the distance varies directly as the square of the  velocity and inversely as the acceleration.  As an example of this relationship, assume  that during takeoff an airplane is, accelerated  uniformly from zero velocity to a takeoff  velocity of 150 knots (253.5 ft. per sec.) with  an acceleration of 6.434 ft. per sec.* (or, 0.2g,  since g=32.17 ft. per sec.*). The takeoff  distance would be:  NAVWEPS 00-801-80  AIRPLANE PERFORMANCE  the runway requirements.  The minimum take-  off distance is obtained by takeoff at some  minimum safe velocity which allows sufficient  margin above stall and provides satisfactory  control and initial rate of climb.  Generally,  the takeoff speed is some fixed percentage of  the stall speed or minimum control speed for  the airplane in the takeoff configuration.  As  such, the takeoff will be accomplished at some  particular value of lift coefficient and angle of  attack. Depending on the airplane character-  istics, the takeoff speed will be anywhere from  1.05 to 1.25 times the stall speed or minimum  control speed.  If the takeoff speed is specified  as 1.10 times the stall speed, the takeoff lift  coefficient is 82.6 percent of CL- and the angle  of attack and lift coeticient for takeoff are  fixed values independent of weight, altitude,  wind, etc. Hence, an angle of attack indicator  can be a valuable aid during takeoff.  If the acceleration during takeoff were reduced  10 percent, the takeoff distance would increase  11.1 percent; if the takeoff velocity were  increased 10 percent, the takeoff distance  would increase 21 percent. These relation-  ships point to the fact that proper accounting  must be made of altitude, temperature, gross  weight, wind, etc. because  any item affecting  acceleration or takeoff velocity will  have a  definite effect on takeoff distance.  To obtain minimum takeoff distance at the  specified  takeoff velocity, the forces which act  on the aircraft must provide the maximum  acceleration during the takeoff roll.  The  various forces acting on the aircraft may or  may not be at the control of the pilot and  various techniques may be necessary  in certain  airplanes to maintain takeoff acceleration at  the highest value.  If an airplane were to land at a velocity of  150 knots and be decelerated uniformly to a  stop with the same acceleration of 0.2g, the  landing stop distance would  be 5,000 ft.  However, the case is not necessarily that an  aircraft may have identical takeoff and landing  performance  but the principle illustrated is that  distance is a function of velocity and accelera-  tion.  As before, a 10 percent lower accelera-  tion increases  stop distance Il.1 percent, and a  10 percent higher landing speed increases  landing distance 21 percent.  Figure 2.32 illustrates the various forces  which act on the aircraft during takeoff roll.  The powerplant thrust is the principal force to  provide the acceleration and, for minimum  takeoff ,distance, the output thrust should be  at a maximum.  Lift and drag are produced as  soon as the airplane has speed and the values  of lift and drag depend on the angle of attack  and dynamic .pressure.  Rolling friction results  when there is a normal force on the wheels  and the friction force is the product of the  normal force and the coefficient of rolling  friction.  The normal force pressing the wheels  against the runway surface  is the net of weight  and lift while the rolling friction coefficient is  a function of the tire type and runway surface  texture.  The general relationship of velocity, accel-  eration, and distance for uniformly accelerated  motion is illustrated by figure 2.31. In this  illustration., acceleration distance is shown as  a function of velocity for various values of  acceleration.  TAKEOFF PERFORMANCE.  The mini-  mum takeoff distance is of primary interest in  the operation of any aircraft because  it defines  = (253.5)*  (2)(6.434)  =5,ooo ft. 