A method of real-time analyzing, with a flight management systems (FMS) of an aircraft , a takeoff sequence of the aircraft on a predetermined runway , the method comprising: receiving at the FMS , real-time aircraft variables associated with the aircraft and real-time condition variables associated with an environment in which the aircraft is located; receiving at the FMS , from sensors on the aircraft , real-time data of an actual velocity (VA) of the aircraft and a real-time acceleration (a) of the aircraft ; estimating , using the FMS , a final estimated velocity (VF) based on the actual velocity (VA) and the real-time acceleration (a), wherein the final estimated velocity (VF) comprises an estimation of a velocity that will occur in the future of the takeoff sequence; the method characterised by : calculating, using the FMS , the takeoff reference velocity , using at least one of the real-time aircraft variables and the real-time condition variables, wherein the takeoff reference velocity represents what a value of the actual velocity of the aircraft should be, at a given time, based on the received real-time aircraft variables and real-time condition variables; comparing , using the FMS , the final estimated velocity (VF) to the takeoff reference velocity to determine if the final estimated velocity (VF) is within a predetermined range of the takeoff reference velocity ; and altering , using the FMS , at least one of a thrust, adjusting a flap mounted to the aircraft, or adjusting a slat mounted to the aircraft when the comparing indicates the final estimated velocity (VF) is not within the predetermined range. receiving at the FMS , real-time aircraft variables associated with the aircraft and real-time condition variables associated with an environment in which the aircraft is located; receiving at the FMS , from sensors on the aircraft , real-time data of an actual velocity (VA) of the aircraft and a real-time acceleration (a) of the aircraft ; estimating , using the FMS , a final estimated velocity (VF) based on the actual velocity (VA) and the real-time acceleration (a), wherein the final estimated velocity (VF) comprises an estimation of a velocity that will occur in the future of the takeoff sequence; the method characterised by : calculating, using the FMS , the takeoff reference velocity , using at least one of the real-time aircraft variables and the real-time condition variables, wherein the takeoff reference velocity represents what a value of the actual velocity of the aircraft should be, at a given time, based on the received real-time aircraft variables and real-time condition variables; comparing , using the FMS , the final estimated velocity (VF) to the takeoff reference velocity to determine if the final estimated velocity (VF) is within a predetermined range of the takeoff reference velocity ; and altering , using the FMS , at least one of a thrust, adjusting a flap mounted to the aircraft, or adjusting a slat mounted to the aircraft when the comparing indicates the final estimated velocity (VF) is not within the predetermined range. calculating, using the FMS , the takeoff reference velocity , using at least one of the real-time aircraft variables and the real-time condition variables, wherein the takeoff reference velocity represents what a value of the actual velocity of the aircraft should be, at a given time, based on the received real-time aircraft variables and real-time condition variables; comparing , using the FMS , the final estimated velocity (VF) to the takeoff reference velocity to determine if the final estimated velocity (VF) is within a predetermined range of the takeoff reference velocity ; and altering , using the FMS , at least one of a thrust, adjusting a flap mounted to the aircraft, or adjusting a slat mounted to the aircraft when the comparing indicates the final estimated velocity (VF) is not within the predetermined range. <EOS>