Aerodynamics of Flight

1,091 x tangent of the bank angle Example Suppose we wanted to know what bank angle ROT = would give us a rate of turn of 5.25° per second airspeed (in knots) at 240 knots. A slight rearrangement of the formula Example The rate of turn for an aircraft in a would indicate it will take a 49° angle of bank to coordinated turn of 30° and traveling at achieve the same ROT used at the lower airspeed 120 knots would have a ROT as follows. of 120 knots. 1,091 x tangent of 30° 1,091 x tangent of X ROT = ROT (5.25) = 120 knots 240 knots 1,091 x 0.5773 (tangent of 30°) 240 x 5.25 = 1,091 x tangent of X ROT = 120 knots 240 x 5.25 = tangent of X 1,091 ROT = 5.25 degrees per second 1.1549 = tangent of X 49° = X 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. What does this mean on a practicable side? If a given arc due to a greater speed. An aircraft traveling at 120 knots airspeed and bank angle produces a specific ROT, additional is able to turn a 360° circle in a tighter radius than an aircraft conclusions can be made. Knowing the ROT is a given number traveling at 240 knots. In order to compensate for the increase of degrees of change per second, the number of seconds it in airspeed, the bank angle would need to be increased. takes to travel 360° (a circle) can be determined by simple division. For example, if moving at 120 knots with a 30° bank The radius of turn (R) can be computed using a simple angle, the ROT is 5.25° per second and it takes 68.6 seconds formula. The radius of turn is equal to the velocity squared (360° divided by 5.25 = 68.6 seconds) to make a complete (V2) divided by 11.26 times the tangent of the bank angle. 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 V2 takes about 137 seconds to complete a 360° circle. Looking at R = 11.26 × tangent of bank angle the formula, any increase in airspeed is directly proportional to the time the aircraft takes to travel an arc. Using the examples provided in Figures 5-56 through 5-58, the turn radius for each of the two speeds can be computed. So why is this important to understand? Once the ROT is understood, a pilot can determine the distance required to Note that if the speed is doubled, the radius is quadrupled. make that particular turn, which is explained in radius of turn. [Figures 5-59 and 5-60] Radius of Turn Another way to determine the radius of turn is speed using The radius of turn is directly linked to the ROT, which feet per second (fps), π (3.1415), and the ROT. In one of the explained earlier is a function of both bank angle and previous examples, it was determined that an aircraft with airspeed. If the bank angle is held constant and the airspeed a ROT of 5.25 degrees per second required 68.6 seconds to is increased, the radius of the turn changes (increases). A make a complete circle. An aircraft’s speed (in knots) can higher airspeed causes the aircraft to travel through a longer 120 knots R = V2 Example Suppose we were to increase the speed to 240 11.26 x tangent of bank angle knots, what is the ROT? Using the same formula from above we see that: 1202 R = 11.26 x tangent of 30° 1,091 x tangent of 30° ROT = 14,400 240 knots R = 11.26 x 0.5773 ROT = 2.62 degrees per second R = 2,215 feet The radius of a turn required by an aircraft traveling at 120 knots An increase in speed causes a decrease in the and using a bank angle of 30° is 2,215 feet ROT when using the same bank angle. Figure 5-59. Radius at 120 knots with bank angle of 30°. Figure 5-57. Rate of turn when increasing speed. 5-39