Flight Crew Flight Instructor; Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 90; Flight Crew Total 1760; Flight Crew Type 690
Troubleshooting; Communication Breakdown
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Weight And Balance; Inflight Event / Encounter Fuel Issue; Inflight Event / Encounter Loss Of Aircraft Control
Flight Crew Regained Aircraft Control
Human Factors; Aircraft
Upon walking out to the aircraft; aircraft was already loaded with fuel.  Total fuel on board was 16;000 pounds.  10;500 pounds of fuel was in the left wing. 5;500 pounds was in the right wing which was a 5;000 pound imbalance; outside the maximum allowable imbalance per the aircraft AFM which is additionally indicated on the graph in the QRH. I did a fuel test to verify the fuel indicators were working properly and upon completion of the fuel test; the indications remained the same. Immediately; I spoke up to the PIC saying the aircraft was out of balance and that we need to balance the fuel for takeoff. The PIC told me that it was fine; he had done it before and it would be alright. I spoke up again and was waved off in an aggressive manner because he didn't not want to hear me bring that up. From the PIC; I was told takeoff would be ok and that he would balance the fuel as much as possible on the ground prior to takeoff and the rest once airborne.The Captain started transfer procedure by turning on the crossflow and turning on both left fuel pumps; while turning the right fuel pumps off.  After approximately 20 minutes; no change was noticed. By then; the aircraft was at the hold short and ready to takeoff.  The Captain stopped the transfer procedure and put the fuel pumps in the normal position for that phase of flight. At this point; the Captain dictated the continuation of the flight. The Captain decided to takeoff.  Immediately upon rotation; the aircraft banked to the left because of the imbalance.  Full right rudder deflection was needed causing a rudder limit CAS message to appear. At the same time; full right aileron deflection was also needed just to maintain the runway heading.  Additionally; I was unable to do the 400 ft altitude callout because I was focusing on the aircraft attitude and control inputs during the initial climb. I considered that the primary importance because it was so abnormal. While continuing the climb; I suggested that we disconnect the auto-throttles and pull the right engine back to idle and advance the left throttle as necessary to maintain our climb speed in order to reduce the fuel flow of the right engine; and increase the fuel flow of the left engine to help balance the fuel.  Additionally; it would reduce the thrust on the right engine allowing us to have more control inputs to the right to counteract the left turning tendency that the right engines thrust produces.  The first time I suggested that; I was told to be quiet and let him focus on flying the aircraft.  I suggested again the same thing; further explaining why we should do that.  At that point; the Captain disconnected the auto throttles and positioned them as previously discussed.In the continuation of the climb; we were told to turn left to a heading which put us on course. While in the left hand turn; the aircraft wanted to continuing rolling left and made it very difficult to stop on the assigned heading.  It should be noted; that the autopilot was not used during the climb and also not on during the majority of the flight.  One of the instructions from ATC was to level the aircraft at 16;000 feet.  As the Captain approached that altitude; I advised him the level off altitude was approaching.  He continued climbing through the assigned altitude to an altitude of 16;450 ft before starting a descent back to the assigned altitude of 16;000 feet.  The reason for this; was the Captain was concentrating on keeping the aircraft on the assigned heading/routing during the climb. No deviation was given from ATC.  Also during the climb; the EICAS screen indicated a yellow CAS message of Retrim Right Wing down which indicated the lateral axis is out of trim.  The Captain proceeded to input 5 degrees of right aileron trim; as well as 5 degrees of right rudder trim. With the trim inputs; nearly full right rudder and right aileron deflection were still needed to keep the aircraft on the assigned headings.  Throughout the flight; the rudder limit stayed on multiple times due to complete rudder deflection.  At no other point; did the retrim right wing down CAS message appear.  Once approaching into ZZZ; ATC assigned a speed of 180 kts and the aircraft was unable to do so because of the controllability [issue]. The slowest speed the aircraft could maintain was 200 kts and I advised ATC.  They had no issue with the increase in required speed; but should be noted the aircraft could not adhere to the speed because of the unsafe situation the aircraft was in.Throughout the flight; after the auto throttles were disconnected in the climb; the right thrust level was flown at idle the whole flight to ZZZ and the left thrust lever flown in an advanced position.  Additionally; the whole flight was flown with near max right rudder input as well as right aileron input near max; more than standard.  All while; the aircraft still banked/leaned to the left while flying the FMS headings. Upon landing; I was visibly shaking after the event that had just occurred.  Once the aircraft was parked; I got off the aircraft and went into the FBO.  I immediately contacted my Chief Pilot; asking if he was available to talk.  He said he was unable to talk via telephone call; but could text.  I proceeded to text him a brief summary of what just happened and asked to be crew swapped asap.  He said he would need safety reports and that there would have to be an investigation into the events before I could swap crew members.  Knowing how this would most likely get swept under the rug if I had just told the Chief Pilot; I then called our Vice President; [who] controls the daily operations at the company and overseas all crew pairings.  On the phone I told [the Vice President] I felt unsafe flying the aircraft with that Captain and needed a crew swap.  I was then told that because of where we were and the remaining flights we had together; the only time I could crew swap would be when we arrived back in ZZZ1; the following day.  After some discussion; I agreed I would be willing to fly the last remaining three trips with that Captain and crew swap back in ZZZ1 in order to minimize the impact of crew swapping would have on the company.  The only condition was that I would not be bullied and intimidated by that Captain into flying the aircraft again in any unsafe manner.  After this phone call; I then went back onto the aircraft and we continued two more flights that day.  From ZZZ to ZZZ2; then from ZZZ2 to ZZZ3 where we were overnighting.   One we arrived at ZZZ3; I again asked the Chief Pilot if it was ok if I called him once I arrived to my hotel since he was now free to talk.  When I arrived to my room; I called the chief pilot.  On the phone call; he told me that I was to not write a safety report which contradicted what he told me earlier via text message.  I told him I wanted to and then he told me the politics of doing so would not be favorable to me.  I then asked him what I should do and he said to just drop it and continue flying with the PIC for all remaining trips; even after reaching ZZZ1.   I told him I was unwilling to do that and that I would like to submit one.  At which point; he said to send only to him; not the safety director.  I told him I would send it to all the necessary people.  I got no response. Once that phone call concluded; I then called another pilot at the company to tell him what happened on the flight and proceeded to tell him how I felt unsafe and needed [to be] swapped in ZZZ1.
Corporate pilot reported the aircraft took off; at the direction of the Captain; with a known fuel imbalance that resulted in extreme aircraft controllability issues.