Closing Angle

[Vone Rotate]

Hi all,

Does anyone know how to work out the 'Closing Angle' for a PA-28 cruise speed of 100kts G/S?

I use this method but wondered how to adjust the closing angle to keep the times to 1nm=1min flying time. I currently use this:

E.g 1 mile off track = turn towards desired track 30deg for:
1 mins @ 120kts G/S
1 1/2 mins @ 90 kts G/S
2 mins @ 60kts G/S

I remember an FI examiner telling me you can work the angle out for your aircraft speed so its 1 min per mile off track to regain your desired track rather than adjust the time as I have done here.

Thanks

[RTN11]

The figures you've used are close enough to work out in the real world. As you turn, the way the wind affects your track will change, so it's never going to be exact. All of these methods just have to be close enough than when you look up you see the reference point you're expecting and go from there.

There are plenty of tips and tricks out there. I prefer to mark halfway points, when you get there see how far off track you are in degrees, double the error and that takes you straight to the destination. This works out as less track miles flown, but the method you've stated has the benefit of getting you back on the line you drew on the map early on, so a feature you were expecting on the left/right should be on the same side.

Another good tip is that while you're in the planning stage with the wind, magnetic variation, and any compass deviation, always round the error the same way, that way when you're off track you know which side of track you expect to be and how you should therefore be correcting it.

[keith williams]

If you sketch out the triangle of velocities you will find that to obtain a closing speed (or cross track speed) the equation is:

Required ground speed = Required closing speed / Sin of closing angle


You have specified a closing speed of 1 nm per minute which is 60 knots, so the equation becomes:

Required ground speed = 60 / Sin of closing angle.

Signs for most practicable angles are less than 1 so mentally dividing by the sign is a bit difficult. So to simplify the task we can multiply by 1/ the sin.

This changes our equation to:

Required ground speed = 60 x 1/Sin of closing angle.


Taking a few angles as examples

Sin 40 degrees = 0.642787609

1/Sin 40 = approximately 1.556

We now have:

Required ground speed = 60 x 1.556

This is probably a bit too difficult to work out mentally so we need to simplify it. We can do this by rounding up to 1.6 to give us

Required ground speed = 60 / x 1.6 which is 96 knots

So if we are 1 nm off track and we use a 40 degree closing angle we need approximately 93 knots to get back on track in one minute.

To test the accuracy use the original equation

Required ground speed = 60 / Sin of closing angle.

Required ground speed = 60 / 0.642787609 which is 93.34 knots.




If we go through the same process for a few other angles we get:

50 degrees Required ground speed = 60 x 1.3 = 78 knots (78.3).

45 degrees Required ground speed = 60 x 1.4 = 84 knots (84.9).

40 degrees Required ground speed = 60 x 1.6 = 96 knots (93.3).

35 degrees Required ground speed = 60 x 1.7 = 102 knots (104.6).

30 degrees Required ground speed = 60 x 2.0 = 120 knots (120).

25 degrees Required ground speed = 60 x 2.4 = 144 knots (141.9).

20 degrees Required ground speed = 60 x 2.9 = 174 knots (175.4).


All of these solutions clearly include some rounding errors (the more accurate figures using 60 / sin are in brackets. If you wish reduce these errors and avoid having to do lots of mental arithmetic in the air, just select a few angle and calculate the required ground speeds using your calculator and the full equation:

Required ground speed = 60 / Sin of closing angle.

Then write down the required ground speeds for the selected angle on your knee pad (or whatever you use). You can read the required ground speeds directly from your knee pad.

[BEagle]

K.I.S.S!!

SCA = 60/(Speed in mi/min), so at 100 kts that's 60/(1⅔), or 180/5, i.e. 360/10 = 36°.

Thus at 100 kt, SCA is 36° and a timing correction of approx 1/4 the time spent correcting a track error should be added to the next time check, if you're happy with the along track velocity being speed x (cos SCA).... If not, just believe it - because it works!

Don't try and make it too complicated though - it's a technique for correcting back to track simply and quickly without too many hard sums. And you can always note down headings ± SCA for each leg before you get airborne!

[Vone Rotate]

That's absolutely perfect! Thanks.

As a CPL student I had all kinds of lines, angles and god knows what else for track errors.

I want to keep it simple for my PPL's and tried this a few times with success. I was after understanding it better so I can teach it with a full understanding! Thanks!

[keith williams]

Actually Beags, not only did I fail to KISS, but I also failed to RTFQ!
(Not a recipe for a happy sex life).

The OP asked how to calculate angle for a given GS. I described how to calculate GS for a given angle.

[dobbin1]

That's absolutely perfect! Thanks.

As a CPL student I had all kinds of lines, angles and god knows what else for track errors.

I want to keep it simple for my PPL's and tried this a few times with success. I was after understanding it better so I can teach it with a full understanding! Thanks!


I teach the Standard Closing Angle technique to my students and I find it to be by far the easiest for them to use. Closing angles of more than 30 degrees are not desirable, so at most spamcan speeds it is better to use half the angle and double the time. I have a PowerPoint briefing on the subject - pm me if you want a copy.

[BEagle]

Closing angles of more than 30 degrees are not desirable, so at most spamcan speeds it is better to use half the angle and double the time.

That's because virtually no-one teaches how to make appropriate timing corrections when using SCAs of 40°..... Does your .ppt brief do so?

[dobbin1]

I have found that using the modified SCA (20 degrees at 90 knots for example) and flying for two minutes for every mile off track there is no need to adjust any timings. My brief does not cover timing changes.

[Ascend Charlie]

Forget that rubbish and track crawl. Look ahead to find a spot that is back on track and fly to it, then re-set your heading to allow for the drift that obviously was different from the forecast - like everything else in the aviation world.

1 in 60, bah, humbug.

[ShyTorque]

Spoken like a true fair weather only pilot.

[Tinstaafl]

I'd like to see you track crawl in Australia's outback. 1:60 for me so I can *choose* an appropriate track regain position - which could be 30 mins up to 2 hours away i.a.w. Oz' position fixing requirements, depending on the fix method.

It's a simple matter to use the same 1:60 distance measurements to find an ETA for the on-track position and destination/turning point - and it will give your the information needed to adjust the subsequent heading needed to maintain track. It's not difficult to do a 1:60 in your head once you measure the 3 distances (I use my calibrated thumb) needed for a track correction.