How does the speed and volume of particles differ in producing thrust in space?

Question

Does a slower detonation velocity push a ship more the same way explosives with a slower detonation velocity moves dirt better?

At the same rate does slower particles produce more thrust from a bigger nozzle then faster particles from a smaller nozzle?

Can the particle velocity be slowed while maintaining particle rate to have a lighter colder running engine and/or nozzle? The trade off would be a much larger surface area to cool the engine.

"I had another question here about Magnetoplasmadynamic Thrust. I've removed it and will ask another question about increasing efficiency of the Magnetoplasmadynamic nozzle by creating high frequency sound before the neck of the nozzle creating pulses to slow the velocity while creating shock waves while retaining average particle rate."

Answer 1

Thrust of a rocket/engine is given by $T=\dot{m}u_{e}$

where, $\dot{m}$ is the mass flow rate of the exhaust of the propellant, $u_{e}$ is the exit velocity of the propellant.

So the mass flow and exhaust velocity for same thrust levels are inter-dependent. If you want to slow down the exhaust velocity, you will have to increase the mass flow rate for the same amount of thrust and vice versa.

The basic premise behind the electric propulsion is this one simple equation, you couple more electric energy into the propellant to increase the exhaust velocity so that you can increase the propellant utilization(meaning for the same mass of fuel you get more thrust over time, which is Isp).

If you are interested in MHD propulsion or EP in general, I would recommend you to read a book by Robert Jahn, Physics of electric propulsion.

Updated after edit:

I really wish the answer could be simple as the question. First and foremost, In space nothing is less durable. Everything is rigoursly tested, e.g. NASA/UMich's X3 hall thruster is being tested for endurance, they will fire it continuously for 10000 hours, by my estimate the cost of propellant should be in order of 10mil USD. It is one of the high power thruster that currently exists, it can take around 100 kWe(kilo-watt electrical).

To come to your actual question, it is not a simple equation, there are very complex scaling laws involved for such thrusters. Thrusters have different efficiency factors like thrust efficiency, thermal efficiency,etc. Even the power unit(PPU) has an effeciency. So the thruster selection is done mission-by-mission basis, it all depends on how much power is available, the delta-V requirement, mission and budget constraints.

Still on a whole, small thrusters can couple so much of electrical energy into the propellant they don't compete with higher power thrusters. To put things into perspective, some very low power arcjets around 100~300 We(watt electric) produces thrust in ranges of 10~50mN(milli-Newton) depending on propellant and similarly the thrust efficiency varies from 10~35%. These types of thrusters have exhaust velocities(Ce) typically around 1000 to 10000 km/s(depending on propellant and power.

On the other hand high power thrusters have exhaust velocities well over 15000km/s (depending on design, power levels and propellant). I think now I have equipped you to dig deeper. If you still are curious, please don't hesitate to ask.

Answer 2

Do slower moving particles create more thrust in space? When using explosives a slow detonation velocity is best when it comes to moving dirt.

In a vacuum, no. There is no external material you can push around.

The property you're looking for is detonation velocity: the speed of the shockwave as it travels through the explosive.

If fragmentation is desired, the best results are obtained when the detonation velocity is at or near the sonic velocity of the rock. If mass movement is more important (as in blast casting) or very large fragments are desired (as in riprap production or slabbing), detonation velocity should be notably below the rock's sonic velocity.

So this is about transferring the energy from the explosive to the surrounding material.

In a rocket engine (of any type in use today), there is no surrounding material. The propellant does not push anything else along. In fact, you want the exhaust speed to be as high as possible. The efficiency of a rocket is expressed as its specific impulse, basically the amount of acceleration you can get out of a set amount of propellant.

$$I_{sp} = \frac{V_e}{g_0}$$

Isp = specific impulse
Ve = exhaust velocity
g0 = standard (Earth) gravity

The effect does happen in the atmosphere.

Turbojet engines are inefficient at low aircraft speeds, because the exhaust speed is not matched well to the speed of the surrounding air. Early jet aircraft needed really long runways because of this.

Turbofan engines take most of the energy from the turbine exhaust and use it to drive a low-speed fan. This means there's a much better match between exhaust speed and the speed of the surrounding air.

Responding to Nathan's comment:

Everything about this answer is correct except for the first line. If there was a way to slow exhaust without outright wasting all the extra energy, it absolutely would increase thrust. Power, thrust, and specific impulse are all directly related, and maintaining the same exhaust power at a lower specific impulse guarantees higher thrust. This is the principle behind the VASIMR's high- and low-"gear" modes.

VASIMR has two modes, they work like this:

• accelerate a small amount of propellant to a high speed (for high efficiency, but low thrust)
• use the same amount of energy to accelerate a larger amount of propellant to a lower speed (for more thrust at a lower efficiency)

So instead of using the engine exhaust to propel surrounding matter, the engine just supplies more exhaust matter.