Length of a Spiral - Can you help a home vegetable grower?

[Guest]

Hi there
I can grow great vegies, but I am terrible at maths!
Can you help me?
I have a circular vegetable bed that is 3.5 metres in diameter.
I want to install a drip irrigation pipe that is (13mm in diameter) in a spiral pattern from the centre expanding outward, and each 'rotation' of the pipe is spaced 30cm apart.
What length of pipe will I need to create a spiral that will water the whole bed?
Thanks so much to anyone that can help me with this!
Cheers Simon

[Baltuilhe]

Hello!

What you want is the Archimedean Spiral.
For your problem, 32.2m is a good size - almost perfect!

For your problem, I think this is the most 'near' solution
Have fun!
https://www.wolframalpha.com/input/?i=polar+plot+r%3D%280.3%2F%282pi%29%29*theta%2C+theta%3D0+to+11.67pi

Spiral from Wolfram

spiral-right.png (56.21 KiB) Viewed 953 times