Math Moron stumped - off track problem!

[sneetch]

Hi all!
I'm a student PPL and just a complete mathmatecal dullard.
This (probably very simple) navigation problem has me a little confused. Here it is:

You are 4nms left of track and 30nms later are 2nms right of track with 20nms to go to your destination. What is the required heading alteration to make your destination?

Please help ........ I'd be very grateful.
You will win naming rights to my first born child if you will please just help me to understand!!! ...... I Promise.



:ok:

[PPPPP]

I made it 17.7 degrees left (nearly).

(12 deg off heading at the waypoint, 6 deg more to turn to destination.)

Similar triangles seems to mean you are 2 nm off track to the right with a baseline of 10nm, so your deviation is (90-(tan-1 10/2) ) deg.
You are 2nmright with 20 to go so you need a further (tan-1 2/20) degrees left.
My , its a long time since I did trig so this could be complete pants...

(edited to justify my answer<G>)
(again to correct duff typing)

[GroundBound]

I think it’s the following, but I would need to do a trig check to be sure.

You have moved 6 nm from left to right, in a distance of 30nm. In other words your actual track is 12 degrees to the right of the desired track.

So, to turn parallel to your track you need a left turn of 12 degrees.

Now you need to regain the 2nm right of track in the next 20 nm, (or 6nm in 60nm), so that's a correction of 6 degrees to the left of the desired track.

So its 12 degrees plus 6 degrees, 18 degrees to the left.

Apologies if this is wrong and someone else can tell you better.

Please don't name your child GroundBound, I'd hate to condemn a poor kid to that for the rest of his/her life.

[Wunper]

Sneech


Answer
18 degrees heading change required to the left.

All based on 1 in 60 rule and similar triangles

1 degree track error over 60units of distance will place you 1 unit of distance off track.

Best to DRAW this to follow it

So you go from 4 nm left of track to 2 nm right of track over 30nm.

Assume you were on track at the start(and not 4 nm left of it) that same heading would place you 6nm (4+2) right of track after 30 nm on the same heading. Multiply both by 2 to get the magic 60 units of distance and you have 12 units right of track and are therefore tracking 12 degrees right of the desired track.

You are 20 nm from destination and 2nm right of track and we know that at this point we are heading 12 degrees right of the heading we should have started with, lets see 3 X 20 = 60 so 3 X 2 = 6 degrees 12+6 =18 degrees


Notice how all the distances are easy multiples of 60?

I hope all this waffle helps you do a search on google for 1 in 60 rule theres heaps out there that explain it better than I do

Wunper
:ok:

[BEagle]

If you're 4 miles left of track, turn right through by your Standard Closing Angle (approx. 60/IAS in miles per minute, i.e. 40 deg at 90KIAS), hold for 4 minutes, then reverse back onto your planned heading. Resynch DI and check the ac is in balance. Adjust your ETA by 1/3 of the 4 minutes, i.e. 1.3 mins if you used a 40 deg SCA.

If you're 2 miles right of track, turn left by SCA, hold for 2 minutes, reverse onto heading, resynch and check. Delay ETA by 2/3 of a minute.

Throw away the hard maths, just use Standard Closing Angle. Trouble is, it's so simple that the dinosaurs don't believe it and continue to force you to suffer hard and pointless mental calculations! SCA is a refinement of the ancient 1 in 60; if it's good enough for the RAF it's good enough for me!

[FlyingForFun]

Sod that.

Assume that there are good visual landmarks nearby (which I think is a reasonable assumption, since otherwise how would you know how far off track you are). You're 2nm right of track, that's not really a huge amount in the grand scheme of things. You're 20nm from your destination - also not very far in the grand scheme of things, certainly not far enough to get lost.

Fly in the direction you'd originally planned, and look out of the left window until you see something you recognise. If the first thing you see is your destination airfield, that's fine - the ATZ will be at least 2nm radius, so you'll be perfectly placed for an overhead join.

There is a place for maths in flying - and unless the maths is very simple, or you've got two pilots on board, that place is on the ground. It's certainly not when you're approaching an airfield, with the extra workload of descending, getting set up for landing, looking for other arriving and departing aircraft which will most likely be at a similar altitude, and looking for the airfield itself.

FFF
-----------------

[stiknruda]

SCA and "snapping for the turn" (using the 1in60 rule) work for me, too.

Doubling the distance off track (if parallel) and turning towards track for 5 mins before reversing half the turn to parallel track used to work in the Dominie - it was just a convenient refinement of the SCA and very easy to remember - even 20 odd years later!

Knowing your g/s in nm/minute makes estimates quite painless -

90 knots = 9nm in 6 mins, 4.5 nm in 3 ergo 1.5 in 1 minute

140kts = 14nm in 6 mins, 7nm in 3, ergo 2and third in 1 minute

Stik

[Chimbu chuckles]

While I have great affinity for the 'turn left a bit an ya carnt missit' in this particular case I also can't help but think the required answer is a little more tech.

For mine I would ignore everything before 2nm right with 20 to run. Double your closing angle and you'll be well inside whatever tolerances anyone wants to make you work to over that small distance. Turn left 12 deg!

When tempted to get to picky about this VFR Nav bit just remind yourself that 1 deg of track error over 60nm travelled is only going to put you 1nm off...and can you stear to 1 deg accuracy?

Well remember a stude of mine who had us Miiiiillllles off track in far west NSW (The outback). After much coaxing he decided he was over something or other and that was 20nm right of track (he was correct). He then pulled out this marvel of clear plastic with lines an numers :} all over it.

Wassat?

That's my new 1 in 60 plotter!!!

Gissalook!

Having perused said item for all of 3 nanoseconds I pitched into the back of the aircraft. For my money if you can't work out the TE for 20 off in 80 and a CA for 20 off in about 90 mentally, hand in said PPL. :E

Then there was the stude who took 4 minutes to work out the time to a turning point 20nm away at a groundspeed of 120kts :uhoh:

Chuckles.

[PPPPP]

Excellent advice from all about what to do in the real world but the original question sounded just like a "homework" one to me. Don't overlook the fact that until the magic bit of paper arrives we have to do it by the book, and that means knowing how to find the exact figures, even if they are unrealistically precise.

[Vedeneyev]

17.24755217 degs left correction

[Evo]

17.24755217 degs left correction


ah, but did you include relativistic corrections to the Einstein-Minkowski metric resulting from the Earths mass? I'll leave the correct answer as an exercise for the reader, but you may wish to consider the analytic and algebraic topology of locally euclidean parameterization of infinitely differentiable Riemannian manifold.

Bozhe moi!

:)

[Chimbu chuckles]

Hmm if they want an answer from the scientific modes of a electronic calc then I would suggest to them they are holding on too tight and should think about turning in their wings:E

But if you insist...eyballing it I would say you crossed track 10 nm back giving a track error of 12 deg (2 off in 10). 2 off with 20 to run is 6 deg closing angle. Turnleft 18deg.

But we're talking < 1/2nm one way or tother here:hmm:

Reminds me of ATPL Nav. It took 30 minutes of button bashing to get the 'right answer' to the PNR question. :ugh:

Given this is the private flying thread I'll let you in on a secret...in real life it takes 2 minutes.

Chuck.