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.
- How to safely reduce the radius of your turn—in case you need to - January 6, 2020
If it gets real tight, why don’t you just apply full throttle, pull up and then stand on preferably left rudder and go the other way? Do a wing over. When it falls off, you are going 180 degrees other way. Works real well unless you are under a bridge or power line.
Agree with Joe. First step is adding full power, convert excess airspeed you started with (assuming cruise speed start) into altitude as you roll into (ideally) upwind turn because as things started getting tight you moved to the downwind side of the valley. Wingover or chandelle depending on what you’re comfortable with, doesn’t have to be pretty, but something you can do consistently. Do it enough to feel it, you won’t have luxury of looking at instruments in situations that demand this maneuver because you need to see what you’re avoiding.
Also suggest you think about maximum three dimensional avoidance maneuvers for if you ever find yourself trying to occupy the same airspace as someone else…full control deflections may be what it takes to save you.
The FAA Airplane Flying Handbook (FAA-H-8083-3B), when discussing turns, states (page 3-11) “the throttle provides thrust which may be used to tighten the turn.” I’m a CFI and ex-fighter pilot with many hours of low-altitude, high-G maneuvering flight (using bank and G to control tightness and throttle to control airspeed). I’ve been trying for 2 years to get someone to explain this FAA paragraph. Does anyone have a good explanation?
This article overly complicates a simple concept. Turn radius is a function of only airspeed and angle of bank. A C172 and B747 will turn at the same radius if they are both at the same airspeed and angle of bank. The suggestions for Chandelle (or wingover if permitted) are the best. You just need to know your stall limits.
Eric, I’m an ex-fighter pilot as well, and I don’t know what they mean either, except maybe to prevent loss of airspeed in a tight turn.
If I get into a box canyon and need to turn around, being permitted to do a wing over is the least of my concerns.
I agree. Also, just after saying he is want a picture rather than equations to describe how to achieve the tightest turn radius, he starts by using equations. The author does not define all the key variables. For example, this is his explanation of the variable Kt: Vs is the stall speed in level flight, in knots calibrated airspeed (KCAS), and Kt is the term which is independent of the airplane.” Not definition of what Kt is. Sorry, but I am not going to look at these performance diagrams, do some quick calculations, and then decide how to get my Turbo Saratoga out of a boxed canyon. I am going to full throttle, pull up, and stand the plane on the wing in a wingover to reverse direction, all the while watching my airspeed and listening for the stall warning horn (and keeping a close eye on the terrain).
I am not an ex-fighter pilot, but I agree with Dick C, if you are going to slow down and yank and bank to do a tight turn, that throttle will absolutely help you from falling out of the sky when your airspeed rapidly decays throughout the turn. We are talking about entering a turn from an already lowest airspeed, so you absolutely must have some throttle available, and sometimes lots of it, to finish the turn without losing airspeed or altitude.
Eric P- Sometimes it helps to look at the opposite in order to understand a concept. What if we remove throttle from the exercise? If we are already at a low airspeed in order to get a tight turning radius, and then our engine dies, can we do a tight 45 or 60 degree turn without losing altitude and without losing airspeed? Of course not. So the FAA is correct: Throttle DOES provide thrust which allows us to tighten the turn (and still maintain altitude and airspeed). No throttle? No tight turn while maintaining. You will be in a descending turn if no throttle.
Exactly right, this article complicates a simple procedure. First of all a LEVEL turn is a semi-aerobatic maneuver and is probably unnecessary in the scenario described. First rule in aviation is don’t get so low and slow you can’t turn, everything else follows that! Power isn’t necessary to do a minimum radius turn if you have altitude to sacrifice and by not doing a level turn you unload the wing and stall angle (NOT SPEED) isn’t an issue.
FWIW, we glider pilots practice “the impossible turn” to deal with a tow rope break, towplane emergency, or other situation that could occur at low altitude. The common altitude threshold for a 180-degree turn back to land on the departure runway (but in the opposite direction) is 200 feet AGL We are taught—and teach—that the appropriate response to a rope break or waveoff from the towplane is to roll smartly into a 45-degree bank, in the direction of the crosswind, & maintain proper airspeed.
Why 45 degrees? My college freshman physics book included this straightforward problem. The aircraft loses the least amount of altitude per degree of heading change when the sine of the bank angle, multiplied by the cosine of the bank angle, is largest—and that happens at 45 degrees of bank. Bank angles less than or greater than 45 degrees cause the glider or airplane to lose more altitude in the turn.
So if you’re performance-limited (high/hot/low-power) & have to give up some altitude to execute the turn, roll to 45 degrees & nail the appropriate airspeed.
And thanks for NOT using the term “unload the wing.”
Most of the discussion above has to do with what fighter pilots call “turning in the vertical”. Performing a Chandelle would be a good example of reducing your effective turn radius because you have in effect – shifted or ‘tilted’ your turn radius from being measured on a the strictly horizontal axis to now being measured on a vertical axis which would reduce the turn radius of an aircraft at any given airspeed if viewed from above while looking down at the radius of the imagined track over the ground.
To illustrate this concept – refer to the “coffee cup” theory of turning in the vertical by picking up a coffee cup or a drinking glass. Now with the coffee cup or glass in hand. Hold it level in your hand as if you were going to drink from it. Look at the rim of the glass and consider the radius or diameter of the rim of the cup as depicting the level-turn radius of an aircraft at any given TAS. Make note of the width of the radius of that turn with the cup held level to the floor as if you were going to drink from it. Now tilt the cup at an angle as if you wanted to pour from the cup. By tilting the cup – you are now turning in the vertical and have effectively reduced the radius of turn required in a level turn to a radius that is considerably reduced from what was required in a level turn at the same TAS. This will work whether you pitch the aircraft nose up or nose down.
Now if you were to combine a reduction in airspeed while simultaneously turning in the vertical, such as in performing a Chandelle – you would achieve turning in the least amount of horizontal distance possible.
I found this article confusing, as the Kt factor is near explained, “and Kt is the term which is independent of the airplane”, what is the value of Kt? How does Kt fit into the equation, the whole thing falls apart.
Continued from above:
The two best extreme examples of ‘turning in the vertical’ would be if you were to perform an Immelmann turn by pitching upwards or a Split-S by rolling with a pitch movement downwards. A zero turn radius would be required in both examples while still changing the direction of flight a complete 180 degrees in direction.
Using those two zero-radius turning maneuvers as examples – you can readily see how using the vertical axis or pitch axis of an aircraft during a turn can reduce the effective horizontal turn radius of that turn. So a modest pitch up or pitch down (airspeed & altitude permitting) to ‘turn in the vertical’ while attempting a minimum radius turn is well worth considering.
There is no mention in the article of the stall horn, but in learning the Chandelle we always want to end up with the stall horn screaming right at the end, to have converted every available amount of energy from forward energy to up and around. In doing tests here, at clear altitude, etc. of course, the stall horn is particularly useful to gauge when one is really at a pending stall (and therefore the tightest possible turn radius for the speed) instead of just being theoretically there or trying to use calculated airspeed numbers. AOA gauges make this even more safe and easy, to stay just at the edge of the yellow and learn where that is in terms of speed/power/bank angle. Again a safety pilot (ideally instructor) is smart to have along.
I learned to fly in Pacific Northwest with mountains to the north and east and ocean to west. It was necessary to obtain a mountain checkout before renting an aircraft for cross-country travel. My three hour checkout below the mountain tops used a Cessna 172. The instructor demonstrated and taught the following emergency procedure for reversing direction in a box canyon or narrow valley: (1) carburetor heat on, (2) engine to idle, (3) flaps full, (4) engine to full power, (5) bank angle 45 degrees or as necessary, and (6) use instruments to maintain control as there is typically no visible horizon. The aircraft feels like it is turning on the head of a pin. It works well.
Or you could just immediately enter a bank to 45 degrees and level out after 180 degrees of turn. If you cannot perform a 45 degree bank while looking outside, how would one be competent enough to do it on instruments? After seven thousand hours of flight time spread between helicopters, airplanes, war birds, and gliders, learn to fly a glider it will teach you how to fly. If you can’t fly an aircraft that weighs almost a ton, 500 miles through the mountains without an engine, how can you call yourself a pilot?
Other aspects of a box canyon escape are that the visuals are deceiving. Typically the terrain is rising with the airplane and the visual relationship of horizon to wing or nose attitude is all off. Yeah, you’re going to look at your AOA and pull it around in a minimum turn. Doesn’t happen like that typically; perhaps the panic of the situation has some effect. Better to avoid box canyons about like thunderstorms.
“Furthermore, increasing the bank angle also increases the stall speed.” WRONG! It is the increased g required for a level flight turn that increases the stall speed, not the bank angle. And who said that the turn had to be level?
This article should never have been published. Aren’t these articles supposed to be vetted?
Time to cancel this subscription!!
Yes this was a very confusing article and agree that the wing over is the most suitable maneuver when altitude isn’t a problem, however when altitude is a problem the author does make some good points. Especially the fact that increased bank angle does not lead to a significant decrease in turn radius, however it does lead to the obvious increase in stall speed.
Very constructive and educative comments. Would like to hear from the author.
We need to start teaching the chandelle at the PP level. It’s the tightest radius turn and largest gain in altitude. Just what you need when trying to escape a box canyon. Don’t understand why the author had to take it to such a theoretical level for something relatively simple. Also as a poster above said, the main thing for any performance maneuver is to practice it often.
Too much useless technical mumbo jumbo. Just give the turn radius formula based on GS, then explain the variables. Unless you are flying a large commercial jet, most SEL or light MEL airplanes should turn 180 within 1nm at approach speed. Any one wanting to cut that short, needs to practice in the clear…..
John, great comment about just knowing the turn radius (Or at least having a good idea about relative turn sizes) and forgetting about Kt, etc. FAA-H-8083-2, Risk Management, gives turn radius formula on page 5-11, but it uses V as ft/sec and R as feet. Converting to Knots for V and Nm for Radius, the formula is Radius = Velocity squared divided by 68,571. Times the tangent of the bank (R=(V*V)/(68586*tangent of bank). Thus, at 75 knots, the turn RADIUS is:
11.6 degree standard rate = 0.4 NM (2428 ft) (180 degree turn takes 60 seconds)
20 degree bank = 0.23 NM (1369 ft)
30 degree bank = 0.14 NM (863 ft)
45 degree bank = 0.08 NM (498 ft) (180 degree turn takes 12 seconds)
Slowing to 60 knots reduces radius to 2/3 these numbers (45 degree radius drops to 319 feet-one football field).
So, if your canyon is less than two football fields wide, be very, very concerned!
Oops, danged AOTA correct. The Radius Formula should have said Radius = Velocity squared divided by the product of 68,571 times the tangent of the bank angle. Auto correct added the period.
In all of these comments, as well as the article above, I have yet to see a single person use the correct terms. This tells me that none of the commenters has actually been through a Mountain Flying course.
The correct terms are “Canyon speed” and “Canyon turn”. If you are flying below the tops of the ridges or canyon, you should be flying a determined Canyon speed for your plane. You should be flying high enough above the floor such that you know the width of the canyon supports a 180 degree Canyon Turn in your aircraft, which is a defined maneuver. No Chandelles, no wing overs, no hammerheads etc.
If you don’t have this knowledge, and haven’t practiced these concepts, then you likely shouldn’t be flying in the mountains. Even with proficiency, and experience, people crash in the mountains. Mountain flying, as fun as it is, has its own particular risks associated with it.
I agree. I fly a Husky and before I got into flying it into serious mountain areas, I took a mountain flying course in ID. After establishing the stall speeds for my particular aircraft, we did practice canyon turns (not in actual canyons, but adjacent to vertical cliffs). It is amazing how tight my airplane will turn in a canyon turn. It was an eye-opener, but also came with a warning – “Don’t get into a situation where you need to use it to survive!”
All of the comments are better than the article (who is editing this crap?). I too was a fighter pilot (SCANG F-102, A-7, F-16) in the 70s and 80s. In visual air-to-air maneuvering against an opponent, power is ALWAYS max. (I disagree with the guy who says throttle is used for airspeed — not so in classic dogfight.) Max thrust helps in many ways, but basically the guy with the most energy can always go vertical on his opponent, lose the airspeed, and turn as tight as he needs. The demo with the rim of the glass is a great illustration.
Same is true for a light airplane. Use max power for max vertical, lowest possible speed combined with greatest possible bank all leads to lowest radius turn. I flew and instructed gliders too, and agree that with NO power, tightest turn is almost always 45 degrees of bank, especially with low altitude, low airspeed rope break.
Directed to Ratso…
This is Walt from above. I used the ‘coffee cup’ illustration to explain turning in the vertical…
I’d like to ask you if you’re still involved in flying planes? Are you living in SC?
I’m in the upstate area myself….with a fully restored Navion. I’d appreciate hearing from you sometime. [email protected]
Thanks, happy landings,