GARMIN TIPS & TRICKS Flying the Hold – Going Beyond the Racetrack

The subject of holding includes a variety of things. Previously I reviewed the how-to routine for putting a hold into your flight plan on the Garmin GTN 650/750. That article did not discuss what a hold looks like when there are winds, nor did it tell you how to fly it perfectly. It turns out there is a precise solution for what a hold should look like, for any value of the wind vector relative to the inbound course. 

Before launching into that I want to review a few other features of holds that are not specific to any particular GPS. First, a hold is a flight leg that’s inserted into your flight plan. There are three kinds of holds, one that you can create, and two that you cannot. Those latter two are inserted on certain procedures when you add the procedure to your flight plan.

The one you can create is a manual hold (HM leg), featured in my previous article. These holds are given enroute when the controller needs to delay you, and also are the last leg of every missed approach. The other two are the hold to an altitude (HA leg) and the hold to a fix (HF leg). This last one is also known as a hold in lieu of a procedure turn, a one-turn hold for course reversal.

Figure 1 shows the HA hold in a departure (on the left) and the HF hold in an approach (on the right), each in its flight plans. The HA leg in this case allows you to climb in that hold to sufficient altitude to get over the rocks west of Yakima before proceeding. The ILS 02 to Sacramento has an HF hold for the purpose of reversing course (we’re approaching in a southerly direction, roughly opposite to the direction of the approach). The HF hold follows the leg ending at the SAC initial approach fix and the hold ends at the SAC final approach fix.

Figure 1. The HA hold as part of a westbound departure from Yakima, Washington (left) and the HF hold in the ILS 02 approach from the north at Sacramento (right).

The differences between these three holds are in the way they sequence. The conventional HM hold requires that you manually sequence out of it. If being held enroute, push the SUSP key when released from the hold and the next time you cross the hold point you will sequence to the next leg. At the missed approach hold, there are no more flight legs. But you might add additional legs to get to your alternate airport, so when ready to depart the hold, again push SUSP.

Sequencing out of the HA hold is automatic when you first cross the hold point above the listed altitude, provided your GPS has a baro-corrected altitude input. Otherwise you have to sequence manually at the altitude (8,000 feet in this case) that ends the leg. Also, sequencing out of the HF hold is automatic after you complete the course reversal. If you want a second turn in that hold, push SUSP while inbound to the hold point. It will sequence automatically after this second circuit.

The topic of hold entries is likely familiar to you so I won’t discuss that. Your GPS has taken all the mental gymnastics of visualization and calculation out of the task. Just put the autopilot in GPSS mode and let it fly the entry that it announces. Flying the hold, with winds, however, is another matter.

You can calculate the shape of the holding pattern for any wind condition. I first learned of these calculations in a paper sent to me for review by its author, Leslie Glatt. More recently, using the formulae of that paper, he developed an app (Holding Pattern Computer – $11.99 on the Apple App store) that will calculate the two parameters you need to determine exactly how to fly the pattern. Those two parameters are the outbound heading and how long to fly it. Using those, with standard-rate turns and constant true airspeed, you’ll do a perfect hold. The GPS does not do this calculation, although in principle it could. Despite that, it does depict some kind of pattern.

The Perfect Hold

How do you fly a perfect hold? Established inbound with the proper crab angle, roll into the outbound turn (at standard rate) at the hold point. Roll out on a heading H (which is unknown) and fly outbound for a time T (also unknown). Turning at standard rate from the outbound leg you will arrive on the inbound course, crabbed at the proper angle, if you chose H and T correctly. If you fly that crabbed heading for the required time/distance (1 min/4 nm) and arrive at the hold point, you’ve done it perfectly.

So it all comes down to knowing H and T. If you have the app on your iPhone or iPad it will tell you those two numbers. For those curious about details on the calculation and formulae for H and T, see my website article, which also gives a number of interesting case studies.

http://www.avionicswest.com/Articles/DriftinHolding.html.

The value of these formulas is in understanding a variety of different cases to get a feel for what you’re up against. For example, you can test the rule of thumb that you triple the inbound crab to get the outbound crab (angle to the reciprocal of the inbound course). That rule arises from the fact that if the winds are light, each of the four legs are about 1 minute duration. A packet of air drifts away from the inbound course by about the same amount while you’re holding course on the inbound and while flying each of the two turns.

So all three of these drifts must be “made up” on the outbound leg, which you can do if you use three times the inbound crab angle while outbound. (Actually, tangents of these angles are involved, but for small angles the tangent is about equal to the angle). This factor of three turns out to be a reasonable guess if the wind fraction f (of your true airspeed) is low, but the number could be vastly different, especially with higher winds.

If there were no wind, the solutions are obvious. The outbound heading H is the reciprocal of the inbound, and the outbound time T is the same as the inbound. If there was a pure tailwind inbound, H is again the reciprocal of the inbound heading, but T is increased over the inbound time by the ratio (1 + 3f)/(1 – f). That is, multiply the inbound time by that ratio to get the outbound time. Holding at 100 knots with a 10-knot inbound tailwind we have f = 0.1 and the ratio is 1.3/0.9 = 1.444. For 60 seconds inbound legs the outbound leg would be 87 seconds. 

For pure headwinds, just reverse the signs in the numerator and denominator in the formula above, so in that case the outbound time is reduced by the fraction 0.7/1.1 = 0.636 and the outbound time is 38 seconds. An interesting case here is with inbound headwinds and f = 1/3.  Then, from our formula, T = 0 and there is no outbound leg; only a continuous turn from the hold point, as shown in Figure 2 (left figure).

Figure 2. Holding pattern without an outbound leg, when the relative wind fraction is 1/3 and there is a pure headwind inbound (left), and the new kind of pattern when the fraction is greater than 1/3 and there is a headwind (30 degrees here) to the inbound course (right). Courtesy of Leslie Glatt.

For pure crosswinds of either direction the ratio is (1 + 3f 2)/(1 – f 2). There is also a formula for the outbound heading (see my web article) which I won’t show here, but needs to be determined by calculation or from the app.

The general case of winds from an arbitrary direction has a pair of equations for H and T that are relatively easy to solve and are given in my article. There are no easy generalizations to come from them however, so they won’t be discussed further. But, Glatt discovered a new type of hold when f > 1/3. For example, with inbound headwinds your outbound turn is less than 90 degrees, and then there is an outbound leg more perpendicular than parallel to the inbound leg, followed by a turn all the way around to the inbound course point. This is also shown in Figure 2 (right) in the specific case of a headwind 30 degrees to the inbound.

  As a further example, suppose there is a quartering headwind inbound (45 degrees to the course). As the wind fraction varies from 0 to 0.3, the outbound time drops from 60 seconds to a minimum or 36 seconds when f = ¼, then rises to 39 seconds at f = 0.3. Over that same range, the outbound crab ranges from 3 to 5.3 times the inbound crab angle. Holding patterns for that case are shown in Figure 3.

Figure 3. Holding pattern with a quartering wind when the winds are into the holding side (blue) and away from the holding side (red). Here, f = 0.3 and turns are to the left. Courtesy of Leslie Glatt.

Clearly, to estimate H and T for your particular situation, in the moment, is quite difficult. So what to do? Your GPS will draw some kind of closed course for the hold, and if you track the magenta line somehow, probably requiring non-standard banking, you’ll get back to the right place. Or, if you have a right seatmate familiar with the holding app, and can get a solution for your winds and wind angle, you could use those numbers. 

Finally, we can hope that the GPS of the future will program in those solutions and the autopilot will fly the perfect hold. Glatt has met with Garmin on implementing those solutions, but that may or may not be in the future. In the meantime, understand how distorted things can get for higher wind fractions and be prepared. One way to reduce the fraction is to fly faster (or stay home).

Dr. Thomassen has a PhD from Stanford and had a career in teaching (MIT, Stanford, UC Berkeley) and research in fusion energy (National Labs at Los Alamos and Livermore). He has been flying for nearly 60 years, has the Wright Brothers Master Pilot Award, and is a current CFII. Read more at www.avionicswest.com