Recreational trigonometry: Fin Spin

Over on YORF, TXFergie was asking about the fin dimensions for the Estes Marauder #1922, and K’Tesh asked for details to help him enter the fins in OpenRocket. I neither have nor am much interested in the Marauder but for some reason I felt like calculating the numbers K’Tesh needed, and then that led to a project…

In OpenRocket you can specify fins as trapezoidal (with the tip and root edges parallel), elliptical, or freeform. The Marauder fins (TIFF file) are trapezoidal, but with the leading and trailing edges parallel, not the tip and root, so it has to be specified as freeform; that means you need the coordinates of each vertex, in a cartesian coordinate system where the x axis is parallel to the body tube. It’s easy enough to measure the sides of the fins and the angles between them, particularly since two of them are right angles, which means the lengths of the corresponding three sides can give you the coordinates in a system where the x axis is parallel to the long side. But then comes the tedious part: calculating (or measuring) the acute angle between the leading and root edges, and then performing a rotation of those coordinates through that angle to get the numbers OR needs.

I did that in a little spreadsheet, and then thought, hm, there might be a use for a tool that lets you do this sort of thing generally. Essentially what I was doing on paper was the equivalent of taking a fin with one edge in the root position and flipping it around to make another edge the root. That might be a cute thing for OR to be able to do for you. (Flipping fins around is sort of the whole marketing premise of the Estes Viking #1949, you may recall, and there are plenty of other instances of people deciding they like their fins better in an orientation other than the design… even if they don’t decide that until after they’re glued on.)

But since it can’t, how about a standalone tool to do it? So I made one. Just to make things even more difficult, I made it in Google Spreadsheets. Spent way too long on it, but now I have a resource that… well, that honestly I may never have a genuine use for. Never mind, it was fun. Okay, so I have a weird idea of fun.

Here it is: Fin Spin. You can’t actually use it from that link, it’s read only; you can copy it to your own Google Drive and use your copy. Or you can download it in Excel or OpenDocs format, though I don’t know how well that will work, not having tried it.

Take your fin and count the number of sides; enter that at the top of the spreadsheet. (Maximum is 9. If you want a 10-sided fin, you’ll have to edit the sheet to add more rows.) Now measure the lengths of all but one of those sides, and the size of all but two of the angles. (Leave out one side and the angles at each end of that side. Fin Spin will calculate them instead.) Enter those in the boxes shown. For example, for an equilateral triangle with sides 2 inches (or cm) long, enter ‘3’ for number of sides, ‘2’ for lengths of first and second sides, and ’60’ for the first and only angle. If you look over on the right, Fin Spin calculates 2 for the length of the third side and 60 for the sizes of the two remaining angles.

On the right you’ll see an outline of the fin, with the first side you entered horizontal. If the fin is too small or too large you can edit the axis limits in the chart. You can also leave them blank and have Fin Spin choose what limits to use, but it won’t use the same scale horizontally and vertically so it may come out distorted.

Now go below and enter three more things: Which side you want as your root (1 for the first side you entered, 2 for the second, and so on); which vertex you want at the origin (normally you’d choose the side number or the side number plus 1), and whether you want to flip the fin horizontally (enter ‘h’), vertically (‘v’), both (‘hv’), or neither (‘n’). Over on the right you’ll see two pictures of the result; the smaller one has automatic axis limits, so you’ll always see the fin but it may be distorted; the other has fixed limits, so the fin won’t be distorted but some or all of it may be out of view. Watch them as you change the inputs… I love how they morph from the old configuration into the new.

To the left of the pictures in the highlighted area are the coordinates of the vertices after rotation and flipping — the numbers to enter into OpenRocket. The first coordinates are duplicated at the end, to make the shape closed in the pictures, but you don’t need to enter the second copy into OpenRocket.

Whatever you do, don’t change anything outside the cells that have borders. Unless, you know, you want to. But you may break it.

There are two sheets (currently), and they’re the same except for the inputs. One has the values for the Estes Marauder, and they agree with the ones I calculated for K’Tesh, fortunately. The other is a more complicated shape, a nonconvex hexagon, just to prove it works.

So, if you have a use for this thing, go ahead and try it… let me know how it works out.



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