Development of a Takeoff Performance Monitoring System

Nomenclature (contlnued) The paper discusses the development and testing of a real-time Takeoff Performance M Pitching moment (ft_lb) Monitoring System. The algorithm is madeup of two MACH Mach number segments: a pretakeoff segment and a real_time p Roll Rate (rad/sec) segment, q Pitch Rate (rad/sec) One_time inputs of ambient conditions and r Yaw Rate (rad/sec) airplane configuration information are used in the S Reference (wing) area (ft2) pretakeoff segment to generate scheduled performance data for that takeoff. TO, TI' T2' T3 The real_tlme segment uses the scheduled Coefficients of the thrust cubic In true performance data generated in the pretakeoff airspeed segment, runway length data, and measured Temp Temperature (°F or °R) parameters to monitor the performance of the THR Engine thrust (ibs) airplane throughout the takeoff roll. Airplane u Linear speed in the X direction and engine performance deficiencies are detected (ft/sec) and annunciated. An important feature of this _ Control input vector algorithm is the one-tlme estimation of the runway rolling friction coefficient, v Linear speed in the Y direction The algorithm was tested using a six degree (ft/sec) of freedom airplane model in a computer vG Ground speed (ft/sec) simulation. Results from a series of sensitivity vT True airspeed (ft/sec) analysis are also included. w Linear speed in the Z direction (ft/sec) Nomenclature W Airplane Weight (ibs) x any appropriate variable a Acceleration (feet/sec2) _x State vector AO' At' A2' A3 r Discrete control effectiveness matrix Coefficients of the acceleration cubic _th Throttle position (deg) in true airspeed CD Drag coefficient ACD Incremental drag coefficient CL Lift coefficient ACL Incremental llft coefficient D Drag force (ibs.) AT Iteration time step (sec) DRW Y Distance along the runway (feet) A_ Incremental friction coefficient eB Pitch attitude (rad) EPR Engine pressure ratio F Force along an axls (Ibs.) _ Runway rolling friction coefficient Discrete transform multiplier g Gravitational acceleration (ft/sec2) p Alr density (slug/ft 3) Rate of change of height (ft/sec) ¢ Discrete state matrix " Iyy Y_axls moment of inertia (slug_ft 2) Superscripts L Lift Force (ibs) LG Landing gear force or moment . Time derivative (lb or ft_Ib) Estimated quantity m Airplane mass (slugs) Subscripts ................ B Body axes brake Due to braking * Aerospace Research Engineer C Command ** Professor of Aerospace Engineering FSP Due to flight spoilers *** Head, Systems Architecture Branch GSP Due to ground spoilers Nomenclature (continued) and rolling friction coefficient estimation. It consists of two segments: a pretakeoff segment and Subscripts (continued) a real-time segment. For each takeoff the pretakeoff segment is utilized to generate nominal M Measured value performance data particular to that takeoff run. n n-th step The real-tlme segment keeps track of the runway n+1 n+1 th step used, the runway remaining, the runway needed to RWY Runway achieve rotation speed, and the runway needed to total Total force/moment bring the airplane to a complete stop. These XB Along body X-axis lengths and a comparison of the actual airplane performance with the nominal value from the ZB Along body Z-axls pretakeoff segment is used to augment the GO/ABORT decision. Introduction The Pretakeoff Segment While the percentage of initiated takeoffs The airplane acceleration performance is that have resulted in accidents is very small, predicted for two extreme values of rolling accidents in this flight phase account for about friction coefficients: a low value (_-0.005) and a 12% of all alcraft related accidents [I]. Also, high value (_-0.040) using the inputs shown in while the accident rate in all other flight phases Table I. The algorithm consists of three parts as has been decreasing in recent years, those in the shown in Figure I and can be run off-line on the takeoff phase have remained almost constant [I]. onboard computers or on ground support computers The concept of takeoff performance monitoring with the results downloaded to the airplane is nothing new. This phase of flight has been of computers. concern since the beginning of regulated aviation The first part performs a flight manual operation. Several single point performance look-up to determine the recommended engine checks have been proposed [2], as well as some pressure ratio for takeoff, the decision speed, that deal with checking the time required to and the rotation speed. The throttle setting attain a prespecified speed [I]. needed to achieve the engine pressure ratio is The takeoff performance monitoring system also computed. described in this paper has the following The second part of this segment computes the features: airplane's scheduled acceleration performance as * The system is carried on the airplane and follows [3,4,5]. First the aerodynamic hence is airport independent, coefficients are extracted from the aerodynamic * The system detects performance deficiencies data base for the airplane as a function of the by comparing the airplane's present motion variables. The aerodynamic forces and performance with a nominal performance for moments are computed in the airplane stability the given conditions, axis system. These forces and moments are then * The system computes the runway used and transformed into the body axis system. The hence the runway available for further components of the engine forces and moments along action, the body axes are determined using the * The system also predicts the runway manufacturer supplied engine model. A required to achieve rotation speed or to manufacturer supplied landing gear model is bring the airplane to a complete halt. utilized in computing the forces and moments * The system can be configured to operate in generated by it along the body axis system. a fully automated mode. Table I: Inputs for the Pretakeoff Segment The algorithm AMBIENT CONDITIONS At any point during the takeoff roll, the Pressure Altitude amount of runway required to achieve rotation Ambient Temperature speed is a function of the instantaneous speed of the airplane and how well it will accelerate until LOADING AND CONFIGURATION INFORMATION rotation speed. The instantaneous acceleration of Airplane Weight the airplane is given by Center of Gravity Location Selected Flap Setting m The resultant forces acting through the The thrust in the above equation is a function of center of gravity along the body X and Z axes are airspeed and not easily estimated onboard an obtained as airplane. Drag and llft vary as the square of the airspeed. The rolling friction coefficient which FX " FXB + THRXB + LG " (2) depends on the runway and tire conditions is a Btota I XB major source of uncertainty. The airplane FZ " FZB + THRzB + LG _ (3) acceleration is seen to represent a composite ZB measure of the performance of the airplane. A Bt°tal comparison of the instantaneous acceleration with a nominal value for the present airspeed is used The resultant moment about the body Y_axis (the to detect performance deficiencies, pitching moment) is given by The algorithm presesented here attempts to circumvent the difficulties associated with thrust