152  NAVWEPS OO-SOT-80  AIRPLANE PERFORMANCE  The forces acting on the airplane during a  climb are shown by the illustration of figure  2.21. When the airplane is in steady flight  with moderate angle of climb, the vertical  component of lift is very nearly the same as the  actual lift.  Such climbing flight would exist  with the lift very nearly equal to the weight.  The net thrust of the powerplant may be in-  clined relative to the flight path but this effect  will be neglectec!  for the sake of simplicity.  Note that the weight of the aircraft is vertical  but a component of weight will act aft along  the flight path.  If it is assumed  that the aircraft is in a steady  climb with essentially small inclination of the  flight path, the summation of forces along the  flight path resolves to the following:  depends on the difference between thrust and  drag (T-D),  or excess thrust.  Of course,  when the excess thrust is zero (T-D=0  or  T=D),  the inclination of, the flight path is  zero-and the airplane is in steady, level flight.  When the thrust is greater than the drag, the  excess  thrust will allow a climb angle depend-  ing on the value of excess  thrust.  Also, when  the thrust is less than the drag. the deficiency  of thrust will allow an angle ~of descent.  The most immediate interest in the climb  angle performance involves obstacle clearance.  The maximum angle of climb would occur  where there exists the greatest difference be-  tweenthrust available and thrust required, i.e.,  maximum (T-D).  Figure 2.21 illustrates the  climb angle performance with the curves of  thrust available and thrust required versus  velocity.  The thrust required, or drag, curve  is nss,~pued  to be ppw=n*~r;.rP nc CnmP  +-+a!  y.“- ..I ‘ ..&. c “I ““IILL  ‘ , y  airplane configuration which could be powered  by either a turbojet or propeller type power-  plant.  The thrust available curves included  are for a characteristic propeller powerplant  and jet powerplant operating at maximum  output.  The thrust curves for the representative  pro-  peller aircraft show the typical propeller thrust  which is high at low velocities and decreases  with an. increase in velocity.  For the pro-  peiler powered airplane, the maximum excess  thrust and angle of climb will occur at some  speed just above the stall speed. Thus, if it  is necessary  to clear an obstacle after takeoff,  the propeller powered airplane will  attain  maximum angle of climb at an airspeed con-  veniently close to-if  not at-the  takeoff  speed.  The thrust curves for the representative jet  aircraft show the typ~ical  turbojet thrust which  is very nearly constant ~with speed. If the  thrust available is essentially constant with  speed, the maximum excess  thrust and angle  of climb will occur where the thrust required  This basic relationship neglects some of the  factors which may be of importance for air-  planes of very high climb performance. For  example, a more detailed consideration would  account for the inclination of thrust from the  flight path, lift not equal to weight, subse-  quent change of induced drag, etc.  However,  this basic relationship will define the principal  factors affecting climb performance. With  this relationship established by the condition  of equilibrium,  the following  relationship  exists to express  the trigonometric sine of the  climb angle, y:  where  Forces forward= Forces aft  T= thrust available, lbs.  D= drag, lbs.  W= weight, lbs.  v=flight  path inclination or angle ,of  climb, degrees  (“gamma”)  This relationship simply states that, for a  given weight airplane, the angle of  climb (7)  T-D  sin y=-  W 