an·ces·tor – wor·ship
Noun phrase
Colloquial slang used to describe the reason for continued use of, or belief in, irrational, unnecessary or inefficient procedures, policies, practices or devices.
A fellow client attending my recent CE-650 (Citation III, VI & VII) initial course arrived without having completed the ATP written – COVID cancellations being one of several valid reasons for the postponements. The rest of the class was more than willing to offer advice and assistance for the upcoming exam, scheduled between our ground school test and his first simulator session – no pressure. We all found ourselves shaking our heads, however, over the requirement that he bring an E6-B to the ATP testing facility – you know, the flight planning “Whiz-Wheel” thingy for making those pilot-y, time-distance TAS/GS and wind-triangle calculations.
When was the last time you saw, let alone used, an E6-B? Probably around the time you whipped out your slide rule at Home Depot or used a typewriter to compose and mail a letter via USPS. The E6-B is fun to play with (like Silly Putty and Etch A Sketch), but inflight use would be sort of student-like and distracting. While ancestor worship may be used as derogatory slang for continued use of outdated reasoning, some old-school pilot-math is nice to keep in our hip pocket – ancestrally derived or not.
Drats: That awkward moment when you finish a math problem and your answer isn’t even close to one of the choices.
Except for geometry and the calculations used in chemistry, college mathematics scared the derivatives out of me. When I talk to prospective youngling pilots, I’m often asked, “How much math is there?” or “What kind of math do pilots use?” While some are curious about health requirements and the plethora of government rules and regulations, many worry that we work complex math calculations before and throughout the flight – and they’d be right. Well, not that complex. Add to that, most have never spoken on a radio where we appear to broadcast confidently, seemingly unrehearsed and impromptu information and requests, speaking and hearing at the speed of light using indecipherable pilot jargon. They think our radio and math skills, perception, and our intuition must be so sharply honed that we view the entire environment with Jedi-like clarity. These factors (math pun intended) all contribute to pilot training apprehension. And the math apprehension can be blamed on east and west-bound trains, pizzas and watermelons.
Math: The only place where people buy 60 watermelons and no one wonders why.
When asked, “Do pilots work story problems?” I ask if they can compute the area of a trapezoid and factor a binomial? And then I quickly add, “Just kidding.” I tell prospective pilots that yes, we do story problems but not like the ones in school. Remember the notorious math question that goes something like this: If a train leaves Chicago at 10:00 a.m. traveling West at 50 mph transporting 300 deep-dish pizzas, and a second train carrying 600 watermelons leaves Phoenix (1,753 miles away) at 11:00 a.m. headed East at a speed of 40 mph, what time will the two trains pass? And if they both are burning 75 gph diesel fuel, how many watermelons and pizzas will each have on board as they pass? Think back to the first time you learned the steps needed to solve the problem.
For me, it was and is paralyzing. You and I have been doing time-distance-fuel calculations for years now, so we can do this problem not only in our heads but in our sleep, right? (NOT – see the admission above). Thankfully, in practice, we need only calculate for one vehicle and we seldom carry 300 pizzas or 600 watermelons (perhaps a dozen cases of Coors in a Cherokee 140, however). That said, piloting does indeed employ several, sometimes complex, math disciplines.
When it comes to inflight math, there are three types of pilots: those who can count and those who can’t.
Why do we still need math, and what types of math do we use? Basic arithmetic, geometry, trigonometry, interpolation, and mental math are all part of being a pilot. We use math to understand principles of flight, computing weight and balance, determining fuel requirements, and in navigation, flight planning, descent planning and calculating crosswind components. We don’t normally stop to think about the various math disciplines involved because they have become intuitive and are nowhere near as daunting and intimidating as this litany would have you believe. Plus, like most aspects of our lives, computers, tablets, smartphones and, for pilots, avionics have relieved us from tedious (often less than perfect) manual math calculations. And this is a good thing not only because of the three types of pilots above but also because four out of three pilots are dyslectic.
WAG’s and TLAR
I tell student aviators that if they can add, subtract, multiply and divide, then that will do just fine. A lot of our math is the “cut it with an ax, measure it with a micrometer” type calculations anyway – meaning that it’s mostly used for estimation and our situational awareness. It’s a WAG (Wild *ss Guess) with a quick “reasonable/reality” check to verify TLAR (That Looks About Right). If the calculations are so critical that we need an answer down to the single mile, to one minute, one gallon, one pound or to several significant digits, then we are probably cutting it way too close – or taking an FAA exam.
Most of our math calculations are used for a time, distance and fuel consumption analysis. The distance we travel in one minute times 60 gives us our GS. We can then divide the distance to our fix/destination by that one-minute calculation to get time remaining to the fix. We multiply the time to the fix by the gph or pph we are burning (with a minor conversion of minutes to hours), and we have fuel used to the fix. We subtract the fuel to the fix from the fuel remaining, and we get fuel remaining at the fix.
All this, plus-or-minus the headwind/tailwind, and we arrive at a TLAR WAG – all accomplished in our head without an Etch A Sketch or E6-B. And speaking of wind, one thing that I find that even experienced pilots often don’t wrap their head around is that once airborne – except for abrupt and significant changes in velocity, direction, density or temperature – the airplane doesn’t know about, or care about, wind. From the airplane’s anthropomorphic perspective, it’s only us math-challenged pilots that need such esoteric information as wind speed and direction relative to the ground. We do all of this (sans E6-B) in order to learn ETA’s, fuel requirements and then crosswind and landing distances when physical contact with the earth is imminent.
If you were to display an E6-B to the passengers or crew when making math calculations, you might get worried stares regarding your competence – kind of like the Chair of the Federal Reserve counting on his fingers during a press conference. Modern avionics, flight planning and weight and balance apps/programs have made preflight and inflight math unnecessary. Airframe and powerplant limitations, V-speed and navigation figures can now be presented on multifunction displays or the engine and flight instruments themselves. Computer-based flight planning programs are common and can be accessed enroute via the internet, Airtext or SATCOM. Enroute climb and descent points, RNAV climb-via and descend-via arrivals and departures, ETA’s, holding patterns and speeds are all calculated by the CADC, GPS, AHARS and FMS. Are there applications of old-school math for pilots that we should remember? You bet – because you never know when some or all of our electronic magic will disappear. Even when our electronics work, most of us still use mental math as backup confirmation for one particular calculation.
Pilot Arithmetic: A Practical Application
The TOD (Top of Descent) calculation is an example of usable old-school math. The easiest way to compute TOD is to use the VSI and a GPS that shows time and distance to the fix. If you want to be over fix ABC at 10,000 and you are at 30,000 now, you have 20,000 to lose. If you begin your descent at 20 minutes to go, that’s 1,000 fpm. If you wait until 10 minutes to go, that’s 2,000 fpm. Often, ATC likes to give us a clearance that may be something like, “Cross 65 miles Southeast of ABC at FL190 and 280 knots, expect to cross ABC at 10,000.” Of course, the easiest way is to enter this in your FMS.
Excluding that, and in order to exercise our math brain cells, subtract the altitude at which you want to be (19,000) from the altitude at which you are (30,000). That’s 11,000. Multiply by 3 and drop the zeros (11,000 x 3 = 33 miles) and add that to the fix distance (65 + 33 = 98 miles) and start down at 98 miles. Recalculate every couple thousand feet and adjust your vertical speed to compensate for changing wind. Do these calculations before you enter it into the FMS so that you may begin the descent immediately if the clearance was given late i.e., a slam dunk. Then, the next descent from 19,000 to 10,000 would be: (19-10) x 3 = 18. Start the descent at 18 miles from the fix. Ah, mathematics – how refreshing when we find a practical application.
Use Your Fingers
Don’t let old-school math scare the derivatives out of you. When working those pilot-y story problems, don’t get distracted by irrelevant components like pizza, watermelons or significant digits. Someday the Whiz-Wheel and memorized math will go the way of the FSS teletype, LORAN and slide rule, replaced by systems and devices that are more accurate and user-friendly. In the meantime, we should keep some of our ancestral pilot-math skills polished, just in case we lose the newfangled electronic gadgetry and need to do some hand flyin’ and mental cipherin.’ I’m sure that our ancestors won’t mind if we use our fingers when calculating a WAG – as long as it’s not in front of the Feds, passengers or during a news conference.
