#oberth effect

[truphysics]

Oberth Effect

Introduction The Oberth effect is a principle in astrodynamics and astronautics that states that the efficiency of a rocket’s propulsion system increases as the speed of the rocket increases. Named after the German scientist Hermann Oberth, who first described the effect, it is a fundamental principle used in mission planning and design for interplanetary travel. Basic Principle The Oberth…

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[tediousfact]

Generation Ship Part 3, Oberth is worthless

This is going to be unfortunately short. I spent about an hour developing a model to let me calculate the benefits, or lack thereof, of trying to leverage the Oberth effect for an interstellar spacecraft. If you didn’t know, the Oberth effect is just the name given to the fact that since kinetic energy is proportional to the square of velocity and a given burn from a rocket results in a fixed increase in velocity, it’s always more energy efficient to burn your rockets when you’re already travelling at a high velocity.

In this case, the idea is that for an interstellar craft using fission pulse propulsion the limit to how hard the craft can accelerate is how much acceleration the craft and the passengers can handle. So, conceivably, our craft could burn half of its mass to accelerate to almost 1% of the speed of light in under five days. And at that speed, it could do most of it’s acceleration while it was still close to the Sun to take advantage of the Oberth Effect.

The case I tested was for craft starting out in an orbit similar to Jupiter, and then using a gravity assist from Jupiter to drop it into an orbit that passes to within half the distance between Mercury and the Sun before lighting up its engines. It was an obnoxious little spreadsheet model that had to account for the changing mass of the spacecraft, the resulting change in acceleration, and the effects of the continually changing potential energy of the craft relative to the Sun as it traveled. And for all of that, I found that a craft taking that path could shave just over ten years off of its travel time to the nearest star... out of 455 years if it just left directly from its original orbit.

So the title is a bit of a lie, it’s a 2% reduction in travel time, even counting the extra couple years spent falling down towards the Sun. And it’s better than using Jupiter to speed up the craft instead, which saves less than two years. 

Dropping from Saturn instead of Jupiter results in a net loss of time, thanks to the relatively small increase in final velocity and the extra three years of falling time. And dropping closer to the Sun helps, but passing twice as close to the Sun only cuts an additional six years off the travel time. So the maneuver would be worth doing, and in general the closer you can pass to the Sun the more benefit you get, but even if you scrape the Sun’s surface you aren’t shaving more than 30 years off your trip and at a certain point the extra damage from approaching the Sun will make getting closer self-defeating.