The Physics
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Altitude of the Highest Toy Balloon Flight

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Bibliographic Entry Result
(w/surrounding text)
The Guinness Book of Records 1999. New York: Bantam, 1999: 528. "In September 1987, British daredevil Ian Ashpole set a world altitude record for toy-balloon flight when he reached a height of 1 mile 1,575 yd. over Ross-on-Wye, England." 3050 m

Everyone had an experience of releasing a balloon into the sky, whether it was an accident or intentional. Once the balloon is released one wonders how high it can fly.

The Guinness Book of Records has recorded the highest toy balloon flight of a 1 foot radius. The record was set in September of 1987. Ian Ashpole of Britain is not afraid of dangerous stunts and therefore pulled off this one. He rose to a height of 3049.52 m in a hot-air balloon. A group of 400 helium-filled balloons were at the same altitude. Ian had attached himself to the group of balloons and descended by releasing them one by one.

I have decided to explore my own ideal scenario. I used party balloons of radius 0.1143 m.

The volume formula for a sphere is:

After substituting the radius of the balloon value into the formula. The volume of the balloon is 0.00625m3. To find the mass of helium, I used the formula:

The density of helium at room temperature of about 20 °C is 0.1663 kg/m. Multiply the density by the volume of the balloon to find the mass of helium. The mass of the balloon is 0.00185 kg. This was measured by placing ten deflated balloons on a scale. The mass of ten balloons was 0.0185 kg therefore the mass of one balloon is 0.00185 kg.

To calculate the total density of the balloon with helium, once again use the density formula:

The density of the balloon with helium is found to be 0.462 kg/m3 at the maximum altitude of 9000 m.

The following graph taken from the US Standard Atmosphere (1976) table in CRC Handbook of Chemistry and Physics, (75th Edition) shows that the density varies with altitude. Altitude decreases as the density increases. The balloon in my calculation would float until it reaches an altitude of 9000 m with a density of 0.462 kg/m3 because after that the density at higher altitudes are lower than my calculated density. Also Ian Ashpole reached a maximum altitude of 3050 M. The altitudes are marked by horizontal lines.

Click for a larger image or to view the raw data file.
Source: CRC Handbook of Chemistry and Physics 75th Edition.

The calculated altitude differs from the record set by Ashpole. This is so because in the record breaking experiment Ashpole's mass was added to the mass of the balloons and therefore the combined density would be greater than the one I calculated. This would prevent Ashpole from reaching the ideal altitude that I calculated.

Jane Rubinshteyn -- 2002

Data and Story Project
    1. Altitude of the highest toy balloon flight
    2. Angular speed of the earth
    3. Height of the tallest building
    4. Highest critical temperature superconductor
    5. Mass of a dog
    6. Number of births in the US
    7. Number of crimes in New York state
    8. Number of pages in a science review book
    9. Number of people in the US
    10. Salary of a baseball player