NAVWEPS 00-801-80  AIRPLANE PERFORMANCE  The total retarding for& on the aircraft is  the sum of drag and rolling friction (D+F)  and, for the majority of configurations, this  sum is nearly Constant or changes only slightly  during the takeoff roll.  The net accelerating  force is then the difference  between the power-  plant thrust and the total retarding force,  The acceleration of the airplane at any  instant during takeoff roll is a function of the  net accelerating force and the airplane mass.  From Newton ’ s second law of motion:  or  where  a=acceleration,~fr. per set  Fn- net accelerating force,  W=weight, lbs.  g? gravitational accelerat  =32.17 ft. per sec.*  M= mass, slugb  = WE  The variation of the net accelerating force  throughout the takeoff roll is shown in figure  2.32. The typical propeller airplane demon-  strates a net accelerating force which decreases  with velocity and the resulting acceleration is  initially  high but decreases  throughout the  takeoff roll.  The typical jet airplane demon-  strates a net accelerating force which is essen-  tially constant throughout the takeoff roll.  As a result, the takeoff performance of the  typical turbojet airpiane will compare closely  with the case  for uniformly accelerated  motion.  The riet aicelerating fdrce on  ‘ the airplane,  F,, is the net of thiust, T, drag, D, and rolling  friction, F.  Thus, the acceleration -at any  instant during takeoff roll is:  The pilot technique required to achieve peak  acceleration throughout takeoff roll can vary  considerably between airplane configurations.  In some instances, maximum acceleration will  be obtained by allowing the airplane to remain  in the three-point attitude throughout the roll  until the airplane simply reaches  lift-equal-to-  weight and flies off the ground. Other air-  planes may require the three-point attitude  until the takeoff speed is reached then rotation  to the takeoff angle of attack to become air-  borne. Still other configurations may require  partial or complete rotation to the takeoff  angle of attack prior to reaching the takeoff  speed. In this case, the procedure may be  necessary  to provide a smaller retarding force  (D+F)  to achieve peak acceleration.  When-  ever any form of pitch rotation is necessary  the  pilot must provide the proper angle of attack  since an excessive angle of attack will cause  excessive drag and hinder (or possibly pre-  clude) a successful  takeoff. Also, irisufficient  rotation may provide added rolling resistance  or require that the airplane accelerate  to some  excessive speed prior to becoming airborne.  Figure 2.32 illustrates the typical variation of  the various fbrces acting on the aircraft  throughout the takeoff roll:  If  ‘ it is assumed  that the aircraft is at essentially constant  angle of attack during takeoff roll, CL and Co  are constant and the forces of lift and drag  vary as the square of the speed.  For the case  of uniformly  accelerated motion,  distance  along the takeoff roll is proportional also to  the square bf the velocity hence velocity  squared and distance can be used almost synon-  omously.  Thus, lift and drag will vary lint  arly with dyriamic pressure (4) or P  from  the point of beginning takeoff roll.  As the  rolling friction coefficient -is esscnti&y un-  affected by velocity, the rolling ftiction will  vary as the normal force on the wheels.  At  zero velocity, the normal force on the wheels  is equal to the airplane weight but, at takeoff  velocity, the lift is equal to the weight and  the normal force is zero.  Hence, rolling fric-  tion decreases  linearly with 4 or Vz from the  beginning of takeoff roll and reaches zero at  the point of takeoff.  Revised January 1965  185  Fn=T-D-F  a=&T-D-F) 