A very much over-simplified explanation of rocket science so that you may apply it to games or real life.
WARNING: This requires A LOT of math, and an understanding of at least 11th grade skills. If you can’t think and breathe at the same time, don’t bother reading this.
The Absolute Basics
1) Rockets function due to Newton’s 3rd Law
Every action has an equal and opposite reaction. Throwing hot particles at stupidly high speeds in the opposite direction of where you are going propels you forward. The particles of burned fuel aren’t that massive, but they have a LOT of speed and energy. This makes them inherently complicated and dangerous, but fun as well.
2) Heavy stuff is bad
Light stuff is good. More weight means more fuel is required to lift it, and fuel is heavy. The effect compounds to ruin your day, and eventually you have 99% fuel and 1% payload. A low dry mass is a great way to boost performance and make life easier.
3) Atmospheres kill your velocity
Do everything you can to stay out of them or leave them as soon as possible unless you wish for all of your speed turned into LETHAL levels of heat and your craft to vaporize into plasma. This does mean that atmospheres are great for getting out of orbit and landing again, though. Just bring a parachute in that case.
4.) A higher orbit is a slower orbit.
The highest point of your orbit is when your craft is at its slowest speed, and the converse is true. Going lower actually speeds you up. This is useful to know when docking two craft together or changing course.
5) Use gravity to your advantage
Planetary gravity wells provide free energy just for stopping by. Steal the planet’s rotational energy as you zoom past for higher speeds. Additionally, the best time to speed up is when you are closest to a planet. As I said in tip 4, this is when you are going the fastest. Due to the Oberth Effect, speeding up is quite a bit cheaper when you do this.
6) Use the right fuel for the job
Some fuels are better for certain applications but have lower energy. Others are easier to access on other planets, making them inherently more useful.
Tsiolcovsky’s Rocket Equation (The Ideal Rocket Equation)
Tsiocovsky was a Russian scientist in the year 1903. He made this rocket equation, which we are about to dissect for fun and hopefully understand better.
This equation is one of the most amazing in rocket science, and one of the first that I learned. It says a lot about how rockets work. Let’s break it down.
/_\ V = Ve * ln ( Mo / Mf )
Change in Velocity = Exhaust Velocity * a natural logarithm of Wet Mass over Dry Mass
This means SO much, but first, let me explain the difference between wet mass and dry mass. Wet mass is the original mass (Mo) when the rocket is fully fueled with liquid propellant (or just fuel in general). Dry mass is the final mass (Mf) the rocket has AFTER you burn all of the fuel.
This means that there is a logarithmic relationship at play, and if you know the weight ratio and exhaust velocity you can calculate how fast and how far you will go.
After you calculate your net speed, you can use the distance formula (Distance = Speed / Time) to find out how far you have gone. You can also calculate speed by using an altimeter in a model rocket and a hand-held stop watch at home like this.
Rockets of all types use this to judge how far they can go based on their payload’s weight. For example, a trip to earth orbit costs just over 2000 m/s of /_\ V. It’s worth making sure you can reach this speed before takeoff or your whole trip will be worthless.
Atmospheric Drag
An atmosphere can cause your vehicle to slow down by stealing its energy and by extension velocity. Tens of thousands of tiny particles bump against your craft and collect upon it, until you reach a speed at which you push them out of the way. They continuously take your energy as they hit your craft’s nose and try to ruin your day. Eventually this energy becomes heat and melts your craft’s outsides (If they don’t just sublimate and ionize into plasma).
Luckily, we can account for this issue. Using, you guessed it, even more ugly looking equations! Yay!
D = Cd * p * v^2 / 2 * A
Drag Force = Coefficient of Drag * Atmospheric Density * 1/2 of Velocity squared * Section of Area
Basically, you can use the values for any planet’s atmosphere and your craft’s area along with its velocity to calculate exactly how much speed will be lost. Account for that when calculating /_\ V on any planet with an atmosphere such as Earth, Mars, Venus, Titan, etc. It is also important to remember that gravity will leech or add some speed as well, depending on how big the planet is. For example, Earth will pull down at 9.8 m/s due to gravity, while Mars pulls at exactly 40% of that due to its low mass.
Nozzles and Combustion Chambers
A rocket nozzle should converge at the throat of its combustion chamber and diverge at the end of the nozzle. This forces the burned fuel particulates to fly out at ludicrous ear-drum shattering speeds beyond Mach-1.
Additionally, a engine should be optimized for its environment. Some generalized rules apply as follows:
1) A larger nozzle works better in a vacuum, while a smaller nozzle works better in normal pressure.
2) The correct combustion cycle should be chosen for efficiency or added thrust, depending on its use conditions.
3) A nozzle should have sufficient cooling for its environment, generally by the use of conducting into the fuel lines or radiating into the -50 degree temperatures of space.
Credit to CMGentry