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:
It also yields the same result from the http://www.csgnetwork.com/e6bcalc.html site that can calculate ground speed:
Using the E6B however, with the same variables, I get a totally different result (10 kts off):
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!