The U.S. e-commerce giant Amazon patented plans for an \"airborne fulfillment ce

Question

The U.S. e-commerce giant Amazon patented plans for an "airborne fulfillment center" (AFC) such as an airship or blimp that would float at an altitude of around 45,000 ft. The airship will be stocked with lots of products that can be delivered by autonomous drones to customers on the ground. If the blimp is filled with helium, what volume is needed to lift one “short” ton (about 2,000 lbf) of goods to this altitude? Explain why the actual blimp will need to be significantly bigger than this. Clearly show how you developed your solution equations, any required assumptions and site sources of any required quantities.

Explanation / Answer

Density of air at 45000 feets(Rho1) = 0.2381 Kg / m3

Density of Helium(Rho2) = 0.164 Kg / m3

Load = 2000 lbs = 907.18 Kg

Doing force balance :0.238

volume *(Rho1- Rho2)*g = load * g

volume = 907.18/(0.2381-0.164)

=12242 m3

The actual bimp has to be bigger in order to account for any change in density of air or increase in future load.

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