Hat TheoryHow to Shape Short Row Pie Wedge Shawl Version: Wedges. 

The spiral version will be coded later.

From The Knitting Fiend.   Guess what?  I'm compiling an index of calculators here.

This page will calculate the ideal rate to knit short rows to shape a pie wedge shawl that turns 180 degrees (or π radians); this is commonly called a U turn.  To do this shape, you cast on at one edge of the shawl and knit around the annulus.

The calculator will permit you to design a shawl with any number of wedges greater than 2.  The wedges are short row regions that cause the knitting to turn giving the pie, (aka. pi, or π ) shawl its curved shape.   Since this calculator is a design tool rather than I pattern, I will try to give sufficient information to help you make some decisions about your shawl.

Enter number of stitches per inch from your swatch.
Enter number of rows per inch from your swatch.
Enter number "wedges" want to divide the shawl into.  The figure shows 4. 
(Based on your input, the target value of the angle α shown in the figure is equal to degrees.)
wedges.
Enter inner radius for shawl or poncho.  This is shown as 'r' on the diagram. 
Based on your current input, the length of the shawl along the inner curve will be inches.

(Note: When rounding, the program will assume you care more about the inner radius than the outer radius. It will also force the outer radius to be larger than the inner radius.)
 inches.
Enter outer radius you want for the shawl or poncho. This is shown as 'R' on the diagram.
The length of the shawl along the outer curve will depend on the method you use to knit this. Read the final instructions.

 inches.


How to Shape the Shawl:

Preface:
The goal is to make a shawl that turns 180 degrees, which is a perfect U turn.  This is done by knitting rectangles and wedges.  All the turning is done in the wedges.  If you are a beginning designer and want a pretty lace shawl, I suggest placing a pretty lace pattern inside the rectangles.  If you are more advanced, you can continue the lace inside the wedges.

The turns are accomplished by knitting the wedges.  However, when calculating, I have to  round to figure the wedge shaping.   Usually, the shawls will not be perfect U turns; they are calculated to be as close to U turns as possible.  I prefer to let you decide how much trouble you want to take to create the prefect shape, so I am providing two possible shaping methods.  The first method I suggest uses the simplest possible shaping. The second uses a slightly more difficult shaping and will come closer to the perfect 180 degree turn. (Occasionally, the two methods work out identically.  That just depends on your gauge and the number wedges.)

The first method is easier to knit. Unless you have a good reason to pick the harder method, I advise using the easier method. If you can't think of a good reason to use the more difficult shaping, you  probably don't have one. (Note to Machine knitters: You won't find the second method too aggravating, so they don't need as good a reason to choose more complicated shaping.  However, you need to understand the directions functionally and figure out how to set up your machine to knit short rows.)

Method 1: This shaping results in a U turn shawl that turns degrees; 180 degrees is a perfect U turn.  The length of the shawl along the inner curve will be inches; the length measured along the outer curve will be inches. 
  1. Cast on stitches. 
  2. Work a half rectangle: Knit rows.
  3. Knit decreasing half of wedge:
    • Row 1: Begin right side facing: Knit across row.
    • Row 2: Begin wrong side facing: Purl across row until stitches remain on the left hand needle.  Wrap and turn.
    • Row 3: Knit to the end of the row.
    • Row 4: Begin wrong side facing: Purl across row until stitches remain on the left hand needle.  Wrap and turn.
    • Work in pattern established,  decreasing the number of stitches knit by stitches every two rows.  Continue until the half wedges has rows.  (Note: The last row in this instruction is a purl row. Also, if I told you to continue decreasing the number of stitches knit, it would not be possible, you'd run out of stitches on the next purl row.) 
  4. Work increasing half of wedge:  To work increasing wedges, mirror the decrease rounds. 
    • The first row you knit will begin knit side facing; knit the number of stitches you knit in the final row of the decreasing wedge.
    • Afterwards, increase the number of stitches knit by every two rows. 
    • The final row will be a purl row, and you will knit across all stitches.
  5. Work a full rectangle by knitting all stitches on the needle for rows.
  6. Repeat 3, 4 and 5 until a total of wedges have been knit. Replace the final rectangle of step 5 with a half rectangle and bind off.





Method 2:  This shaping results in a U turn shawl will  turn degrees; 180 degrees is a perfect U turn. The length of the shawl along the inner curve will be inches; the length measured along the outer curve will be inches. 
  1. Cast on stitches. 
  2. Work a half rectangle: Knit rows.
  3. Knit decreasing half of wedge:
  4. Work increasing half of wedge:  To work increasing wedges, mirror decrease wedges,
  5. Work a full rectangle: Knit rows.
  6. Repeat 3, 4 and 5 until wedges have been knit.  End with a half rectangle. ( Note: There will be 4 wedges, 3 full rectangles and 2 half rectangles.)





Have fun knitting!
Lucia