Turn performance is measured using two different parameters, turn rate and turn radius. Turn rate (ω) is the rate of heading change, measured in degrees per second. Turn radius (r) is a measure of the radius of the circle the flight path scribes. Turn performance in a level coordinated turn is controlled only by airspeed and angle of bank. Weight, altitude, load factor, stalling angle of attack, engine performance, and wing loading may limit either the airspeed or angle of bank. This would limit maximum turn rate or minimum turn radius, however, the actual performance would still be determined using only airspeed and angle of bank. The formulas for determining the turn rate and turn radius for an airplane in coordinated flight are on the attached image:
where ω = turn rate, r = turn radius, V = velocity, φ = angle of bank and g = gravity.
If velocity is increased for a given angle of bank, turn rate will decrease, and turn radius will increase. An example of this would be turning a very sharp corner on a bicycle at 5 mph versus trying to turn the same corner at 30 mph. If angle of bank is increased for a given velocity, turn rate will increase, and turn radius will decrease.
The maximum turn rate and minimum turn radius would be achieved in a 90 degrees angle of bank turn, at the airplane’s minimum velocity. However, there are limits on angle of bank and velocity. Minimum velocity, stall speed, is determined by CLmax AOA. Maximum turn performance will be achieved at the accelerated stall speed for whatever angle of bank is being flown. An increase in angle of bank increases the accelerated stall speed, and vice versa.
If an airplane’s limit load is 2 Gs, the maximum angle of bank that it could maintain will be 60 degrees (Figure 1-11-2). An airplane’s thrust limit may also limit its turn performance. Since induced drag is directly proportional to lift squared, an airplane pulling 5 Gs would produce 25 times as much induced drag as in level flight. If the maximum thrust available can only overcome 16 times as much induced drag, then the airplane can only maintain level flight at 4 Gs.
Of the three factors that limit turn performance, CLmax AOA and the limit load factor are found on the V-n diagram at the maneuver point. Assuming the airplane’s angle of bank is not thrust limited, this is where maximum turn performance is achieved. Any deviation from the maneuver point produces an undesired result. If velocity increases at a constant load factor, turn rate will decrease and turn radius will increase. If velocity decreases at a constant load factor, the airplane will stall. If angle of bank increases at a constant velocity, the airplane will stall. If angle of bank decreases at a constant velocity, turn radius will increase and turn rate will decrease.
Turn rate and turn radius are independent of weight. Any two airplanes capable of flying at the same velocity and same angle of bank can fly in formation, regardless of their weights. The load factor and turn performance for both airplanes will be the same, although the heavier airplane will be producing more lift.
Instrument flight requires that turns be made at a standard rate. A Standard Rate Turn (SRT) is one in which 3 degrees of turn are completed every second.
