PHAK 5-39

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. Figure 5-56. Rate of turn for a given airspeed (knots, TAS) and bank angle. 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: Figure 5-57. Rate of turn when increasing speed. 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. Figure 5-58. To achieve the same rate of turn of an aircraft traveling at 120 knots, an increase of bank angle is required. 120 knots 11.26 x tangent of bank angle R = 1202 11.26 x tangent of 30° R = V2 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 Figure 5-59. Radius at 120 knots with bank angle of 30°. 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. 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 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. The radius of turn (R) can be computed using a simple formula. The radius of turn is equal to the velocity squared (V2) divided by 11.26 times the tangent of the bank angle. R = V2 11.26 × tangent of bank angle Using the examples provided in Figures 5-56 through 5-58, the turn radius for each of the two speeds can be computed. Note that if the speed is doubled, the radius is quadrupled. [Figures 5-59 and 5-60] Another way to determine the radius of turn is speed using feet per second (fps), π (3.1415), and the ROT. In one of the 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