Why Balloon Boy Never Could Have Been
Alby Reid
alby@bleary-id.co.uk
@Alby
October 27, 2009
Abstract
The case of Balloon Boy Falcon Heene cost emergency services a
signi cant amount of money and resulted in considerable distress to cable
news viewers. This paper sets out the physics behind a helium lifting
balloon and explains why it should have been obvious to both emergency
services and news organisations that Falcon Heene was never aboard.
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1 Could the Heene Balloon have lifted Falcon
Heene?
We can calculate the lifting capability of the Heene Balloon using Archimedes'
Principle, which states that the buoyant force on an object submerged in a uid
is equal to the weight of the uid displaced. To calculate the lifting capability
of the Heene Balloon we need to know the volume of the balloon, the density of
the surrounding air and the density of the helium contained within the balloon.
1.1 Density of Surrounding Air and Helium
The density of a gas is given by:
pM
ρ=
RT
Where p is the pressure of the gas; M is the molar mass of the gas (M air =
0.0290kgmol−1 , M He = 0.00400kgmol−1 ); R is the molar gas constant (8.31Jmol−1 K−1 );
T is the temperature of the air.
Fort Collins, Colorado is 1525m above sea level and at 1115 on 15th October
2009, when the balloon took o, the temperature was 291K and the pressure
was 1020.2hPa[2]; this gives the density of the air at ground level in Fort Collins
−3
as 1.22kgm . As the balloon was not rigidly in ated we can assume that the
pressure of the helium was the same as the pressure of the surrounding air,
−3
giving the density of the helium as 0.169kgm .
1.2 Lifting Capability
The upthrust force (Fupthrust ) on a helium balloon oating in air is equal to the
buoyant force (Fbuoyant ) less the weight of the helium (WHe ). By Archimedes'
Principle the buoyant force is equal to the weight of the air displaced (Wair ) so
that:
Fupthrust = Wair − WHe
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Using the gures for density calculated above 1m of air has a weight of 12.0N
3
and 1m of helium has a weight of 1.66N, thus the upthrust on a helium balloon
−3
is 10.31Nm . This is a maximum possible value as it ignores the weight of the
balloon material itself. The lifting capability of the balloon would decrease with
height, as the density of the air is proportional to the pressure and the pressure
is inversely proportional to the height of the balloon:
gM
Lh RL
p = p0 1−
T0
Where p0 is standard atmospheric pressure (1013.25hPa); L is the rate at
−1
which the temperature decreases with height (6.5mKm ); h is the height above
sea level; T0 is standard temperature (288K); g is gravitational eld strength
−1
(9.81Nkg ).
The Heene Balloon was an oblate spheroid, the volume of which is given by:
2
4 2
V = πa c
3
Where a is the rst semiaxis; c is the third semiaxis. The Heene Balloon
was approximately 6.1m (20ft) wide and 1.5m (5ft) high, giving the balloon a
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volume of 29.2m and therefore a maximum lifting capability of 301N, assuming
the balloon is completely lled and ignoring the weight of the balloon itself. The
CDC gives the average weight of a six year old as 206N (46.2lb)[?], meaning that,
discounting other components, the Heene Balloon would have been capable of
lifting Falcon Heene, assuming he is of average weight.
1.3 Weight of Balloon
1.3.1 Envelope
The surface area of a spheroid is given by:
c2 tanh−1 1− c2
a2
A = 2π a2 +
a2 −c2
a2
Which, using the dimensions previously given, gives the Heene Balloon an
2
area of 78.0m . Assuming the Heene Balloon is made of a material similar to
−2
ve micron aluminised Mylar, which has a density of 6.8gm the weight of the
balloon's envelope would be only 5.20N.
1.3.2 Basket
Estimating the weight of the balloon's basket, said to have been made of ply-
wood, is much harder as the dimensions of the basket and the details of its
construction are unknown. Assuming that the remaining 89.8N of upthrust is
2
accounted for by the plywood allows for only 9.09kg or 1.21m of 12.5mm-thick
(1/2”) plywood (assuming ρplywood = 600kgm−3 ). It is unlikely that it would be
possible to create a basket large enough to hold a six year old boy using this
limited quantity of wood.
1.3.3 Miscellaneous
As details of the balloon's construction are unknown it is not possible to estimate
the weight of parts other than the envelope and basket, such as the connections
holding parts together. Some sources have reported that the balloon initially
had an attached gondola which fell away shortly into the ight. This would
have further reduced the balloon's initial lifting capability.
2 Shape
The real giveaway as to the absence of Falcon Heene aboard the Heene Balloon
is the balloon's shape. A load-carrying balloon has a characteristic inverted
raindrop shape, as seen in Figure 1. The absence of any structural support
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Figure 1: Load carrying balloons (Images from NASA)
(obvious due to the balloon's shifting shape and size during its ight) means
that the presence of a 200N weight aboard the balloon would have distorted the
balloon's shape very noticeably.
3 Conclusion
Given that the balloon was not fully in ated, and that the plywood used for
the basket would contribute a signi cant amount of weight, it should have been
immediately obvious that the Heene Balloon was not capable of lifting a six year
old boy, especially when the rate of climb and its ability to reach an altitude of
more than 3000m is considered. The absence of the correct shape of the balloon
should have further reinforced the absence of Falcon Heene aboard the balloon.
A knowledge of basic physics on the part of the emergency services and news
organisations would have avoided a great deal of wasted time, eort and money
and prevented a great deal of distress.
References
[1] Weather Underground, Data for Loveland Municipal Airport (KFNL), Fort
Collins, http://bit.ly/4t0r14
[2] CDC Growth Charts, Percentile Data Files with LMS Values,
http://bit.ly/4tYYgb
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