Mathematics, 11.02.2021 07:10, nsuleban9524

1. Find the height of the parabolic balloon arch for the prom when the position of the bottom anchors are at x = 3 feet and x = 7 feet.

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answered: 727

lculator: Single Row Arch or Garland

For a 'String of Pearls' arch (i.e a floating arch with a single row of balloons) you'll need about 3 x 11" balloons per meter (this translates into 0.91 x 11" balloons per foot).

Example: Let's say your arch is 6m (20') wide and 6.7m (22') high. As your arch is taller than wide, formula 3 from above applies to calculate the arch length:

(2 x 6.7m) + 6.0m = 13.4m + 6.0m = 19.4 m

So your arch is roughly 20m long, which means you need 60 x 11" balloons (20m x 3 balloons per meter).

How Many Balloons Do You Need for a Clustered Arch or Garland?

If the length of the balloon arch or garland and the diameter of balloons are in the same units (both in ft, in, m, cm, mm ) you can use this formula for an arch with clusters of 4 balloons:

Divide the diameter of the balloon into the length of the arch and multiple by 4.8 to get the number of balloons needed (thanks to Sean O'Kelly from balloondecor.com.au who shared this formula with our readers).

Length of arch (unit)

x 4.8 = number of balloons

Diameter of balloon (same unit)

Example:

You want to make an arch that is 6.1m (20') wide and 3.7m (12') high. You plan to use 11" balloons (28cm diameter). As your arch is wider than tall, formula 1 from above applies. We'll calculate everything in cm to stay with the same unit.

Arch length: 610cm + 370cm = 980cm

Number of balloons: 980cm / 28cm * 4.8 = 168 balloons

Number of 4 balloon clusters: 168 / 4 = 42

If you calculate everything in feet and inches, here's an easier way to estimate the number of balloons you need for a 4 balloon per cluster arch...

5 inch balloons = 12 per foot

9 inch balloons = 8 per foot

11 inch balloons = 6 per foot

14 inch balloons = 4 per foot

16 inch balloons = 4 per foot

Is your head spinning from all these numbers and formulas? Fear not. I've calculated the number of balloons for various arch or garland lengths for you.

Balloon Arch / Garland Chart

Balloon arch or garland chart

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