Suppose you have a two uniform beams of equal weight balanced on pivots. You have two equal weights. With one
beam you attached a weight to each end - so the balance point remains in the centre of the beam. With the second beam
you attach both weights to the same end - so the balance point is move nearer to the heavier end. The pivot is positioned
so that both beams still balance.
Suppose you now add (blue) identical weights to the beam while keeping the beams balanced. With the beam with the balance point in the middle you can add 9 weights, the full length of the beam. With the other beam you can only add 6 blue weights. Add any more weights (the red ones) and the beam is going to tip up.
The balanced beams (blue weights only) don't move so there is an upward force by the pivot on the beam equalling the downward gravity force on the beam. Looking at the weights only and ignoring the beam itself then for the beam with the balance point in the centre (zero FOC) the force acting downwards on the beam is 9 times the value of each blue mass and for the beam with the balance point nearer one end (positive FOC) the force acting downwards on the beam is 6 times the value of each blue mass. In both cases this force acts through the beam balance point (its centre of gravity).
The red weights are identical to the blue weights, apart from the colour. We can add 3 red weights to the beam with the positive FOC. Obviously the downward force from these weights is 3 times the value of each weight. Because adding these red weights would tip the beam clearly the downward force from them doesn't act through the pivot but somewhere else as illustrated. (this point on the beam is what is called the 'Centre of Pressure').
OK, now for the conceptual jump. Instead of beams on a pivot suppose we have two arrow shafts magically suspended in mid
air. Same as the beam, one has an identical weight at each end (zero FOC) and one has the two weights at the same end (positive
FOC). We have a large fan and the arrows are initially the same distance from the fan. We switch the fan on so we get an airlow
across the arrows. The air flow creates a drag force on the arrow shafts. We can replace the force generated by the weights
on the beam with the force generated by the drag on the arrow shaft (each weight corresponds with the drag force over the
corresponding length of arrow shaft).
So with the zero FOC arrow the force acting through the arrow centre of gravity is 9 and with the positive FOC arrow the force acting through the arrow centre of gravity is 6 with an addional force of 3 acting through the centre of pressure. Both arrows get blown downwind intially at the same acceleration. However the arrow with the positive FOC tips and this reduces the drag force blowing it downwind. Both arrows have the same mass so the zero FOC arrow which has a higher drag force acting on it gets blown downwind faster than the arrow with the positive FOC.
Last Revision 1 July 2009