Why is the centre of mass located ahead of the centre of pressure? And what would happen if centre of mass would be too close or too far away from the centre of pressure?
On most airplanes, the horizontal stabilizer provides a downward lift. The center of mass is between the nose gear and the main gears.
If the center of mass is too aft:
- Stall (and spin) recovery will be difficult or even impossible
- Increases the chance of tail strike
- The plane will tip on its tail if the main gears are not moved aft
If center of mass is aft of center of pressure, then the horizontal stabilizer must provide positive (upward) lift; the tail structure must be made stronger to support the higher lift. The wings will be moved forward of the main gears to keep the aircraft balanced on the ground. Such designs are called Tandem wing. See also this question.
Consider an arrow. Its center of pressure is behind the middle of the arrow due to the fletching (feathers) at its back (aft) end, but its center of gravity is close to the middle. If it isn't pointing directly into the path it is taking, the center of pressure, being behind the center of gravity, pushes in the direction to restore it to pointing where it is going. Were it the other way around, the center of pressure would cause it to diverge from that direction, ultimately turning around. That's why arrows are shot with the feathers in the back, not the front.
Note that the vertical surfaces on an airplane (i.e. the vertical stabilizer and rudder) are on the back of the airplane for the same reason.