Tuesday, June 28, 2011

Pocket Protector Optional

A calculus professor once told me the only tools a real mathematician needs are a pen, a piece of paper the size of a postage stamp, and his or her brain. That may be the case if one is sitting at a desk, quietly contemplating the theoretical. Controlling an aircraft that is hurtling through the air at two miles per minute or more while simultaneously listening and talking on the radio? That endeavor has the unfortunate side effect of dropping everyone's IQ by several points, which is why pilots have adopted a few tools to help them deal with the flying world's challenging mix of theoretical and practical. One such tool is the E6B calculator.

For older, traditionalist pilots, the E6B is synonymous with "slide rule" and the mere mention of electronic E6B calculators and smartphone apps will get them on their soapbox in a heartbeat, praising the slide rule and preaching against the dangers of new-fangled electronic contraptions. Young upstart pilots, having likely never used a slide rule, may find this attachment a bit odd. Frankly I do too. But even as electronic E6Bs are becoming widespread, there is still a place for the old fashioned E6B slide rule.

Tried and True

The advantages of the E6B slide rule are many: It requires no batteries, it does a variety of calculations, and it is relatively lightweight. The "front" side of the E6B can accomplish a dizzying array of calculations and conversions: Ground speed, distance, time, fuel consumption, endurance, knots to nautical mile - provided the user has been properly initiated. The back side of the E6B, sometimes called the "wind side," is used to calculate wind correction angles and determine winds aloft.

The disadvantage of any slide rule is that in order to use it, the user must provide most of the problem-solving context. In a high-workload environment, user-supplied context is less than ideal. If you don't understand how to arrange the slide rule scales to solve your problem, you won't get very far. Even after you have a grasp on the slide rule basics, you must still use common sense to ensure that your answer is not off by an order of magnitude.

Some might argue that having to provide this sort of context and judgement is the very thing that ensures an understanding level of knowledge about the calculations be performed. That rings hollow to me because in flight what is most desirable is speed and accuracy. It's possible to go through the motions of slide rule calculations, mimicking what you've seen, arrive at an answer (correct or incorrect), and still not understand how you got there. Yet for kinesthetic and tactile learners, the E6B is an ideal tool, probably more so than an electronic calculator. Instructors who are unsure of their student's learning strengths can always have them take one of the many learning style inventory tests available on-line.

In spite of its apparent simplicity, the slide rule E6B is by no means foolproof. Tiny screws hold the main section together. With age, these screws can come loose and if that happens in flight, you'll have an interesting project on your hands. The wind side has a transparent plastic disk that is meant to be marked with a pencil, but that plastic can become cloudy, brittle, and riddled with marks. APR Industries has developed an innovative E6B design that uses a rotating windspeed cursor arm on the wind side so that you don't have to make any pencil marks. Who says you can't teach old dogs new tricks?

If you are up for a challenge, grab the E6B of your choice and try tackling one of the Safety and Flight Evaluation Conference (SAFECON) Practice Exams

Flashy and New

There seems to be a endless supply of E6B apps out there for smart phones like the iPhone and the Android. At last count there were over 30 E6B apps at the iTunes store, some included as a feature inside an app. Perhaps creating E6B apps is a rite of passage, like writing your first "Hello world" program.

My favorite iPhone/iPad E6B app continues to be PFMA since it has a very simple, shallow menu structure. You provide the information you know and PFMA provides the missing information. No need to first locate the type of problem you're trying to solve in a complex and multi-layered menu structure. There are a few conversions that PFMA doesn't do and some obscure calculations that are missing, but it's easy to use in flight and a very good deal at $5.99.

For those of you wondering, that other calculator is an ancient HP-16C Computer Scientist that still works flawlessly. What can I say? I love RNP calculators and you never know when you might need to calculate the 2's compliment of a binary number.

Regardless which E6B app you choose, remember you won't be allowed to take your smartphone or other multi-purpose electronic device into an FAA knowledge test session.  Hmm ... Maybe there's life in that old E6B after all. Or purchase one of the dedicated E6B electronic calculators like the ones sold by Sporty's. I still have one of the Sporty's models, though the LCD display has long since given up the ghost.

Required Knowledge?

Like sailors before them, aeronautical navigators aboard airliners of yore used a sextant to plot their position. Thinking about this got me wanting to learn something about celestial navigation, even though it has been supplanted by satellite-based navigation. So in my spare time, I'll be working on building my own (very simple) sextant. When completed, I plan to try plotting my position in a few locations on the ground and compare the results to a handheld GPS or Google Maps on my iPhone. This project is for my own amusement and just because I find it interesting doesn't mean I'll soon be requiring my students to build their own sextants.

Ron wrote a cogent rejoinder to my post about digital versus paper charts, pointing out that most any pilot can blindly follow a magenta line into oblivion if they have lost (or perhaps never learned) basic flight planning and navigation skills. Many instructors might see that lack of skill and interpret it to mean that the pilot needs more training, but a deeper question seems to emerge: "What knowledge should the FAA (and, by extension, DPEs and CFIs) require pilots to demonstrate in the first place?" I believe the answer lies in thoughtfully combining the use of hand calculations, slide rule and electronic E6Bs, paper and digital charts, and paper navigation logs with computerized flight planning.

Tradition versus Progress

There's a undeniable pride student pilots feel once they have mastered basic calculations with an E6B. That's understandable because acquiring slide rule prowess is like learning a magic trick. Your friends are bound to be impressed, especially if the E6B you use is contained on the face of a flashy pilot watch. Pushing buttons on a calculator? Anyone can do that! For my part, I'll continue to teach my students how to use paper charts and a slide rule E6B, but I also won't discourage them from embracing new technology. I never tire of hearing students marvel "So pilots really used to fly this way?"


Hamish said...

"A calculus professor once told me the only tools a real mathematician needs are a pen, a piece of paper the size of a postage stamp, and his or her brain."

You forgot the coffee :-) (can't imagine how I would have survived either post-grad maths or IFR training without it…).

toddgrx said...

I can honestly say that if I needed to calculate the 2's component of a binary number, I wouldn't know I needed to.

Also, purchased my Sporty's Electronic E6B about 6 months before iPad came out and then Sporty's E6B iPad app... anyone wanna rarely used Sporty's Electronic E6B with yoke mount?

Eddie said...

Love the blog. Can't wait for your next one.

rodrop said...

Great article! Love it!