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Pilot’s Handbook of Aeronautical Knowledge

FAA-H-8083-25C Version October 20, 2025
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Chapter 5

Aerodynamics of Flight

Rate of turn when increasing speed.
Figure 5-57. Rate of turn when increasing speed.
To achieve the same rate of turn of an aircraft traveling at 120 knots, an increase of bank angle is required.
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 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.

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]

Radius at 120 knots with bank angle of 30°.
Figure 5-59. Radius at 120 knots with bank angle of 30°.
Radius at 240 knots.
Figure 5-60. Radius at 240 knots.

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 be converted to fps by multiplying it by a constant of 1.69. Therefore, an aircraft traveling at 120 knots (TAS) travels at 202.8 fps. Knowing the speed in fps (202.8) multiplied by the time an aircraft takes to complete a circle (68.6 seconds) can determine the size of the circle; 202.8 times 68.6 equals 13,912 feet. Dividing by π yields a diameter of 4,428 feet, which when divided by 2 equals a radius of 2,214 feet [Figure 5-61], a foot within that determined through use of the formula in Figure 5-59.

Another formula that can be used for radius.
Figure 5-61. Another formula that can be used for radius.

In Figure 5-62, the pilot enters a canyon and decides to turn 180° to exit. The pilot uses a 30° bank angle in his turn.

Comparison of 180-degree turn radius at 120 and 140 knots inside a 5,000-foot-wide canyon.
Figure 5-62. Two aircraft have flown into a canyon by error. The canyon is 5,000 feet across and has sheer cliffs on both sides. The pilot in the top image is flying at 120 knots. After realizing the error, the pilot banks hard and uses a 30° bank angle to reverse course. This aircraft requires about 4,000 feet to turn 180°, and makes it out of the canyon safely. The pilot in the bottom image is flying at 140 knots and also uses a 30° angle of bank in an attempt to reverse course. The aircraft, although flying just 20 knots faster than the aircraft in the top image, requires over 6,000 feet to reverse course to safety. Unfortunately, the canyon is only 5,000 feet across and the aircraft will hit the canyon wall. The point is that airspeed is the most influential factor in determining how much distance is required to turn. Many pilots have made the error of increasing the steepness of their bank angle when a simple reduction of speed would have been more appropriate.

Weight and Balance

The aircraft’s weight and balance data is important information for a pilot that must be frequently reevaluated. Although the aircraft was weighed during the certification process, this information is not valid indefinitely. Equipment changes or modifications affect the weight and balance data. Too often pilots reduce the aircraft weight and balance into a rule of thumb, such as: “If I have three passengers, I can load only 100 gallons of fuel; four passengers, 70 gallons.”

Weight and balance computations should be part of every preflight briefing. Never assume three passengers are always of equal weight. Instead, do a full computation of all items to be loaded on the aircraft, including baggage, as well as the pilot and passenger. It is recommended that all bags be weighed to make a precise computation of how the aircraft CG is positioned.

The importance of the CG was stressed in the discussion of stability, controllability, and performance. Unequal load distribution causes accidents. A competent pilot understands and respects the effects of CG on an aircraft.