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.
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.
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.