NAVWEPS 00-6OT-60  STABILITY AND CONTROL  where  pb  Generally, the maximum values of rVobtained  by control in roll are approximately 0.1 to 0.07.  The helix angle of roll, $i, is, actually a com-  mon denominator of rolling performance.  If the airplane is unrestrained and sideslip is  allowed, the affect of the directional stability  and dihedral effect can be appreciated. The  conventional airplane will  develop adverse  yawing moments due to aileron deflection and  rolling motio6.  Adverse yaw tends to produce  yawing displacements and sideslip but this is  resisted by the directional stability of the air-  plane. If adverse yaw produces sideslip, di-  hedral effect  creates  a rolling moment opposing  the roll and tends to reduce the roll rate. The  typical transient motions (A) and (B) of the  time history diagram of figure 4.29 show that  high directional stability with low dihedral  effect is the preferable combination.  Such a  combination provides an airplane which has  no extreme requirement of coordinating aileron  and rudder in order to achieve satisfactory  rolling performance. While the coupled mo-  tion of the airplane in roll  is important,  further discussion of lateral control will  be  directed to pure uncoupled rolling performance.  and, one radian=S7.3 degrees  Roll helix angle=&; (radians)  p=rate of roll, radians per second  6=wing span, ft.  V=airplane flight velocity, ft. per sec.  ROLLING PERFORMANCE. The required  rolling performance  of an airplane is generally  specified as certain necessary  values of the roll 1  helix angle, &I$  However, in certain condi-  tions of flight, it may be more appropriate to  specify minimum times for the airplane to  accelerate through a given angle of roll.  Usually, the maximum value of 2% should be  on the order of 0.10.  Of course, fighters and  attack airplanes have a more specific require-  ment for high rolling performance and 0.09  Pb  may be considered a minimum necessary  2v.  Patrol, transport, and bomberairplaneshaveless  requirement for high rolling performance  and a  Pb  2-V of 0.07 may be adequate for these types.  The ailerons or spoilers must be powerful  Pb  enough to provide the required rV’  While  the size and effectiveness  of the lateral control  devices is important, consideration must be  The deflection of the lateral control surfaces  creates the differential lift and the rolling  moment to accelerate  the airplane in roll.  The  roll rate increases  until an equal and opposite  moment is created by the resistance to rolling  motion or “damping  in roll.”  The second  illustration of figure 4.29 defines the source  of the damping in roll.  When the airplane  is given a rolling velocity to the right, the  downgoing wing experiences an increase in  angle of attack due to the helix angle of roll.  Of course, the upgoing wing experiences a  decrease  in angle of attack.  In flight at angles  of attack less than that for maximum lift, the  downgoing wing experiences an increase in  lift and the upgoing wing experiences a de-  crease  in lift and a rolling moment is developed  which opposes  the rolling motion.  Thus, the  steady state rolling motion occurs when the  damping moment equals the control moment.  The response  of the airplane to aileron deflec-  tion is shown by the time history diagram of  figure 4.29. When the airplane is restrained  so that pure rolling motion is obtained, the  initial response to an aileron deflection is a  steady increase in roll rate. As the roll rate  increases  so does the damping moment and the  roll  acceleration decreases. Finally,  the  damping moment approaches the control mo-  ment and a steady state roll rate is achieved.  Revised January 1965  301 