Land and Hold Short

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.

My Warrior’s altimeter is probably the simplest instrument on the panel, really nothing more than a calibrated barometer. It doesn’t even tell me my real altitude — on a very warm or very cold day it can be off by a thousand feet or more. Still, when I sat down to think about it, I surprised myself by coming up with four uses for this piece of low-tech steam gadgetry beyond finding my current altitude, starting with weather forecasting (note: I make no guarantee that any of these is practical or reliable).

Weather Forecasting

Because the altimeter is a barometer, I can use it to forecast the weather in a clumsy way. With any barometer, when the mercury is falling, the weather is probably getting worse, since a low-pressure system is likely moving in; when the mercury is rising, the weather is probably getting better, since a high-pressure system is likely moving in.

So, let’s say that I land at a small, unattended airport for a leisurely lunch with a friend. Before I tie down the plane, I set the altimeter so that it shows the field elevation of 550 feet. Three hours later, I come back and the altimeter reads 750 feet — that means that the pressure has fallen by 1/5 of an inch of mercury in three hours (one inch of mercury is 1,000 feet), and the weather is going down. Where I live, in central Canada, the prevailing winds are from the west, so that’s probably where the low-pressure system is moving in from. That means that I can look up at the sky at the current weather, and then make a reasonable guess that if I fly west, towards the low, the weather will get worse than what I see right now, and if I fly east, away from the low, the weather will get better; north and south, of course, are anybody’s guess. If I came back after three hours and the altimeter read 1,550 feet, then the pressure is falling fast (one inch of mercury in three hours), and the weather change will probably be more severe.

The same thing works in the air — if the altimeter settings from airports along my route are getting lower, there’s a good chance that I’m flying towards worsening weather; if they’re getting higher, there’s a good chance I’m flying towards improving weather. In the air, that works moving north and south as well.

Detecting Inversions

The thermometer tells me the outside air temperature at my current altitude, but not the temperature of the air below me. However, I can use the altimeter to at least get a clue about what’s going on underneath if I compare its reading with the elevation displayed on a GPS (preferably one with WAAS). The altimeter is calibrated to show my altitude +/- 50 feet only when it has the correct altimeter setting and the air temperature is exactly 15 degrees Celsius at sea level and the temperature follows a standard lapse rate of 1.98 degC for every 1,000 ft up to my altitude.

On a cold winter day, the altimeter should show me much higher than I really am: for example, the altimeter might read 10,000 feet while the GPS shows me at 9,100 feet. On a hot summer day, the opposite is true: the altimeter might read 10,000 feet while the GPS shows me at 10,500 feet. When I don’t see the error I expect, that tells me that something unusual is going on beneath the plane — for example, if I’m at 10,000 feet indicated with an outside air temperature of -30 degC and the GPS shows that I actually am near 10,000 feet, I can take a fairly reasonable guess that I’m in cold air overrunning an inversion, and that things will get much warmer if I descend a bit (which could be bad in the winter, since I might end up in the ideal icing zone of 0 degC to -10 degC). Likewise, if my actual altitude isn’t above my indicated altitude on a hotter than average day, it’s a sign that there might be cooler air below me.

This is something I’d like to work on a bit. I’m still not sure how practical it would be in the cockpit.

Finding Vertical Air Currents

Glider pilots know all about using thermals and other vertical air currents to gain altitude. Unfortunately, those of us who fly underpowered planes also end up having to learn about these currents, since sometimes they’re the only way we can climb past 9,000 or 10,000 feet on a hot summer day in a fully-loaded plane. The vertical speed indicator lags a fair bit, so it’s not all that useful for finding rising air — by the time it shows a climb, I might already be past the air current. The altimeter, on the other hand, reacts almost instantly, and used together with the airspeed indicator, it tells me when I’m in rising air during a climb:

• If the altimeter needle starts moving faster and the indicated airspeed stays the same or increases, I’m in a column of rising air; often, I’ll slow down the plane below Vy to spend more time in the column. If the indicated airspeed is decreasing, then turbulence has probably just pitched the nose up.
• If the altimeter needle starts moving slower (or even falling) and the indicated airspeed stays the same or decreases, I’m in a column of falling air; often, I’ll speed up the plane well above Vy to spend less time in the column, even if it means levelling out or descending a bit. If the indicated airspeed is increasing, the turbulence has probably just pitched the nose down.

These will sound funny to people who fly behind big, powerful engines, but they matter a lot to someone dragging four people behind a 160 hp O-320. In level cruise, finding the currents is a bit simpler: assuming a constant power setting, if I have to push the yoke forward to keep the altimeter needle still, I’m in rising air, and if I have to pull the yoke backward, I’m in falling air.

Maintaining Attitude in IMC

Finally, the altimeter can help me maintain my attitude in IMC, especially in stratus cloud (where vertical currents are rare). Along with a rising airspeed, a falling altimeter needle is one of the first signs that the wings are not level — if the attitude indicator shows that I’m level and the engine is still producing the same power but the altimeter shows me descending from cruise or descending faster than expected in a planned descent, it’s time to cross-check the turn coordinator, vacuum gauge and compass to see if the attitude indicator is malfunctioning. This is especially useful during instrument approaches, when the altimeter is near the centre of the scan: it’s one of the first places I should be able to detect the beginning of a spiral.

In fact, in a severe partial panel situation (losing all gyros), the altimeter could be essential for maintaining attitude, though that kind of situation is very rare and very difficult to manage if it does happen.