Starting a hat: disks and cones

A pattern for a skull-fitting chu'llu hat (from Knitting With Balls)
knit in the round begins:

1. Cast on 8 stitches.

2. Knit 1 rnd.

3. Kfb into every st (16 stitches).

4. Knit 1 rnd.

5. * Kfb K1 repeat from * (24 stitches).

6. Knit 1 rnd.

7, etc.: add 8 stitches every other round up to 88 stitches.

With a gauge of 4" = 18 sts and 24 rows,

1 st = 4/18 inches = 2/9 inches
1 row = 4/24 inches = 1/6 inches

At the end of every even numbered step N above, the piece measures

N rows = (1/6)N inches from center to edge
8(N/2) st = 4N st = (8/9)N inches around

Applying geometry and an inverse sine, this yields not a disk or even a
near disk, but a cone with an angle at the peak of 116 degrees. This is
rather pointy.

The reason I ran through this computation is that when I tried this
pattern a cone is what I got. I wanted to see if I had done anything
wrong, but the arithmetic confirms my result.

If I were to add 9 stitches every other round, my cone would flatten out
considerably, to about 145 degrees at the peak. This would seem to make
more sense, conforming more closely to the shape of the top of the head.

Or does this all work itself out at blocking time?

What do you think?

In article ,
Harlan Messinger wrote:
A pattern for a skull-fitting chu'llu hat (from Knitting With Balls)

Which is it, I wonder: a skullcap (tight and smooth to the head)
or a chu'llu (the South American hats I've seen all had a noticeably
pointy top).

knit in the round begins:

1. Cast on 8 stitches.
2. Knit 1 rnd.
3. Kfb into every st (16 stitches).
4. Knit 1 rnd.
5. * Kfb K1 repeat from * (24 stitches).
6. Knit 1 rnd.
7, etc.: add 8 stitches every other round up to 88 stitches.

This is pretty much the same pattern idea in Barbara Walker's
book, Knitting From The Top.

88 stitches tells me you're using bulky yarn or very big needles.
With US worsted-weight I use 96 stitches on US size 8 needles
(old UK size 6) and even that can be made too small for an adult
if I strand too tightly.

snip math
Applying geometry and an inverse sine, this yields not a disk or
even a near disk, but a cone with an angle at the peak of 116 degrees.
This is rather pointy.

The reason I ran through this computation is that when I tried this
pattern a cone is what I got. I wanted to see if I had done anything
wrong, but the arithmetic confirms my result.

If I were to add 9 stitches every other round, my cone would flatten out
considerably, to about 145 degrees at the peak. This would seem to make
more sense, conforming more closely to the shape of the top of the head.

Or does this all work itself out at blocking time?

It would work out if you are using 100% wool, which can be reshaped
with steam and pressure to an amazing degree. Also, a mild point
will flatten once the hat is put on.

Or you could use bigger needles, or knit looser.

Knitting math is more complicated than non-stretchy materials math
because of the stretch factor, and because knit stitches are not
exactly square.

The pattern as given adds 8 stitches every other round;
that is equal to four stitches every round. (With finer yarns you
can play with the spacing of the increases even more, because of
the stretchiness factor.)

I think I have this right, but check carefully, because when I try
to do math and type, I often get it wrong:

For a circle, C = 2*pi*R
so for each round, you have to increase enough stitches around the
circumference to offset the increase in diameter. For each round,
you would have to increase the circumference by 2*pi, that is
2x3.14... or 6.28 stitches _if_ the stitches measured the same for
both height and width. But for most people, knitting stitches are
not square.

If stitches were exactly as high as they are wide, increasing
eight stitches every other round (four stitches every round)
wouldn't be nearly enough, so you get a cone.

If stitches are very high and narrow, the work comes out even more
cone-shaped. If stitches are wide and flat, the work is flatter.
But for only four stitches per round to make a shallow/flat top,
the stitches have to be very wide and flat. That means they need
to be loose enough to stretch sideways.

To make your cone into a flatter dome, if not a disk, you need
to use bigger needles or knit looser.

=Tamar

in all flat circular knits i made the amount of stiches between
increases grows ,,,but the number of increasing per round stay the
same
mirjam

A pattern for a skull-fitting chu'llu hat (from Knitting With Balls)
knit in the round begins:

1. Cast on 8 stitches.

2. Knit 1 rnd.

3. Kfb into every st (16 stitches).

4. Knit 1 rnd.

5. * Kfb K1 repeat from * (24 stitches).

6. Knit 1 rnd.

7, etc.: add 8 stitches every other round up to 88 stitches.

With a gauge of 4" = 18 sts and 24 rows,

1 st = 4/18 inches = 2/9 inches
1 row = 4/24 inches = 1/6 inches

At the end of every even numbered step N above, the piece measures

N rows = (1/6)N inches from center to edge
8(N/2) st = 4N st = (8/9)N inches around

Applying geometry and an inverse sine, this yields not a disk or even a
near disk, but a cone with an angle at the peak of 116 degrees. This is
rather pointy.

The reason I ran through this computation is that when I tried this
pattern a cone is what I got. I wanted to see if I had done anything
wrong, but the arithmetic confirms my result.

If I were to add 9 stitches every other round, my cone would flatten out
considerably, to about 145 degrees at the peak. This would seem to make
more sense, conforming more closely to the shape of the top of the head.

Or does this all work itself out at blocking time?

What do you think?