Determining Compass Bearing from Resultant Angle

[Vector1961]

We are using a smart phone app to add vectors; once we get the resultant angle, we need to determine what direction the vector is based on the compass. Can someone easily explain how to do this?

Example: Using the app, we input a 2 knot current toward 230 degrees and a 0.7 knot wind speed from 320 degrees. The resultant values are 2.119 magnitude, angle of 30.710 degrees and a vector of <1.82, 1.08>

What we need is an EASY way to compute the compass direction from the 30.710 angle. I know this has something to do with what quadrant the vector resides in and it involves adding or subtracting 180 or 360 degrees, but I don't have a physics background and am looking for an "easy" and repeatable means of converting. Thank you in advance for any assistance. I can provide additional information via email if required.

 

[Simon Bridge]

Welcome to PF;
Bearing are usually measured clockwise from due north.
http://en.wikipedia.org/wiki/Bearing_(navigation )

If that is the convention you used, then east is 90deg, south is 180deg, and west is either -90deg or +270deg.
It helps to sketch the vectors.

When you set up vector equations, be very careful to write down what the vector representation means in terms of the compass - so if 230deg is clockwise from north, then that is a bit west of SW. But sometimes angles are taken from due east or something else. Only you know, since you are the one inputting the numbers.

I don't know how the app works, so I cannot comment - ask the apps designer and/or consult the documentation.

 

[maimonides]

Maybe a nitpick, but:
Are you sure you want/need to add wind speed and (water) current?
(I assume water because of "current" and the values you use)

 

[Vector1961]

To clarify, we want to determine the speed and direction of oil when spilled when there is current AND wind. We are only using a vector app because of speed, accuracy and ability to use in the field. Looking at the example above, we know from using the app what our magnitude (oil speed) is, what our angle is and the vector. What we want to do from here is compute from the angle what the actual bearing of the oil is based on the compass (N, S, E, W, etc.) I've done some research and came up with this, but need to verify:
IF THE RESULTANT ANGLE IS POSITIVE AND IN:
• Quadrant I: The reference angle is the resultant angle
• Quadrant II: The reference angle is 180° minus the resultant angle
• Quadrant III: The reference angle is the resultant angle minus 180°
• Quadrant IV: The reference angle is 360° minus the resultant angle

 

[pmacias]

To determine the compass direction from the resultant angle, you will need to consider the quadrant in which the vector resides. In this case, the vector is in the first quadrant, which means the angle is between 0 and 90 degrees. To convert this angle to a compass direction, you will need to add 90 degrees to the angle. In this case, the compass direction would be 120 degrees (30.710 + 90 = 120). This indicates a southeast direction.

To make this process easier, you can follow a general rule for converting angles to compass directions. For angles in the first quadrant, add 90 degrees to the angle. For angles in the second quadrant, subtract the angle from 180 degrees. For angles in the third quadrant, subtract the angle from 270 degrees. And for angles in the fourth quadrant, subtract the angle from 360 degrees.

In your example, the resultant angle of 30.710 degrees is in the first quadrant, so you would add 90 degrees to get the compass direction of 120 degrees. This rule can be repeated for any angle in any quadrant, making it a simple and repeatable method for converting angles to compass directions.

Additionally, it may be helpful to remember that the four main compass directions are north (0 degrees), east (90 degrees), south (180 degrees), and west (270 degrees). So, for angles close to these values, you can easily determine the corresponding compass direction without needing to use the conversion rule.

I hope this explanation helps and please feel free to reach out with any additional questions or clarifications.