Expansion ratio is an expression of how fast the burn space behind the bullet expands as the bullet goes forward inside the barrel � how much, IOW, that space expands per inch, for example, of the bullet's forward travel.
A barrel ahead of a cylindrical case has a high expansion ratio � a smaller-diameter barrel ahead of a necked-down case has a lower expansion ratio, because the smaller-diameter bullet has to travel farther to expand the burn space behind it by as much as a case-body-diameter bullet expands it in a much shorter forward travel.
In two barrels of the same length, the bullet's trip to the muzzle can quickly double the burn space in a cylindrical case (in about the same distance in the rifling as the distance from the primer vent to the base of the seated bullet), but the burn space behind a bullet from an extremely necked-down case may not double before the bullet reaches the muzzle of a very short barrel.
Another way to look at it is how many times the bullet's travel to the muzzle expands the burn space behind it in a given length of barrel, for a given cartridge. A .22 Long Rifle has a much higher expansion ratio than a .220 Swift � because the bore volume of a rifle-length Long Rifle barrel is several times as much as the net volume of the case's powder cavity. The bullet from a .220 Swift would need an incredibly long barrel for its travel to expand the burn space an equal number of times the volume of the Swift cases's net powder cavity.
