I need help building an equation

[BrendonTW]

Hey folks,

I've got a very different question for these forums, and I looked all over online and this seemed to be the best place to ask for help.

I own a landscape company and we are venturing into Christmas lighting, specifically wrapping tree trunks with strands of Christmas lights.

I need to build an equation to where I can plug in two numbers for tree trunk measurements and light spacing, and know how many strands of lights I will have.

I need to be able to enter:

Trunk Diameter
Trunk Height

And I need the product to be X strands of lights. Here's what I know:

We use 23 foot strands of lights. They are all 23' and that will not change.
6" diameter trunk gives 15.64 inches of rise (wrapping from the bottom up)
12" diameter trunk gives 7.82 inches of rise
21" diameter trunk gives 4.3 inches of rise

I need to go on properties and take measurements. Our pricing is per strand. For example, I have a customer who has a 36" diameter tree trunk which is only 72" tall. I need to be able to plug in those two numbers and come up with a number of strands required. Any help is GREATLY appreciated!

Also - if circumference would be easier than diameter, I could measure that too.

 

[Deleted member 4993]

Hey folks,

I've got a very different question for these forums, and I looked all over online and this seemed to be the best place to ask for help.

I own a landscape company and we are venturing into Christmas lighting, specifically wrapping tree trunks with strands of Christmas lights.

I need to build an equation to where I can plug in two numbers for tree trunk measurements and light spacing, and know how many strands of lights I will have.

I need to be able to enter:

Trunk Diameter
Trunk Height

And I need the product to be X strands of lights. Here's what I know:

We use 23 foot strands of lights. They are all 23' and that will not change.
6" diameter trunk gives 15.64 inches of rise (wrapping from the bottom up)
12" diameter trunk gives 7.82 inches of rise
21" diameter trunk gives 4.3 inches of rise

I need to go on properties and take measurements. Our pricing is per strand. For example, I have a customer who has a 36" diameter tree trunk which is only 72" tall. I need to be able to plug in those two numbers and come up with a number of strands required. Any help is GREATLY appreciated!

Also - if circumference would be easier than diameter, I could measure that too.

Are you wrapping the strand around the trunk as close as possible - or are leaving some gap between each wrap?

 

[Ishuda]

Hey folks,

I've got a very different question for these forums, and I looked all over online and this seemed to be the best place to ask for help.

I own a landscape company and we are venturing into Christmas lighting, specifically wrapping tree trunks with strands of Christmas lights.

I need to build an equation to where I can plug in two numbers for tree trunk measurements and light spacing, and know how many strands of lights I will have.

I need to be able to enter:

Trunk Diameter
Trunk Height

And I need the product to be X strands of lights. Here's what I know:

We use 23 foot strands of lights. They are all 23' and that will not change.
6" diameter trunk gives 15.64 inches of rise (wrapping from the bottom up)
12" diameter trunk gives 7.82 inches of rise
21" diameter trunk gives 4.3 inches of rise

I need to go on properties and take measurements. Our pricing is per strand. For example, I have a customer who has a 36" diameter tree trunk which is only 72" tall. I need to be able to plug in those two numbers and come up with a number of strands required. Any help is GREATLY appreciated!

Also - if circumference would be easier than diameter, I could measure that too.

As Subhotosh Khan indicates, it will change depending on how close you want the wraps. The values you give appears to be a close wrap as the rise is approximately the 23' [276''] divided by the circumference.

dia	cir	276/cir	mea rise
6	18.85	14.64	15.64
12	37.70	7.32	7.82
21	65.97	4.18	4.3

If that is the case the formula
Strands = (Height in inches / Circumference in inches) rounded up to the next strand.
should probably work out if you just use complete strands. If you want to be more cautious use
S = 1.05 H / C
and adjust after a few of complete wraps.

 

[hoosie]

Christmas Lights Problem: How many strands?

Question:



Trunk Diameter
Trunk Height

And I need the product to be X strands of lights. Here's what I know:

We use 23 foot strands of lights. They are all 23' and that will not change.
6" diameter trunk gives 15.64 inches of rise (wrapping from the bottom up)
12" diameter trunk gives 7.82 inches of rise
21" diameter trunk gives 4.3 inches of rise

I need to go on properties and take measurements. Our pricing is per strand. For example, I have a customer who has a 36" diameter tree trunk which is only 72" tall. I need to be able to plug in those two numbers and come up with a number of strands required. Any help is GREATLY appreciated!

Also - if circumference would be easier than diameter, I could measure that too.


Solution:

Circumference of a circle is given by:
C = πd where π = 3.14159 and d = diameter

d = 6" C = 6π = 18.8496"
d = 12" C = 12π = 37.6991"
d = 21" C = 21π = 65.9734"

Strand length
= 23′
= 276″


6" diameter trunk:

To calculate how many times one strand wraps around the trunk we divide the strand length by the length of one wrap (circumference):


276/18.8496 = 14.6422


Strand passes around trunk 14.6 times


Rise of one strand = 15.64"

To calculate the distance between each wrap we divide the rise of one strand by the number of times the strand wraps around the trunk.

15.64/14.6 = 1.0712
First wrap starts at height 1.07"
14 * 1.0712 = 14.9968
Wrap 14 finishes at height 15.00"
14.6 * 1.0712 = 15.6395
Wrap 14.6 finishes at height 15.64"




12" diameter trunk:


276/37.6991 = 7.3211 7.82 inches of rise


Strand passes around trunk 7.3 times

7.82/7.3 = 1.0712
First wrap starts at height 1.07"
Wrap 7 finishes at height 7.50"
Wrap 7.3 finishes at height 7.82"





21" diameter trunk:


276/65.9734 = 4.1835 4.3 inches of rise

Strand passes around trunk 4.2 times

4.3/4.2 = 1.0238
First wrap starts at height 1.02"
Wrap 4 finishes at height 4.10"
Wrap 4.2 finishes at height 4.30"


If we make it so that 21" diameter trunk has distance of 1.07" between wraps (same as other two trunks) then using 4.2 wraps we can work out the rise:
4.2 * 1.0712 = 4.4990
The rise in this case would be 4.50"

4.5/4.2 = 1.0714
First wrap starts at height 1.07"
Wrap 4 finishes at height 4.29"
Wrap 4.2 finishes at height 4.50"




Summary:

Distance between each wrap = 1.07"

Diameter 6 Rise 15.64"276/18.8496 = 14.6422

Diameter 12 Rise 7.82"276/37.6991 = 7.3211

Diameter 21 Rise 4.50"276/65.9734 = 4.1835


Rise = (276/πd)* 1.0712

= 295.6512/πd

If given height of trunk = h and number of strands required = n then:


n = h/(295.6512/πd)

n = πhd/295.6512

Example 1:

How many 23′ strands are required to wrap a trunk with diameter 6″ and height 120″?

n = πhd/295.6512 where h = 120, d = 6, π = 3.14159


n = (3.14159*120*6)/295.6512

= 7.65

8 strands would be needed

Example 2:

How many 23′ strands are required to wrap a trunk with diameter 36″ and height 72″?




n = πhd/295.6512 where h = 72, d = 36, π = 3.14159


n = (3.14159*72*36)/295.6512

= 27.54

28 strands would be needed

Example 3:

How many 23′ strands are required to wrap a trunk with diameter 12″ and height 96″?



n = πhd/295.6512 where h = 96, d = 12, π = 3.14159


n = (3.14159*96*12)/295.6512

= 12.24




13 strands would be needed



Formula Required:

n = πhd/295.6512

h = height of trunk (in inches)

d = diameter (in inches)

π = 3.14159


Hope this helps to solve your problem.