Les Glatt, Ph.D., ATP/CFI-AI, AGI/IGI
As a requirement in the certification for the Private Pilot Certificate, the Candidate must be proficient in the execution of three Ground Reference maneuvers. These are: (a) Rectangular Course, (b) S-Turns Across a Road, and (c) Turns Around a Point. All three maneuvers depend on understanding how wind affects the ground track of the aircraft.
In most texts on performing ground reference maneuvers, the subject of Tracking a Road, is treated fairly well. However, when it comes to the Turn Around a Point, the discussion is not very detailed. As an example, the FAA “Airplane Flying Handbook” (FAA-H-8083-3A) indicates that the maximum bank angle will occur when the aircraft is on the downwind and the minimum bank angle will occur when the aircraft is on the headwind. In addition, the Handbook states, “Thus, if a maximum bank angle of 45 degrees is desired, the initial bank will be 45 degrees, if the aircraft is at the correct distance from the point. Thereafter, the bank is shallowed gradually until the point is reached where the aircraft is headed directly upwind. At this point the bank should begradually steepened until the steepest bank is again attained when heading downwind at the initial point of entry.” Thus, it is left to the Pilot as to what is meant by gradually changing the bank angle and what should be the radius of the turn that allows the maximum bank angle to be no more than 45 degrees on the downwind.
In order to answer these questions and provide the Flight Instructor and the Pilot with the very information he/she needs to fly the Turn Around a Point maneuver with precision, we derive the exact solution to the Turn Around a Point maneuver. The exact solution provides the following information to the Pilot: (1) Rate of turn, (2) Bank angle, (3) Wind correction angle, and (4) Groundspeed ratio (i.e., the ratio of the groundspeed to the TAS), as a function of the angular position of the aircraft around the circle. We show that the solution is dependent on a single parameter, the wind speed ratio (i.e., VWind /VTAS), with both the rate of turn and bank angle around the circle proportional to the square of the groundspeed.
However, what is most intriguing is the solution also provides a crucial piece of information to the Pilot, which is the “gradient bank angle”. The “gradient bank angle” is the number of degrees the bank angle must change per degree of angular displacement around the circle, as a function of where the aircraft is relative to the tailwind position. The “gradient bank angle” is found to be nearly a linear function of the wind speed ratio. The resultant behavior of the variation of the “gradient bank angle” is one of the root causes of why Pilots have trouble flying the maneuver with a wind of 10 knots or more.
If we follow the aircraft around the circle starting at the point when the aircraft is on the tailwind, the change in bank angle is zero, i.e. the bank is being held constant at its maximum value as we pass the downwind point. As we move toward the downwind side, the bank angle is being decreased; however, the rate at which the bank angle is decreased is increasing and reaches a maximum near the crosswind point (on the downwind side). For winds speed ratios of 0.3 or less, this maximum value of the “gradient bank angle” is less than 3 degrees per every 10 degrees of angular movement around the circle. During the time the aircraft is progressing from the crosswind point to the headwind point, the bank angle is continuing to decrease; however, the rate of change is also decreasing, until at the headwind point, the bank angle is being held constant at its minimum value. As the aircraft progresses from the headwind point to the opposite crosswind point (i.e. upwind side), the bank angle is increasing, with the rate increasing until it reaches a maximum in the neighborhood of the crosswind point. Again, this maximum in “gradient bank angle” is less than 3 degrees per every 10 degrees of angular movement around the circle. As the aircraft passes the crosswind point, the bank angle continues to increase with the rate of change decreasing until the bank angle is at maximum again on the tailwind, at which time, the bank angle is being held constant at its maximum value for a short period of time. This process than repeats itself.
Since the “gradient bank angle” is the key to the precise execution of the Turn Around a Point, we show that the “gradient groundspeed” parameter, which is the rate of change in the groundspeed around the circle, closely replicates the “gradient bank angle” parameter, and thus can be used as a guide in how to adjust the rate of change of the bank angle around the circle. In addition, we show that there are two primary variables the Pilot needs to observe around the circle. These are the radius of the turn and the groundspeed. The wind correction angle is shown not to be a primary variable since if the radius is correct, the wind correction angle must also be correct.
It is important to understand that these bank angle changes for wind speed ratios less than or equal to 0.3 are less than 3 degrees for every 10 degrees around the circle, and thus the term “gradually” is now quantified. In addition, the exact solution of the Turn Around a Point has been used to determine the radius of the turn which will ensure that the maximum bank angle is never greater than 45 degrees at the downwind point.
Using the information in this White Paper will allow both the Flight Instructor and Pilot not only to be able to fly a more precise Turn Around a Point, but have a better understanding of what is taking place during the execution of the maneuver.
Download the paper here: Flying-a-Precision-Turn-Around-a-Point.pdf