Calculating angle of attack

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lcorinth

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Is there a method for calculating the angle of attack of the effective flow direction of air over a rocket's fins?

So, let's say that the rocket is traveling upwards at 50mph (0 degree angle of attack), and then is hit with a wind from the side going at 50mph (90 degree angle of attack), my understanding is that the angle of attack of the effective flow would be 45 degrees, due to these combined forces, because wind from both directions is going the same speed.

But, let's say the rocket is traveling upwards at 150mph and the crosswind is, let's say, 15mph. Is there a way to calculate what the angle of attack the rocket would be experiencing?

Full disclosure, I might be asking for something which is mathematically beyond me, but I want to see if I can understand this.
 
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Draw a right triangle, the base the length of the wind speed the side the length of the rocket speed. The hypotenuse is the effective airflow, the angle is the angle of attack and the length is the air speed. This assumes the wind and rocket travel are perpendicular, if not you have to draw the sides at the correct angle to each other.

https://www.mathsisfun.com/algebra/vectors.html
 
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You might find this easier to do https://www.carbidedepot.com/formulas-trigright.asp
Side A is the speed of your rocket
Side B is the speed of your cross wind (for this calculator it is at 90 degrees to the flight)
Side C is the speed of the air flowing over your fins
Angle B is the angle of attack.

Wow, that is much simpler than I'd thought. I'm not sure if this actually surprising, but it kind of blows my mind that this can be calculated with a simple triangle. At least, it's convenient.

Thank you! I'm trying to write a blog post about stability, which is taking a long time, because I want to get the information correct but understandable. But after fiddling around with that calculator, OpenRocket and Microsoft Paint, I came up with this little picture:

Trig Calc 07.png
 
Much off mechanical engineering and physics boils down to drawing vector triangles.
 
This is accurate if the wind is completely sudden, or when the rocket is still constrained by a launch device. In any other case, the rocket will gain lateral momentum with the wind after an instant. In the constant wind case this can be simulated by Open Rocket.
 
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