Pete, try this trick. It works well for some, especially those of us a little slower at mental math, and I think you'll like it.
Picture a DG on a heading of 360. With a standard rate (2 minute turn) the number directly on you tail (180 -- visualize the DG or grab a picture online, or take a few minutes in a parked airplane to do this) is exactly one minute.
The number on the right wingtip is 1/2 of a minute. 30 seconds.
Same with the number on the left wingtip. 30 seconds.
Don't do the math in your head. Visualize the points on the DG in a time reference. sSee the DG as a clock.
Now spilt those into quarters. The right 45 degree angle (045) is :15 seconds. The right 90 + 45 more (135) is :30 plus :15 ... Easy to do that math in your head, it's 45 seconds.
Same the other direction. The heading directly under the 45 degree line (if you have one, or just look halfway between the heading you're flying and the left wingtip line, is :15 seconds to the left.
225 is directly on that right aft 45 degree line. That's :30 plus :15.
Use the DG like a very odd clock. You can also "slice and dice" your DG up in 3.3 second intervals for every 10 degrees if you want to get real precise. Knowing that every 10 degrees is just over 3 seconds works great as an add-on, read on for how.
Same deal, but now let's start out on a heading of 200. Look at the DG. The heading, whatever it is, directly on the tail is one minute away. It just happens to be 020, but don't get hung up on the heading numbers reading this. It's a visualization exercise. Imagine you look at the DG and whatever number is on that tail line right now, is a one minute turn away.
Now imagine a controller says "turn right heading 290". Don't jump to trying to do mental math, just LOOK at the DG and hey, that's right under the right wingtip line. We know the right wingtip line is :30 of turn no matter what the number under it is.
You can be on a heading of 045 and your right wingtip is on 135 and your left on 315. They're both a :30 second turn away. Think about the DG as a clock that takes 2 minutes to go all the way around it.
Pretending your DG is like an old style wristwatch or clock with one minute directly on the tail, anyone can closely guesstimate a timed turn to any heading on the clock face.
No it won't nail it with 100% accuracy if your instructor is trying to get you to do the mental math for an exact number, that comes with practice.
But in real-world flying where you need to look at the DG in a second or so and ascertain how long of a turn you should expect after a controller gives you a heading, you just look, see what quadrant it's in, guesstimate the angle and you'll have a rough number from your "DG clock" without bogging down your brain too much with any math.
The cardinal headings, no matter what they are on the DG, at the 90 left and right are always half a minute, :30, and the 45's are always 1/4 of the dial, and 1/4 of a minute, :15 or half the way plus another quarter
30 plus :15)... :45. Directly behind you is always one full arc of the dial :60.
Think of a minute hand that only goes from the top to the bottom. 1/4 of a minute as it traces it's sweep around if you were to hold heading, it would point at 045 off the nose, either direction. 1/2 of a minute it would point at 090 off the nose -- the wingtips. Etc. Keep going around the dial.
Draw yourself a DG in time on a piece of paper. 0 seconds at the top. 60 seconds at the bottom. Fill in with ten degree increments. Study and memorize it. Now you can mentally "overlay" that onto any DG with any heading at the top.
If you have access to a PC based flight sim, play with this. Put the sim on any heading and have someone (or yourself) call out a random heading. Don't turn. Look at the DG. Is your heading about 2/3s of the way around one side of the dial toward your tail? That's 2/3s of one minute. Or... 40 seconds.
Don't get bogged down in the number of degrees it is off your heading or try to do the math when first visualizing this. Just use the DG like a clock.
Now if your flying something that has a sweep second hand on the clock instead of a digital display, you can apply this visual-angular technique to the clock itself.
To make this easy at first, wait until the second hand is pointed straight up. As you get better you can pick your starting point on the sweep hand.
Want to turn 45 degrees right? When the second hand is pointed 1/4 of the way around the dial, or straight out to the right (since the clock only runs clockwise) that's 45 degrees. Doesn't matter if you're turning right or left, straight out to the right is a 45 degree turn.
1/2 way around the dial, or straight down, would be 90 degrees of turn. All the way around is a course-reversal or 180 degrees.
You can also use this trick...
We know that three degrees per second is what we're doing. To turn 30 degrees either direction, look at the clock and start your turn. When 10 seconds have passed, roll wings level. This divides evenly and nicely at 30, 60, and 90 degrees. In-between you'll have to do some memorization or use one of the other techniques.
The whole point of these exercises is to get your brain thinking in clock face angles. Not counting seconds. Some people do exceedingly well with the math quickly in their heads, but just by visualizing the DG as a clock, or a sweep clock as if it had degrees printed on it all the way around, you can get the job done very quickly if you have a good "visual overlay" imagination and have drawn it out on paper a few times.
I'm imagining if you're a gamer, you like games where you can see the angles and know how much movement it takes your mouse across the table to line up cross-hairs or similar. Turn the DG and/or the clock into the opposite type of instrument in your mind's eye and it's a simple matter of waiting for the angle to line up on the clock or seeing the angle on the DG before starting the turn and knowing "that angle is the right wingtip and that's always :30 seconds away.
Put the two techniques together and you're flying along on a heading of say 035 and a controller says "turn left heading 270". You can either mess with the mental math and figure that is X number of degrees or you can slice and dice a little in your head, like this.
3 deg/sec means 36 would be easier math. 12 seconds to 000. (close enough)
At 000/360 heading, 270 is exactly at the :30 line.
:30 plus :12 will get me damn close.
Punch the start button on your handy dandy digital timer and/or pick a straight up, straight right, straight down, or straight left indication on the sweep second hand clock and start the turn, visualizing stopping it at just before three 1/4 chunks of the clock have gone by. It's :42 seconds, which is just 3 seconds under :45 which is three 1/4 clock "pie wedges". To keep it simple, let's say you started the turn at 12 straight up. You know you'll stop just before 9, straight left, which is three 1/4 pie-wedges from now.
It takes a little practice, and if you're of a younger generation without many clocks with hands on them, you can probably just toss this whole reply out and work harder on the mental math. This angular relationship between time and a second hand isn't imprinted enough on the brain.
But for Gen-X and older, this can make the mental math go away. The clock is mentally marked in degrees from 0 straight up, to 45 at 3 o'clock, 90 at 6 o'clock, 135 at 9 o'clock, and 180 back at the top.
The DG is marked in time with :15 at the 45 degree mark, :30 at the 90 degree wingtip mark, :45 at the 135 degree (45 behind) mark, and :60 at the bottom. Both sides.
Clear as mud, or does it help? It's damn fast in the cockpit with a little practice, but completely foreign to how it's taught on written tests and by CFIs who are fast at mental math.
If you do go the mental math route, remember rounding a little and knowing the effect is okay too. If someone says "40 degrees right is how many seconds?", quick long division will tell you that it's 13+ right? 10 x 3 = 30, 3 x 3 is 9 = 39. We also know 45 degrees is always :15. So it's easy to swag. 14 seconds is close enough. But saying "just over 13 seconds" if you did the long-division in your head, or "just under 15 seconds" by working your angles in your head, in anything flying Cessna bugsmasher speeds is also going to get you to the answer you need, just fine.
