What is it about?
Previous derivations of the "rocket equation" that go back to Tsiolkovsky (1903) make the assumption that a rocket expels its exhaust at a constant relative velocity to itself. But if a rocket propels itself by ejecting discrete chunks of matter ("pellets") this assumption breaks down. I argue that a more physically accurate model of such propulsion is that chemical energy is converted at a constant value per unit mass (typically by exploding the fuel mixture). I show that a rocket can propel itself to the highest final speed by expelling all if its fuel in one go. But in the limit of many small pellets, the rocket's final speed approaches, from above, that predicted by the standard rocket equation.
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Photo by SpaceX on Unsplash
Why is it important?
The literature on rocket propulsion by discrete ejection of matter has been confusing, since different authors made different assumptions. My "constant energy per unit mass" assumption is closer to how rockets actually work, and encompasses propulsion by springs or nuclear explosions. One application is the ejection of multiple nanosats from a rack via use of small springs or pyrotechnics. To separate the rack from the nanosats as quickly as possibe, it should eject the nanosats on one side all at once, as opposed to one-by-one.
Perspectives
I got annoyed with the confusing published work on discrete rocket propulsion, including some back-and-forth in Physics Education journal, and the traditional "constant relative velocity of the exhaust" model did not sit well with me. So while waiting around for jury duty I started with simple momentum conservation between a rocket and an ejected pellet, which divides the energy generated per unit mass between them, and proceeded from there. This paper is the result. I hope it clears up the confusion (which I discuss in detail in the Supplement, freely accessible at the link below.) It was also fun for me to discover that the "utilisation" of a rocket fuel's energy has a maximum of about 65%, with the rest of the energy going into the exhaust. Then I discovered that Tsiolkovksy had derived this in his original, seminal paper! So a nice re-discovery that I was glad to highlight.
Dr. Philip Blanco
Grossmont College
Read the Original
This page is a summary of: A discrete, energetic approach to rocket propulsion, Physics Education, August 2019, Institute of Physics Publishing,
DOI: 10.1088/1361-6552/ab315b.
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