I agree a 3S is not adequate for an EDF. I have a Hyperion 4S 3300mAh 35C and it fits in the Hawk. I can get 5+ minutes, but I do not fly WOT the whole time. I have found that the battery has to be mounted way back on the tray, i.e. toward the wing, to get the CG right. The manual shows the 3S mounted more toward the front. I see no reason that a 4000mAh would not fit, but just make sure the CG is OK. I have the ESC mounted with a velcro strap around the vent holes in the belly and it could be moved back more to help the CG with a heavier battery.