Land and Hold Short

I’ve finally gotten around to adding free data downloads to OurAirports. You can now download nightly CSV-formatted data dumps of all the airports, countries, and regions in OurAirports at

http://www.ourairports.com/data/

These will open with most spreadsheet and database programs (make sure you import them as UTF-8).

All data is released into the Public Domain and comes with no warranty. If you have any corrections or additions, please make them in the spreadsheet and then send them back to me.

If you were building a mapping application that could show only (say) 20 airports on the screen at once at any given zoom level, how would you decide which airports are most important, using only publicly-available data sets? Here are some possibilities:

• Points for being in the list of the top 100 passenger airports.
• Points for having an ICAO code.
• Points for having an IATA code (rarer, so more points than an ICAO code).
• Points for each localizer and glideslope (since they’re unambiguously associated with the airport).
• Points for having a TAF.
• Points for having a METAR.
• Points for each long, paved runway.

These are all easy to measure, but I’m not sure that they capture enough of what makes an airport important for mapping purposes. Really big airports often cluster around urban areas — think of JFK, EWR, and LGA around New York, or LHR, LGW, and LCY around London. These are all busy airports, but they’re very short drives from each other (traffic permitting), so perhaps they don’t have the same kind of importance on a map as the main airport in a smaller country, the only airport serving an isolated community or an island, etc.

I’ve done some experimenting trying to measure isolation: for example, I’ve tried limiting the map to one airport in each 30×30 deg square (world level) or 10×10 deg square (continent level), but the map still ends up with huge clusters of airports in the U.S. and Western Europe and none in most of the rest of the world, and even a 10×10 square means that Toronto’s and Montreal’s main airports won’t show up (same square as JFK and EWR). What would Google do?

Recently, in the cold weather, my Warrior’s battery has barely managed one try starting the plane — any more, and it goes flat. Most recently, it happened after I’d just been flying 1.7 hours and tried to restart after a short fuel stop. I had to figure out whether the problem was the battery or the alternator (or regulator).

I was reading through an article on pilotage [Wikipedia] in the December AOPA Pilot. In general, I found the article enjoyable, but one thing stuck out like a wart — the author’s assumption that people should always read a chart track up (with the chart rotated for the direction they’re heading) rather than north up.

I have no objection to the suggestion that people try using a chart track up, but frequent claim that it’s easier — and some pundits’ and instructors’ insistence that it’s the only proper way — grates a bit. In informal surveys on aviation mailing lists, I’ve found people split about 50:50 between north up and track up, and I suspect that it has to do with how different people’s brains work, something along the lines of left-handedness and right-handedness.

Personally, if I’m flying west, my mind already pictures me flying right to left, so it’s by far easier to hold the chart north up so that it lines up with what I’m seeing in my head. Track up would be a double annoyance, since (1) I’d have to rotate everything in my head, and (2) all the text on the chart might be sideways or upside down. Likewise, when I’m walking, cycling, or driving around a city, I think of myself as heading northwest, south, etc. — I never memorize a trip as a series of left or right turns. I imagine that people who do navigate that way probably also find track up easier.

So if you fly, hike, boat, or whatever, do you prefer to hold your charts (or set your GPS display) north up or track up? Why? If you’re an instructor (aviation, seach-and-rescue, orienteering, etc.), have your students generally found one or the other easier? Has anyone every done a proper scientific study?

Check out the low-level upper wind forecast (FD) for Ottawa tomorrow — it looks like the gales of November are coming calling a couple of days early:

In plain language, that means that at 18,000 ft the wind will be from the northwest at 97 knots (180 km/h). My Warrior cannot fly that high (the theoretical ceiling is around 14,000 ft, with a lightly-loaded plane and lots of patience), but many light piston singles and twins can. Even at 12,000 ft, the winds are strong enough that I could point the plane into the wind, drop flaps, pitch for slow flight, and fly backwards over Ottawa; at 9,000 ft, I could still pretty-much hover or move backwards very slowly.

(kias: knots indicated airspeed; kcas: knots calibrated airspeed; ktas knots true airspeed)

V speeds [Wikipedia] are the critical performance speeds of an aircraft — while some of them are illustrated on the face of the airspeed indicator using lines and bands of different colours, a pilot is usually expected to be able to cite them from memory for each aircraft she flies, off by heart, backwards, while standing on her head drinking a glass of water. For example, my Warrior stalls
at 44 kias dirty (Vso) and 50 kias clean (Vs), best angle of climb (Vx) is 63 kias, best rate of climb (Vy) is 79 kias, and so on. Simply memorizing isn’t always enough, however, because of a couple of gotchas.

Gotcha #1: indicated vs. calibrated airspeed

The first gotcha isn’t usually too serious, but it’s worth keeping in mind when comparing different aircraft, and it becomes critically important for gotcha #2. All of the V speeds are given as indicated airspeed, so that the pilot can read them straight off the airspeed indicator. With the flaps up in the middle speed range, usually around Vy, indicated and calibrated airspeed are about the same; however, under other circumstances, it gives a distorted picture of how fast you’re actually going:

• at lower speeds, indicated airspeed is almost always slower than the real, calibrated airspeed; for example, the Cessna 172p has a Vs (stall, clean) of 44 kias, but that’s actually more like 51 or 52 kcas — the plane’s not actually landing as slowly as you think it is, though the performance tables in the POH take that into account
• at higher speeds, indicated airspeed is almost always faster than the real, calibrated airspeed; for example, the Cessna 172p cruises at about 111 kias at 75% power (120 ktas at 8,000 ft), but that’s actually more like 108 kcas
• flaps distort the airspeed indication even more — dropping 10° flaps in the 172p at slow speeds makes the indicated airspeed read 9 knots slower than the calibrated airspeed

It’s easy to notice that these errors tend to work in the aircraft manufacturer’s favour — who doesn’t want a plane that lands slower but cruises faster? There may be other engineering reasons not to mess with the airspeed indicator, but it does not look like it would be difficult to design an ASI that shows something closer to the actual calibrated airspeed, at least with the flaps up.

Gotcha #2: weight, balance, and wing loading

Most of the V speeds apply only when the aircraft is being flown straight and level in coordinated flight at maximum gross weight with the centre of gravity (CG) somewhere in the middle of its allowed range. Shifting the CG has only a tiny effect on V speeds (typically a knot or two), but the other factors can play big.

Roughly speaking, most V speeds will vary proportionally to the square root of the aircraft’s weight. For example, if an aircraft stalls at 50 kcas at 2440 lb, it will stall somewhere around 46 kcas at 2000 lb. Here’s the formula, for anyone who’s interested:

sqrt(weight / maximum weight) * V speed

2000 divided by 2400 is 0.82, the square root of that is 0.91, and 0.91 * 50 is 45.5. Note however, that you have to do the math on the calibrated airspeed, not the indicated airspeed, to get this right, especially since the variation between the two gets huge near the stall speed.

This math works in your favour when you’re flying light, but it works against you in a turn. In a coordinated, non-descending 60° bank, the aircraft is double its normal weight, so a 2440 lb aircraft actually weighs 4880 lb. Running the same formula, the stall speed will be multiplied by sqrt(2), or approximately 1.4. If the aircraft normally stalls at 50 kcas, it will stall at about 71 kcas in that turn. Smaller bank angles still have a significant effect on stall speed, and can be especially dangerous while maneuvering right after takeoff or just before landing, when the aircraft is already slow.

Maneuvering speed

One place that the POHs do take this into account is the maneuvering speed (Va), the maximum speed for abrupt maneuvers, such as recovering from upsets in moderate or severe turbulence. Typically for light, non-aerobatic aircraft, Va is roughly double the stall speed (calculated using calibrated speeds), so that the wing will stall under a load of more than 4Gs (double the speed will lift four times as much weight, more or less). This is critically important not only for protecting lifting surfaces like the wings and horizontal and vertical stabilators from excessive loads, but also for keeping the engine from ripping off its mount though sudden accelerations. As a result, POHs generally give VA not as a single number, but as a range — for my Warrior, it ranges from 88 kias (89 kcas) at 1531 lb to 111 kias (108 kcas) at 2440 lb. Running the above formula on the 108 kcas at 2440 lb gives a result of 86 kcas at 1531 lb, which is 3 knots low, but pretty close.

Cutting speeds to increase safety margins

As mentioned earlier, nearly all of the V speeds actually work this way. Most of the time, pilots don’t have to worry, but if you’re flying in and out of short, obstructed fields, doing the math can be a huge help. For example, if you normally fly an approach with full flaps at 63 kcas at 2,440 lb, and your plane is loaded only to 1,900 lb, you can fly the approach at 56 kcas (don’t forget to convert to kias!) and shorten your landing distance without giving up your safety margin; likewise, if your Vx (best angle climb airspeed) is 60 kcas at 2,440 lb, you can climb out at 53 kcas and clear the trees by a few more feet. If you want to get above the turbulence quickly to keep from getting sick, you can adjust Vy down as well — if you normally climb out at 79 kcas, climbing at 70 kcas will get up higher, faster, at this light weight (though it might not let your engine get enough airflow for cooling).

Of course, if you have a long runway, no trees in the way, etc., you probably don’t need to worry about these calculations, since the published V speeds give you an extra safety margin. Just make sure that you don’t add an extra extra margin when you’re flying light — if your normal approach speed is 70 kias, the plane is lightly loaded, and the air is a bit rough, you already have about a 9 kt safety margin, so there’s no need to add another 10 kt and approach at 80 kias, increasing your landing distance even further. One reason that people claim that more powerful aircraft “float a lot” on landing is that those aircraft often have much higher maximum gross weights, so when a pilot is flying one of them alone (and thus, very light), he usually approaches way too fast.

Airliners and other larger aircraft make calculations like these for every flight. There is no fixed V speed to do a takeoff or landing in a 747, for example; instead, the dispatcher or a computer on board calculates the optimal speeds based on fuel, cargo, and passenger load for each trip. After all, for a 747, an 8,000 ft runway is a short-field landing.

The lean-of-peak debate, which I’ve written about before, has just gone mainstream — check out this Forbes piece, part of a series of online articles about institutional stupidity. The focus is on Lycoming’s business practices (deny evidence that you cannot refute while insulting your customers in the process) rather than the technical fine points of LOP operation, but still, there it is, out of the pilot-geek closet.

I just read this TAF for Watertown International Airport (KART):

KART 	121738Z 121818 19008KT P6SM SKC
FM0600 17006KT P6SM SCT250 WS015/23035KT
FM1400 19012KT P6SM BKN250 WS015/23045KT

The tricky parts are the phrases “WS015/23035KT” and “WS015/23045KT” — those might be common out in the prairies, but I don’t see that kind of thing often in TAFs around the Great Lakes. The “WS” stands for “wind shear”. The following number is the altitude of the shear layer above ground level (1,500 feet in both cases), followed by the wind direction and speed at that altitude.

So starting at 06:00z tomorrow morning (that’s 01:00 EST), the wind will be from 170 degrees true at 6 knots on the ground, but from 230 degrees true at 35 knots just 1,500 feet up; from 14:00z (09:00 EST), the wind will be from 190 at 12 knots on the ground, but from 230 at 45 knots 1,500 feet up.

What does that mean, practically speaking? As you approach to land on runway 25 at 10:00 am local time tomorrow morning, you’ll be facing a headwind of 43 knots until 1,500 feet AGL, at which point the headwind will drop abruptly to about 8 knots — that means that your airspeed will suddenly drop by 35 knots as you descend through the shear layer, until your plane has time to reestablish its trimmed airspeed. If you’re approaching at 80 knots calibrated airspeed, you’ll suddenly find yourself at 45 knots with your nose swinging hard towards the ground trying to make up the missing speed (you’ll probably also be in moderate-to-severe turbulence). In a light aircraft, you may have room to recover at 1,500 feet; in something heavier, like a commuter turboprop, I’m not so sure.

When you take off from runway 25, exactly the opposite will happen. As you climb through the shear layer (and turbulence), your airspeed will suddenly increase by 35 knots, and the nose will shoot up to the sky to try to regain the plane’s trimmed airspeed. For a brief time, the climb rate will be spectacular, but you’ll have to make sure that you get the nose down before the extra speed decays on you and leaves you nose-high and slow.

The exact effect will depend on how thin the transition layer is and how fast the plane is descending or climbing. A slow descent or climb, or a thicker transition layer, will give more time for a gradual adjustment.

Anyone for some touch-and-goes at Watertown tomorrow?

Update: WordPress tells me that this is my 100th post. Whoopie!

Update 2: I went for another test flight on Friday, and the problem is fixed.

When you land after a flight, do you know — within a gallon/a few liters — how much fuel your plane should take? Some people always take off with full tanks and limit their legs to 2-3 hours, so they figure they never have to worry.

On Tuesday, I took my Warrior for its second post-maintenance test flight. I started with full tanks, flew for 2.75 hours at 75% power, then filled up again. The plane took 146 liters of fuel, over 50% more than expected, indicating that I landed with less than 45 minutes of fuel remaining. Upon closer investigation, there was some blue staining on the wing and a bit of streaking coming from under the left side of the cowling. My new fuel pump was leaking, throwing fuel overboard as I flew. I probably leaked fuel on my first flight as well, but since I didn’t start with full tanks, it was harder to be certain (I mentioned my concern to my AME then, but we saw no evidence of leaks inside the cowling).

I’m glad that I insisted on a second test flight before making the 800 nm trip to Atlanta, but I’m also glad that I routinely track my fuel consumption and know what to expect at the pump — it’s as important as being able to read the panel instruments during flight. Unlike a Cessna (with its “both” fuel setting), my Piper would have warned me of a problem when the first tank ran dry, giving me a few minutes to land with the remaining tank, but fortunately it didn’t come to that. A new fuel pump will arrive by courier tomorrow (Thursday) morning from the engine shop.

The featured article of the day on Wikipedia for Saturday 29 October is Metrication, the process of converting a country to metric from various historical units of measure. Now that Ireland has switched, the only three countries left not officially using metric (or in the process of changing) are Liberia, Myanmar (Burma), and the United States, though many people still informally use older systems for some things — for example, I use metric for temperature and distance (on the ground) and for buying food, but not for weighing myself, measuring my height, or buying lumber.

Because Canada and Mexico are metric while the U.S. is not, we’ve come up with a funny mishmash for North American aviation. We use nautical miles for distance and knots for speed (even most Americans don’t know those); statute miles for visibility (or feet under conditions of very low visibility); feet for elevation, altitude, and runway dimensions; inches of mercury for air pressure; and Celsius for outside air temperature (but not for cylinder head or oil temperature). Got all that? That’s right, if you’re six miles from the airport and there’s six miles visibility, don’t expect to see the airport, because six statute miles of visibility is 9,656 meters, while six nautical miles of distance is 11,112 meters, about a kilometer and a half further. Even American pilots use Celsius for temperature: you can always tell which Americans visiting Canada are pilots, because they’re the only Americans who understand the temperature on the Canadian weather report.

In Europe and most of the rest of the world, I know that they give runway dimensions in meters and air pressure in hectopascals (millibars), but I’m not sure if they use kilometers for distance, and I’m pretty sure they don’t use meters for altitude (or else standard altitudes wouldn’t mesh up). If the U.S. were finally to give in and go metric, would we switch to metric for all of aviation? It would certainly make things simpler for someone building a new plane or learning to fly from scratch, but there would be a lot of gauges to recalibrate, a lot of weight-and-balance to recalculate, and probably a lot of accidents caused by unit confusion until we straightened everything out. Remember that the Gimli Glider was, mainly, a result of confusion during metrication at Air Canada.

Here’s some flying Greek from a flying geek:

(I hope that the Greek characters show up in your browser.)

This is only a selection — if you want more (much more), grab a used copy of Jan Roskam’s Airplane Flight Dynamics and Automatic Flight Controls, part one, which I used as a reference for this list.

Very often, I see people write that low-wing planes like my Piper Warrior have a longer flare (i.e. they float longer) than high-wing planes like the Cessna 172, usually based on the argument that lower wings benefit more from ground effect.

In fact, that does not seem to be the case: the numbers in the POH all indicate that the Warrior actually has a slightly shorter flare and shorter landing distance than the 172. My own personal experience is more dramatic: I find that the Warrior’s flare decays very rapidly at the end compared to that of the 172, and it took me a while to learn to land the plane smoothly without dropping a foot or two at the end. Other Piper owners have reported similar experiences, though, obviously, the differences are much smaller than going from either the Warrior or the 172 to a more heavily wing-loaded plane like the 182. The condition and rigging of any individual plane will also make a huge difference — if someone is flying battered, badly-rigged 172s and then switches to a clean, well-rigged Warrior, the Warrior will certainly flare better.

So what’s going on? Why would a plane with lower wings and about the same gross weight float less, when the wings are closer to the ground and should benefit more from ground effect? Here are two possibilities:

1. The Warrior has a wing loading of 14.4 lb/ft^2, vs 13.8 lb/ft^2 for the 172P. That’s not a huge difference, but it will affect the plane’s floating ability. By comparison, the Cessna 182P has a wing loading of 16.9 lb/ft^2 (note that all of these apply at maximum gross weight, not with just one or two people on board).
2. The Warrior’s wings have a lot more dihedral than the 172’s wings. Low-wing planes need more dihedral to get the same roll stability as high-wing planes, and the dihedral creates a lot of drag, as well as putting the wing tips (though not the roots) fairly high off the ground. Both the dihedral on the Warrior and the wing struts on the 172 cause drag, but I suspect that the struts produce only parasite drag, which is fairly constant, while the Warrior’s dihedral affects induced drag, which can increase dramatically near the stall (hence the abrupt end to a Warrior’s landing flare).

Basically, these two factors overwhelm any benefit gained from ground effect, increasing the Warrior’s stall speed and decreasing its flare and landing distance compared to the 172, as can be verified by the numbers in the POH. With no flaps, the 172P stalls at 51 kcas (44 kias), while the Warrior stalls at 56 kcas (50 kias); with full flaps, the 172P (with its huge fowler flaps) stalls at 40 kcas (33 kias), while the Warrior stalls at 50 kcas (44 kias) — since both planes have the same approach speed, a higher stall speed means a shorter flare.

As a final confirmation, the published landing distance over a 50 ft obstacle at sea level/ISA/maximum gross weight is about 50 ft longer for a 172P than a Warrior.

Kris Johnson has a posting on holy wars in aviation, including the two variants of the very dangerous teaching that you control airspeed with pitch and power. The idea is that students learn to look out the window (which is good) and, for any given RPM — assuming a fixed-pitch prop — memorize what pitch attitude will give them what airspeed. I believe that this teaching approach has two significant consequences:

1. it gets student pilots to first solo faster; and
2. it kills some of those pilots (and their friends and families) after they get their licenses.

While we all want to save money on flying lessons, I think this is a lousy tradeoff. The only way to make a given pitch/RPM combination produce a given airspeed is to make sure that gross weight, density altitude, CG, sideslip, and bank are always exactly the same. During training, while these conditions are not always exactly the same, they’re usually pretty close, so instructors can get away with this little cheat, students solo sooner, and everyone’s happy.

Departure Stall

Some day soon, though, the new private pilot is going to want to do more than fly around the same area under the same conditions with zero-to-one passengers on board, and unfortunately, he or she is going to be in for a big surprise. Consider this: after training through the fall, winter, and spring, the pilot (we’ll make it a male) finally has his PPL, just in time for summer vacation. He loads his wife and two children on board a Cessna 172 or Cherokee, secures the baggage in the back, and fills the tanks (making sure to stay withing W&B, of course). It’s a bit of a hot, humid day, but it’s a low elevation airport and a nice long runway, and the pilot must have taken off here 50 times during training, so it shouldn’t be a problem.

It takes the plane a lot longer to get up to rotation speed in the takeoff roll, but the pilot expected that — that’s why they have those takeoff-distance charts in the POH. It’s also much harder to unstick the plane from the runway; in fact, it seems to want to settle right back down again. Finally, though, the plane is climbing … well, sort of. The pilot is used to about 700 fpm with half tanks and an instructor on board, and 1,000 fpm or better when he’s solo; a quick glance at the VSI, though, shows only about 200 fpm. HUH? Well, the pitch is wrong — the nose is too low compared to every other climbout the pilot ever did — so he pulls the nose up a bit to get closer to the normal climb pitch. The VSI jumps up to 500 fpm, so this was obviously the right choice … except that three seconds later, it’s down to less than 100 fpm. The plane isn’t climbing at all, for any practical purpose. OK, pull the nose up a bit more (the tach shows full power, and the nose is still lower than usual), and sure enough, the VSI jumps up a bit more, before it settles down again, this time with no climb at all.

You can see where this is leading — one or two more pullups (still below the normal climb pitch angle from training) and the flight ends up as one of the many, many summer stall-spin accidents on takeoff. According to the Transportation Safety Board of Canada statistics, from 20-33% of accidents take place during takeoff, literally during the first few seconds of flight. In this case, a glance at the ASI should have told the pilot that the nose was too high, not too low, but the problem was that the nose looked too low, because the pitch was too low, and pitch + power = performance. Normally, the pilot could barely see the ground ahead at all in a Vx or even Vy climb, but this time, the ground seemed to fill a third of the windshield. Even if the pilot did look at the ASI, he might have had trouble believing it, since it was outvoted by the pitch (which showed the nose too low), the power (which showed the correct RPM), and the VSI (which showed the climb rate way too low), and all of that was combined with the stress of having the family on board for the first time, etc. etc.

Angle of attack, angle of attack, angle of attack …

Here’s the problem — it’s not pitch and power, but angle of attack that controls airspeed. The pilot studied angle of attack during groundschool, of course, but it never seemed all that practical, and the instructor’s “pitch + power = performance ” mantra seemed simpler and more logical. As long as the plane was flying under similar conditions (density altitude, gross weight, etc.) you could pretty-much map pitch angle to angle of attack during each phase of flight — there was a “climb attitude”, a “cruise attitude”, and an “approach attitude”. In the example above, however, there was a significant change to some of the conditions, so the mapping didn’t work any more.

My Warrior, for example, might climb as fast as at 1,200 fpm on a winter’s day near sea level with just me on board and half fuel; it can barely manage 400 fpm (at Vy) from the same airport with the whole family, dog, baggage, and full fuel on a hot summer day. Since Vy for my Warrior is 80 knots, assuming no wind I’ll fly forward about 8,100 feet every minute — if I’m climbing at 1,200 fpm, I’ll follow an angle of climb of nearly 9 degrees (!!); if I’m climbing at 400 fpm, I’ll follow an angle of climb of about 3 degrees. Now, my angle of attack, which controls my airspeed, goes on top of that. Let’s say that a 4-degree angle of attack gives me Vy (I’m just guessing):

• when I’m flying light on a cold day, my pitch angle will be 4 degrees for angle of attack, minus (say) 2 degrees for the incidence angle of the wings (which are normally tilted up a bit), plus 9 degrees for the angle of climb, giving me a pitch angle of 11 degrees — I’ll see nothing but clouds and sky outside the windshield.
• when I’m flying heavy on a hot day, my pitch angle will be 4 degrees for angle of attack, minus 2 degrees for the incidence angle of the wings, plus 3 degrees for the angle of climb, giving me a pitch angle of 5 degrees — the bottom third of the windshield will be filled with the ground.

In one case, a pitch of 13 degrees + full power = 80 knots; in the other case, a pitch of 5 degrees + full power = 80 knots. Different pitch, but same airspeed and same power. Clearly pitch + power != performance.

Why do some instructors do this?

Of course, there are many instructors who know the dangers of the pitch + power thing and teach it properly: you have to get to the right airspeed first, and then choose the pitch angle that gives you that airspeed at that power setting at that particular moment — it might be different every time. And you have to choose a new pitch angle not only for every flight, but for every power change in that flight (and even for the same power setting over a long trip, as you burn off fuel and get lighter). Taking the shortcut — memorizing preset pitch angles — might get you to first solo faster, but it might also kill you.

Part of the problem with the instructors who get it wrong might be the fact that a lot of them — especially the ones using flight instruction as a career step — have a surprisingly limited exposure to aviation. It’s even possible that some of the ones who are building time to get into the airlines might never have gone on a really long cross country (the one for the CPL is only a few hundred miles), never have flown a low-powered plane near gross weight on a hot day, never have taken off from a short, obstructed grass strip, never have flown an approach in actual low IMC, never have tried to maintain control inside a TCU with lightning flashing around them, never have done a continuous 180 descent from close downwind to landing to avoid holding up three jets on final at a busy airport, etc. etc. Their experience doesn’t really match much that their PPL students will be doing if they choose to remain private pilots, so instead, they pass on platitudes and old chestnuts that they learned from their instructors, and spend a lot of time on relatively pointless exercises designed to get the student past the flight test rather than helping him or her become a safe pilot.

Since both countries have statistics for 2003 available (U.S. stats, Canadian stats), and I thought it would be interesting to compare trends in Canada and the U.S. Unfortunately, statistics for the two countries do not follow the same categories, so comparison is sometimes tricky. With this posting, I’ll start by looking at how many hours we logged on both sides of the border for civil aviation (obviously, the U.S. logs a lot more military hours).

Total hours

The U.S. logged a lot more civilian flight hours than Canada did relative to its population: a full 33% more per person. In many ways, that makes sense: while Canada is a bigger country in land mass, most of our population is concentrated in the south along the U.S. border; even more importantly, about half of Canada’s population and a much larger proportion of its businesses live in the Quebec City-Windsor corridor. A business traveller in the U.S. will frequently be making long flights from New York to Chicago to Los Angeles to Denver and so on; a business traveller in Canada is more likely to take a one-hour flight (or a even a six-hour drive) from Toronto to Montreal, with only the occasional hop out west to Edmonton, Calgary, or Vancouver. Many small communities in the Canadian north rely on aviation as their only transportation link, but they are small and few, and probably not enough to tip the statistics.

General Aviation

It is much trickier to come up with general aviation numbers. The U.S. NTSB statistics divide civil aviation into three categories:

1. Part 121 Operators
2. Part 135 Operators
3. General Aviation

The Canadian statistics, on the other hand, divide civil aviation into seven categories:

1. Airliners
2. Commuter Aircraft
3. Air Taxi
4. Aerial Work
5. State
6. Corporate/Private/Other
7. Helicopters

How do we reconcile these? It is entirely possible, for example, for a helicopter to be carrying out scheduled air service or making a private flight. My best approximation (and this isn’t a very good one) is to take Aerial Work, State, Corporate/Private/Other, and Helicopters as very roughly equivalent to the U.S. General Aviation category. With that enormous caveat in mind, here’s how general aviation compares in Canada and the United States:

Again, there’s a big difference between the two countries. Allowing for the comparison difficulties, it looks like general aviation accounts for well over half of air traffic in the U.S., but well under half in Canada. So Canadians log fewer hours per person, and we log more of them on commercial or airline flights. That’s not what I initially expected to find, given that so much of Canada is sparsely populated and accessible only by air, but again, the explanation is probably the concentration of Canadian population near the U.S. border, and especially along the Quebec City-Windsor corridor.

In future postings, I’ll take a look at the differences (if any) in accident statistics between the two countries.

A comment by a fellow pilot got me thinking about headwinds and tailwinds. I started flying with serious misconceptions about how a headwind or tailwind affects a flight, and some of the bogus rules of thumb only makes things worse. I’m going to take a quick look at three popular misconceptions here — that you make up for a headwind on the return trip, that your average groundspeed over many trips is a good indication of your plane’s true airspeed, and that you should fly faster into a headwind to save fuel.

Making up for a headwind

First, the easiest one. Let’s say that you’re flying on a round trip in a single day, and the wind is forecast to be the same all day. On your way outbound, you will have a headwind, and on your way back home, you will have a tailwind. Sounds about even, right? To try it out, consider a plane with a 120 kt true airspeed (like a Warrior or a Cessna 172) flying 300 nm each way:

In other words, you never make the time up, because you spend more of the flight in the headwind than the tailwind, by definition. There are tricks, of course, like flying low westbound to get a weaker headwind and flying high eastbound to get a stronger tailwind, but averaged over many flights, the best wind is still no wind at all.

Average ground speed

And that comes to the second point. When people want to challenge the true airspeed figures put out by the airplane manufacturers, they often pull out their average groundspeeds, which are inevitably 10 knots slower or more, for which they usually blame the manufacturer’s marketing department. Part of the difference can be explained away by density altitude (nobody always flies at 7,000-8,000 feet density altitude), low power settings (many pilots are shy about setting 75% power), or climb, approach, etc., when the plane is flying outside its optimum conditions, but another big part of the difference is the wind. For example, in the table above, the plane’s average groundspeed would be 120 kt with no wind, 117 kt with a 20 kt wind, or 107 kt with a 40 kt wind. Average groundspeed is a more accurate indication of how long trips will take in a plane, but it is a different measurement than the plane’s true airspeed, because any wind at all hurts the average, and there’s almost always some wind.

Fly faster into a headwind

Flying faster into a headwind will definitely get you home sooner, but it won’t usually save gas, despite what many pilots, including flight instructors and textbook writers, try to tell you. To demonstrate, I’ll use another table. At 8,000 ft density altitude, a Cessna 172p will fly 121 ktas burning 8.6 gph at 75% power, 112 ktas burning 7.4 gph at 65% power, and 100 ktas burning 6.2 gph at 55% power according to its POH; this table shows the time and fuel to fly 300 nm with different headwinds:

Obviously, if you just want to get home, you are better off speeding up and paying for the small amount of extra gas–you’d have to be pretty dedicated to fuel savings to make your trip an hour longer to save 1.5 gallons of fuel. However, if you’re worried about running dry and there’s nowhere to turn around to (let’s say that you’re halfway between Greenland and Iceland), speeding up is not necessarily the best choice. Even at 55% power, you’re still burning half a gallon less gas than at 65% power and almost two gallons less than at 75% power flying directly into a 30 kt headwind. With a 40 kt headwind, speeding up to 65% power starts to make sense, but 75% will still burn a full gallon more fuel; in fact, you need to get up to a 60 kt direct headwind before you will save fuel by speeding up to 75% power.

Note that these numbers are for a very slow plane. If you’re flying a fast single, like a Lancair or Cirrus, or a twin, you will probably always be considerably better off at 55% for conserving fuel, unless you’re flying into a hurricane. I imagine that cross-ocean ferry pilots pretty-much always fly at low power settings, no matter what the wind is like.

My Warrior is one of the slower planes on the apron. It’s not as slow as some people claim, of course — under ideal conditions, I actually can get within 2-3 knots of the 127 knots true airspeed promised by the POH — but it makes long work of short trips compared to (say) the Mooneys or Barons, not to mention the new Cirrus and Lancair planes. I thought it would be interesting to find out just how big that difference is in real life, and what the cost is, so I plugged the best performance numbers I could find for a bunch of light aircraft into a spreadsheet, and figured out cruise time and fuel for a 400 nautical mile trip with no wind, a 20 knot headwind (normal for a low-altitude westbound trip), and a 20 knot tailwind (normal for a low-altitude eastbound trip). The results follow.

No Wind

As far as I can determine, these are all performance numbers for the plane’s optimal altitudes (depending on the engines). Unfortunately, I have not been able to find good numbers for the Lancair Columbia, so I’ve left it out: its performance should be similar to but slightly better than the SR-22. For a 400 nm trip, ignoring taxi, climb, and descent, here are the numbers:

Some of the slower planes are surprisingly fuel efficient in this table: for example, the Cessna 172 and the Piper Warrior are almost as fuel-efficient as the Mooney 201, though they take a fair bit longer to complete the trip. The range of fuel efficiency is quite large: from 6.8 nm/gal for the Seneca, to 16.9 nm/gal for the TwinStar.

20 kt Headwind

A headwind should improve the relative fuel efficiency of the faster planes, since they spend less time in it than the slower ones. It will also greatly increase the time spread between the fastest and slowest planes:

At this point, the slower planes (including the Cessna 182) really start to suffer. With 40 gallon tanks, the Cessna 172M is pretty-much at the limits of its fuel reserves for this trip; the Warrior, with its 48 gallon tanks is still safe (probably even for IFR), but both make for a very long trip. The Seneca is now almost twice as fast as the Cessna 172 and Warrior. Note, though, that the Baron still has only a half hour advantage over the Mooney, while burning more than double the fuel.

20 knot Tailwind

A tailwind should eliminate some of the advantage of the faster planes: they will burn more fuel, but won’t get you there all that sooner:

Reflections

All of these numbers are a little misleading, of course. For example, the first part of any trip is spent climbing, and a plane that climbs slowly (like the 172M or the Warrior) will spend relatively longer than a plane that climbs fast (like the twins), slowing it down a bit. There’s also the matter of maneuvering around weather enroute, long vectors for approaches at the destination, and so on. All of these planes, then, will take a little longer for the trip than these numbers suggest — my Warrior, for example, more typically needs 4:00 takeoff to landing for a 400 nm westbound trip with a moderate headwind, and 3:00 for a 400 nm eastbound trip when you factor all of that in.

The twins are not much faster than the high-performance singles but burn a lot more gas. Of course, they have other benefits, such as a redundant engine and (often) deicing equipment, but those come at a very high price. The one exception is the TwinStar, which actually outperforms its single-engine sibling both on speed and fuel burn.

So, in practical terms, what would it mean to me to upgrade to a faster plane, like a Mooney 201 or even a Cirrus? On this hypothetical 400 nm round trip with a headwind outbound and a tailwind inbound, my Warrior uses 6:38 flying time and burns 55 gallons of AvGas (about USD 190.00 at current fuel prices). A Mooney 201 would use 5:03 flying time and burn 53 gallons: that’s a hour and a half faster and about USD 10.00 less fuel to boot. A Cirrus SR-22 would get me there and back in only 4:30, for a two-hour saving, but would burn 74 gallons, adding about USD 90.00 to the fuel cost. In other words, the Cirrus saves only a half hour over the Mooney at a cost of USD 100 extra in fuel. Most of the twins are too expensive to even bother calculating, except for the TwinStar, which manages the trip in the same time as the Cirrus using even less fuel than the Mooney.

In general, pilots are a pretty smart bunch of people, so I’m always surprised reading aviation mailing lists and newsgroups to learn how many of them don’t seem to have the slightest understanding of how to control their planes’ airspeed and power. This ignorance will typically come out in a statement like “a Cessna 172p really only flies about 105 knots” (it can really fly around 120 knots true airspeed if the pilot knows how to operate it). I thought it would be interesting to look at how pilots actually set speed and power in planes with fixed-pitch propellers, and what they get for their trouble.

Marketing Writers

So the POH says that your plane will fly at 120 knots, but you never seem to get that — typically, pilots blame marketing writers for making up numbers so that their planes look better. In reality, the POH’s do usually try to put the plane’s speed in the best light, but the numbers are not made up. Normally, a plane with a normally-aspirated piston engine (like a 172 or Cherokee) will have its true airspeed will be calculated at between 7,000 and 8,000 feet density altitude, where the plane flies at its fastest: any lower, and the dense air slows you down; any higher, and there’s not enough oxygen for the engine to produce 75% power. If you normally fly below 7,000 feet or above 8,000 feet, you can expect to see a slower true airspeed. Some manufacturers will also test with the plane lightly loaded, providing a boost of a couple of extra knots (that’s the case for my Warrior) — if you put the whole family on board, you can expect to fly a bit slower.

One of the biggest problems, though, is the wind. It is a simple fact that you will spend longer (possibly much longer) flying with headwinds than tailwinds, because headwinds slow you down — for example, a trip might take three hours outbound against the wind and only two hours return with the wind, meaning that you spend 60% of your trip with headwinds. As a result, your average groundspeed will always be lower than your plane’s best true airspeed, possibly by 10% or more if you fly a lot with strong winds. That difference does not mean that the POH lied about the true airspeed, which should be as advertised (more or less), but just that wind is a big pain.

So how do pilots control true airspeed and fuel burn? It turns out that it’s easy to manage one or the other, but managing both can be a bit of a challenge.

The Constant-RPM Pilot

To start, consider the pilot who always flies with the same tachometer reading (say 2400 rpm), letting the indicated airspeed rise or fall as it will. Using a constant RPM will give a nearly constant true airspeed at any altitude, so this seems like a simple system: according to the POH, 2400 rpm will give a true airspeed of 109 knots at 2,000 feet density altitude, 107 knots at 6,000 feet density altitude, and 105 knots at 10,000 feet density altitude. That’s easily close enough, and makes flight planning simple: set the power to 2400 rpm and assume 105 knots true airspeed (to allow for old paint, chips in the propeller, draggy antennas, etc.), and everything will usually work out for any cruise altitude, plus or minus the wind.

Unfortunately, for this pilot fuel burn will vary. At 2,000 feet density altitude, the Skyhawk’s O-320 Lycoming engine spinning the propeller at 2400 rpm will be producing 69% power (110 hp) and burning 7.7 gallons of fuel per hour; at 12,000 feet density altitude, the engine will be producing 56% power (90 hp) and burning 6.3 gallons of fuel per hour — that’s an almost 20% difference in fuel consumption. Since fuel consumption seems unpredictable, the pilot has learned to fly short legs (so that there’s always lots of extra gas in the tank), making IFR flight difficult. The pilot also might decide to spend thousands on speed mods to get 3 or 4 extra knots, when simply using the right power setting at 7,000 or 8,000 feet density altitude would give an extra 12 knots without any modification to the plane. This is the pilot who goes on mailing lists and claims that his or her plane is much slower thant he POH says it should be.

The Constant-Indicated-Airspeed Pilot

Next, consider the pilot who always flies with the same indicated airspeed, varying the RPM as required. Let’s say that the pilot chooses 114 knots indicated (111 knots calibrated), which will give the maximum cruise performance for the Cessna 172p. At 2,000 feet density altitude, the pilot needs to set the engine to 2500 rpm to maintain this airspeed; at 8,000 feet, the pilot needs to set the engine to 2650 rpm (at 10,000 feet, the plane is no longer capable of this speed in level cruise). By using a fixed indicated airspeed, the pilot is actually using a fixed power setting, and that means a fixed fuel consumption: at either 2,000 feet or 8,000 feet density altitude, the fuel burn will be the same (about 8.5 gallons per hour according to the POH).

Unfortunately, for this pilot true airspeed will vary, making flight planning trickier. At 2,000 feet density altitude, the plane’s true airspeed will be 114 knots; at 8,000 feet density altitude, the plane’s true airspeed will be 121 knots. There’s also the problem that the plane might be draggier than the one used to calculate the POH numbers, so 114 knots might actually push the engine up to 80% power or higher, burning extra fuel and risking detonation.

Power Setting

So the constant-RPM pilots know how fast they will fly but not how much fuel they will burn, while the constant-indicated-airspeed pilots know how much fuel they will burn per hour, but not how fast they will fly.

Right about this point, a lot of people will argue that that’s not the case — after all, if a pilot always flies at about the same density altitude, he or she will find the fuel burn and true airspeed pretty predictable with either technique. The problem comes, however, when one of those pilots flies somewhere different than the normal summer cross-country at 3,000 feet (or whatever normal means for that pilot). For example, where I live, in Ottawa, it gets cold enough in the winter that the density altitude at 3,000 feet is sometimes still negative. A constant-RPM pilot who flies under these conditions will burn far more fuel than expected, and could end up landing with near-empty tanks when expecting a half-hour reserve; a constant-indicated-airspeed pilot who flies under these conditions will fly far slower than expected, and could end up landing with near-empty tanks (again) because of the extra travel time. I believe strongly that this is why some good, experienced pilots run out of fuel: something changes from their normal flying routine (colder weather, different cruise altitude, etc.), their normal technique produces abnormal results, and they do not understand how to compensate for it.

Knowing your power setting requires calculating your density altitude and then looking up your RPM in a table or graph, which is a big pain, but it does allow you to get maximum performance (true airspeed and range) out of your airplane safely. You do not have to do that for every flight, of course — once you know your indicated airspeed at any given power setting, and have confirmed your fuel burn, you can use a variation of the constant-indicated-airspeed approach, as long as you do the calculations to get your true airspeed. The alternative is believing that your plane is 10 knots slower than it really is, or never knowing quite how fast you’ll fly or how much fuel you’ll burn.

Following my 1:60 rules of thumb, here are some rules of thumb that apply to altitude. Some of these, like pressure altitude, are basic stuff from any ground school, but some are not well understood. Density altitude is especially useful, because it lets you forget about all the temperature-correction interpolations in the performance tables in your POH and just read the numbers you need directly.

Pressure Altitude

OK, if you don’t know this one, stop flying. The altimeter setting for the standard atmosphere is 29.92 inHg (inches of Mercury). For every inch below that, your pressure altitude goes up by 1,000 ft; for every inch above, your pressure altitude goes down by 1,000 ft. Of course, the easiest way to figure this one out is to temporarily change your altimeter to 29.92 inHg and read the pressure altitude directly, but the calculation isn’t really trick. For example, if your altitude is 2,000 ft and the altimeter setting is 29.40, the difference from standard is -0.52, so you have to add 520 feet to get your pressure altitude (PA) of 2,520 ft.

Standard Temperature at Altitude

Standard temperature at altitude, at least below the flight levels, is even easier than pressure altitude, and again, everyone knows this from ground school. At sea level, the standard temperature is 15 degC, and it decreases by 2 degC for every 1,000 ft. So the standard temperature for 5,000 ft is 5 degC, the standard temperature at 10,000 ft is -5 degC, and so on.

Density Altitude

Density altitude is the key to airplane performance. For example, whether you are at 8,000 ft with an altimeter setting of 31.00 inHg and an outside air temperature of -23 degC, or at 2,000 ft with an altimeter setting of 29.00 inHg and an outside air temperature of 19 degC, you are at the same density altitude — 4,000 ft — and will see the same cruise speeds, the same climb rate, the same fuel consumption, and the same takeoff and landing distances.

If you have been muttering about wasting your time with the first two examples, here’s a chance to put them into practice: density altitude is, roughly, just pressure altitude +/- 120 ft for every 1 degC difference from the standard temperature at that pressure altitude. So if the pressure altitude is 5,000 ft and the outside air temperature is 30 degC, the difference from standard temperature (5 degC) is 25, and 25 * 120 is 3,000: that means that your density altitude is about 8,000 ft: your plane will be flying (and burning fuel) as if it was at 8,000 ft, not 5,000 ft; if you’re on the ground in the mountains, your plane will also take off and climb as if it were at 8,000 ft, so you might want to wait until the sun goes down and things cool off a bit.

Density altitude is also interesting in the winter, because it can drop thousands of feet below sea level, allowing your engine to produce far more than its rated horsepower. It’s easy to get spoiled watching your climb rate improve by 50% and your takeoff roll shrink to a few seconds, but remember that you’re also burning a lot more gas than you’re used to unless you throttle back a bit.

Takeoff Distance and Density Altitude

I’m not entirely sure about this one, so check your own manual, but in all of the POH’s I’ve looked at, takeoff distance is linear with density altitude: however many feet you add to your sea-level takeoff distance for 1,000 ft DA, you add double that for 2,000 ft DA, and so on. For my Warrior II loaded all the way up to 2,440 lb, the POH says that I need 1,100 ft of runway at sea level, 1,400 ft at 1,000 ft DA, 1,700 ft at 2,000 ft DA, and so on, so my magic number is 300 ft for every 1,000 ft of density altitude (of course, I always leave a big safety margin, and don’t fly out of short fields at full weight anyway).

Line of Sight and VHF/UHF Reception

If your thumb can do square roots, you can use it (or your pocket calculator) for figure out approximate VHF/UHF reception distance at any altitude, assuming the signal is strong enough and there are no mountains or tall buildings in the way. To get the reception range in nautical miles, multiply 1.23 * your altitude above the transmitter in feet. So, if a VOR/DME transmitter is at 1,000 ft MSL and you’re flying at 9,000 ft MSL, you can expect to receive it at 1.23 * sqrt(8,000), or 110 nm away.

Since VHF and UHF both work on line-of-sight, this is actually the calculation for how far away you can see something in clear air before the curvature of the earth blocks it. So on a clear night, this might also give you a clue about how far away you can expect to see a city’s lights. At 3,000 ft AGL, you might be able to start seeing them when you’re 1.23 * sqrt(3,000), or 67 nm away (of course, you may make out the glow reflected from clouds above the city sooner). Sometimes the atmosphere plays tricks and bends light a bit around the horizon so that you can see things even further, but I don’t claim to know enough science to explain that; if someone who knows writes in, I’ll add an update.

The Lying Altimeter

Finally, there is the issue of altimeter error. Temperature affects the density of the air (remember density altitude), which affects the pressure gradient, so on a hot day, the altimeter will say that the plane is lower than it actually is, and on a cold day, the altimeter will say that the plane is higher. The formula is 4 feet for every 1 degC deviation from the standard for every 1,000 feet above the station reporting the altimeter setting.

So, let’s say that you take off from an airport at 2,000 ft MSL (with its altimeter setting) and climb to 12,000 ft MSL to cross a 11,000 ft mountain chain. If the outside temperature is -30 degC, what’s your real altitude when the altimeter reads 12,000 ft? Standard temperature at 12,000 ft is -9 degC, so the difference will be 4 * 21 or 84 feet for every thousand. Since you are 10,000 feet above the station, you will actually be about 840 ft lower than your altimeter says — you’ll fly across the 11,000 ft mountains at 11,160 ft, give-or-take.

After reading my posting on the Rule of 60, Malcolm Teas kindly pointed me to a 1996 Usenet posting by Barry Silverman (originally written ten years ago, in October 1994) describing the French method of teaching pilot navigation. He also recommended a couple of books on mental math for pilots, for those of us who wear propeller beanies over our headsets — if you’ve read this far, you know you’re one of us.

The French method divides 60 by your true airspeed (there’s no escaping the number 60) to get a factor F, which you can use in mental calculations to estimate time enroute and wind correction angle without requiring an E6B or calculator: see the link to the original posting for details.

Malcolm also recommended two books for people who enjoy flying by numbers: Diversion Planning: How to Navigate Around the World with a Stopwatch and a Pencil (USD 8.95), written by a retired British RAF navigator named Martyn Smith, and Mental Math for Pilots (USD 27.95), written by Ronald D. McElroy, Pam Ryan, and Carol Core. To these, I’ll also add the Cross-Country Flying chapter of John S. Decker’s excellent (and free) online flying text, See How it Flies.

I enjoy the numbers in flying. That’s not to say that I’m one of those people who try to calculate everything to five decimal places like the FAA and Transport Canada (unrealistically) require on their tests; rather, I like the kinds of numbers that you can actually play with in your head while you’re flying the plane: they keep you awake and improve your situational awareness, so they’re a win-win. I’ve been collecting these rules of thumb for a while, from many different sources, and one of my favourites is the 1:60 rule: one degree equals approximately one unit (foot, mile, whatever) sideways for every 60 units forward.

Distance to a navaid

On Canadian written flight exams, and I assume on those of other countries as well, the 1:60 rule usually appears in a cryptic and almost totally useless question about calculating the time to a VOR or an NDB. The 1:60 rule says that 10 degrees should account for a unit sideways for every six units forward (60/10), so however long it takes you to change your radial or inbound track by ten degrees, it will take you six times as long to get to the navaid. For example, imagine that you are tracking inbound on the 260 radial of a VOR (i.e. your track is about 80 degrees), you turn right to 170, and it takes five minutes before you intercept the 250 radial. That means that your approximate time to get to the VOR is 6 * 5, or 30 minutes in the unlikely event that there is little or no wind to mess up your calculation (but of course you just wasted 5 minutes finding that out, and if you are IFR, you have ATC screaming at you over the radio and rerouting traffic all over the sector to stay out of your way). Let’s be realistic: if you’re VFR, just look out the window; if you’re IFR, check the DME or GPS, or even just your time since the last checkpoint, or call ATC and ask where you are. The only time that this stunt might make sense would be if you were completely lost with no GPS, DME, or ATC radar coverage.

Calculating the crosswind

Fortunately, there are more useful things you can do with the 1:60 rule, including calculating the crosswind component: this trick works especially well if you have your track and groundspeed from either a VOR/DME or a GPS. First, divide your groundspeed by 60 (approximately) — that gives you the amount of crosswind represented by each degree of crosswind correction; next multiply that number by the difference between your track (GPS or VOR) and your actual compass heading, and you have the crosswind component in knots or miles per hour, as applicable. For example, if your groundspeed is 110 knots, then each degree accounts for 110/60 or just under 2 knots of crosswind. If you are tracking the 133 radial outbound and your heading is 141, then your crosswind correction is 8 degrees right and the crosswind at your altitude is a bit under 8 * 2 knots: let’s call it 15 knots.

If you’re really bored and want to keep your brain awake during a long flight, you can go on and estimate what direction the wind is coming from. To do that, start by figuring out your headwind or tailwind component by subtracting your groundspeed from your true airspeed or vice versa: for example, if your true airspeed is 125 knots and your groundspeed is 110 knots, then you have a 15 knot headwind component. If the headwind and crosswind (from the right) are both 15 knots, then the wind is blowing at about 45 degrees to your right — just trace your finger around 45 degrees on the heading indicator or VOR, and you’ll see where the wind is coming from (in this case, you can round it off to 180 degrees, or due south, so there’s a good chance that there’s a low pressure system directly to the east of you: the 1:60 rule is even useful for weather observation and forecasting, just like the ).

45 degrees is easy, because the cross wind and headwind are equal. It’s also easy to calculate when you have a pure headwind (the crosswind is 0 or very small) and a pure crosswind (the headwind is fairly small). At 30 degrees, the crosswind will be about 60% of the headwind; at 60 degrees, the headwind will be about 60% of the crosswind. So if the headwind were 6 and the crosswind were 11 from the right, you’d have the wind blowing from approximately 2 o’clock (there’s no need to be more accurate than that). Being able to perform this kind of calculation is especially useful during IFR training or an IFR flight test when you’re on your way to a VOR for a hold.

Climb and glide angle

Many light, fixed-gear planes like the Cherokee and Skyhawk glide at about 1:10 when fully loaded: they move forward ten units (feet, miles, etc.) for every unit they descend. Since 1:60 represents a single degree, 1:10 represents six degrees — that’s your glidepath. If you plane glided at 1:12, your glidepath would be about 5 degrees (60/12); if it glided at 1:6, your glidepath would be about 10 degrees (60/6). When you consider that a typical VASI/PAPI or glidescope is set up to bring you in on a slope of 3 degrees, you can see that you won’t have much chance of gliding to the runway if you lost the engine on final.

The 1:60 rule also gives you your climb angle, as long as you convert miles/hour to feet/minute first — one knot is just a bit over 100 fpm, so it’s an easy conversion. For example, if your plane climbs at 70 kt (~7,000 fpm), then your climb angle is 1 degree for every 117 fpm (7,000/60 — call it 120 fpm) that you can climb at that speed. If your climb rate is 640 fpm, then your angle of climb is a bit over 5 degrees (640/120). This calculation is easier to perform at home, with a calculator.

Navaid accuracy

The 1:60 rule is useful, if a little frightening, for figuring out navaid accuracy. In Canada, a VOR receiver has to be accurate within +/- 6 degrees, which, obviously, means 1:10. That means that if you are 50 nm from a VOR, you could be 5 nm (50/10) left or right of the airway with your receiver in tolerance; at 100 nm, you could be 10 nm left or right. Air traffic control is so used to GPS these days that they used to call me to check if I was two miles off an airway centreline halfway between two widely-spaced VORs — unfortunately, the equipment isn’t any more accurate than that. I’m just glad that I don’t have to rely on the VOR for flying through mountain passes.

Deliberate deviation

You can also use the 1:60 rule to change your heading deliberately to miss a target. For example, let’s say that you’re dead-reckoning from inland to a city on the coast. To make sure you don’t miss the city, you decide that you want to hit the coast 20 nm to the left of the city and then turn right and follow the coast in. How much should you change your heading if you’re 120 nm away? That’s 2 nm for every degree (120/60), or a course change 10 degrees to the left.

With cheap, portable GPS in almost every cockpit now, this stuff is not as important as it used to be, but it can still be a lot of fun, especially when you’re sitting in your chair on a bad day, wishing you could be up flying.