How do you fly a holding pattern? Most of us probably learned to fly turns at a standard rate with the inbound leg defined by a course to the fix and the time or distance to fly it. The challenge is how to fly the outbound leg – what course and how long to fly it. At issue is the significant distortion of the racetrack pattern with large winds, say about 20 to 30 percent of your airspeed. However, there are alternative ways to fly a hold, including RNAV holding. In the Aeronautical Information Manual (AIM) section on holding, as listed in the Appendix, it allows this option if you have an RNAV system, using either constant bank angle or constant radius turns. Here we review three of the four ways to do holding. Some of you may find the subject of holding interesting but irrelevant to your flying, but to remain IFR current you must fly a hold at least once in 6 months.
Let’s begin with the original way to fly holds using standard rate turns without a GPS or FMS to draw a pattern. The headings and leg times to be flown for an arbitrary wind speed and direction and inbound course can be determined exactly from trajectory equations developed and solved by Les Glatt. Those equations and solutions are described in my website article, “Flying the Perfect Hold,” that refers to Glatt’s articles. The equations determine the outbound heading and how long to fly it, and the solutions are used in his app “Holding Pattern Computer” from Aviation Mobile Apps for your tablet or phone. His papers are also available on the app. The latest version 3.0 now includes entries as well.
In Figure 1, sent to me by Glatt, are two cases for 30 percent quartering winds, left turns, and 1 min inbound legs. They have 45-degree headwinds or tailwinds from the holding side and illustrate the distortions of the patterns that make them so difficult to fly. The x and y scales here are distance but normalized by the true airspeed. Winds are responsible for stretching or shrinking the inbound legs on this plot. The inbound tailwinds in the blue plot show that you cover more ground in a minute.
Figure 1. Two left turn holding patterns for a significant wind of 30 percent of your true airspeed. Here, winds are from 45 degrees (red) and 135 degrees (blue) from the holding side. Figures by Les Glatt.
Without the app on a tablet in the cockpit, these would be impossible to fly correctly. Both cases have 1-minute inbound legs, and the red track has a 35 second outbound leg and an outbound crab angle 5.6 times the inbound crab angle. The blue track has a 137 second outbound leg into the wind, with a crab angle ratio of 1.9. The suggestion that the outbound crab should be 3 times the inbound crab is clearly not correct, since that only applies for very small wind fractions, just a few percent of your true airspeed. And, you would have no way to guess the outbound time.
But with the advent of RNAV navigation systems there are different ways to create and fly holds, which may not be as well known to the general aviation pilot. They’re used in the corporate and commercial aviation sectors, using flight management systems (FMS). These have parallel inbound and outbound legs.
As mentioned in the AIM, you can create holds with constant radius turns. Such turns are also done in the turn-around-a-point maneuver and in RF (radius to fix) legs found in RNP procedures. This hold gives a “pure” racetrack pattern that your RNAV system must create, for which roll steering commands will be generated for lateral tracking with an autopilot. As with the turn-around-a-point maneuver these are flown with a continuously varying bank angle to maintain the radius in a wind.
To create this pattern, its size must be determined and your RNAV system must calculate it. The size includes the spacing between straight sections, which is twice the radius of the turns. There are FAA rules for inbound time or distance given your altitude. Longer inbound times and higher speeds are authorized as you go higher. The radius R of the turns is dependent on the bank angle f, and groundspeed Vg. The AIM suggests a bank angle limit of 25 degrees.
For those who are interested, the formula (See FAA Order 8260.58C, p 1-18) relating the variables is g R tan (f) = Vg2 where g is the gravitational constant 9.8 m/sec2 in MKS units (meters, kilograms, seconds). The largest bank angle occurs when you have a pure tailwind (maximum groundspeed), which occurs somewhere on the downwind turn. Then the radius is chosen from that maximum groundspeed (equal to your airspeed plus the wind speed) and the maximum permitted bank angle. If that maximum bank angle is 25 degrees then the formula is 4.57 R = Vg2. Here, R is in meters and speed is in m/sec (1 nm = 1853 m and 100 knots = 51.4 m/s). With a 25 percent wind speed and 150 knot true airspeed the radius is 2,032 m or 1.1 nm.
The minimum bank angle on the other turn at the upwind point is determined the same way using this radius and solving for tan (f) with a groundspeed that’s now the difference of the TAS and wind speed. That angle is 9.5 degrees in this example, so there is a continuous bank angle change on the turns between 25 degrees and 9.5 degrees. Your GPS/FMS will figure this out and draw the pattern.
This racetrack pattern is used in FMS systems like the Honeywell Apex system as shown here in Figure 2 (left). In addition to the holding pattern, their system creates both parallel and teardrop hold entries as required for your direction of flight relative to the inbound leg. The parallel entry here encroaches significantly on the non-holding side airspace, so the FAA has also created RNP holding to ameliorate that. RNP procedures use RF legs and require crew and equipment authorization. To limit the incursion on the non-holding side, RNP holds allow RF leg turns before reaching the holding fix to keep you inside the racetrack as shown in Figure 2.
Figure 2. A Honeywell Apex FMS flying a constant radius hold and entry (left) as in the video here. An RNP hold entry (right), from a 2011 MITRE study for the FAA on RNAV holds, avoids entering airspace on the non-holding side.
Garmin was one of the seven FMS manufacturers participating in the RNAV hold study for the FAA by the MITRE Corp referenced in the Figure 2 caption. They used their G1000 in a Cessna Citation Mustang, but this RNAV (GPS) is widely used in general aviation. The G700 autopilot is intrinsic to the G1000 and can track turns that require constantly changing bank angles and RF leg turn radii that are small compared to the typical radius of AF (arc to fix) legs. But the key point is that the G1000 can determine the hold pattern, display the hold, and provide autopilot guidance. It has the necessary data to create them, namely the wind, airspeed, inbound course, and time or distance to the fix.
However, in a video showing the G1000 flying a hold in a Cirrus aircraft, their methodology appears to be a variation of the constant radius hold, one that still has parallel inbound and outbound tracks. The video scenario has a 29-knot near crosswind from the non-holding side (about 20 percent of their 150-knot speed) and they flew the (downwind) outbound turn at a constant 3-degrees per second rate as shown on the PFD in Figure 3 and commented on in the video. This is not the varying bank angle that would produce a constant radius turn. They compensated on the inbound turn with a shallow rate, again constant but at about half rate. As shown on the MFD the racetrack pattern has parallel inbound and outbound legs.
Figure 3. RNAV Holding pattern on a G1000 showing a racetrack pattern. There is a 20 percent direct crosswind from the non-holding side. In the video from which this was taken the outbound turn is flown at standard rate and the inbound leg at about half that rate to stay on course. The outbound leg is parallel to the inbound leg. View the video here
So, what methodology are they using? For an arbitrary wind direction, you can’t simply roll into a standard rate turn outbound. For example, if the pure crosswind was from the holding side you would be blown towards the inbound leg during the outbound turn and then need a steeper downwind turn on the inbound, nearly double the standard rate.
One possibility for a general method of flying holds with arbitrary winds and parallel inbound and outbound ground tracks, is to use a standard rate turn on the downwind turn and a lesser constant rate on the upwind turn. When I suggested this idea to Glatt he extended the thought by pointing out that this general case could easily be solved with his general holding pattern equations, and he’s now done that. We’re calling this the “dual rate turn” holding option.
Instead of having a single turn rate and solving for the outbound time and heading, you specify the downwind turn rate (say 3 degrees per second) and solve for the lesser upwind rate and for the outbound time. The outbound heading is known here since you would roll out on the heading that gives a ground track parallel to the inbound course. That heading has a crab angle equal to that on the inbound but in the opposite direction.
What do these patterns (with dual rate turns) look like with strong winds? Figure 4 has right turn patterns calculated by Glatt for 20 percent crosswinds and for 20 percent quartering headwinds, each from both the holding and non-holding directions. The coordinates are distance, not time, and the scales are the same for each. The inbound times are 1 minute. For direct crosswinds as in Figure 4 (left) the outbound and inbound times are equal but the turns are either slightly bulged in or out compared to a constant radius curve, which would be between them.
Figure 4. Dual rate turn holding patterns (right turns) with a 20 percent wind factor, for pure crosswinds (left) and quartering headwinds (right). Downwind turns are at standard rate and the upwind turns are at a smaller turn rate. Patterns from Les Glatt.
As you would expect, the downwind turn at standard rate is stretched in the wind direction so the curve is slightly inside a constant radius. The upwind turn is bulged out from a constant radius and the turn rate is 53 percent of standard in this 20 percent case, which is the scenario in the Garmin video. The curves look to be close to a constant radius turn but they are not. With wind, turns are not 180 degrees since you enter them at some crab angle to the straight legs and exit at the opposite crab angle. The turn into the wind is less than 180 degrees and the downwind turn is greater than 180 degrees.
For strong quartering winds that have components along the straightaways, the outbound time can be significantly different from the inbound. For example, for a 20 percent quartering headwind the outbound leg is 26 seconds, and the shallower turn is 64 percent of standard. You roll out past the abeam point (to the fix) and roll in before being abeam of the start of the inbound leg. The inbound distances are shorter than those for the crosswind cases because of the headwind component.
For quartering tailwinds, imagine that the holding fix is at the end of the outbound leg in Figure 4 (right). This would be a hold with a 26 second inbound leg and 1 min outbound. Stretching each leg an amount that makes the new inbound leg 1 minute results in a new outbound leg longer than 1 minute by an amount you could calculate from these winds and directions. In each case the distortion from a constant radius turn is apparent but is not nearly as distorted as those patterns in Figure 1.
The spacing between inbound and outbound tracks is calculated on the downwind turn using the radius of a 3 degree per second turn in the airmass at your airspeed. Then add twice the radius to the distance the airmass travels perpendicular to the pattern in the time you’re executing the turn (more than 180 degrees on this turn, so more than 60 seconds).
This variation of the RNAV hold is easily implemented in a GPS or FMS system. Their use is required to fly the hold since it must first draw patterns using the solutions for the lesser bank rate and time to fly the outbound straight section. Using a constant but different turn rate on each turn has some advantage over flying varying bank rates throughout the turns, in that the latter are not passenger friendly and are harder to hand fly and hold course. It could also be implemented in the Holding Computer App (and might) so that you could fly it if your GPS doesn’t draw it.
Is this the algorithm that Garmin is using in its G1000? Perhaps, but what is Garmin doing for their other GPS systems? My GTN 750 draws patterns that do not have parallel inbound and outbound straightaways, possibly because it might not be coupled with an autopilot to fly it. What are other manufacturers like Avidyne doing about RNAV holding? While these questions have answers I don’t know them, but I find it intriguing that there are these two different RNAV holding options that each satisfy the AIM holding guidance.
In summary, to fly a holding pattern using a constant 3-degree roll rate is easy in strong winds only if you have the Holding Computer App on a tablet in the aircraft for guidance. Otherwise, they are difficult if not impossible to do correctly. The remaining holds require RNAV to compute and draw the patterns. Either of the two racetrack patterns described here, with constant radius turns and varying bank angle or one using two different bank angles in the turns, is sanctioned by the FAA for RNAV systems and are appealing alternatives to the original standard rate turn holding. What does your RNAV system do?
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 65 years, has the Wright Brothers Master Pilot Award, and is a current CFII. See his website on all his manuals plus numerous articles on GPS and other aviation topics.
