Default Turret Bullet damage type is None (regular ammo).
I will edit in the damage scaling formula later . (it is 923.498 for lvl 34 axton ; 1147.906 / 35; 1415.057 / 36; 1465.762/ 37 o_O missing something ?). Measured ROF in game seems slightly less than 5 bullets per second or 300 RPM. ~1.2 second pauses between bursts.
Scorched Earth rocket damage type is explosive. The ROF of the missile launcher is (to test - but it seems not quite 1 per bullet burst).
Since the damage type is explosive it can benefit from own double up provided slagging.
Impact damage per missile pod = ModifiedScaledBulletDamage * 1.2
I said modified since Either Scorched earth or Double Up LOWER turret bullet damage by 1/1.15 and if you take them both the reduction to bullet damage is 1/1.3 .
Double Up - CHANGES the turret’s bullet damage type from NONE TO SLAG. Which means on UVHM the turret’s bullet damage will get boosted by Slag vs Slag modifier 150% instead of None vs Slag 300%. (you’ll have to slag for your turret AND YOURSELF via other means) … It DOES FIRE DOUBLE the number of bullets per same length of time (doubles gun ROF). 30% chance to slag vs on level enemies per bullet.
Double up provides a lazy way to slag for gun centric Axton but at the cost of potential turret DPS output.