It’s a plane? No it’s… a house?

A physics analysis of the Movie Up

How many balloons did Mr. Fredricksen need to fly his house?

Up is a timeless classic

• Follows Mr. Fredricksen and a young boy named Russell as they fulfill Mr. Fredricksen's wife's dying wish of getting their house to Paradise Falls
• Paradise falls is a fictional waterfall based off a real waterfall in Venezuela
• So I was wondering how many balloons it would take to get the house off the ground
• Let alone flying it to another continent

How many balloons did Mr. Fredricksen need to fly his house?

To answer this I had to:

F_{g house} = F_{B balloons} ~~ mg = ⲣV_dg

• Find the value of F_{g house}
• Weight of the house
• Weight of his belongings
• Find the value of F_{B balloons}
• Solve for V_displaced

275 pounds per square foot + 200,000 lbs foundation

​

Mr Fredricksen as a unit of measure

Old man Mr. Fredricksen is about 5ft 9in

4 and 6/10 Mr Fredricksens (26.45 ft)

House floor plan:

2 Bedrooms

1 Bathroom

Full kitchen

9 rooms total

Black line = 4.6 Mr. Fredricksens

Overlapped the Blue line over the Black line

Found the blue line to be 34.4% of the Black line

​

Blue line = (0.344)Black line = 1.58 Mr. Fredricksens = 9.085 ft

Black line + Blue line = 26.45 + 9.085 = 35.535 ft

​

The house is:

26.45 * 35.535 = 939.90075 ft²

275 pounds per square foot

939.90075 * 275 = 258472.7063 lbs

258472.7063 lbs = 117241.247 kg

F_{g house} = (117241.247)(9.8) = 2533032.521 N

Items(simplified):

• 18 tables
• 1 bench
• 8 chairs
• 1 king sized bed
• 1 crib
• 2 desks
• 1 oven
• 2 sinks
• 1 fridge
• 1 bathtub
• 1 toilet

~~1733 lbs = 786.0756 kg

F_{g stuff} = (786.0756)(9.8) = 7703.54 N

F_{g house} = F_{B balloons}

m_houseg + m_stuffg = ⲣV_dg ⲣ_air = 1.225 kg/m³

​

2533032.521 N + 7703.54 N = (1.225)V_d(9.8)

​

211639.8219 m³ = V_d -> Volume displaced by balloons

Number of balloons need for 211454.6826 m³

Party Balloons

Average diameter of a party balloon is about 11 inches ~~ 0.2794 m

SO

211639.8219 = x(4/3ℼ0.1397³)

x = 18531883.41

​

Mr. Fredricksen would need at least 18,531,884 balloons to make his house fly

​

He rich

• Party Balloons in 2009 costed around $0.16
• So 18,531,884 balloons would cost $2,965,101.44
• In 2022 helium costs $3.10 per cubic meter
• Accounting for inflation that was around $2.30 in 2009
• So to fill 211454.6826 m³ with helium it would cost $486,345.77
• His trip costed at least $3,451,447.21

Where did he get this kind of money just for balloons???

​

Work Cited

“Balloon Size Chart.” Party Wholesale Centre - Main Balloons & Party Supplies in Singapore, https://www.partywholesale.com.sg/balloon-size-chart/.

City, Party. “Graduation.” Party City, https://www.partycity.com/balloons-latex.

Ella, and acesu143. “Up Characters: Heights and Ages Comparison.” Endless Awesome, 9 Mar. 2022, https://endlessawesome.com/2022/01/04/up-characters-heights-and-ages-comparison/.

“Inflation Rate between 2009-2022: Inflation Calculator.” $3,400 In 2009 → 2022 | Inflation Calculator, https://www.in2013dollars.com/us/inflation/2009?amount=3400#:~:text=The%20dollar%20had%20an%20average,Labor%20Statistics%20consumer%20price%20index.

USGS Online Publications Directory, https://pubs.usgs.gov/periodicals/mcs2020/.