Monday, December 1, 2014

All of the Lights

One of my family's favorite Christmas movie is National Lampoon's Christmas Vacation. So since it's getting close and it's that time of the year, I thought I would look into something Christmas related. This weekend, since the weather was nice (no more snow and not too cold!), my family dug out the Christmas lights to put them up. And it got me thinking of that movie and all those lights. How many and how much would it cost to decorate a house as done in the movie - the entire roof and all around the entire sides.

First, I went to find out what sort of lights were used. Based on a picture in a movie, they're larger than the sort I'm used to. So then I searched Christmas lights. I know that there are all sorts of places to buy lights but I choose Home-Depot. The lights cost $8.48/each for a strand of 25 lights at a length of 25 feet. You can however only connect at most 2 sets. But I'm guessing by the looks of it with any lights you wouldn't be able to create that long of a strand. So we're just going to assume that we can attach them all together no matter.

So now how to figure out how many strands are needed. After a little searching, hoping to find the house dimensions (and then go round trying to figure out how many strands), I was able to find that house was decorated with 25,000 lights! That's a ton and no wonder. So divide that by the nice easy 25 lights per strand and you would need 1,000 strands of lights. And based on the website, you'd have to travel to several stores to pick them up - the one near me only has 20 on stock. These lights being bigger than usual, already cost a lot. Multiplying the cost of a strand at $8.48 by the number of strands, it ends up costing $8480.00 dollars. No thank you. I could pay to study abroad instead!

And the length of all those strands, at 25 feet per strand ends up being the same as the number of lights - 25,000 feet.

So then I thought: how tall of a tree would you need to use that many lights? I'm going to use a cone to represent a tree to find this out. Since lights go around the tree, I'm going to look at the surface area of a cone minus the base: pi*r*l. The variable "l" of the cone represents the slant height, which in terms of height equals sqrt(h2 + r2 ). So our formula becomes: pi*r*sqrt(h2 + r2 ). Just looking at my own tree, the height is about 3 times the radius of the tree. Using this I can narrow the formula down to having only one variable, height: pi*h/3*sqrt(h2 + (h/3)2 ). Now to simply the equation a bit:

= pi*h/3*sqrt((4h/3)2 )
= pi*h/3*4h/3
= pi*4h2/9

To make things simple, just like the house we'll cover the entire tree with lights! Which I think would hurt to look at up close haha. The width of the light strands is about 2 inches or 1/6 of a foot, so the area of all the light strands is  feet squared. Setting this equal to the surface area and solving:

4166.67 = pi*4h2/9
37500 = pi*4h2
54.63 = h

So the height of the tree is about 55 feet. A little too small to be the tree at Rockefeller Center (69 to 100ft). If the spacing between the lights was increased from nothing to something, the height of the tree would just continue to grow. So again, like I thought, I'm going to pass. I'd rather keep with tradition and continue to put up the fake tree and string a few lights.