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I agree that the FDL should have the jump range roughly compatible to the vulture (16-17 ly). 13 ly in a full combat loadout is just punishingly awful, that's as bad as a fully loaded type 9. The problem with moving the FDL to a class 5 FSD is it will then have a better jump range than the asp (which has a class 5 FSD and is heavier than the FDL). The FDL is in that awkward position where it's too heavy for a class 4 FSD, and too light for a class 5 FSD. FDL carries overcharged (and thus heavy) components for its hull mass, e.g. a class 6 distributor. This makes it a great combat performer, but tanks the jump range.
I am not sure what the solution is, maybe military drives (can't use scoop fuel, but lighter and bigger range)?
Wall of text slightly off topic incoming:
The Viper doesn't necessarily make for a better combat ship compared to the Cobra. It's shields are superior yes, but just like with all of the combat ships its loadout is dictated by the power capacity. The Cobra on the other hand has the same amount of power capacity as the Vulture. Yet the Vulture costs 15 times as much to buy stock. That gives the Cobra the edge in combat, IMO, just based on the fact it has more options when it comes to weapons and internal modules. IE: can support plasma acc or rail guns, as well as more room for shield cells. The Cobra is also double the cost to kit out however so the comparison is kind of moot.
I agree that the Vulture whoops Asp when it comes to combat, but the Asp isn't what I would call a true multi-role ship (Well, actually, it may be the only true multi-role ship in the game if you are not going by the other "multi-role" ships in the game) It's more of an explorer/miner that is capable (to a point) of defending itself while carrying out these other roles. IMO, both ships are in a good spot when it comes to each being able to perform it's duty. With the exception that the Vulture's shields may be a tad OP, while the Asp's may be a tad underwhelming.
The FDL vs Python is a fight that I would love to see performed by better pilots than myself. Both ships, at similar price points, pack one hell of a punch. The difference is the Python can be taken to the nth degree when it comes to outfitting while the FDL tops out fairly quickly (and cheaply). With the biggest disadvantage, as far as the FDL goes, being it's jump range and internal module capacity.
End wall of text and back on topic now:
The best way to balance the FDL's jump range while making it not as crazy as the Asp's (and to make it not suck) is to up it's base tonnage enough to compensate for the added oomph of a C5 FSD. You would also have to balance this with it's speed so a boost to the thrusters may also be necessary. Then again boosting the thrusters to C6 would also throw off the power balance. So something would have to be done about that as well.