to reaching the target.  This "time of flight" affects the time in which the downward acceleration acts on the arrow.  The longer an arrow is in flight the "faster" it is dropping by virtue of its downward acceleration. This flight of the arrow therefore creates velocity/force vectors, both horizontal and vertical components which are added together to produce a magnitude and direction resulting from both components.

The higher the downward velocity vector AND the lower the horizontal velocity vectors are (more time in flight), the more the resultant force/velocity points downward giving the perception that the arrow's point is dropping faster than the back.  It is, however, not due to the FOC, but more so the resultant velocity vectors.

Hope this makes sense.

awbowman, sounds good for different mass/speed arrows, OP specified different foc with same weight 800gr arrow.

Now take the 800gr high foc arow and put tiny A&A fletches on and compare to the normal foc 800gr 3x 5". I would think the high foc would drop less at distance since it stabilizes earlier and retains more energy.

Here are my unscientific results to testing foc and efoc.  I shot three arrows ICS Bowhunter 500's with a arrow weight of 535 gr, with 250 gr, upfront.  Easton 2018's with 125 gr. up front and a total weight of 565 gr.  And one cx heritage 150's with a total weight of 500 gr with 250 gr. upfront. I shot a group of 5 ICS, 2 Eastons and 1 cx per group.  I could not find nay difference from 20 to 40 yards.  Except for the brain fart fliers the arrows grouped well enough to not matter.  At 40 if I had to call teh good shots ( and at 40 I am not good) the ICS's grouped about an inch or two higher.  The Cx was about 6" lower.  Total mass seemed to mean more than foc.

Is there data out there measuring trajectory with a "bow machine" for arrows with the same weight, same velocity,  same profile, only different FOC?

QuoteOriginally posted by gordydog:
Is there data out there measuring trajectory with a "bow machine" for arrows with the same weight, same velocity,  same profile, only different FOC?

This would be the test I'd like to see and I'd like to see it done into a test medium to study penetration too