## Monday, May 11, 2015

### Rocket Propulsion

Rocket propulsion is interesting; it's not like anything else we normally encounter when moving on Earth. Originally a lot of this post was going to be in the last post, to explain about how the engine stats related to real world science, but it grew far too big. Last week's simple answer is likely to be enough for anyone deciding for engine parts, but here's how things work behind the curtains. I hope that anyone reading this finds the topic as interesting as I do.

First, let me reference cars, as I believe anyone reading this is quite familiar with them in principle. A car accelerates by spinning its tires that then push against the Earth. At the same time, there's friction pushing back against the car, mostly from wind resistance whenever the car is moving. In practice, we spend most of the energy from the engine to equal out this wind resistance acceleration, and so move at a constant speed. Even though all the car can do is accelerate, we think of its movement in terms of speed and raw distance, and this is reflected in how we measure a car's performance.

Think of all the terms of measurement you use when talking about vehicles. Some big ones are the ones that relate to practical matters. I rate the efficiency of the vehicle in terms of miles per gallon. Similarly, I can take that number and the amount of gas I have left in order to roughly calculate how many miles I can travel before refueling. For performance I'll usually use max speed, rather than using horsepower or acceleration.

With rockets, everything is different, though there are a lot of similarities to a regular car. For a rocket to move forward, you must throw stuff out the back. The rocket gains the momentum of the stuff sent backwards, in a similar way to the car gaining momentum by pushing against the Earth. (For those that have forgotten from science class, momentum is mass * velocity, and momentum must be conserved in a given system) We call this "stuff" propellant, reaction mass, or remass, though I'm very sure we'll have more names for the stuff as it enters popular speech. (Do not call this stuff fuel, or rocket enthusiasts will be very angry with you. Unless it is fuel, as with chemical rockets, which muck everything up naming-wise)

I'm sure most people are aware of this, but space is overwhelmingly empty. For a rocket in space, this means there's no friction until you crash into something. Compared to how we think of movement on Earth, this difference is huge. The distance of a trip starting at rest, the distance gone is a function of acceleration versus time. Normally, we ignore the acceleration and consider it in terms of velocity - why would I care about the 6 seconds of acceleration I have when I'm traveling for an hour? Even though I constantly accelerate forward when using a car, my speed will not change, as it is countered by the acceleration due to friction. But with a rocket, the acceleration needs to be accounted for, and this is shown with all the terms of measurement in use with them.

Now, to keep things as simple as possible, I'll try to relate these terms to those of a normal car, but remember that the comparison is not exact; they differ in key points. This is muddled further by the tendency to talk about a rocket by its engine, while we talk about a vehicle in terms of the entire vehicle. For example, I'll give a rocket's performance measurement in terms of thrust (given in Newtons (N)), whereas a vehicle's performance is done in max speed. The vehicle's engine performance however is given in horsepower, which is similar to the engine's thrust.

With rockets, measuring how far it can go is a useless measurement. If we pick a good trajectory, the rocket can travel light years, though it will take eons. Instead, it's more useful to measure a rocket's ability to change velocity, dV (pronounced delta V, and measured in meters/second). And now we get to the fun part: measuring an engine's efficiency. That's measured either as specific impulse (labeled Isp and given in seconds) or effective exhaust velocity, measured in meters per second. Why is it fun? It's like labeling a car's efficiency in horsepower per pound of fuel. If you're interested in learning how it relates to efficiency, read the next paragraph, or feel free to skip if you want to take my word for it.

First. Let me define Isp more clearly. Impulse is (roughly) defined as the change in momentum, and calling it specific means using it in relation to something else. In this case, we use impulse in terms of pounds of propellant. (Note the word pound: measure the propellant in terms of weight, not mass) Instead of measuring propellant by weight, we can use mass. This other value is known as the effective exhaust velocity (more colloquially known as exhaust velocity), and also measures the average speed of the propellant as it leaves the rocket (when done outside an atmosphere). Specific impulse is more useful for other aspects relating to rocket design and so engines are rated in terms of specific impulse. Exhaust velocity is easier to understand, and much nicer for calculating dV, and so is what I'll tend to use. The calculation is dV = exhaust velocity * ln(ratio of total rocket mass to propellant mass)

It should be noted that thrust and exhaust velocity are not intrinsically linked. For a given engine power, it's usually possible to increase the thrust at the expense of exhaust velocity or vice versa. I can also increase the engine power to get an increase in both thrust and exhaust velocity compared to the old engine. This isn't always possible though, unfortunately. The ion engine is sadly stuck forever in having a very low thrust, to give an example.

Hope that helped clear some things up and gave people some interest in the matter. Remember, leave a comment if you have any questions, and I'll be sure to answer it!