Wednesday, July 13, 2016

Getting Your Head Around Balloon Formulas - How Many Balloons Does it Take to Fill a Room?

When I left school I thought my days of trying to understand mathematical formulas were well and truly over... how wrong I was!

Balloon Filled Room 

Recently, I was asked to quote a price for a balloon-filled room. Many years ago I would have tried to guess, but as we all know that can be very costly in many ways. So where do you start?  Before anything else you will need some information from the client:
  • Room Length - 6.3m
  • Room Width - 3.82m
  • Room Height, or how high the balloons need to go to if they do not want the whole room completely filled - 1.5m
  • What size of balloons would they like to be used? - 16"
My client had seen a high-profile event on the Internet, where a room had been filled with 16" white balloons, and that was exactly what she wanted me to recreate. 

So basically we need to work out the Volume of a Rectangle - 

length x height x width

Because we use the measurement of inches when we work with balloons, it is easier for me to change the room dimensions into feet and inches first.

6.3m = 20.66ft
3.82m = 12.53ft
1.5m = 4.92ft

To calculate the total volume of space that I would need to fill in cubic feet, multiply the dimensions as shown below.

20.66 x 12.53 x 4.92  = 1,273 cubic feet.

The client requested 16" balloons but agreed that it would be better if we only inflated the 16" balloons to 14" to make them more durable.  So, all my calculations need to be for a balloon inflated to 14".

The next step is to work out the radius of the balloon using the Volume of a Sphere 4/3π𝒓3   equation. 
This formula is used for figuring how much space an inflated balloon occupies, or how much gas it takes to fill a balloon to a round shape.

4 ÷ 3 x 3.14 x 7 x 7 x 7 = 1,436 cubic inches per 16" balloon inflated to 14"

12" x 12" x 12" = 1,728 cubic inches per cubic foot

1,436 ÷ 1,728 = 0.83 cubic feet per balloon

Our result shows us that each 14" balloon  occupies a minimum of .83 cubic feet

The balloons will not pack perfectly together. The balloons might take up as much space as an equivalent cubic shape if there is no packing at all.

14 x 14 x 14 = 2,744

2,744 ÷ 1,728 = 1.58 cubic feet per balloon

Our results show us that each 14" balloon occupies a maximum of 1.58 cubic feet.

1273 ÷ .83 = 1,532 maximum number of balloons to completely fill the room.
1273 ÷ 1.58 = 805 minimum number of balloons to completely fill the room.

Therefore, I would take the mean average number of balloons and quote for the job using that figure.

1,531+ 805 ÷ 2 = 1,168 16" balloons inflated to 14"

I asked Luc Bertrand, CBA, of wAw Balloons in Vichte, Belgium, if he agreed with me.

In theory the calculations are correct. If I design with round balloons and they fitted in five perfectly interlocking layers, it would result in 986 balloons being used.
However, balloons are not round, and on top of that, it is not likely that they will perfectly organise themselves in grids. We all know they have their own will. So I would go for an absolute max of three layers resulting in using more like 595 balloons.”

Luc shows us using a mathematical method to check his findings.

The space to be filled in the room is;
6.3m = 248"
3.82 = 150"
1.5m = 59"

Therefore, the volume of space in inches is 248" x 150" x 59" = 2,194,800 inches.

If the 14" balloon, when inflated, is 17" in length, the volume of a balloon as a cube is 

14" x 14" x 17" = 3,332"

The volume of the space to fill ÷ volume of the "cube" balloon.

2,194,800 ÷ 3,332 = 658 balloons

So now we need to consider the fact that balloons do not fall in a nice orderly manner,and therefore we should allow extra balloons for this. If you look at Luc's diagram below, you will see that Luc shows layers of balloons. He shows balloons standing upright and laying flat. This demonstrates how many balloons will fit into the room falling in different patterns.

Luc concludes;

“So I would go for an absolute max of four layers resulting in using more like 782 balloons, if perfectly organised.”

“If you want only one layer to fill a ceiling, this could be calculated as  square balloons. Some will stand up some will be flat. If multiple layers, use the cube method and add up to 20% to be on the safe side as the more layers the more they will organise and pack.

 658 balloons + 20% = 789

This is a very interesting result, the difference in the two suggested totals (1,168 and 789)  is quite different. This is caused by calculating the balloon size using the volume of a totally round sphere versus using the actual balloon size. 

I really like Luc's method. I think that it is logical and makes this exercise easier to understand and calculate.

Maths has never been my strong point, but I really enjoyed working on this project as I feel that I understand it much better now than I ever did before. 

Since writing this blog, I have actually filled two rooms with balloons! I was very happy that on both occasions using the math formula above worked perfectly!

This is a panoramic photo of the one of the rooms that I filled. The floor cover
reached a height of about 1.5 m plus we filled the ceiling with 16" helium filled balloons!

Happy Ballooning!



Christine Maentz said...

Math is not my forte either and I feared the day someone would ask for this! Thanks for sharing - I'm going to save this info - you never know when it will come in handy!

Unknown said...

I entered your dimensions into my Balloon Calculator and the balloon size and it came up with the answer with out all the math. 761 balloons

Sue Bowler (Marston-Weston) said...

That's great Gary! How do people find out about your Balloon Calculator? I also believe that it is important that people understand how to work out this for themselves, as it does give you more confidence when working on projects such as this. Thank you for your feedback!

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superk said...

Wonderful explanation of a SERIOUSLY complicated calculation. Without the proper calculations a decor job and reputation can be left lacking or could cost you in over purchasing stock you may not be able to return.
Thank you for the topic