Wednesday, February 11, 2015

Flying "teardrop" procedure turns

An interesting situation was brought to my attention a few days ago by a reader (and former instrument student). He (for reasons known only to him) decided to fly the RMN ILS OR LOC RWY 33, in the simulator, using only one VOR and an ADF. Yes, your guess as to why is as good as mine. However, he (correctly) identified that the turn radius depicted by the initial segment starting at HIGAP and arcing to (AFUWY) is way larger than needed in the airplane he was flying (a typical four-place single).

Let’s talk about this type of procedure turn a bit, since you don’t see them very often. Actually, many pilots studying for the instrument written for the last 10 or 20 years have probably seen one at least once, as the Duncan, OK (DUC) LOC RWY 35 used to be an example procedure on the test, and used to have this type of procedure turn. However, it has since been modified and has a (regular) procedure turn. And may not be on the test any longer, though I’ll have to defer to those of you studying for it to let me know about that.

Regardless, it had the same geographic setup as RMN – a VOR a few miles away on final, but offset to one side a couple of miles. How to use it to get turned around and lined up on final? This is a situation where the teardrop procedure turn can be used by the procedure developer. Essentially, from the BRV VORTAC you fly the 122 radial outbound until 10 DME (or intersection with the 279 bearing to EZF), then begin a right turn around to intercept the final approach course on the localizer.

Of course, that turn radius depicted has to cover all speeds of airplanes, right? Accordingly, it is WAY larger than you would need for a light single-engine airplane. If you measure the distance between HIGAP and (AFUWY), it’s about 5.7 nm, meaning a turn radius of half that. But what is the turn radius of, say, a Cessna 172 at 90kts in a standard rate turn?

(Note – way geeky content ahead. CLICK HERE to just skip ahead to the answer and keep reading from there.)

You can easily figure this out if you pull out your copy of “Aerodynamics for Naval Aviators”. What, you say you don’t have one? Of course you do, this is 2015 after all:

This book really has a lot of good stuff in it, which is why it’s still used as a reference, unchanged, since 1965. A quick (?) browse will take you to page 178, which has formulas for turn radius and turn rate. As we are in a standard rate turn, we know our Rate Of Turn (ROT) is 3 degrees per second. What we need to determine is our bank angle from the second equation, then use that in the turn radius formula.

In the second question, solving for phi:

Using V = 90 KTAS and ROT = 3 degrees per second, phi (angle of bank) = 13.9 degrees.

Inserting phi = 13.9 into the first equation gives us a turn radius of……….

2907 ft.

Alternately, you can use Figure 2.29 on the next page if you prefer a chart format. Notice there are two sets of “bank angle”  curves, you use one to solve for radius and the other for rate. Since we know rate, we can work backwards from there. Personally, I prefer the formula method, but that’s me.

Okay, so if you skipped right to here, the radius of a standard rate turn at 90 KTAS is about 2900 feet, or about 1 nm in diameter.

So back to the RMN ILS teardrop – if we entered a standard rate turn at HIGAP, we would be well right of the final approach course after completing the turn. So how to combat that – fly a half-standard-rate turn? Quarter standard rate? No, no need to try to stay on the line – it’s not a DME arc. Instead, begin your turn at HIGAP but then roll out to establish a normal intercept angle to the final approach course. Don’t worry, that whole area between the outbound and inbound legs has been evaluated for obstacles, and as long as you stay at or above 3000 feet until on final, you’ll be safe.

Remember the effect that wind might have on your ground track – a north or northeast wind will tend to push you toward final quicker than normal, and a wind from the west will have the opposite effect, “holding you back” from intercepting the final approach course. The segment between HIGAP and intercepting final is essentially a dead-reckoning course.

Alternately, another solution could be to fly a 10 DME arc from the VORTAC - but obviously this would only work if the facility had DME and the value was published. 

I know what you’re wondering, because I was too. What true airspeed would allow an aircraft to maintain that arc in a standard-rate turn (no wind)? I calculate about 536 KTAS (the method how is left as an exercise for the reader). Not too likely in a Skyhawk, and even more, a “standard-rate”, 3 degrees per second turn at 536 knots requires a bank angle of about 56 degrees. That’s “slightly” past the limit for passenger comfort in commercial air travel, and 536 ktas is “slightly” above the speed limit of 250 KIAS below 10,000 feet anyway (yes, I know, the speed limit is “indicated airspeed” not “true”, but c’mon now).

So what’s the deal with this huge turn radius on the approach?

Above about 180 KTAS, a standard rate turn requires greater than 25 degrees of bank. As a result, faster aircraft use 25 degrees of bank as a maximum, regardless of the “degrees-per-second” that result. (Note I am not a jet pilot, but this comes from AIM 5-3-8j6, which admittedly only references holding patterns. Please correct me if I am wrong.)

At 25 degrees of bank, the speed necessary for that 4.7 nm diameter circle is “only” 273 KTAS. Still pretty quick, but not out of the realm of possibility at the maximum 250 KIAS, depending on atmospheric conditions!

This type of teardrop used to be seen quite often on the military “HI” approach charts, where the idea was to cross the field at a high altitude then have an outbound and inbound leg long enough for the descent – a “high-altitude penetration turn”. But even then, many U.S. military bases do not have them anymore. I’ll have to defer to any military aviators who read this to let me know why.

I have no idea how many of these teardrop procedure turns are around. It doesn’t seem to be very many, and the number is likely getting smaller as the teardrop is replaced with other options. But if you see one, now you know what it’s all about!


  1. Interesting analysis Russ. Thanks for posting!

    1. Thanks Wylie! I'll admit I had a good time coming up with the turn radius numbers, but I had always kind of wondered about that.

  2. Hi Russ!

    Believe it or not, here in Chile teardrops are the rule, procedures turns are inexistents and TAA are almost unknown.

    Of course, our Civil Aviation Authority design teardrops having in mind Airbuses and Boeings, then we face exactly the same situacion you describe.

    Look at my base airport main approach plate:
    At 100 knots in a tipical GA plane, you will have to fly 6 minutes outbound!!!

    What we do? The same you recommend:

    1) To fly a half standard turn.

    2) To fly a less than a half standard turn, normally using a bank angle equivalent to 0,5 or 1,0 times our speed expressed in tenths of knots.

    3) To make, initially a standard turn to intercept the inbound leg with 60º to 90 degrees.

    Greetings from Chile


    1. Oscar, thanks very much for the reply! It's very interesting to me to read about procedures in other countries (and nice to see that we face some of the same issues - and the same solutions).

      Also, thank you for attaching the approach procedure. I much prefer the Spanish version of the term "Missed Approach" - "Apch Frustrada" - while I believe the actual translation is "Failed Approach", it sure seems to read "Frustrated Approach", which is certainly what most missed approaches are!

      Thanks for reading and for the additional information. I am glad to know I have readers outside the U.S. Please feel free to respond to any other articles letting me know how things work in your country - it's fascinating!


  3. Very interesting... nice to see a formula for turn radius. It can boil down to 1 mile per 90 knots for a ROT/easy math.

    1. Thanks, I definitely like rules of thumb! I'm sure you meant a 1 nm turn _diameter_ per 90 knots, but I like it. Easy!