Author notes

299 - The Plunge

El Cid

on Feb. 26, 2020

* Author's Note: “Yog” is a reference to Yog-Sothoth, the all-knowing Outer God from H.P. Lovecraft's Cthulhu mythos.

For some reason, when Rohan speaks, I hear Wil Willis' voice, from Forged In Fire. I'll confess, I've watched way too much of that show!

Don't worry, there are only two more pages of this stupid game show thing and then the actual story picks up! Hang in there!





So, you want the spaceships in your space opera to have realistic performance… but it turns out rocket science is a bit complicated, and you don't know how to make heads or tails out of it? Well, as it turns out, with some quick and easy hacks, you can cut through a lot of the complex math.

If you're doing any sort of grounded sci fi, then your spaceship is likely propelling itself through space in one of two ways: Either some kind of sail (light, laser, magnetic, etc.), or more likely a rocket. If it is a rocket, then its maximum velocity can be calculated with the Tsiolkovsky rocket equation:


What does all that gobbledygook mean? What the heck is “Δv?” Well, “delta v” (that triangle thing is the Greek letter “delta”) means “change of velocity.” In a nutshell, that's how much net velocity change your engine can impart on the spaceship before it burns through all of its fuel. In practice, unless it's a one way trip, your maximum velocity is going to be half the delta v, because it takes equal amounts of fuel to accelerate as it does to decelerate. Basically, you use half your fuel getting up to speed, then you coast, then you turn the ship around and burn the other half of your fuel to slow down (obviously, this is an oversimplification, but that's the point of this whole blurb). “vₑ” is effective exhaust velocity. “m₀” is your ship's initial mass (when the fuel tanks are full), and “mf” is its final mass (when the tanks are empty). If you've looked up the specs on your sci fi rocket and they don't give the effective exhaust velocity, then you can instead calculate it by multiplying its specific impulse (Isp) by Earth's standard gravity 9.81 meters per second square (and no, you don't use a different gravity value for different planets or whatnot; it's just a convention of how you convert the units).

It's a complicated calculation because the amount of thrust your rocket is able to generate is directly related to how much mass it needs to push… but the mass is constantly changing, because your ship is accelerating by expelling mass.

Thankfully, there's an easy way to condense this into a handy rule of thumb. The natural log of Euler's number (2.71828…) is 1. So, looking at the rocket equation, if your ship has a fuel to dry mass ratio equal to Euler's number (approximately 63 percent fuel and 37 percent dry mass), then you're multiplying by 1, so your delta v is basically equal to your exhaust velocity… meaning your maximum speed is roughly half the exhaust velocity. In order to have a maximum speed equal to your exhaust velocity, your spaceship needs to be about 86.5 percent fuel. Here's a handy dandy chart to show some useful ratios.



So now that you know all of this, next time you build a spaceship for your sci fi story, you can do so with the physics involved in mind. You'll want to build it with the fuel-to-dry mass ratio in mind, and then you can pop over to the Project Rho Engine List page to find an engine that works for your sci fi universe. Plug in the specs, and you now know exactly how fast your spaceship can go (though it's worth keeping in mind that spaceships typically don't travel in straight lines, but that's a whole other can of worms).

And I know what you're thinking: “Hmm, so if my exhaust velocity is the speed of light…” Sorry but no, you can't use this to build an FTL starship. It's a different equation when you're dealing with relativistic speeds. Einstein shits in everyone's Cheerios.

That's enough for today, folks. See you next week!