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Croucher: Good Rules of Thumb

Sorting Out Directions on the Fly

It is probably true that most pilots, once they complete their licence exams, throw away their books with relief, thinking “That’s it! I don’t need to bother with that stuff any more!” Naturally, at the time, much of the stuff you’ve been made to learn looks fairly useless, and it’s only years later, when you’re trying to figure something that you wish you’d studied harder, or at least kept the books!
For example, I’ve ended up in trouble more than once with surveyors because it appeared that I “wasn’t using my GPS properly” when they reported back to management at the end of the flight. On one occasion I was handed a page or two of coordinates the evening before a flight around a series of compressor stations. “That’s nice,” I said to myself. “Looks like a busy day.” It never occurred to me for one minute that the surveyor expected me to waste several hours punching the numbers into an antiquated display that had no keyboard.

The fact of the matter was that, after four years of aerial survey experience in a previous life, I was able to work out approximate distances and bearings in my head and merely had to allow for drift and read the map properly. Of course, I also used to watch the Lat & Long numbers run down on the GPS display as confirmation, making slight adjustments here and there to get over the target.

As far as direction goes, it’s easy enough to visualize the approximate quarter of the compass in which you will be operating. If you are at latitude 51°N, for example (Calgary), and you have to proceed to Grande Prairie at 56°N, it’s not hard to figure out that you will be going north! Similarly, as Calgary is at longitude 114°W and Grande Prairie is more or less at 119°W, you need to go a little bit west as well. Just adjust for such combinations and within a very short time you will be able to calculate headings to within 10° or so. The real trick is the distance, and this is something I learned on my pilot exams in Europe.

You know that as you go north from the Equator, the coverage of the surface by one degree of longitude gets smaller because the lines of longitude converge in a cosine relationship (time to dig out those math books!) In fact, you can find the true length of a degree at any latitude by multiplying the change of longitude (in minutes) by the cosine of the latitude, so at 60°N, the distance between meridians will be 30 nm, since the cosine of 60° is 0.5 (this is called the departure formula).

Say, from a location roughly on latitude 54°N (such as Edmonton), you need to find a location roughly 3° to the east. At the Equator, this would be 180 nm as 1 minute is equal to 1 nautical mile and there are 60 of those to a degree. However, we are not at the Equator. The cosine of 54° is 0.59, or 0.6 for ease of calculation. Multiply 180 by that number and you get 105.8 nm, or 106. Remember that your calculations do not have to be that accurate, as you cannot carry complete tables of figures around in your head, but this is a good method of sorting out your direction on the fly while keeping your eyes outside the cockpit, which is good for flight safety (also, the mathematical model of the Earth on which operation of the GPS is based is a sphere which, of course, it is not, so excessive reliance on machinery should be avoided).

You can also do this on the flight computer, if you still have one. The cosine of 54° is the same as the sine of 90° – 54°, which is 36°, so:You have 106 nm to travel, so it will take around an hour in a Bell 206. Using the 1 in 60 rule for our trip from Calgary to Grande Prairie, you have to divide 177 (distance west) by 300 (distance north) and multiply by 60, to get 35° which, subtracted from 360 gives you a nil-wind heading to steer of 325°. Easy, no?

I have found that if you tell somebody why they are learning something, or give them a use for the subject matter, it makes the learning process a whole lot easier.

Your feedback on this or any other topic is always welcome. Please contact the editor at dmccarthy@annexweb.com or go to www.helicoptersmagazine.com to post a comment in our blog section.

Phil Croucher is a longtime industry expert and author of Professional Helicopter Pilot Studies.