Calculating wind vectors
Question:
Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
Response:
Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
Given: TC, TAS, WD, WS Find: TH, GS WCA (wind correction angle) = arcsin( (WS/TAS) * sin(WD-TC) ) TH = TC + WCA (limit between 0-360 degrees) GS = sqrt( TAS**2 + WS**2 – 2*TAS*WS*cos(TH-WD) ) Watch your trig functions; make sure you keep radians and degrees straight. –Tom Turton
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Hi. For ordinary, garden-variety flying in a light a/c, you can do well enough by remembering two things: (1) The hypotenuse of a 45 degree right triangle is 1.4 times the length of a side. (2) A "60-30" triangle (one with angles of 90, 60 and 30 degrees) has a hypotenuse that is twice the length of the short side. Draw some "wind triangles" on paper and you’ll soon get a feel for how your track and ground speed are affected by a wind that is 30, 45, 60 or 90 degrees from your heading. Then you can just interpolate for winds that are between those directions. Yes, it’s inexact. But so are forecast winds, and who holds a heading within two degrees on a cross country, while enjoying the scenery? I find that above works just fine for a two- or -three hour flight in a Cherokee. If after an hour I find that I’m drifting off ocurse, I can adjust the heading. However, the wind changes, too, by the time I’ve flown a hundred miles. I’m not recommending this for transatlantic flights, but as I said at the outset, it works fine for vfr cross-country flying in small a/c. There’s a 40-year-old E6B in my bag, that I carry "just in case." But it hasn’t been out of that bag for a long time. vince norris writes:Path: news.cac.psu.edu!news.ems.psu.edu!news.math.psu.edu!chi-news.cic.net!newsxf er2. – Hide quoted text — Show quoted text -Organization: InfoRamp Inc., Toronto, Ontario (416) 363-9100 Lines: 7 NNTP-Posting-Host: ts16-14.tor.inforamp.net Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Mailer: Mozilla 2.0 (Macintosh; I; PPC) Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
Response:
Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time.
Quick course in trig. Draw a triangle, with sides of length A, B, and C. Label the three angles a, b, and c, with an angle’s name matching the side opposite it. a C b / / B / A / * c Two basic laws of triangles. sin(a) sin(b) sin(c) Law of Sines: —– = —— = —– A B C Law of Cosines: A^2 + B^2 – 2*A*B*cos(c) = C^2 Notice that if you make C a right angle, cos(90)=0 so the last term on the left side drops out and you’re left with A^2 + B^2 = C^2, which is the famous Pythagorean Theorm which every high school student learns, and which the Scarecrow in The Wizard Of Oz recited upon getting his brain. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
Starting with the two laws above, you should be able to work out the rest. If unsure you’ve got the right answer, confirm with pencil and paper drawings, or use a whiz-wheel. — Hippocrates Project, Department of Microbiology, Coles 202 NYU School of Medicine, 550 First Avenue, New York, NY 10016 "This never happened to Bart Simpson."
Response:
Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
Attached is a 123 spreadsheet "wca.wk4" Hope this helps Contact me if you have any questions. Miro
WCA.WK4
8K Download
Response:
writes: Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
I always draw a little picture in the margin. It shows my intended course with a vector labeled with my TAS. The wind speed vector gets added to the picture with the "right" relative angle, the WCA. Then resolve the WS vector into a component along the heading and a component perpendicular to it. The one that affects your ground speed is |WS| cos(WCA) and the crosswind component is |WS| sin(WCA). If you figure out how an E6-B works, this is it. You are creating the wind vector and then rotating it graphically! But be careful about the angles: Written wind directions are usually True, but controllers convert them to Magnetic. Then you have to worry about magnetic variation in your area and compass deviation in your airplane. Good stuff to know if you can’t use VOR navigation some day and don’t own a GPS! –Bill Wm W. Plummer, 7 Country Club D., Chelmsford MA 01824 508-256-9570 PP-ASEL,G
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Path:
dodo.global.co.za!hermes.is.co.za!news.uoregon.edu!usenet.eel.ufl.edu!newsf eed.inte rnetmci.com!swrinde!hookup!news.nstn.ca!inforamp.net!usenet – Hide quoted text — Show quoted text – Newsgroups: rec.aviation.piloting Organization: InfoRamp Inc., Toronto, Ontario (416) 363-9100 Lines: 7 NNTP-Posting-Host: ts16-14.tor.inforamp.net Mime-Version: 1.0 X-Mailer: Mozilla 2.0 (Macintosh; I; PPC) Status: N Does anybody know how to calculate wind vectors mathematicaly. It seems that I cannot remember by high-school trigonometry well enough to do so. I am trying to incorporate the calculations into a spreadsheet so I don’t have to use my E6-B every time. Specifically, given 4 out of 6 of TH, TAS, WD, WS, TR, GS, what is the formula for calculating the other 2?
When you have 4 out of the 6 variables, you should be able to use either the sine rule or cosine rule which apply to any triangle. sin A / a = sin B / b = sin C / c a2 = b2 + c2 – 2*b*c*cos A where a, b, c are the lengths of the sides of the triangle, and A, B C are the angles opposite the side of teh same name (e.g. A is included between sides b and c). a2 means a squared, etc You should be able to identify which of the two formulae applies to the problem by checking which contains only one unknown. In a spreadsheet, the calculation should be trivial. Neil A Fraser TEL: 27 (11) 468 2892 FAX: 27 (11) 468 2895 ** There’s more fun in getting there than being there **
