Rocket Dynamics
A
rocket is broadly defined as any machine that accelerates itself by expelling part of its mass at high velocity, gaining momentum via classical energy conservation. The fundamental principle of rocketry is the Law of Reaction (occasionally referred to as
Newton’s Third Law): every action has an equal and opposite reaction. Under the generally accepted workings of classical physics, there is no way to move in a vacuum without expelling reaction mass. Simplified, this means that since there is no medium in space to push against, a spacecraft must carry its own push-fodder with it. The faster the push, the greater the acceleration; the greater the push-fodder-to-rocket ratio, the higher the final speed. All of this is boiled down to the
ideal rocket equation, famously called “
Tsiolkovsky’s equation” by
humans, which looks like this:
Δv = (Isp • g0) • ln(m0 / mF)
where
- Δv is the total velocity the craft is capable of reaching in meters per second
- Isp is the total burn time of the engine, or "specific impulse," in seconds
- g0 is Earth’s gravity (9.8 m/s2)
- ln is the natural logarithm function
- m0 is the total mass of the craft, or "wet mass," in kilograms
- mF is the mass of the craft minus the mass of its fuel, or "dry mass," in kilograms
It can be simplified further into:
Δv = ve • ln(mR)
where
- Δv is the total velocity the craft is capable of reaching in meters per second
- ve is the effective exhaust velocity of the propellant in meters per second
- ln is the natural logarithm function
- mR is the fuel-to-body mass ratio of the craft, which has no units
This equation governs all of aerospace engineering across every known technoculture. The two main methods of increasing the Δ
v of rockets are to increase the exhaust velocity and improve the mass ratio, with the best results being achieved with both combined. However, most modern crewed spacecraft opt for a stronger emphasis on the former option, as vessels that are 90% propellant are both unwieldy and dangerous. Based on the various methods of maximizing delta-V, there are three broad classes of reaction engine: ballistic, marathon, and torch.
Engine Classes
Ballistic
- High thrust (>100kN)
- Low specific impulse (<3600s)
- High propellant flow
- Low exhaust velocity
Marathon
- Low thrust (<100kN)
- High specific impulse (>3600s)
- Low propellant flow
- High exhaust velocity
Torch
- High thrust (>100kN)
- High specific impulse (>3600s)
- Medium propellant flow
- High exhaust velocity
Ballistic
Ballistic-class rockets have high thrust but low specific impulse, meaning they provide a lot of acceleration over a short period of time. They don’t actually pack a lot of push-power (low exhaust velocity) so they compensate by using a very large amount of fuel (high propellant flow). These are usually
thermal or chemical rockets like
aerospikes. Ballistic engines are typically used for transatmospheric and orbital flight, and are commonly used for interplanetary travel in the earlier stages of spacefaring.
Marathon
Marathon-class rockets have
low thrust but
high specific impulse, meaning they provide a small amount of acceleration for a very long time. They do this by expelling a tiny amount of propellant at ridiculous speeds (low propellant flow with high exhaust velocity). These are usually
ion or
positron drives, which are almost always used on autonomous spacecraft because of the transit times involved.
Electrodynamic thrusters are also considered to be marathon-class engines, though these are exclusively used for orbital navigation because they require a large external magnetic field to operate within.
Torch
Torch-class engines are the apex of spaceflight engineering: high thrust
and high specific impulse; a lot of acceleration for a long time. They use a relatively small amount of propellant expelled at extremely high speeds (medium-low propellant flow with high exhaust velocity) to achieve this. Generally the only reactions with a high enough energy density to achieve these requirements are nuclear in nature, most commonly
fusion or
antimatter reactions. Vessels equipped with torch drives are referred to as "torchships," and are capable of taking
brachistochrones on interplanetary flights or attaining relativistic interstellar velocities within a reasonable amount of time. Current
USSC torch drives are of the
Blazar or
Pulsar types.
This is really cool! I like how you included the equations to help ground the designs in reality.
Thank you! The Tsiolkovsky equation is the most essential thing needed to understand how rockets work, and also what the stats mean for the specific engine designs I'll be posting in the coming days. Δv, specific impulse, and mass ratios are all terms that pop up again and again.