One interesting idea that sometimes shows up in discussions of turning flight is that of an "unloaded" turn, a turn in which you bank, but avoid the load factor normally incurred by the bank by not simultaneously increasing the AoA by pulling back on the yoke.

The advantage of this technique, so proponents say, is that you get the turn but avoid the increase in stall speed associated with a loaded turn. So there is a free lunch after all.

Well, not really. There are two problems with this technique:

1. It's primarily the load factor which is responsible for the increased rate of turn in a bank, so you're giving that up, and
2. Without increasing the AoA, the airspeed of the aircraft will increase while the bank is held until the load factor ends up where it should have been based on your bank angle.

So is there any value at all in the technique? Let's run some numbers, using this diagram and formula as the basis of our calculations:

In the table below, the first three entries in the table are "true banked turns" where the AoA is increased as the bank is entered to keep the airspeed the same. I use the term "true banked turn" to refer to a turn in which your turn rate is appropriate for your angle of bank. When this is not the case, such as in a slip or skid, the apparent gravity inside the airplane not acting through the center of your body, but at an angle, tending to slide you along the seat towards the inside or outside of the turn. The present situation is exactly the same as a slip, where the turn rate is less than what you'd expect based on the bank angle.

The entry highlighted in yellow is the unloaded turn. I show two values for some entries in the unloaded turn row, because the airspeed increases steadily during the maneuver.

Here are some interesting observations regarding the calculations:

• The smallest turn radius occurs with the 60° true banked turn, as you’d expect, but in this case, the aircraft stalls.
• The next best turn radius occurs with the 45° bank, with a 11 knot margin over the stall speed.
• The unloaded 60° banked turn has the third best performance, but the aircraft will steadily accelerate, generating an increasing load factor and increasing stall speed. Interestingly, the turn radius does not change as the load factor increases, because the increased velocity exactly compensates for it.

The unloaded turn doesn't get the expected performance because it only generates half of the centripetal force that a true banked 60° turn would. So in terms of safety and performance, you're better off maneuvering at the proper airspeed for the bank angle you've chosen.