Holding pattern heading calculator?

[peter-h]

There seems to be a large number of devices which tell you how to enter a holding pattern, but that operation is usually obvious anyway

What I have not found is a device, or a program, which takes in the current wind vector, your TAS, the bearing of the inbound track (the track to the holding fix) of the hold, and it works out the optimal inbound and outbound headings and the outbound timing.

It must be something that many people have worked out in the past, and modern airliners can fly holding patterns automatically so they must have solved it.

But the only thing I found on google was some patent on a device which does it...

The calculation is fairly simple but does involve nontrivial trigonometry because you need to take proper account of the wind effect on the turns. Just adding 3x the drift on the outbound leg works only for small values of wind/TAS.

It would be useful to have this on say an Ipad, because once airborne it is easy enough to do the "current wind" calculation knowing your heading, TAS, GS, and track.

Here in the UK, in IR training, we have to fly NDB holds and they are much harder than the VOR holds I was doing in the FAA IR. With an NDB hold, you have very poor lateral track guidance on the track inbound to the fix.

 

[Sac Arrow]

My guess is an airliners' flight director or other sophisticated autopilot is just flying the ground track of the hold and automatically compensating for wind drift at any given time, negating the need for calculated heading corrections on the downwind leg, the same as if you "flew the magenta line" of the hold by watching your GPS.

 

[peter-h]

That would suprise me, because you are not supposed to tighten up the Rate 1 (or Rate 0.5, for large jets) turn rate.

There is no way to fly a geometrically perfect (nil wind shape) hold while maintaining a constant rate turn, if there is any wind across the hold.

One could do it by flying one of the turns at less than R1, with the "less than" ratio being precomputed so that the opposite turn is no tighter than R1; then you could fly a pattern on which the two straight legs are parallel.

But I think the jet FMSs precompute the headings, using airdata. Otherwise, if you just turned onto say the inbound track at a heading equal to the track, and the wind was say 100kt across the hold, the autopilot would have to make a big roll correction to achieve the tracking.

 

[HPNPilot1200]

But I think the jet FMSs precompute the headings, using airdata. Otherwise, if you just turned onto say the inbound track at a heading equal to the track, and the wind was say 100kt across the hold, the autopilot would have to make a big roll correction to achieve the tracking.

I believe the box indeed crunches the numbers using the ADC computed wind direction and velocity and comes up with a corrected heading to fly during the entry and turns in the hold. The flight director is usually limited to 25 or 30 degrees of bank.

 

[poadeleted20]

AFAIK, there is no system which does all that. The closest you get is the way the Garmin 430W/530W do it, which is to "draw" the holding pattern based on the charted inbound course and the turns based on standard rate at the current ground speed, and then do its best within bank angle limitations to fly that path. Length is based on either published length in miles, or starting the inbound turn when it computes that it will roll out with one minute to the fix. If you watch it work, you'll see the length and width of the pattern change as your ground speed changes. There is no heading computation at all -- it's all based on turning to make track good, not heading.

 

[Jaybird180]

It would be useful to have this on say an Ipad, because once airborne it is easy enough to do the "current wind" calculation knowing your heading, TAS, GS, and track.

Sorry for threadjacking, but I was also thinking that 'somebody has surely written an app for that'.

 

[peter-h]

You would think so but I haven't found one.

OTOH in the FAA system you don't get the anal attachment to NDB holds which we have here in Europe I never needed fancy heading estimates for the VOR holds I was doing in the FAA IR.

EASA, in its war with the USA, is proposing to force all FAA licensed pilots based in Europe (that is a simple way of putting it) to have to get EASA papers, by April 2014.

I am nearly done with the Euro IR but am having a lot of trouble with NDB holds.

Sure one can work it all out with the circular wind calculator but that is a lot of work while hand flying the aircraft Preparing the hold headings on the ground, from forecast winds, is usually too far out.

 

[HPNPilot1200]

Sure one can work it all out with the circular wind calculator but that is a lot of work while hand flying the aircraft Preparing the hold headings on the ground, from forecast winds, is usually too far out.

Do you fly with a GPS? If so, does it display DTK and TRK side by side?

 

[peter-h]

Yes, and it's trivial to fly holds with a GPS, but that wasn't the Q I was asking

Here in the UK, the portions of the IR test which involve NDB procedures must not involve the sight of any GPS data. GPS is permitted only in the past year or so, and only for enroute sections (in simple terms).

 

[lgtech]

Hi Jason,
The calculator that you describe is an approximate method that was patented by a fellow named Holcomb. This calculator is a very complex tool. However, However, to address your statement above, there is an exact solution to the holding pattern under any wind speed and wind direction relative to the inbound course. This solution gives the pilot the exact inbound wind correction angle, outbound heading and outbound time (measured from the wings level outbound heading) which will will allow the pilot to intercept the inbound course with the CDI centered and with exactly a one minute time to the fix. It has never been published in the open literature. It is very simple to derive, and I was suprised that nobody derived these two simple equations previously. There are two parameters that control the outbound heading and time and these are the wind speed ratio (Vwind/VTAS) and the wind angle relative to the inbound course.
The exact solution show why pilots have a significant amount of trouble holding with a wind speed ratio of more than 0.2. In fact the FAA is the root cause of the problem with the recommendation of using an outbound wind correction angle of 3 times the inbound. This multiplicative factor can vary from a very large number when tracking inbound on a headwind component to one less than two on a tailwind when inbound. In fact when the wind speed ratio is above 1/3 and when inbound on a headwind component, the aircraft is turned less than 90 degrees for the outbound heading and the actual holding pattern looks nothing like you see in any figure on holding patterns. I have called this type of holding pattern a "Type 2" pattern compared to the one we see in textbooks on holding patterns (a "Type 1"). I have taken the exact solution I derived and tested in out on a Frasca 131 simulator flying both "Type 1" and "Type 2" holding patterns. In both cases the aircraft intercepted the inbound radial with the CDI inside the donut and the the inbound time within 1 sec of 1 minute. Unless the pilot understands the "Type 2" holding pattern there is no way he will every get it right using the standard trial and error method.
In fact, one can take these two simple equations and program it into the GPS so that
the pilot has the exact outbound heading and outbouond time before he crosses the fix, thus allowing him to nail the holding pattern on the second circuit after entering the hold.
Les

 

[N175PT]

"Hold Here" is a nice little ap, works pretty well once you figure out how to make it swivel around with your fingers.
Tim

 

[poadeleted20]

Unless you're flying something for which the holding pattern speed limits are an issue, or the winds aloft are upwards of 60 knots at low altitudes, it's darn near impossible to blunder outside the holding pattern airspace unless you do something really weird. In my experience as an instrument instructor, folks who use these little calculator gizmos spend too much effort on the gizmos and not enough on basic VOR orientation/interception skills, which if they had down pat, would obviate the need for the gizmos.

 

[lgtech]

Hi Ron,
There are a number of reasons for a holding pattern. ATC issues one, or lost comm or
troubleshooting an equipment problem. In any event, the pilot should be using this time to prepare for the approach, not worrying about trying to fly the holding pattern. Therefore, If I give you the answer to the holding pattern before you get to the fix, one can concentrate on the preparing for the approach.

As I pointed out in my previous comment , the exact solution of the holding pattern under any wind condition does not require any gizmo's to fiddle with. It shows that the the holding pattern changes character when the wind speed ratio gets above 1/3. In the case of a general aviation aircraft holding at a true airspeed of 100 Kts this corresponds to a wind speed above 30 kts. Just to give you a feel for what I am talking about, try out this particular scenario. Wind speed 40 kts. Wind direction 30 degrees to the left of the inbound course. True airspeed 100kts. Assume this is a non-standard holding pattern. The exact solution to the holding pattern requires the aircraft to turn 68 degrees to the left after passing the fix and fly outbound for 35 seconds. The aircraft then turns left to the inbound course plus and 11.5 degree wind correction angle. The time from the inbound radial intercept to the fix will be exactly 1 minute. If you sketch out the holding pattern you will see that the undershoot/overshoot is not controlled by the outbound heading but by the outbound time. The inbound time is being controlled by the outbound heading. This is exactly the reverse of the method used in the classical holding pattern, where inbound time is controlled by outbound time and undershoot/overshoot of the inbound course is controlled by the outbound heading. My whole point here is that if the pilot is provided with this information through the GPS (which a simple software update can be made), none of the above issues ever come up and the pilot can devote his time to preparing for the approach.
Les

 

[poadeleted20]

There are a number of reasons for a holding pattern. ATC issues one, or lost comm or
troubleshooting an equipment problem. In any event, the pilot should be using this time to prepare for the approach, not worrying about trying to fly the holding pattern. Therefore, If I give you the answer to the holding pattern before you get to the fix, one can concentrate on the preparing for the approach.

All true, but not relevant to the question of whether those hand-held holding pattern entry maneuver selection gadgets are a help or a hindrance. My feeling based on observing a lot of pilots learning how to enter holding patterns is that they're a hindrance, but YMMV.

 

[midlifeflyer]

I've always wondered why instructional texts always make holding far more complicated than it needs to be. Must be the silly gadget lobby.

 

[lgtech]

When I posted my original comment on the holding pattern wind calculator patented by Holcomb in the 90's (by the way he also patented the holding pattern entry calculator) I was in no way supporting the use of the holding pattern entry calculator. I agree there are much easier visual concepts to make the holding entry very easy without the use of the calculator. My comment was based on the use of the holding pattern wind calculator that Peter-h posted. As I stated previously, this was a complex device for determining the outbound time and heading for the hold and was based on an approximate method. In Mark's recent comment,"I've always wondered why instructional texts always make holding far more complicated than it needs to be", is the reason that I derived the exact solution to the holding pattern.
The method that is used to fly the holding pattern with a wind is based on the old method of "trial and error". Anytime a maneuver is based on the "trial and error" method there is always provided what we call "Rules of Thumb". If you look up the definition of "Rules of Thumb" what you find is that one must provide limitations on the use of the "Rules of Thumb". These limitations are usually never provided by either the FAA or CFII's. The exact solution of the holding pattern was derived in order to provide the complete limitiations of any "Rule of Thumb" regarding flying a holding pattern in the presence of a wind. These "Rules of Thumb' relate to both timing and wind correction in the holding pattern. The "Rules of "Thumb" that relate to holding pattern will usually only apply to light winds and when the winds get stronger, these "Rules of Thumb" basically go down the drain quickly. In fact, using these "Rules of Thumb" require the pilot to fly additional circuits to get the holding pattern correct. Even with the exact solution shown on a simple graph so the pilot could pick off the outbound time and outbound heading (or number of degrees to turn from the inbound course) is still too much of an effort for the IFR pilot to perform while in the clouds. However, it is still better the the pattented holding pattern wind calculator.
In any event, I am not proposing that every IFR pilot has this graph in front of him while holding. What I am pushing is to implement two simple formulas (for outbound time and outbound heading) into the GPS software that will spit out this information directly to the pilot while he is inbound to the fix so that he does not need to do anything but fly the outbound heading and outbound time upon reaching the fix. In fact, since the winds can have variablility on the order of minutes, everytime the pilot is inbound to the fix he will have a new update of the outbound time and outbound heading.
In regard to Mark's comment "I've always wondered why instructional texts always make holding far more complicated than it needs to be.", I will answer with the following statement"
"How flying such a simple geometrical racetrack holding pattern without a wind can be loaded with "gotcha's" when flying in the presence of a wind".
The exact solution of the holding pattern shows how truely complex the holding pattern can get as the wind speed ratio gets above 0.2.
I just recently presented a FAASTeam Seminar in the Van Nuys Calif area, entitled "Holding Patterns 101: A New and Novel Approach to Understanding the Pitfalls and Misconceptions of Timing and Wind Correction in the Holding Pattern". In fact what I point out is that the exact solution of the holding pattern shows why there are distinct advantages to always starting the outbound time when the aircraft rolls out on the outbound heading rather than starting the time at the abeam point. It also shows under what wind speed ratio the holding pattern transitions from a "Type 1" (outbound turn is more than 90 degrees relative to the inbound course) to a "Type 2" (outbound turn is less than 90 degrees). I have never observed any textbook ever show a "Type 2" holding pattern or even discuss the possiblitly of such a holding pattern, and I bet that 99% of the IFR pilots (including CFII's)are not aware of the so-called "Type 2" holding patterns.
As a CFII for over 35 years my goal is to try to make the IFR pilots aware of the complexity of the holding pattern in the presence of a wind, as well as to find ways to allow to pilot to take the mental math out of the "Trial and Error" method when flying the holding pattern.
Les