What is the formula for spacing wire around a conical Christmas tree?

In summary, the individual has built a large Christmas tree with 1200 lights in their front yard. The tree is 6m high, with a 2m diameter base and a constant cone shape. They are looking for a formula to calculate the spacing of the wire around the cone to achieve a neat finish at the top. A good approximation for this calculation is 20/(wire length) in meters.
  • #1
Rsole
1
0
So here's my problem.
For the past few years i have built a very large christmas tree in my front yard.
1200 lights or so... looks awesome

it is 6m high, a 2m ring at the bottom and is a constant cone shape to the top point.
To install the lights i start from the bottom and progress to the top, coiling the wire around the cone at a constant spacing
i know the length of lighting wire (its written of the packet), and would like to know the formula to calculate the spacing of wire around the cone to achieve a theoretical neat finish at the top
Rus
 

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  • #2
Rsole said:
So here's my problem.
For the past few years i have built a very large christmas tree in my front yard.
1200 lights or so... looks awesome

it is 6m high, a 2m ring at the bottom and is a constant cone shape to the top point.
To install the lights i start from the bottom and progress to the top, coiling the wire around the cone at a constant spacing
i know the length of lighting wire (its written of the packet), and would like to know the formula to calculate the spacing of wire around the cone to achieve a theoretical neat finish at the top
https://www.physicsforums.com/attachments/90625

Rus
There's some kind of problem with your attachment. It can't be viewed.
 
  • #3
For your 2m diameter base and 6m high conical tree, a good approximation in meters is: spacing = 20/(wire length).

You might want to start at the top since final adjustments at the bottom should be easier.
 

1. How do you calculate the length of wire around a cone?

The formula for the length of wire around a cone is L = πr√(r² + h²), where L is the length of wire, r is the radius of the base of the cone, and h is the height of the cone.

2. What does the radius represent in the formula for the length of wire around a cone?

The radius in the formula represents the distance from the center of the base of the cone to the edge of the base.

3. Can the length of wire around a cone be negative?

No, the length of wire around a cone cannot be negative because it is a measurement of distance, which cannot be negative.

4. Is there a simpler formula for calculating the length of wire around a cone?

Yes, there is a simpler formula for calculating the length of wire around a cone called the slant height formula, which is L = πr√(r² + s²), where s is the slant height of the cone.

5. How does the height of the cone affect the length of wire around it?

The height of the cone directly affects the length of wire around it because the longer the height, the longer the slant height and therefore the longer the wire needed to wrap around the cone.

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