Figure 5-56.  Rate of turn for a given airspeed (knots, TAS) and  bank angle. Figure 5-58.  To achieve the same rate of turn of an aircraft traveling  at 120 knots, an increase of bank angle is required.  Figure 5-57.  Rate of turn when increasing speed. Figure 5-59.  Radius at 120 knots with bank angle of 30 ° .  5-39 What does this mean on a practicable side? If a given  airspeed and bank angle produces a specific ROT, additional  conclusions can be made. Knowing the ROT is a given number  of degrees of change per second, the number of seconds it  takes to travel 360° (a circle) can be determined by simple  division. For example, if moving at 120 knots with a 30° bank  angle, the ROT is 5.25° per second and it takes 68.6 seconds  (360° divided by 5.25 = 68.6 seconds) to make a complete  circle. Likewise, if flying at 240 knots TAS and using a 30°  angle of bank, the ROT is only about 2.63° per second and it  takes about 137 seconds to complete a 360° circle. Looking at  the formula, any increase in airspeed is directly proportional  to the time the aircraft takes to travel an arc.  So why is this important to understand? Once the ROT is  understood, a pilot can determine the distance required to  make that particular turn, which is explained in radius of turn.  The radius of turn is directly linked to the ROT, which  explained earlier is a function of both bank angle and  airspeed. If the bank angle is held constant and the airspeed  is increased, the radius of the turn changes (increases). A  higher airspeed causes the aircraft to travel through a longer  Another way to determine the radius of turn is speed using  fGLYPH<df00>GLYPH<df00>t pGLYPH<df00>r sGLYPH<df00>cond (fps), π (3.1415), and thGLYPH<df00> ROT. In onGLYPH<df00> of thGLYPH<df00>  previous examples, it was determined that an aircraft with  a ROT of 5.25 degrees per second required 68.6 seconds to  make a complete circle. An aircraft’s speed (in knots) can  Note that if the speed is doubled, the radius is quadrupled.  [Figures 5-59  and  5-60]  Using the examples provided in  Figures 5-56  through  5-58,  the  turn radius for each of the two speeds can be computed.  The radius of turn (R) can be computed using a simple  formula. The radius of turn is equal to the velocity squared  (V$^{2}$) divided by 11.26 times the tangent of the bank angle.  arc due to a greater speed. An aircraft traveling at 120 knots  is able to turn a 360° circle in a tighter radius than an aircraft  traveling at 240 knots. In order to compensate for the increase  in airspeed, the bank angle would need to be increased.  Radius of Turn  V 2  R = 11.26  ×  tangent of bank angle   1,091 x tangent of the bank angle  airspeed (in knots)  ROT =  1,091 x tangent of 30°  120 knots  ROT =  1,091 x 0.5773 (tangent of 30°)  120 knots  ROT =  ROT = 5.25 degrees per second  Example  The rate of turn for an aircraft in a  coordinated turn of 30° and traveling at  120 knots would have a ROT as follows.  1,091 x tangent of X  240 knots ROT (5.25) =  240 x 5.25 = 1,091 x tangent of X  240 x 5.25  = tangent of X 1,091  1.1549 = tangent of X  49° = X  Example  Suppose we wanted to know what bank angle  would give us a rate of turn of 5.25° per second  at 240 knots. A slight rearrangement of the formula  would indicate it will take a 49° angle of bank to  achieve the same ROT used at the lower airspeed  of 120 knots.  1,091 x tangent of 30°  240 knots  ROT =  ROT = 2.62 degrees per second  An increase in speed causes a decrease in the  ROT when using the same bank angle.  Example  Suppose we were to increase the speed to 240  knots, what is the ROT? Using the same  formula from above we see that:  120 knots  11.26 x tangent of bank angle  R =  120 2  11.26 x tangent of 30°  R =  V 2  R =  11.26 x 0.5773  14,400  R = 2,215 feet  The radius of a turn required by an aircraft traveling at 120 knots  and using a bank angle of 30° is 2,215 feet 