## Final Exams, and Project Orion

Due to final exams and their associated studying, I’ve been nose deep in books or tests for the past couple of weeks, but now that my spring break has arrived I have the opportunity to relax a bit and focus on my recreational interests. Behold my most recent fixation: Project Orion!

Project Orion studied the feasibility of using atomic and/or nuclear bombs as a form of propulsion: in a nutshell, you toss out an atomic bomb behind your spaceship, explode it, and ride the blast in the direction you want to go. If you repeat this process enough times, you can pick up an incredible amount of speed – projections ranging as high as 3% the speed of light, according to Freeman Dyson[1]. The fancy term for this arrangement is nuclear pulse propulsion.

In aerospace systems, we measure engine performance in two ways: thrust and specific impulse. Thrust refers to the “kick” one gets from accelerating fuel out the back end of the engine; mathematically, it is $\frac{dm}{dt} \mathbf{v} = \mathbf{T}$, where $\mathbf{T}$ is the thrust, $\mathbf{v}$ is the velocity of the exhaust gases, and $\frac{dm}{dt}$ is the mass flow of the exhaust (so many grams per second, for example). Thrust is a force, and so is measured in Newtons, pounds, or other appropriate units.

Specific impulse, denoted Isp, refers to the change in change in momentum of the reaction mass (the exhaust gases) per unit reaction mass, or more simply, how much thrust you get from a given amount of fuel; mathematically, it is $\frac{v_e}{g_0} = I_{sp}$, where ${v_e}$ is the exhaust velocity, ${g_0} = 9.8 m/s^2$, and $I_{sp}$ is the specific impulse. It is interesting to note that the specific impulse given by this formula is in seconds; for a complete discussion, check out the specific impulse Wikipedia page.

Normally, a drive system will have great thrust, but low specific impulse (like a rocket) or poor thrust, but great specific impulse (like an ion drive):

 Drive System Thrust Specific Impulse Space Shuttle Main Engines 2170 kN 453 s NSTAR (ion drive) 92 mN* 3300 s

(*Note: mN is the abbreviation for milli-Newton, or 10-3 Newtons)

In contrast, the type of engine contemplated by Project Orion has both high thrust and high specific impulse. According to a General Atomics document[2], Orions would produce meganewtons of thrust (106 Newtons) with a specific impulse between 5,000 and 10,000 seconds. This specific impulse is governed by $I_{sp} = \frac{C_0 V_e}{g_0}$, where $C_0$ is a collimation factor no greater than .5, ${v_e}$ is the plasma debris velocity of the nuclear device, and ${g_0} = 9.8 m/s^2$. This equation is nearly identical to that given above, so why is the Orion drive possessed of such superior performance?

The reason Orion drives have such a high $I_{sp}$ relative to chemical rockets is hiding in the $V_e$ term. In a chemical rocket, exhaust velocities are in the range of a few km/s. In an Orion drive, exhaust velocities start at roughly 100 km/s, and increase from there as the bomb yield increases. Similarly, the thrust is directly related to the exhaust velocity – the Orion’s higher exhaust velocities give it the advantage once again.

Now, there are some downsides to all of this. None of the proposed Orion designs can actually land on a planet, so you’ll still need chemical rockets for that. Also, there’s that whole “nuclear fallout is generally a bad thing” – proposed designs generally call for a single launch to detonate roughly a thousand nuclear bombs, which is going to introduce significant amounts of radiation and radioactive contamination to the atmosphere. Finally, the cost of developing and constructing an Orion-based vehicle is enormous; the most optimistic estimates put R&D at $1.2 billion in 1960 dollars, which is roughly$8-$10 billion today, plus the construction costs, which can easily reach tens of billions of dollars. In contrast, the entire Apollo program cost roughly the same$1.2 billion, and included 17 missions, 6 of which were moon landings.

Footnotes:

Dyson, Freeman. “Interstellar Transport.” Physics Today vol 21, issue 10, October 1968, pp. 41-45. DOI:10.1063/1.3034534.

Ross, F. “Propulsive System Specific Impulse.” General Atomics GAMD-1293 8 Feb. 1960.