text: ai, Fn, = acceleration and net accelerating 
  force corresponding to sea level 
  aa, Fn, = acceleration and net accelerating 
  force corresponding to altitude 
  
  ~=altitude density ratio 
  
  In order to evaluate the effect of these items on 
  takeoff distance, the following 
  relationships 
  are used : 
  
  if an increase in altitude does not alter ac- 
  celeration, the principal effect would be 
  due to the greater TAS 
  
  ;=(g,yxe) 
  
  f2 1 
  -=- 
  $1 (T 
  
  where 
  
  Si=standard sea level takeoff distance 
  St= takeoff distance at altitude 
  o-altitude density ratio 
  
  From the previous table, some approximate 
  rules of thumb may be derived to illustrated 
  the differences between the various airplane 
  types. A 1,ooo-ft. increase in density altitude  if an increase in altitude reduces accelera- 
  tion in addition to the increase in TAS, the 
  
  191 