In two recent posts I've been dissecting hold timing. The goal is to fly a racetrack pattern such that, despite winds, it takes exactly one minute to fly the inbound leg. Clearly, if the first inbound leg takes you less than a minute, you need to fly longer outbound, and if the first inbound leg takes more than one minute, you need to fly for a shorter time outbound. The challenge lies in how much more or less.
As I mentioned before, I subtract two thirds of any excess inbound time from my outbound leg, and add one and a third times any shortfall. A colleague just hacks off half the excess and adds all the shortfall. He's good at math, and conscientious, so I pulled out Excel to find out what he knew that I didn't.
As I made up the table below I realized that if the first calculation gives me an inbound time of less than 20 seconds inbound, I fly for 20 seconds, which helps me not overshoot. I also don't make a correction based on the very first inbound leg, because that's part of the entry, and not to be trusted. I probably have more arbitrary rules like these that I haven't even noticed.
The values in the table below use the inbound leg distance calculations from my last hold post and the formula distance equals speed times time, with speed being the true airspeed of the airplane plus a tailwind or minus a headwind.
|IB #1 time||OB #2 my way||OB #2 his way||IB #2 my way||IB #2 his way||OB #3 my way||OB #3 his way||IB #3 my way||IB #3 his way|
The above data leads me to conclude that with light to medium winds, both methods work fine, mine a bit better, but not worth bragging about. For strong headwinds on the outbound, giving an initially very short times on the inbound, adding one and a third the shortfall works better than just adding the shortfall. For strong tailwinds on the outbound, subtracting the whole excess works faster than subtracting two thirds of it. Which makes perfect sense.
I initially set up my spreadsheet looking at aircraft of different speeds in different winds, but discovered that it makes no difference what combination of wind speed and airspeed produce a given inbound time, any initial inbound time corresponds to a particular outbound time that will give a one minute inbound. One could make a computerized hold timer that contained a database, such that when you hit stop on the inbound leg it automatically looked up the value and set up a countdown timer for the appropriate time on the outbound leg. Or you could have a printed table stuffed in with your approach plates, giving the same effect.
No one needs to, because as long as you are correcting in the appropriate direction, a few iterations will converge on the appropriate outbound time. I even tried setting up my spreadsheet so that the correction was a random number and if I limited the number so that the values didn't overshoot, after four turns in the hold, the timing was within a few seconds.
Why do we do this? Why don't they protect airspace based on a one minute outbound, and tracking inbound, so no one would have to calculate anything? I think they even do that in Europe. Perhaps it's a bit like the practice of putting mirrors in elevator lobbies. It gives you something to do while you are waiting, thus making the wait seem shorter.
I've had enough of holds for now, even though I haven't touched correction angles or hold entries.