Discussion of The Rocket Equation and Different Types of Rocket Propulsion

[scaesare]

I realize that the 10,000 m/s number was just wild guesstimate, but I wonder what the practical limits of this tech would be...

Given liquid chemical exhaust velocity is around 4.4Km/s which therefore limiting the total delta-V than can practically be achieved, this will be interesting to see as it develops...

 

[Young]

I realize that the 10,000 m/s number was just wild guesstimate, but I wonder what the practical limits of this tech would be...

Given liquid chemical exhaust velocity is around 4.4Km/s which therefore limiting the total delta-V than can practically be achieved, this will be interesting to see as it develops...

It probably depends on how hot you can heat the gas. Roughly 0.5 * M * V^2 ~ k * T.
k is the Bottzmann cost. T is temperature. M is the mass of the molecule. V is the velocity.

By the way, the fastest exhaust out there is photons.

 

[bxr140]

Somewhat adjacent, but as a data point practical/real in (or near in) service electric thrusters are typically in the 10-25km/s range. Aspirational is upwards of 50km/s.

(Erosion at the business end of the thruster is a major life limiter at those velocities; while obviously not the same propulsive environment I’d expect that to be a significant factor in nuclear solutions that are intended to drive around the solar system)

 

[ecarfan]

k is the Bottzmann cost

Darn auto correct. In case anyone is confused, what @Young intended to type is Boltzmann Constant.

The Boltzmann constant (kB or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas.

 

[JB47394]

I realize that the 10,000 m/s number was just wild guesstimate, but I wonder what the practical limits of this tech would be...

Using the ideal rocket equation that @Young references, you get a chart that looks like this, taken from a Stanford online course page.

The NERVA engine got its propellant up to 2558K on one run. Also, there's a great 2018 paper (PDF) from NASA (Nuclear Thermal Propulsion (NTP): A Proven Growth Technology for Human NEO / Mars Exploration Missions) that goes through all sorts of number crunching about nuclear thermal propulsion for a trip to Mars. Table 2 on Page 9 has the summary of the numbers, including an exhaust temperature of 2940K using the latest lab results, which is close to the 3000K mark, which gives about 10,000 m/s.

So it seems plausible. For anyone who read my prior version of this, my apologies. It calculated numbers using the root mean square velocity formula, which is not applicable to rocket exhaust speed calculations.

 

[scaesare]

Somewhat adjacent, but as a data point practical/real in (or near in) service electric thrusters are typically in the 10-25km/s range. Aspirational is upwards of 50km/s.

(Erosion at the business end of the thruster is a major life limiter at those velocities; while obviously not the same propulsive environment I’d expect that to be a significant factor in nuclear solutions that are intended to drive around the solar system)

But very low thrust... so for a relatively massive ship, assume not as practical as the proposed nuclear/H2 for > chemical velocities...

 

[scaesare]

Using the ideal rocket equation that @Young references, you get a chart that looks like this, taken from a Stanford online course page.

View attachment 1038558

The NERVA engine got its propellant up to 2558K on one run. Also, there's a great 2018 paper (PDF) from NASA (Nuclear Thermal Propulsion (NTP): A Proven Growth Technology for Human NEO / Mars Exploration Missions) that goes through all sorts of number crunching about nuclear thermal propulsion for a trip to Mars. Table 2 on Page 9 has the summary of the numbers, including an exhaust temperature of 2940K using the latest lab results, which is close to the 3000K mark, which gives about 10,000 m/s.

So it seems plausible. For anyone who read my prior version of this, my apologies. It calculated numbers using the root mean square velocity formula, which is not applicable to rocket exhaust speed calculations.

So the exhaust velocity for Nuclear is in the neighborhood of 2.25x chemical. With something the mass of Starship, it will be interesting to see the practical speeds they could reach and what that would mean for a trip to Mars...

 

[nativewolf]

Completely fascinating. As usual, nothing to add. Just fascinating. Maybe actually see this approach reality before I die.

 

[JB47394]

With something the mass of Starship, it will be interesting to see the practical speeds they could reach and what that would mean for a trip to Mars...

I'm not going to show my work on this one, but if we assume a 1200 ton propellant load, 100 ton ship, 100 ton cargo load and 10,000 m/s exhaust velocity, then after the outbound burn, the ship is up to 6,931 m/s. A Hohmann transfer orbit calls for 3,900 m/s and takes 260 days (8 months, 20 days). Naively assuming that time is proportional to speed, the NTP rocket would take 146 days (4 months, 26 days).

Lockheed Martin claims that they could knock travel times down to 1 month, 15 days. I have no idea how.

For reference, the NERVA engine massed 18 tons and generated 25 tons of thrust. I'm assuming that a more modern implementation would have a higher thrust-weight ratio.

 

[nativewolf]

well there is no chance of going to mars on vacation with my wife, no way either of us could stand seeing each other all day for 45 days.

 

[Young]

I'm not going to show my work on this one, but if we assume a 1200 ton propellant load, 100 ton ship, 100 ton cargo load and 10,000 m/s exhaust velocity, then after the outbound burn, the ship is up to 6,931 m/s. A Hohmann transfer orbit calls for 3,900 m/s and takes 260 days (8 months, 20 days). Naively assuming that time is proportional to speed, the NTP rocket would take 146 days (4 months, 26 days).

Lockheed Martin claims that they could knock travel times down to 1 month, 15 days. I have no idea how.

For reference, the NERVA engine massed 18 tons and generated 25 tons of thrust. I'm assuming that a more modern implementation would have a higher thrust-weight ratio.

One thing that needs to be considered is your speed vs. that of exhaust. Once you reach the speed of exhaust, it does not help you very much.
You need the speed of exhaust as fast as possible.
Ultimately, you want to use ion engine or photons to propel your rocket to go very far.

 

[Young]

This is a common fallacy. The thrust doesn't change just because of the speed of the rocket.

You are right. The rocket still gains speed.

 

[Young]

You are right. The rocket still gains speed.

It was a long time ago when I calculated the speed gain vs energy spent by the rocket. I reworked that and it shows that the ratio is decreasing as the speed of the rocket increases compared to that of exhaust. Sorry I was not very clear.

 

[mongo]

It was a long time ago when I calculated the speed gain vs energy spent by the rocket. I reworked that and it shows that the ratio is decreasing as the speed of the rocket increases compared to that of exhaust. Sorry I was not very clear.

The exhaust motion is in the frame of the rocket and exhaust velocity is constant so momentum imparted is also. Impact of momentum depends on rocket mass, of course.
Kinetic energy = 1/2mv², so the faster a rocket is going the more energy it gains for the same delta-V. That is utilized on escape orbits by timing the burn for perigee.

 

[JB47394]

Kinetic energy = 1/2mv², so the faster a rocket is going the more energy it gains for the same delta-V.

I've read the Oberth Effect article at Wikipedia, but what it fails to communicate with me is how kinetic energy translates to delta-V. I keep reading that the delta-V is constant, but that the change in kinetic energy goes up, and that means the rocket goes faster. But the delta-V remains constant. What's going on?

 

[Young]

The exhaust motion is in the frame of the rocket and exhaust velocity is constant so momentum imparted is also. Impact of momentum depends on rocket mass, of course.
Kinetic energy = 1/2mv², so the faster a rocket is going the more energy it gains for the same delta-V. That is utilized on escape orbits by timing the burn for perigee.

Roughly, rocket's final speed is ~Ve / (propellant portion of the rocket). If you through in this condition, chemical propulsion may not do.

 

[mongo]

Roughly, rocket's final speed is ~Ve / (propellant portion of the rocket). If you through in this condition, chemical propulsion may not do.

With a log function added. Speed change due to engines is Ve*ln(finalMass/startingMass)
So a mass ratio of e (2.7ish) gets a rocket from 0 velocity up to the speed of the exhaust. Double requires 2.7 times higher ratio and triple is ~20x propellant to dry.

Tsiolkovsky rocket equation - Wikipedia

 

[mongo]

I've read the Oberth Effect article at Wikipedia, but what it fails to communicate with me is how kinetic energy translates to delta-V. I keep reading that the delta-V is constant, but that the change in kinetic energy goes up, and that means the rocket goes faster. But the delta-V remains constant. What's going on?

The work section of that article helps bridge the difference. The engine thrust acts over a longer distance (due to higher speed) and imparts more mechanical energy. The exhaust itself loses more energy due to its velocity decreasing (in a prograde burn).
Momentum and kinetic energy themselves are not always stongly linked (inelastic collisions).

 

[scaesare]

Fascinating, and counterintuitive (at least to me). But thinking about it, if I have this right, the fact that the work done is really within the combustion chamber and nozzle....and the time the rocket exhaust pushes against those to generate thrust is determined by the chemical ration and thus static.... let's call it 1ms. If the rocket is moving at speed X, then the work done is the propulsive force of the exhaust over the distance travelled in X * 1ms. If you are traveling 10X than the total work done is 10 times as much (10X x 1ms).

I would not have expected this.

 

[scaesare]

This is a common fallacy. The thrust doesn't change just because of the speed of the rocket.

Nor did I realize this until this thread... It makes sense now after going through the thought exercise though...

Thanks.