Comment on the “Impossible Turn” (This is a long post but it is packed with a lot of important information)
The so-called “Impossible Turn” was coined when pilots incurred an engine failure and attempted to turn back and land at the airport they had just departed. The reason it was termed the “impossible Turn” was the fact the pilots attempted to make the turnback without any understanding of (1) How much altitude was necessary to make the turnback successful and (2) If one new how much altitude was necessary for the turnback, what return flight profile was used to obtain that given altitude. Many flight instructors would go out and practice this turnback maneuver by reducing the power to idle and trying various bank angles and airspeeds to see what scenario would provide them with the least altitude loss. In some cases they would determine the altitude loss for a 180 degree turn and some would use a 270 degree turn. The problem is that without a true understanding of both the geometry of the turnback maneuver and the aerodynamics of the turnback maneuver, attempting to extrapolate this altitude loss from one set of conditions to another can be fatal. There are three variables that determine whether the turnback maneuver is “impossible” or “possible”. The first is the aerodynamics of the aircraft you are flying. The second is the environment (i.e. wind), and the third is the pilot skills. I am not going to address the issue of obstacles around the airport because this can be addressed after the first three issues above. If a combination of the aerodynamics and environment tells you that it is truly an “Impossible Turn” for the altitude you are at when the engine fails, then it is an “Impossible Turn” no matter how good your stick and rudder skills may be.
There are various types of turnback scenarios that one can utilize, but the one that is the optimal from the standpoint of the minimum runway length required, is the teardrop turnback maneuver. This maneuver has three segments starting at the point where the turnback is initiated. Under no wind conditions, the first segment is a turn from the upwind heading rolling out on a heading that points directly at the departure end of the runway. The second segment is a wings level glide toward the departure end of the runway (DER). The third segment is a final turn that aligns the aircraft over the centerline of the runway with the wings level. Each segment may have to be flown at different indicated airspeeds. Therefore, from an aerodynamics standpoint we have two segments involving gliding turns and one segment involving a wings level glide. If we all understand “basic aerodynamics” (i.e. what’s in the Handbooks of Aeronautical Knowledge, Chapters 3, 4, and 10), we know that the wings level glide should be flow at the angle-of-attack for maximum L/D.
In regard to the gliding turn segments, in order to minimize the altitude loss in the turns, one needs to minimize the altitude loss per degree of turn. Again, “basic aerodynamics” allows one to determine the altitude loss per degree of turn. It is obtained by dividing the aircraft rate of descent by the aircraft rate of turn. When you determine this quantity you find the following:
Altitude loss per degree of turn = (F1 * F3) /(F2*F4)
Where F1 is the wing loading (W/S)
F2 is the density of the air
F3 is the bank angle function
F4 is the aerodynamic function and is equal to CL *(L/D)
CL is the lift coefficient
L/D is the lift to drag ratio
The entire information on the altitude loss during the turning portion of the turnback maneuver is in this simple formula. These are four independent parameters that can be varied in any manner. If you want to minimize the altitude loss per degree of turn one, wants to minimize F1 and F3and maximize F2 and F4.. It is easy to see that lower aircraft weight and higher air density will reduce the altitude loss in the turn. However, all the information that we as pilots want to know about how to perform the turnback maneuver is contained in the bank angle function (F3) and the aerodynamic function (F4 ). One finds that to minimize the bank angle function the turnback maneuver must be flown at a bank angle between 45 and 46 degrees ( there is a slight dependence on the L/D ratio),. However, one also finds that the variation in F3 is very small between 40 and 50 degrees of bank (only varies by a few percent), so flying exactly a 45 degree bank angle is not very important (40 degrees will do just as well). The aerodynamic function is where the real issue comes into play. This function maximizes just as the aircraft approaches the accelerated stall speed for the bank angle being flown. Thus, if one really wants to minimize the altitude loss per degree of turn, one would need to fly just above the accelerated stall speed for the corresponding weight of the aircraft and bank angle used in the turnback. This is not practical from a safety standpoint, since I would suggest that if you flew at a hair below the stall angle-of-attack you would probably be attempting the “impossible turn”. If one flies at 5-10% above the accelerated stall speed you will only give up about a 5-10% increase in altitude loss per degree of turn. The importance of the formula for the altitude loss per degree of turn is that one can determine how much penalty in altitude loss per degree of turn you get by changing the aircraft weight, density altitude, bank angle, and angle-of-attack. With the above information you can now determine the altitude loss as a function of distance from the departure end of the runway.
The above covers just the basic aerodynamics of the tunback maneuver. If we now consider the geometry of the teardrop turnback maneuver in a no wind condition, it is easy to show that there are two important characteristics of the teardrop pattern. First, when the aircraft completes the first turning segment and is pointed directly at the departure end of the runway, the distance from that point to the runway is exactly equal to the distance from the departure end of the runway to the point that the turnback was initiated. Second, the angle of intercept between the aircraft heading and the runway centerline is only a function of the radius of the first turning segment divided by the distance from the departure end of the runway to the point at which the turnback is initiated. Thus, the geometry tells one that there is a region close to the runway equal to the diameter of the first segment that would force to aircraft to come in perpendicular to the runway right at the departure end of the runway. This is what is called the “region of impossible turn”, because the aircraft would require a 90 degree turn at very low altitude to get over the runway center (a very dangerous type of turn, especially when on a tailwind and very close to the ground).
With the above information one can estimate the minimum altitude required for a “potentially successful” turnback maneuver. This altitude will not be constant but will be a function of distance from the departure end of the runway. So determining some minimum altitude and using this for the turnback can be potentially fatal. If one asks is there a way to obtain an upper bound on what the required altitude would be the answer is “yes”. In order to get this estimate one must add the altitude loss in the two turns to the altitude loss in the wings level glide. If the pilot flies the aircraft at the angle-of-attack for maximum L/D (need to fly the correct speed for the weight of the aircraft), the altitude lost in the wings level glide is just the distance from the runway to the point where the turnback is initiated divided by the L/D ratio. Just as a point of information, the maximum L/D is achieved at a fixed pitch attitude and is independent of the weight of the aircraft or the altitude. So if you know the proper pitch attitude for maximum L/D, you just fly the pitch attitude and you will be at the proper airspeed for the weight of the aircraft.
That’s the easy part. The first and third segments are the gliding turns and there is where one needs to utilize the above formula for the altitude loss per degree of turn. Since the turnback maneuver will always involve a first segment turn of no more than 270 degrees, one can calculate the altitude loss by multiplying the altitude loss per degree of turn by 270 degrees. Since there are four variables in the formula, the best way to handle that is by assuming the aircraft is at gross weight, sea level density, bank angle of 45 degrees and angle-of-attack just above the accelerated stall speed. Then one can correct that for aircraft weight, air density, bank angle being utilized and how close to the accelerated stall you want to fly the maneuver. This would allow you to obtain the maximum altitude loss in the first turning segment. The last turning segment would be bounded by a 90 degree turn back to the runway heading. Thus, one could similarly determine the altitude loss in this 90 degree turn. Note that one might want to use a much shallower bank angle when close to the ground for this final turn. This would increase the altitude loss because the bank angle function will increase significantly.
Finally, I suppose that if you fly aircraft at high altitude and high speed you have heard the term “coffin corner”. There is an equivalent “coffin corner” for the turnback maneuver. It occurs on the third segment of the turnback maneuver, i.e the final gliding turn at low altitude. If the pilot finds himself beginning to overshoot the centerline of the runway, there is the urge to steepen the bank angle to prevent the overshoot. Without power, the only way to increase airspeed to prevent the aircraft from entering an accelerated stall is to lower the nose and thus give up the remaining precious altitude. Therefore, pilots must understand that the maximum bank angle in the final turn is going to be controlled by the wings level glide speed flown in the second segment. The bank angle must never exceed this value to prevent an accelerated stall from occurring. When we bring in the wind issue, the pilot will be on a tailwind on this final segment and thus the potential for overbanking and entering an accelerated stall will always be there.
Once you have calculated this altitude, you will now need to add a pad for both pilot skills and the fact that the aircraft is not aerodynamically perfect. One should add the same factor for the aerodynamic imperfection on both the turning segments and the wings level segment, however, pilot skills should be weighted more heavily on the turning segment than on the wings level segment. Finally, since this minimum altitude required for the turnback maneuver is based on flying a given teardrop pattern, the pilot must fly this teardrop pattern exactly, and only modify it slightly to dissipate excess altitude. If you change the geometry of the turnback pattern, all bets are off on the success of the turnback maneuver. There is additional information in regard to incorporating the effects of the wind that I will not discuss in this post. But if anyone is interested I can provide you that information.
As a final point of information, even if one new the minimum required altitude for the turnback as a function of the distance from the departure end of the runway (I doubt anyone can remember what that altitude would be at any distance from the runway after an engine failure), a decision would have to be made whether to turn back or not. This is not a good way to mitigate the risk of estimating the wrong required minimum altitude and actually flying an “Impossible Turn”. A way to mitigate the risk is to use the knowledge of the required minimum altitude for the turnback and convert that into a minimum runway length as a function of distance from the departure end of the runway at which the turnback is initiated. Thus, the pilot can view the minimum runway requirement prior to takeoff, and if it greater than the available runway length, you have an “Impossible Turn”. If the required runway length is shorter than the available runway length, one has a “potentially successful” turnback maneuver. However, one may find the runway is only long enough for turnback maneuver within a certain distance from the departure end of the runway. Thus, there would be a narrow envelope for a “potentially successful” turnback.
Although this is a very long post, I hope you can now understand how flying such a geometrically simple teardrop maneuver can be riddled with potentially “fatal gotcha’s”.
Les Glatt
