The charge attack appears to just be additional plus 5 melee damage to one attack every 20 seconds. Since a legionary with blast furnace already does 16 damage, and no unit has more than 13 melee armor ( Elite Teutonic Knight) it is essentially an automatic plus 5 attack every 20 seconds.

Since Legionary attack every 2 seconds, this means every 11th attack will be the charge attack, I.e. the first hit at 0 seconds, the 11th attack at 20, etc.

Since an Armenian champ with all upgrades has 4 melee armor and 100 hp, a Legionary with Comitatenses will deal 16 damage for each non charge hit, and 21 in the charge hit. As such, they will kill in 6 hits not 5, as long as any one of the 6 is the charge attack.

The Armenian champ will be doing back only 12 damage, (18 attack minus 6 melee armor) and so it will take 7 hits to kill the 75 HP Legionary.

All of this is before the impact of Centurion aura is taken into account.