Circle Skirt tutorial, part 2: 1/2 and 3/4 circles

According to Google Analytics, my Circle Skirt tutorial is the second most popular hit on my blog, and gets more searches than any other page.  How fun is that?  I'm pleased that there is so much interest!  I recently had a question regarding drafting a pattern for a 3/4 or 1/2 circle skirt, and how that would differ.  Since there is a bit more math involved, I thought that it deserved a post of it's own.
As you probably have surmised, a circle skirt is just a big doughnut, with the waist measurement as the circumference of the inner circle and the length as the distance between the inner and outer circles.  When you change this to a skirt that is less than a full circle, you now have just a segment of a circle (an arc) as your inner and outer measurements, so instead of using the formula for the circumference of a circle to find the radius of your inner arc, you need the formula for arc length.  I'm not going to bore you with derivations and reductions (although if you are interested, here is where I got my geometry refresher), but the formula you'll need to draft your pattern is this:

r(radius)=360l(arc length)/2 pi m(angle).

If that makes you nervous, don't worry!  I'm going to take you through the steps for a 1/2 or 3/4 circle skirt.  It'll be easy!  Stick with me.

OK, here is the info that you will need: Your waist measurement (That is, where you want the skirt to sit) and the final length that you want your skirt.  Measure this from your waist to wherever you want the skirt to end.  Let's get to work!  I'm going to show you how to draft the waist part of the1/2 and 3/4 circle skirt.

If you've already watched the video on the Circle Skirt tutorial, then you are ready to start.  If you haven't please go there and watch it, so that you know what I'm talking about.  Don't worry, it's short.  The first thing that we need to calculate is the radius of our inner arc.  The formula up there will give it to us.  For the 1/2 circle m=180 and for the 3/4 circle m=270.  The formula you will need to use is:

r=l/pi for the 1/2 circle
r=(2l)/(3 pi) for the 3/4 circle
where l=your waist measurement.

For example, if your waist measurement is 26, you would have a 8.3 inch radius for your 1/2 circle skirt and a 5.5 inch radius for your 3/4 circle skirt.
Now, we have to draft.  The first thing to do is choose a midpoint on your drafting paper, and draw lines representing the edges of your skirt.  For the 1/2 circle, that would be a straight line (that is a 180 degree angle)

and for the 3/4 circle, you would draw a 90 degree (270 on the skirt side) angle.  This is easier if you are working on or with gridded paper.

You'll use these lines as the boundary of your pattern piece, since you aren't making a full circle, so draw them as long as you plan your skirt to be, plus the radius you calculated.  This will be the total size of your pattern piece and the full size of your skirt, if you seamed the long edges together.  You'll probably need a pretty big piece of tracing paper for this...
For the waist measurement, you already know what to do if you watched the video.  Use the radius you calculated to draw the arc you need for your waist measurement.  Here's what it looks like with our hypothetical 26 inch waist.
For the 1/2 circle,

and for the 3/4 circle.

Now to complete the pattern piece, make your outer arc, using the length of your finished skirt plus the radius.  Since you drew your initial lines to this measurement, you should just have to connect the endpoints, but with a semicircle.  Your final pattern pieces should look like either a half circle or a 3/4 circle.  You can even try it on to see how your skirt will fit!  To get a pattern piece, fold this giant thing in half.  You can either make this cut on the fold (if your fabric is wide enough) or you can cut two and use one as the front of your skirt and one as the back.
Now to finish your skirt, head over to the original tutorial to see how to subdivide your pattern piece into panels, and how to construct your skirt.  I hope this is helpful!
Happy sewing!