If you’re asked about the minimum ground turning radius of the airplane you fly, you probably know the number or at least you know where to find it in the Pilot’s Operating Handbook (POH). What if the question is about the minimum turning radius when the airplane is flying? The answer might not be that simple, given the number of factors it depends on. However, can you provide an approximate number? What bank angle and airspeed would you adopt to fly such a turn? How much bank is actually worth it for the type of airplane you’re flying? What are your minimums, so to speak?
If you aren’t so sure about your answers, this article might be just right for you—especially if you fly low-powered airplanes.
As you know, the knowledge and the practice of this maneuver can be an important safety factor if you fly near mountain areas, if you do aerial work, or in general if you ever need to take an evasive action which requires a tight turn while maintaining altitude.
Wouldn’t it be nice to have a pictorial tool, independent of the type of airplane, which allows a discussion of the main factors that determine a turn with a minimum radius? Here we keep the equations to an absolute minimum, but the numbers, which are important, can be calculated.
The main factors that determine a turn with a minimum radius are a combination of slow airspeed and a high bank angle. In a coordinated level turn, the increase of the bank angle is mainly limited by the engine power available and by the maximum load factor. The latter depends on the airplane category: normal, utility or acrobatic, which, in turn, depends on its weight and configuration (gear and flaps). As you know, maximum load factors must be respected to ensure the structural integrity of the aircraft.
Furthermore, increasing the bank angle also increases the stall speed. This increase can be represented by a factor. For example, a bank angle of 60 degrees implies a 41% increase on the stall speed. This can be represented by the factor Ks = 1.41. Let us call this the Stall Speed Factor.
Because the bank angle increases the stall speed, the reduction of the airspeed is dictated by the impending stall if engine power is not a problem. In practice, we want to fly with a safety margin above the stall. Therefore, we can express the airspeed as a percentage above the stall speed. We will call this the Safety Speed Factor, Ka. For example, Ka = 1.2 means that the turn is flown at an airspeed 20% higher than stall speed.
By now, you’re probably wondering why we need these factors, Ka and Ks. The reason is, as mentioned before, we want to keep this discussion generic and independent of the airplane. Since the stall speed is very dependent on the type of airplane we need to introduce yet another factor: the Turning Radius Factor. Now, we can express the turning radius, in meters, as follows:
Vs² x Kt
where Vs is the stall speed in level flight, in knots calibrated airspeed (KCAS), and Kt is the term which is independent of the airplane. This equation is valid as long as the turn is executed in still air, in coordinated level flight, with a constant airspeed and the air compressibility can be neglected.
The equation tells us that small turning radii can be obtained by decreasing the stall speed or by decreasing Kt or both. Even a small reduction of Vs has an impact on the turn radius given its dependency on the square of the speed. For example, if Kt is kept constant, a 4-knot reduction on a stall speed of 50 knots reduces the turning radius by 15%. Note that a reduction of Vs can be achieved by deploying flaps.
While Vs can be estimated by consulting the airplane POH, the Turning Radius Factor can be determined using the figure provided. This figure displays the relationships between the Turning Radius (through the Turning Radius Factor, Kt), the stall speed (through the Stall Speed Factor, Ks), the Load Factor, the airspeed (through the Safety Speed Factor, Ka), and the density altitude (DA). This is accomplished for bank angles ranging from 20 to 70 degrees. The example provided in this figure illustrates how Kt is evaluated by following the various guide lines displayed in red. Note that graphical interpolation is required.
Besides the numbers, the figure tells us some important facts: as expected, a decrease of Kt—and consequently of the turning radius—requires a decrease of the aircraft speed, by reducing Ka as much as possible to a value near 1.0, and by increasing the bank angle. Also, Kt decreases when flying in lower density altitudes.
Note that increasing the bank angle up to 45 degrees decreases Kt significantly while keeping the stall speed factor below 1.2, that is, an increase up to about 20%. Also, the load factor is less than 1.5. This can be important since the maximum load factor with flaps extended—for a great number of airplanes—is 2.0. This sets a limit of 60 degrees on the bank angle.
On the other hand, when the bank angle is increased from 45 to 70 degrees, the decrease of Kt is not as significant as before. However, the stall speed factor increases up to 70% and the load factor increases up to 2.9. Remember that as the bank angle increases, more engine power is required to sustain level flight. Just to make matters worse, when the airspeed is close to the stall, the airplane will be flying in the region of reverse command of the speed-drag curve, which also demands engine power.
Thus, in a relatively low-powered airplane we might lose the benefit of the increased bank angle beyond 45 degrees, if the speed margin also has to be increased to get out of the “trap” given by this region of the speed-drag curve. For example, consider a bank angle of 60 degrees. If a safety speed factor of 1.3 is required to sustain level flight, Kt is about the same as that given by a 45-degree bank combined with a safety speed factor of 1.2. This is also a direct consequence of the strong dependence of the turning radius on (the square of) the airspeed. In fact, for a chosen bank angle, we see that increasing Ka from 1.0 to 1.1 means a 21% increase in the turn radius; an increase from 1.0 to 1.2 means an increase of 44%, and an increase from 1.0 to 1.3 implies an increase of 69%.
About the density altitude, the figure reveals that Kt increases by about 3% for each 1000 ft increase of DA. Therefore, it should be of no surprise if you get different values for the turning radius when the density altitude varies—even if we fly the same indicated airspeed. Recall that higher density altitudes are associated with high altitudes, combined with a hot and humid atmosphere.
As suggested, we might want to fly the turn with flaps extended. However, remember that, while a first stage of flaps decreases Vs without much increased drag, a full flaps configuration causes a lot of drag. Thus, flying steep turns with full flaps at slow airspeeds might require engine power which is not available. Again, the consideration about an aircraft operating in the region of reverse command of the speed-drag curve applies.
Finally, from this discussion we suggest that, for most low-powered airplanes, a bank angle between 45 to 55 degrees combined with a small setting of flaps might be a good compromise to achieve turns with small radii. The actual choice of speed margin above stall depends on the engine power available and pilot skills. Recall that the onset of the stall warning provides some margin above the stall.
Now, you might want go out there and practice some tight turns. But, before you do, please take into account these practical aspects:
- Consult the POH to get the stall speeds for different flap configurations. Note that these speeds are usually given for specific flight conditions (e.g. idle power). These might not match those that apply when high engine RPM settings are used. If this is the case, they are the best guess.
- Practice in VMC at a safe altitude and place (remember your HASELL checks).
- Consider taking a flight instructor with you or doing a detailed briefing. When was the last time you practiced the recovery from a fully developed stall or spin?
- Consider starting the practice with small bank angles—25 or 30 degrees, for example—and gradually increasing these values. On the other hand, consider starting with higher Safety Speed Factors and, gradually, reducing them. Whatever your course of action, you can use the figure to determine:
- The load factors. Make sure these are within limits by checking the POH.
- The stall speeds for the corresponding bank angles.
- The airspeeds to be flown during the turn, by applying the corresponding safety speed factors. Consult the POH for conversions between CAS and IAS.
- The turning radii (still air) for the various conditions. Use the actual density altitude. DA calculators usually required the QNH, elevation and temperature.
- Write these numbers on your kneeboard.
- If you use flaps, consider extending them gradually. Again, observe load factor limitations and make sure that the airspeed is less than Vfe.
- This discussion does not account for the finite rate-of-bank (roll-in and roll-out rates) which will influence the turning radius; the lower the rate-of-bank, the higher the turning radius. Be aware that abrupt banking can significantly increase the angle of attack which, at low speeds, already tends to be high. This can be a recipe for a stall and a spin. Anyway, remember that abrupt and full deflection of flight controls must not be attempted at airspeeds exceeding Va.
- The airspeed and the setting of flaps should be adjusted before starting the turn. As you roll in, increase power and angle of attack (pull the elevator) to maintain the airspeed and level flight. The inverse applies as you roll out. Keep a coordinated turn (ball centered).
- The turning radius depends on the wind conditions. You can take advantage if you’re able to turn into the wind.
- We suggest the practice of 180-degree turns. The 360 degree turn is also a good exercise but you might encounter your own wake turbulence.
- 180-degree turns (or higher) take a physical space which is twice the turning radius.
- Take your GPS with you and record your maneuvers and achievements. How do they compare with the numbers? Don’t forget to include the number of times you’ve heard the stall warning. It will be good fun to tell your friends all about it in your clubhouse or hangar!
As a final note: the actual turning radius will also depend on other factors such as the aircraft condition and its actual weight, human factors, weather conditions such as turbulence, etc. So, be advised—no equations or formulae replace the outcome of the actual practice. Fly safe and have fun.