Date: 201604
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: VMC
Light: Daylight
Aircraft: Large Transport; Low Wing; 2 Turbojet Eng
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Takeoff / Launch
ATC / advisory: Tower ZZZ
Second aircraft: Commercial Fixed Wing
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Communication Breakdown; Situational Awareness
Second reporter function: Local; Handoff / Assist
Anomaly: ATC Issue All Types; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: In-flight
Result: General None Reported / Taken
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: My leg. Tower cleared us to line up and wait on Runway XXL. As we began to taxi onto runway and still perpendicular to runway heading; tower cleared us for takeoff. Spacing seemed tight; but we still had to make the 90 degree turn before we could start takeoff roll. Even so; I listened to FO's readback of takeoff clearance and no subsequent transmission from tower. So everything seemed totally normal as preceding aircraft was now at normal spacing ahead. So I applied takeoff power and started our takeoff roll. As we accelerated through approximately 100 to 110 knots; I noticed a business jet crossing the runway well ahead of us. I instantly calculated that this aircraft would clear the runway well before we got to his position. I also; at the same time watched to make sure that two other air carrier aircraft waiting to cross runway were holding their position. They were and I continued the takeoff roll. Also at the same time I pointed out to the FO and our jumpseater of the aircraft crossing in front of us. We made normal takeoff and tower told us to switch to departure as if nothing happened. FO readback the handoff transmission. Then he informed tower that the business jet had crossed the runway in front of us during our takeoff roll. This was followed by silence on tower frequency as we switched to departure. We continued on to our destination.


Second narrative: I was working Local Assist. I observed LE1 controller somewhat confused about something that just happened which I did not catch because I was temporarily distracted with watching the traffic operations on another landing runway making sure that the aircraft landed safely. I did not hear what happened but I knew something was not right by the way the local controller was acting. I asked him if everything was ok and he said no. He then was kind of confused because he thought he did not issue a takeoff clearance to an aircraft in position because he was crossing the departure runway at three different points. Because I did not hear what had transpired I was very unsure of what happened myself but I did hear the local controller say that he thinks he just had a runway incursion. I found out later that a business jet crossed Runway XXL with an aircraft departing it at the same time. From my understanding Local Control was trying to issue a landing clearance to Flight X who had just checked on for Runway XXC but local control mistakenly said 'Flight X Runway XXC cleared for takeoff' and the air carrier who was holding in position took it as his departure clearance. The air carrier rolled and lifted with a business jet jet crossing in front of him; but was well clear of the runway before the air carrier was anywhere near his intersection.Personally I feel that I could have done a better job of assisting LE1 but I feel also that we should have had Runway XXR position with another local controller.


Synopsis: Air carrier flight crew and Local Controller reported the First Officer accepted a takeoff clearance that was not for them and they took off while a business jet was crossing downfield. The Local Controller mistakenly said 'cleared for takeoff' with the call sign of an aircraft on final when he meant to say 'cleared to land.'