Date: 201905
Local time of day: 0601-1200
Location: ZZZ.Airport, US
Flight conditions: Mixed
Light: Daylight
Aircraft: B737-700
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Climb
Airspace: Class B ZZZ
ATC / advisory: TRACON ZZZ
Aircraft component: Flap Fairing
Component problem: Failed
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Anomaly: Aircraft Equipment Problem Less Severe; Inflight Event / Encounter Other / Unknown
Detector: Person Flight Crew
When detected: In-flight
Result: Aircraft Aircraft Damaged; Flight Crew Landed As Precaution; Flight Crew Diverted
Contributing factors: Aircraft
Primary problem: Aircraft

Narrative: This was the first leg of day two of a three day. Great FO (First Officer); and we flew the whole month together. Although we were both experiencing continued fatigue and cumulative sleep loss all month due to chronic flight cancellations and re-routes; we both determined that we were fit for duty. All preflight duties were normal; uneventful and not rushed; and we departed on-time. Taxi and takeoff were routine and uneventful. During departure; at approximately 2;000 feet MSL I engaged the A Autopilot and we both confirmed LNAV and MCP Speed on the FMA's (Flight Mode Annunciators). Shortly thereafter; we both noticed that the control yokes appeared to be deflected approximately 4 degrees to the right. I then attempted to 'trim-out' that deflection with right rudder trim; which took approximately 3.5 degrees.We also verified that the engine instruments were all normal and symmetrical as well as the fuel (we were feeding out of the center tank at the time). The aircraft was tracking the LNAV courses satisfactorily at all times; and we were in and out of various scattered-to-broken cloud layers throughout the departure; complete with the usual multiple; frequent frequency changes. We discussed; coordinated and analyzed our situation among ourselves throughout the departure and climbout; we both agreed that the aircraft was in a satisfactory and safe condition; but that there was something unusual with regard to the position of the control yokes and the amount of rudder trim required. We elected to continue toward our destination initially while we continued to evaluate what we were seeing; we discussed numerous suitable airports we could divert to if we decided it was necessary.We continually discussed our observations as well as our options and also our mutual concerns about how the aircraft might handle with landing flaps selected. With the autopilot disengaged; balanced fuel tank indications; symmetrical engine thrust; the aircraft required three degrees of right rudder trim and one degree of right aileron input; and that still resulted in a slight drift (skid) to the left. There was never any abnormal indication with the trailing edge flaps nor the LED's (Leading Edge Devices); no asymmetry and no disagreement; all indications matched flap handle position(s) at every phase/setting; from flaps 10 to 5 to 1 to UP on departure; from UP to 1; 5; 15; 25 and finally 30 during approach. Dispatch forwarded to us an updated TAF for ZZZ1 that indicated we could expect marginal conditions (at or near CAT 1 ILS minimums); 1/2 Mile visibility; OVC 002 hundred ceiling; FG and SN. We became increasingly concerned about that expected weather at destination while feeling conflicted with the desire to get our Passengers to ZZZ1 as well as our ZZZ1-based Cabin Crew as this was the end of their pairing.The FO and I agreed that it was inadvisable to continue to ZZZ1 and the marginal weather there; given that there was some unknown defect and therefore; degradation; with the aircraft. We advised Dispatch that we had an abnormality with our flight controls and that we were going to divert to ZZZ; which was 125 NM off our right wing with VMC conditions and light winds right down the runway in case of any further escalation of the problem. We informed the Cabin Crew of the situation as well as the Passengers and proceeded to ZZZ. Our approach and landing were uneventful and we taxied to the gate. Upon arrival and standing underneath the right wing; we could visually see a 'control rod' protruding through the top of the flap track fairing; commonly referred to as a 'canoe.'Having no further information about this event currently; I am assuming this was simply a mechanical failure; it was not visible to the Crew nor from the cabin.




Synopsis: B737-700 Captain reported a flight control problem inflight requiring excessive trim correction.