Hi @Brandon,
Let me break down John D’Errico’s insights to clarify your concerns further. He has more years of technical expertise and knowledge. He has provided some excellent key points such as:
Multiple Solutions in Trigonometry
As noted, trigonometric functions such as sine and cosine are periodic, meaning they can yield multiple angles for a given value. This is why you see four distinct solutions when you solve for AlphaS and BetaS. It’s essential to understand that while all solutions are mathematically valid, you will need to determine which one fits your physical context.
Understanding Forces versus Angles
Your attempt to convert the force (F2S) from Newtons to degrees was identified as an error. Forces should remain in their units (Newtons), while angles should be expressed in degrees or radians as appropriate. This distinction is crucial to prevent bugs in your calculations.
Selecting the Appropriate Solution
Among the four solutions provided for AlphaS and BetaS, you will need to choose based on practical considerations related to your ship's configuration and operational context. Typically, the solution that keeps both angles within the first quadrant (0° to 90°) is most applicable for real-world scenarios.
If you require further assistance from us, please feel free to reach out!