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Keeping your distanceKeeping your distance

The science of turns around a point

By Nihad E. Daidzic

Ground reference maneuvers are more important than you may think. Frequently regarded as unimportant or boring, ground reference maneuver training is often limited to a few minutes of flight instructor demonstration and brief student practice.

Keeping Your Distance
Illustration by Kevin Hand

However, ground reference maneuvers are an essential part of airport traffic pattern operations, hence of every takeoff and landing. Lack of understanding and poor execution of ground reference maneuvers can result in inconsistent and unstabilized approaches.

According to the FAA, the purpose of ground reference maneuvers is to train pilot applicants to maintain desired ground tracks and airplane control in the presence of winds at low heights above the ground. Ground reference maneuvers require simultaneous division of attention between airplane control, visual scanning for traffic and collision avoidance, and flying proper ground track while maintaining coordinated flight.

Typical training ground reference maneuvers are rectangular patterns/courses, S-turns (across a road), and turns around a point, all part of the private pilot airplane single-engine syllabus. An airplane commercial pilot applicant will practice eights on pylons—one of the more difficult maneuvers to perform consistently. Other ground reference maneuvers such as eights along a road, eights across a road, and eights around pylons (none of which is required on FAA checkrides) may combine the elementary ground reference maneuvers. The best description of ground reference maneuvers that I have seen is in The Student Pilot’s Flight Manual by the late William K. Kershner.

It is often said that good landings are the result of good approaches. Moreover, good approaches are, to a large degree, the result of flying traffic patterns and circuits accurately in arbitrary winds. At the same time, dissipation of an airplane’s total energy (airspeed and altitude) must be accurately managed for required vertical flight path control. These skills are essential when performing challenging low-visibility circle-to-land segments on instrument approaches.

The basics of turns around a point

A particular focus here is on the science behind a turn around a point: a constant-radius and constant-altitude turn around a fixed point on the ground. The maneuver has other practical applications, such as circling over a designated area for surveillance, sightseeing, search-and-rescue operations, or aerial photography. Altitude and power generally remain constant, while bank angle and angle of attack change. An airplane is constantly accelerating and decelerating somewhat while turning. The FAA standard to maintain airspeed within plus or minus 10 knots may sometimes only be possible if the power is managed.

Turns around a point are normally entered downwind at altitudes of 600 to 1,000 feet above ground level (agl) to simulate light general aviation airplane traffic pattern operations. Under no circumstances should the pilot be lower than 500 feet agl. Before practicing any ground reference maneuver, clear the area and complete a premaneuvering checklist, while ensuring plenty of emergency landing sites exist should the engine fail. There are not many gliding options from such low altitudes.

Since the entry is directly downwind, here the groundspeed is fastest, the bank angle is steepest, and the rate of turn highest. The maximum bank angle should not exceed 45 degrees. The entire maneuver is flown by continually and smoothly changing the bank angle and varying the rate of turn to enable a constant-radius turn.

A horizontal (not slant) distance from a reference point is typically 1,500 to 2,000 feet. There is no FAA standard for how accurately the constant radius must be maintained. It is difficult to judge such distances and we often use slant distance, which is OK as long as the altitude remains constant. Distance variations of no more than plus or minus 100 feet should be the goal. Ideally, maximum steady winds should not exceed 30 percent of the airplane’s true airspeed.

Keeping Your Distance
Enter a turn around a point facing downwind. The tailwind increases your groundspeed, so you’ll need the steepest bank of the maneuver at this point to maintain a constant radius. The shallowest bank of the turn is on the opposite side, when the airplane has a direct headwind.



Keeping Your Distance

  1. Entering downwind, bank and groundspeed are at maximum, rate of turn is at its maximum, and the wind correction angle is zero.
  2. Bank angle, groundspeed, and rate of turn decrease and the wind correction angle increases toward the center of the turn.
  3. Crab angle reaches maximum perpendicular to the wind and then decreases, along with bank angle, groundspeed, and rate of turn.
  4. Wind correction returns to zero 180 degrees from the starting point. Angle of bank, groundspeed, and rate of turn are at minimum.
  5. Bank angle, groundspeed, and rate of turn increase as the wind correction angle increases to the outside of the turn.
  6. Crab angle reaches maximum perpendicular to the wind.

Maintaining a constant radius from point A requires constant changes to bank angle and rate of turn. The airplane’s lateral axis always points to B. In this scenario altitude, true airspeed, and power remain constant. The maneuver should be conducted above 500 feet agl and at bank angles of no more than 45 degrees.



Master’s class

In calm winds, a turn around a point is simple; bank angle, groundspeed, and rate of turn remain constant. Consider a steady circular turn at 100 knots true airspeed (KTAS) with a radius of 1,500 feet in no wind: A steady bank angle of 30.6 degrees produces a rate of turn of 6.45 degrees per second. It will take about 56 seconds to complete a 360-degree turn.

Add winds, and the maneuver gets more complicated. Bank angle, groundspeed, and rate of turn are constantly changing, and the maneuver takes a bit longer. With 20 knots of wind and an identical circular ground track, for example, the groundspeed at the turn entry point (zero degrees in the figure on page 37) is 120 knots, with a bank angle of 40.4 degrees. The rate of turn at entry is 7.74 degrees per second. With a straight headwind (180-degree point) the groundspeed is 80 knots, the bank angle is 20.7 degrees, and the rate of turn drops to about 5.2 degrees per second. The groundspeed with a direct crosswind at 90 and 270 degrees is about 98 knots.

With a direct tailwind or headwind, no wind correction angle is necessary. But at the 90-degree and 270-degree points, instantaneous wind correction angle is at its maximum—in this case, about 11.5 degrees (right and left, respectively).

Interestingly, another reference point appears. Draw a line through the airplane’s lateral axis, and it will always point to B (above). This reference point is on a line perpendicular to the wind vector. It could be a few hundred feet on either side of the center depending on the ratio of wind to true airspeed.

The instantaneous wind correction angle is the angle between the true airspeed vector and the groundspeed vector, which are constantly changing. The true airspeed vector is always perpendicular to the instantaneous and variable radius of turn, which is measured from B. The groundspeed vector is always tangent to the circle and perpendicular to the constant radius-of-turn over the ground—from the center. The true airspeed vector lags the groundspeed vector on the upwind side and leads the groundspeed vector on the downwind side of the circle. In a no-wind case, the two centers merge and the rate of turn, bank angle, and groundspeed values are numerically between the maximum and minimum values in turns with steady wind.

While all this may look overly complex (and the science behind it certainly is), the skills you learn performing turns around a point will change many aspects of your flying with improved flight path accuracy and safety. FT

Nihad E. Daidzic is president and chief engineer at AAR Aerospace Consulting and a professor at Minnesota State University, Mankato. He is an ATP airplane multiengine land, gold seal flight instructor, and a FAASTeam representative.


This more in-depth diagram shows approximate still-air ground tracks, wind correction angles, ground- and airspeed, and more.

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