# Energy of Commercial Space Transportation

## Introduction

 Fig. 1: Diagram of the elements in Tsiolkovsky's rocket equation. (Source: Wikimedia Commons).

SpaceX CEO Elon Musk has revealed his newest vision for the BFR spacecraft: as a interplanetary rocket system for long-distance travel on Earth. Musk claims that it will allow passengers to travel most popular long-distance trips in just 30 minutes. Other entrepreneurs such as Richard Branson's, also envision transporting people between cities on Earth via space. While the concept of rocket travel is definitely cool and exciting, does it make sense from a cost perspective. In order for this dream to turn into reality, the cost of travel using a rocket has to be understood.

## Fuel Requirement to Launch a Rocket

Using the Tsiolkovsky's rocket equation, we can estimate the fuel needed to launch a rocket from earth's surface to low earth orbit (LEO). Tsiolkovsky's rocket equation says

ΔV = Veln(mo/mf)
MR = eΔV/Ve

where ΔV is the velocity change of the rocket, Ve is the exhaust velocity of the rocket, and MR is the mass ratio. A diagram representing the elements of Tsiolkovsky's rocket equation is show in Fig. 1. If we wish to place a payload in low Earth orbit (LEO), the spacecraft must be accelerated to about 9.7 km/s. Furthermore, assuming a specific impulse of 330s or (3.2 km/s), the rocket would have a ΔV/Ve ratio of approximately 3. This means that approximately 19 kg of propellant are required for every kilogram of unfueled rocket (engine, structure, and payload). A payload of 50,000 kg would require 9.5 × 105 kg in propellant. At an oxidizer to fuel ratio of approximately 2.5, the rocket will require 2.7 × 105 kg of fuel and 6.8 × 105 kg of liquid oxygen (LOX).

In comparison, a Boeing 747-400 has a maximum fuel capacity of 164,064 kg. [1] Therefore, even if a 747 used up all of its fuel on a flight, a rocket would still require 1.65 times more fuel. In my previous calculation, I calculated the propellant necessary to travel to LEO, however in reality, commercial space transportation would most likely follow a ballistic trajectory. Yet a ballistic trajectory would be subjugated to atmospheric drag for the entirety of flight, reducing the effective exhaust velocity. Putting aside many other factors such as atmospheric drag, novelty of rocket travel, re-usability, location of launch, etc. it can be assumed a ticket for rocket travel will be, at best, 1.65 times more expensive than current intercontinental airline travel.

## Feasibility and Affordability

According to SpaceX's own website, the "standard payment plan" for a 2018 launch of its Falcon 9 rocket cost around \$62 million. Musk has revealed that the BFR has supposedly a passenger capacity similar to an Airbus A380 (~ 850 passengers). On Twitter, Musk estimates the "cost per seat should be about the same as full fare economy in an aircraft." At \$500 per ticket at 850 tickets, SpaceX is looking at an earning of \$425,000 for a full capacity flight. However with a launch cost of \$62 million, ticket sales won't nearly turn a profit. Furthermore, faster air travel is not an unfamiliar concept. British Airway's Mach 2 Concorde was decommissioned in 2003 due to fuel-ticket cost profitability and a higher value placed on passenger comfort over travel time.

Additionally in 2010 the US Department of Transportation submitted an assessment of "Point-to-Point Commercial Space Transportation", in which serious financial and regulatory risks, present in commercial space transportation, exist. [2] Passenger accommodations, security, and emergency response are all issues that need to be addressed for viable commercial space transportation.

## Conclusion

It seems highly unlikely that commercial space travel will be an economical, viable form of transportation; at least anywhere in the near future. Once the cost of sending rockets to space comes down, then we can begin seriously considering traveling by rocket.

© Nicholas Kau. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

[1] "747-500 Airplane Characteristics for Airport Planning," Boeing Corporation, D6-58326-1, December 2002.

[2] "Point-to-Point Commericial Space Transportation in National Aviation System," U.S. Department of Transportation, 10 Mar 10.