True wind/apparent wind?

Can anyone give me the formula fore calculating:
1: true wind, when you know apparent wind and boatspeed? (speed and angle)
2: apparent wind, when you know true wind and boatspeed?

If possible on a exel file...? ;-)



(General) Thanks to everyone that contribute in this forum !

 

I dont have to have it on a ecel file!
I can do that my self, but I cant find the formula anywhere!

 

Good, that makes it a lot easier.

Taking the angle between the boat's heading and the direction the wind is coming FROM,
first get the longitudinal (x) and lateral (y) components of the wind velocity:
(V means speed, a means apparent, t means true)
(A means angle in DEGREES)

Vay = Vtrue*sin(3.1416*Atrue/180)
Vax = Vtrue*cos(3.1416*Atrue/180) + Vboat

Vapparent = square root of (Vax squared + Vay squared)
Aapparent = (180/3.1416)*arctan (Vay/Vax)

To go the other way, switch true and apparent everywhere, and put a minus sign in the Vx equation:

Vty = Vapparent*sin(3.1416*Aapparent/180)
Vtx = Vapparent*cos(3.1416*Aapparent/180) - Vboat

Vtrue = square root of (Vtx squared + Vty squared)
Atrue = (180/3.1416)*arctan(Vty/Vtx)

 

Truble

(Im a bit tired now, it's 23.59 here)
I'll have a closer look tomorrow, if not anybody can have a look and help me in the mean time?

 

I put this sheet together quickly a couple of years ago. Seems about right until App Angle >90. I just input your calc in RED. Doesn't seem to work. Maybe someone can check both calcs.

 

http://www.sailingusa.info/true_wind_calculator.htm

Try this link.