Sunday, November 27, 2016

Buoyancy with the Thanksgiving Day Parade

When I was watching the Macy’s Thanksgiving Day Parade, I noticed how each of the balloons in the parade needed to have several ‘walkers’ to hold it down. I was curious as to why this is, so I reached it a little bit further. It turns out that the balloons are filled with a mixture of helium gas and some air; in fact, the average balloon is filled with 12,000 ft3 of helium! At 300 K (about 80 ˚F), Helium has a density of 0.164 kg/m3 while air has a density of 1.161 kg/m3. I thus released that the principles of buoyancy that we learned about it class must be at play!

This can be shown by a simple calculation (seen below). For this example, I will be using the information for the Pikachu balloon. The balloon alone has a mass of 373 lbs. and it is filled with 13,200 ft3 of helium!  If we assume that the helium accounts for the total volume of the balloon, then the Pikachu balloon displaces 373.78 m3 of air. This means there would be a buoyant force of 4,250 N. However, the gravity would only account for a downward force of 2,260 N. This means there would still be a net upward force of 1,990 N. This explains why they need handlers! The handlers would apply a downward tension force through ropes, allowing there to be a net-zero y-force on the balloon!

Vhelium = 13,200 ft3 x (1 m / 3.28084 ft)3 = 13,200 ft3 x 1 m3 / 35.31467 ft3 = 373.78 m3 = 374 m3

mtotal = mballoon + mhelium added = 169.19 kg + 61.14 kg = 230.326075 kg = 230. kg

mballoon = 373 lbs. x 1 kg / 2.20462 lbs. = 169.190155 kg = 169 kg

mhelium added = V x ρ = 372.78 m3 x 0.164 kg / 1 m3 = 61.13592 kg = 61.1 kg

Fbuoyant = ρfluid x Vfluid x g = 1.161 kg/m3 x 373.78 m3 x 9.8 m/s2 = 4,252.79408 N = 4,250 N

Fgravity = - (mtotal x g) = -(230.326075 kg x 9.8 m/s2) = -2,257.19554 N = -2,260 N

ΣF = Fbuoyant + Fgravity = 4,250 N + -2,260 N = 1,990 N

In other words, the applied force from the handlers must be -1,990 N in the y-direction for there to be no y-movement of the balloon. This is what Macy’s wants, as it would be bad for the balloon to fly away or come crashing to the ground. Fifty-four people each year are required to “walk” the Pikachu balloon—this means that 54 people in total apply a -1,990 N force. In other words, each person, on average, applies a -36.9 N force in the y-direction. There would obviously have to be some +x force for the balloon to move forward. This would also come from an applied tension force through the rope, but this problem only examined the need for “walkers” to balance out the buoyant force!
            Fapplied = ΣF – (Fbuoyant + Fgravity) = 0 – (4,250 N + -2,260 N) = -1,990 N
            Fper person = -1,990 N / 54 people = -36.9 N / person

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