How do you use sin & cosin to work out drift?

[deano14]

Hi - anyone know how to do this using sin & cosin? (using pen and paper only - no computer/calculator)

IAS 120kts
Wind is 030/30kts
Required track 090

What is the drift?

[jsf]

At 120 kts your Max drift wil be 15 degrees.

Wind is 60 degrees off track from left. Using clock rule 60 degrees is all the max drift so 090 degrees - 15 drift for wind from the left equals a heading of 075.

With wind at 60 degrees off your heading the rule is at its maximum error, and you are turning 15 degrees into wind!!! But hey the wind strength and direction are only a guess anyway.

jsf

PS Not sine and cosine directly but that's where it all comes from.

[Send Clowns]

The question you ask is a lot more complicated than simple sine or cosine, to get an accurate answer. Don't bother - use a CRP-5. If you really need it I can show you the calculation, but the maths is to above GCSE standard.

[fintan]

Is this the correct formula for drift

ws over tas x 60 = drift

[sawotanao]

Send clowns, I know its not entirely linked to this thread but wondered if you knew a way how to work out the reciprocal of any HDG by mental arithmatic without looking at the HSI / DI. Somebody told me a dead simple way a few years back but i've totally forgotten.
Cheers. saw'

[Knightsky]

Send Clowns and jsf are both right. The mathematics of applying sine and cosine become more complicated as you change heading to compensate for wind because this heading change causes the amount of drift that you are esposed to to change. jsf is also right for a practical application of the clock code but what is that?

Draw yourself a circle( a clockface) and divide it into four quaters.
At the 3oclock position mark 15 (15 minutes past the hour)
At the 6oclock position mark 30 (30 minutes past the hour)
At the 9oclock position mark 45 (45 minutes past the hour)
At the 12oclock position mark 60 (60 minutes past the hour)

Sine 15 is about .2588 or approx 0.25 so mark 1/4 at the 3 oclock position

Sine 30 is 1/2 so mark this at the 6 oclock position
Sine 45 is .707 which can be rounded up to 3/4 for the 9 oclock position.
Sine 60 is 0.866 so rounf this up to 1.0 and place in the 12 oclock position.

So for crosswind calculations you can now memorise this little chart.
If the wind is 15 degrees off the nose then you apply 1/4 of the wind component as a crosswind. So for a twenty knot wind this would equate to a 5 knot crosswind.

At 60 knots you would apply 5 degrees of drift ,at 120 knots you wouls apply half that etc.

If the wind is for instance 20 degrees off you can intepolate your chart and say that 20 mins past the hour is 1/3. Sine 20 is very nearly equal to 1/3.

Once the angle >60 then 0.866 or greater is so nearly 1 then just apply the full wind component.

These rules of thumb dont give you precise answers but if you can fly to these rule of thumb tolorences your aerolpane will be on track.

Cosine???

Well cosine 15 is 0.9659.
Cosine 30 is 0.866
Cosine 45 is 0.707
Cosine 60 is 1/2

Use them for head/tail wind calcs

Up to 30 degrees 0.866 just apply the full head or tail component to calucate ground speed.
At 60 degrees off the nose you have a half head/tail component.

Rule of thumb. Forget memorising cosines
Take the crosswind angle away from 90 and use this figure to re-enter your memorised clockcode and apply the relevant fraction.

From your intial example 90-60 =30 (sine 30=1/2) therfore apply 1/2 the headwind component to your airspeed to calculate groundspeed ie; 105 knots.

Of course if you want to be clever you are now heading 075 and therefore the crosswind is now only 45 degrees and your headwind exposure has increaed to 45 degrees ie 3/4 so ground speed closer to 98 knots.

Hope this helps

[moku]

sawotanao,


The way I used to use was simply to add two and subtract two from the first two digits. (or as I remember it add 2 take 2)

i.e 180 is 1+2=3, 8-2=6 ans 360.
That is probably the same way.

or if you are going the other way around the compass subtract two then add two.

Moku.

[sawotanao]

moku,

Cheers for that its all come back now! Many thanks saw'

[High Wing Drifter]

Get RANT (or download the demo). It has a bunch of tutorials, some of which are mental math. Now do a flight in RANT and mentally calculate all your headings and descent profiles on on the fly. Is good fun and the knowledge sticks.

[Chintito]

sawotanao, to get reciprocals just add 200 and take away 20 or take away 200 and add 20.
eg. reciprocal of 270... take away 200 = 70... and add 20 = 90

" " 156 = add 200= 356... minus 20 = 336

[Tinstaafl]

Covered a while ago here (http://www.pprune.org/forums/showthread.php?s=&threadid=53523)

[deano14]

Thanks to those of you who offered advice re my original question. Happy flying....

[mrfox]

hi deano14

It'll be a lot easier to explain if I can somehow draw a picture.

---------------------------------**30 deg
---------------------------*---*--*
--------------120kt--*--------*---*
---------------*-------------*----*Length B
---------*--------------30kt*-----*
---*-----------------------*------*
****************************
Angle A

Cosine = Adj/Hyp
Cos 30 = Length B/30
Length B = 30xCos30

Sin = Opp/Hyp
Sin (Angle A) = Length B/120
Sin (Angle A) = (30xCos30)/120
Angle A = Arcsin ((30xCos30)/120)

Arcsin((30xcos30)/120)=12.5 degrees correction

EDIT cuz the picture looks like crap!

[deano14]

mrfox - thanks for the diagram(?!) - it makes sense and is a lot of help. Regards.

[razzele]

this thread is another fearful confirmation that the nerds have been breeding !!

r

[Port Strobe]

Saw, the simplest way I know of, and consequently use, is given that you'll always have a rough idea of what a reciprocal heading should be, then if you add together the first two digits of your current heading (say 150 degrees) then the reciprocal will ALWAYS have the same sum, in this case 330, which acts as a good check to see that it is correct. I say only the first two digits because the last digit is going to be the same by adding an integer multiple of ten to it. Heading roughly south east I know the reciprocal will probably begin with a 3 so all I need to do now is decided 3+what = 1+5. That's not difficult for anyone. That rule works for any heading change that is an integer multiple of 90 degrees, its very useful. Hope this helps.