Mathematical calculation of heading
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Mathematical calculation of heading
Hi,
I'm looking for a mathematical formula for calculating heading and groundspeed from TAS, track and wind. While it is easy to work out the track and groundspeed from the TAS, heading and wind using sin, cos and Pythagoras, I can't seem to scratch up enough memory of high school maths to work out the formula I'm looking for.
For example :-
TAS = 90Kts
Wind = 030/15
Track required = 060
What is the heading to be flown to achieve the track and what will the groundspeed be?
It's easy enough to put this into a flight computer and get a result, and I'm not pretending anybody should expect to fly to this level of accuracy, but the maths has currently got me stumped.
TIA
D
I'm looking for a mathematical formula for calculating heading and groundspeed from TAS, track and wind. While it is easy to work out the track and groundspeed from the TAS, heading and wind using sin, cos and Pythagoras, I can't seem to scratch up enough memory of high school maths to work out the formula I'm looking for.
For example :-
TAS = 90Kts
Wind = 030/15
Track required = 060
What is the heading to be flown to achieve the track and what will the groundspeed be?
It's easy enough to put this into a flight computer and get a result, and I'm not pretending anybody should expect to fly to this level of accuracy, but the maths has currently got me stumped.
TIA
D
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Dufwer,
I wrote a computer program that performed such calculations a year ago. I remember the derivation requiring some A Level Maths knowledge:
The sin rule: A / Sin a = B / Sin b = C / Sin c
And the cosine rule: A^2 = B^2 + C^2 - 2BC Cos A
If I find the code tonight at home, and nobody beats me to it, I'll post the formula on here.
I wrote a computer program that performed such calculations a year ago. I remember the derivation requiring some A Level Maths knowledge:
The sin rule: A / Sin a = B / Sin b = C / Sin c
And the cosine rule: A^2 = B^2 + C^2 - 2BC Cos A
If I find the code tonight at home, and nobody beats me to it, I'll post the formula on here.
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This kind of thing is required to be worked out in your head when your doing the CPL.......Ive got some infor for you although not easy to understand!!
First you work out your max Drift...Ie the max you will drift in one hour.
Max drift = 60/TAS x Wind speed
In your example the max drift would be :
60/90knots x 15 = 10 deg MAX DRIFT
Then you have to factor the drift according to how many degrees the wind direction is off the nose. This is basically done using the simple 'Clock Rule'
0 deg Head/Tail = 0 x Max drift
15 deg Head/Tail= 1/4 x Max drift
30 deg Head/ Tail = 1/2 Max drift
60 deg Head/ Tail = 1x max drift (full)
In your example the new heading would be calculated like this :
TRK= 060
W/V = 030/15
Max dft= 10 degrees
030 is 30 degrees off the nose therefore you will alter your heading by 1/2 the max drift (5 degrees) so your new heading will be 5 degrees into wind = 055
There is also a way for calculating the ground speed but its a little
complicated so maybe i'll type it another time!!
Hope that helps!
Rowley!
First you work out your max Drift...Ie the max you will drift in one hour.
Max drift = 60/TAS x Wind speed
In your example the max drift would be :
60/90knots x 15 = 10 deg MAX DRIFT
Then you have to factor the drift according to how many degrees the wind direction is off the nose. This is basically done using the simple 'Clock Rule'
0 deg Head/Tail = 0 x Max drift
15 deg Head/Tail= 1/4 x Max drift
30 deg Head/ Tail = 1/2 Max drift
60 deg Head/ Tail = 1x max drift (full)
In your example the new heading would be calculated like this :
TRK= 060
W/V = 030/15
Max dft= 10 degrees
030 is 30 degrees off the nose therefore you will alter your heading by 1/2 the max drift (5 degrees) so your new heading will be 5 degrees into wind = 055
There is also a way for calculating the ground speed but its a little
complicated so maybe i'll type it another time!!Hope that helps!
Rowley!
Why do it if it's not fun?
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This kind of thing is required to be worked out in your head when your doing the CPL
Rowley, there's nothing wrong with using the Max Drift rules in practice. If you do need to work things out in flight (not for the CPL, but for any other reason), or even on the ground if you don't have a flight computer handy, that's fine.
But at the end of the day, it's just an approximation.
However, Dufwer was after the exact formula, not an approximiation. Just purely as a theoretical exercise, because we all know that neither the forecasts nor our flying are accurate enough to get any real benefit from dusting off our scientific calculators to get the exact numbers - but that doesn't stop it being a useful exercise in trigonometry, as long as we all agree that that's all it is.
This thread has definitely got my brain-cells going... I had a go at solving this before PA28 and Oxford Blue posted, but couldn't remember enough of my A-Level maths to be able to do it. It's slowly coming back to me now though
FFF
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FFF, I was taught the method RowleyUK describes when I did my PPL. I, too, would be interested to know what method you used in the CPL. Did you describe it in your CPL diary anywhere?
D
D
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Dufwer/PA28,
I used a CRP1 to calculate the drift on the ground. In the air, for diversions, I just used a sensible estimate, and then used the 1/4-way method to make corrections. The max drift and 1/60 rule would have worked just as well, as would a number of other methods, but I wasn't told to use them and managed perfectly well without them.
This was last November, though, and I know that diversions have changed, or are about to change, not sure which - I had to my diversion under the hood, but I don't think that's the case any more. I don't think that affects calculation of drift, though.
FFF
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I used a CRP1 to calculate the drift on the ground. In the air, for diversions, I just used a sensible estimate, and then used the 1/4-way method to make corrections. The max drift and 1/60 rule would have worked just as well, as would a number of other methods, but I wasn't told to use them and managed perfectly well without them.
This was last November, though, and I know that diversions have changed, or are about to change, not sure which - I had to my diversion under the hood, but I don't think that's the case any more. I don't think that affects calculation of drift, though.
FFF
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