*22 May 2010*

Thanks to feedback from Lesley, I have modified this tute. I have broken it into Easy Method and Hard Method.

**Easy Method**

For this example, I want to draw a bottom with circumference = 20".

All my curves are drawn using a radius of 2" and they make up a quadrant.

What you need:

A compass drawing instrument

Paper

Calculator

Pencil

Ruler

1) Take your compass, measure off 2" (let's call this R) and draw an arc length such that you end up with a quadrant. The image above show you what you should get.

2) Next, you need to calculate the total length of the curved line you have drawn.

We need 4 arc lengths in our bag bottom.

Since each arc length make a quadrant, together, they make up a circle.

Total Arc length = Circumference of circle = 2 X pi X R

where R is the amount(radius) we measure off to draw our quadrant, pi is 22/7 or 3.14

Total Arc length= 2 X 22/7 X 2 = 88/7" = 12 4/7" (let's round off to 12.5")

3) This next step shows you the thought process. You don't need to construct anything yet.

Total arc length calculated in previous step is 12.5"

Total circumference of bag bottom we want is 20"

Look at the image above. What we need to figure out next is how much "a" and "b" should be.

For my example, I want 0.5" for a.

Therefore b = (20 - 12.5 - 0.5 - 0.5) / 2 = 3.25" or 3 1/4"

4) Now complete the pattern by drawing in the "a" and "b" and the remaining 3 quadrants. You should get the same pattern as seen above.

5) If you want to construct your own bag bottom pattern, just change the following variables to suit your needs:

circumference of bag bottom

R (step 1)

"a"

"b"

*edited:*

If you sew in cm, there's no difference in the formula. Your variables (step 5) will be in cm.

**

This is an example of another bag bottom you can achieve by just using 2 semi-circles. The only difference here is the variable "a" is omitted. The formula remains the same.

Note: Please go thru' Easy Method first before using Hard Method.

**Hard Method**

What you need:

A compass drawing instrument

Paper

Calculator

Pencil

Ruler

Protractor

1) Take your compass, measure off 2" (let's call this R) and draw an arc length.

2) Next, you need to calculate the length of the arc you have drawn.

Use the protractor to calculate the angle of your arc.

In my example (see image above) my angle is 50 deg.

Arc length = R(2 X pi X C) / 360)

where R is the amount(radius) we measure off to draw our arc length, pi is 22/7 or 3.14 and C is angle of arc which we measured with our protractor.

4 Arc length is 2 ( (2 X 3.14 X 50) / 360 ) X 4 = 6.97" (round off to 7")

3) This next step shows you the thought process. You don't need to construct anything yet.

Total arc length calculated in previous step is 7"

Total circumference of bag bottom we want is 20"

Note: If you don't understand what "a" and "b" are, please refer to Easy Method.

I want 2" for a.

Therefore b = (20 - 7 - 2 - 2) / 2 = 4.5"

4) Now complete the pattern by drawing in the "a" and "b" and the remaining 3 arcs.

5) If you want to construct your own bag bottom pattern, just change the following variables to suit your needs:

circumference of bag bottom

R (step 1)

"a"

"b"

This image gives you an idea how you can combine 2 different arc length constructed using different radius.

Any errors or questions, please put in the comment form. Thank you.

**Tute guideline**: All content on my tutes are my original ideas. Please don't copy or re-distribute or lift content from my tute. Please don't re-phrase my content and write a similar tute. You are however free to link to my blog or my post. Thank you.

Lastly, some notes on matching the base of a bag to the bag bottom.

If the circumference of your bag bottom pattern is 20", the circumference of your bag base is logically 20" (after having side seams sewn). But take note when you sew the base to the bottom, the base will be slightly bigger. You will end up with some pleats.

My personal preference is to have the circumference of my bag base (after having side seams sewn) 1" smaller than the circumference of the bottom. That way, I have fewer pleats to take care of. You can experiment to see what suits you best.

If you like having a lot of pleats on your bag base, just make the bag bottom much smaller than the bag base.

Happy sewing!

* * *

Below are my bag patterns which are available for sale at Etsy (instant download). Clicking on the images will take you to my Etsy shop.

For more Applique Resources

For more Tutorials

## 4 comments:

Thanks for this Jane, I always struggle with bottoms!

Hello Jane - I love your blog and your bags! I've been reading you for quite some time now. You are so clever, and so generous with all you share.

I'm de-lurking because in your calculations, above, wouldn't be a lot easier to calculate the length of the four arcs all together as the circumfernce of a circle with a 2-inch radius? A simple 2 x pi x R - then add the extra length for the four straight bits?

How nice, a lurker!

About your question, the reason I use the "arc length" formula is because I thought there might be some folks out there who don't want to use quadrants and try using different values for the angle.

But you are right. If a quadrant is what you want, then 2xpixR will give you the answer.

Thanks

Jane

I am amazed at your math abilities! I wish I could figure it all out, thank you again for your tutorials, I also hate the exposed raw edges!!

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