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I have been trying to create an excel formula for calculating the ground speed of an airplane using the TAS, Course, Wind Dir, and Wind Velocity.

The issue that I am finding is that I can't properly calculate ground speed. Using pythagorean's theorem, you can use both this site: https://www.mathsisfun.com/algebra/vector-calculator.html and this site http://www.csgnetwork.com/e6bcalc.html to calculate your ground speed. This is how my excel sheet works. However, using the E6B(https://www.e6bx.com/e6b/), I get very different results.

For example: TAS(Tas) = 100 Course(C) = 120 Wind Dir(Wd) = 40 Wind Speed(Ws) = -20 (20 kts coming from 40 degrees(used in E6B), so -20 in the direction of 40 for pythag)

Using Pythagorean theorem, GS = sqrt((Tascos(C) + Wscos(Wd))^2 + (Tascos(C) + Wscos(Wd))^2).

This will yield a GS of 99 kts using a raw vector addition calculator:

enter image description here

It also yields the same result from the http://www.csgnetwork.com/e6bcalc.html site that can calculate ground speed:

enter image description here

Using the E6B however, with the same variables, I get a totally different result (10 kts off):

enter image description here

I guess in my mind there are 3 possibilities, 1) I have made a mistake somewhere or have a misunderstanding of vector addition, 2) The E6B uses more information than I know about, or 3) the E6B isn't 100% accurate.

Please shed some light on this if you understand! Thank you!

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    $\begingroup$ You're asking for somebody to debug your program, and that's awfully close to not being on-topic here at Av.SE. Your best bet, honestly, is to take some problems with known, accurate, solutions, and run them in both of the calculators you have. One should match the accurate solution, and hopefully the other won't. Then, knowing that "this" answer is wrong, you can start looking to see in what ways it is wrong and what needs to be changed to make it right. $\endgroup$ – Ralph J Jun 6 '18 at 4:30
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    $\begingroup$ @RalphJ No i am not. I didn't post a single line of code I was using. The sites I posted are open to the public, and the algorithm i wrote up there is just the formula for magnitude given 2 vectors... And the correct answer was about the difference between heading and course, not a debugging of any equation. The question was really : which solution is accurate of these 3 websites where i put in (what I thought) was the same formula. $\endgroup$ – Ryan Jun 6 '18 at 11:21
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Course and heading are not the same. Course is the direction of your path over the ground. Heading is the direction you are pointed (and the direction you would travel through a still airmass).

In your second site you entered 120 as a heading, not a course. Correct that and you get the same figures as the final site.

http://www.csgnetwork.com figures

You're doing the same thing in your calculation: treating the angle as a heading and calculating the resulting course. The simple vector calculation is that the airplane path through the air (TAS@HDG) plus the movement of the air mass (WS@WD) becomes a resultant path over the ground (GS@C).

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