Adding Multiple Vectors

February 19, 2005 3:31 PM

Mathematical imbecile question: what's the simplest, most universal way to add a list of vectors?

I need a one-size-fits-all formula that I can pop into Excel (or, indeed, an add-in); all my Google searching seems to turn up is high-school methods involving drawing diagrams and measuring angles with a protractor, or a "step-by-step" approach that I can't get my head around moving into a spreadsheet. I just want to be able to put a list of angles and magnitudes in a couple of columns, and come out with the resultant vector at the end.

posted by Jimbob to Science & Nature (7 answers total)

Highlight the column to the left of the other columns. Click once on the "Sigma" ("sum") button in the toolbar. Excel is usually smart enough to figure out you want the highlighted column to contain sums of the row entries from the other columns.
posted by AlexReynolds at 3:39 PM on February 19, 2005

In the future, go directly to Mathworld, not Google.

1. Add more columns to turn your polar coordinates into cartesian.

2. Add them

3. Convert back if necessary
posted by vacapinta at 3:39 PM on February 19, 2005

Pseudocode:

Result = (Summation of magnitude*(cosine of angle))i + (Summation of magnitude*(sine of angle))j.
posted by Gyan at 3:40 PM on February 19, 2005

Beautiful, that works like a charm vacapinta, and was pretty obvious. I think the main thing that was confusing me was the need to convert between degrees and radians at various points.
posted by Jimbob at 4:08 PM on February 19, 2005

Actually, just to sum up exactly what I've done in Excel for anyone else wanting this in the future:

Column A: Magnitude
Column B: Direction, in degrees, clockwise from "North"
Column C: =90-B
Column D: =RADIANS(IF(C<0,C+360, C))

Columns C and D convert the angle into radians anti-clockwise from the X-axis.

Column E: =A*COS(D)
Column F: =A*SIN(D)

I then calculate the sum of all the rows of column E (call that X) and the sum of all rows of column F (call that Y)

Angle =DEGREES(ATAN(Y/X))
Magnitude =SQRT(X^2+Y^2)
posted by Jimbob at 4:17 PM on February 19, 2005

No, I lie, calculating that last angle gives the wrong answer. I'll try to work it out.
posted by Jimbob at 4:27 PM on February 19, 2005

Oh okay, that last angle has to be subtracted from 90 to get it back into "compass" angles, and you add 180 to it if the X-coordinate is negative. Done. Cheers!
posted by Jimbob at 4:38 PM on February 19, 2005