triangle of velocities formula

[slast]

I need to back calculate the actual wind from heading and IAS plus track and G/S, but all the formulae I've found so far use wind as an input? Anyone got a quick solution I can plug into a spreadsheet?

[gonebutnotforgotten]

Steve,

Try the cosine rule....relates two sides to the third knowing the included angle between the known sides, sorry, can't paste it in here.

[RAT 5]

Bring back the Dalton computer & chinograph. I've no idea how it did it, or what the formula was, sorry, but it worked. Have any 4 from 6 and calculate the other 2: long before pilots became dependant on 'japanese brains'. Indeed I've never seen formula; it was pictorial on graph paper with ruler & compasses on a desk, or the DC slide on your knee as you did your nav-ex.

[FCeng84]

Try this:

Wind component along airplane heading:
Vground * cos(crab angle) - Vtas

Wind component across airplane heading:
Vground * sin(crab angle)

Total Wind velocity:
Take the square root of the sum of the squares of the two above

Difference between airplane heading and wind angle:
Take the inverse tangent of the cross component divided by the along airplane heading component. (Always sanity check to make sure it makes sense by drawing your triangle picture.)

Cheers

[galaxy flyer]

Simpler method:

Subtract your TAS from you GS for tail or head component. TAS equals your IAS plus 2% per thousand feet of altitude. Ex.: 300 IAS at F200 equals 300 + (40% of 300) equals 420 knots TAS

Multiply your crab angle by your TAS in nm per minute equals your crosswind component. Ex.: 420 knots equals 7 nm per minute, so a 6* crab equals 42 knots of crosswind.

Then, scale them out on the HSI.

Ex.: 100 knots of tail and 42 knots of right cross, starting with the airplane symbol, the outer edge is 100, the middle of the right side is about half way (50 knots), so a little inside that is 42 knots. Then connect the two points with a pencil slide the pencil or the line over the airplane symbol. The length of the line compared to the distance of 100 is the speed of the wind; the heading is read on the HSI.

Not perfectly accurate, but close and good sanity check. Too much time in old fashioned planes and not a math major, besides the FMS figures it all out anyway. Are you really going to use a spreadsheet in a plane?

[FCeng84]

I concur with the simpler approach that GF has provided. Here a small angle assumption is made without much loss in accuracy. Cosine of a small angle is approximately 1. Sine of a small angle is approximately that angle in units of radians. Conversion from radians to degrees is 57.3 that is almost the same as the hours to minutes factor of 60 that the GF method uses.

All good

[slast]

Simpler method:

Are you really going to use a spreadsheet in a plane?
Thanks GF, no that's not the problem! I have some data readouts from an FDR, which give me the flight parameters once a second, and I am trying to extract what winds the aircraft was actually exposed to as it descended, in particular whether there were big changes (shears /gusts etc). And I no longer have my trusty old Dalton E6B!

[galaxy flyer]

Well, if you’re working FDR data, you might well need the more accurate methods.

[slast]

Exactly! I also have a problem with temperature, I have total air temp and IAS but it is ISA-20 so have to calculate a more accurate TAS as well.... about 180 times!

[KayPam]

Hello,

I elected to put some formulae on wikipedia :
https://fr.wikipedia.org/wiki/Altitudes_et_vitesses_(a%C3%A9ronautique)#Vitesse_du_vent

Here are the reverted formulae :

alpha = atan(tas*sin(da)/(tas*cos(da)-GS)
Vw = tas²*sin(da)² + (tas*cos(da)-GS)²

where :
alpha = wind direction - track
da = heading - track
Vw= wind velocity
Careful : formula needs a correction on drift angle, if there is non zero sideslip

What is the aircraft in question ?
It may have more precise info available.