Acceleration of First Stage of Rocket Not using chemicals

tahanson43206 · 2023-06-27 10:05:00

For SpaceNut re new topic ...

We did not have a topic in Science, Technology and Astronomy that included the word "acceleration" in the title.

This topic is created to (hopefully) provide Calliban with a runway to develop his recently published first stage alternate design concept.

Humans have been accelerating mass without using chemical propulsion for thousands of years.

Heavy mass was routinely launched using stored energy in the Middle Ages, and before, when large stones were given momentum from stored energy.

In recent times, the amount of mass has increased substantially, but it is still measured in tens of tons and not hundreds of tons.

This topic is available for Calliban (and anyone else so inspired) to describe a design for a non-chemical acceleration of a 100+ ton mass to 500 meters per second.

To start the topic off, I'll quote Calliban's recent post:

text

(th)

tahanson43206 · 2023-06-27 10:06:31

Quoting from Stage Separation topic...

Calliban wrote:

One option that I will throw into the mix here. If we use some sort of launch assist, that boosts rocket takeoff velocity to a minimum of 500m/s, we can dispense with the need for a two stage rocket and go SSTO. The space shuttle used about 1/3 of its fuel mass accelerating to 1000mph. Launch assist could save sufficient fuel to allow an SSTO to be possible. For small rockets, a modified gun (look up Project Harp) could serve this function. For larger rockets, a steam or natural gas powered cannon or rocket sled can provide the required velocity boost. The spin launch technology may offer some value here.
The challenge for a man rated rocket is acceleration. High acceleration also imposes high loads on the structure of the vehicle during the boost phase. So launch assist may increase structural margins, eating into the payload budget. Nothing comes for free.

(th)

tahanson43206 · 2023-06-27 10:12:58

An option that is most certainly "feasible" in the sense that physics does not preclude it, is the Dry Ice launcher concept.

Here is a web site that offers a product for educational purposes:

https://www.chillistick.com/all-products/rocket.html

The Rocket Pack is a fun science experiment and one of our favourite demonstrations.
The rocket is an empty drinks container which will travel 10 metres vertically and so this experiment must be done outside.
Pack Contents
The pack includes:
1 Rocket Bottle
1 Bung
1 Funnel Loader
1 Jug Launcher
1 Set of Polyurethane Gloves
1 Set Of Instructions
Important: This pack does not include dry ice - please select the dry ice pack you require.
How Does It Work?
Using the funnel place 5 pieces of dry ice in the top of the bottle. Place the plastic bottle plug so that it rests on the top of the bottle and then place the jug over the bottle. As you push down on the jug you will push the plug into the bottle

I presume (do not ** know **) that this principle could be applied to the problem of launching a mass of hundreds of tons to 500 meters per second.

The "bottle" for this system would be quite a feat of engineering. There may well be some upper limit to the size such a bottle might reach in the Real Universe, but I presume it is likely a mass of 10 kilograms could be launched upwards at 500 meters per second with known engineering methods and known materials.

(th)

tahanson43206 · 2023-06-27 11:08:44

The ChatGPT transcript at the link below explores the technology of the Dry Ice Rocket for a first stage launcher:

https://www.dropbox.com/s/bl2sjdt1at3nr … ocket?dl=0

The basic concept is to store mechanical energy in a volume of gas, before releasing the stored energy to propel a payload.

ChatGPT dealt with this challenge in a series of approximations, as the conditions of the thought experiment were clarified.

The concluding number of moles required is interesting. It may or may not have any correlation to the task at hand.

I asked ChatGPT to list the inputs it needs if we decide to pursue this further.

For one thing, I'd like to point out that Dr. John Hunter uses this exact same scenario in his proposal to launch a payload to low Earth orbit. That payload would include a solid state rocket to handle second stage responsibilities. The difference is that Dr. Hunter's design calls for Hydrogen as the working fluid.

The only reason I used carbon dioxide was that I was starting with the familiar dry ice rocket.

In practice, it would seem reasonable to use compressed air to provide the impetus for the launch, since air is so readily available, and because the desired exit velocity is only 500 meters per second.

(th)

tahanson43206 · 2023-06-27 11:59:37

For SpaceNut .... if you have a bit of time, please report on the use of compressed air to launch ballistic missiles from submarines.

I understand (from vague recollection of news reports) that ballistic missiles are routinely launched from submarines using compressed air. The rockets launched using this method are pushed up through ocean water until they are above the surface, at which point (or so I understand) they ignite and continue their journey.

If you can find any non-classified information about this launch method it would seem a good fit for this topic.

(th)

Calliban · 2023-06-27 12:10:05

A steam cannon is technically easiest. It allows us to accumulate energy in hot rock or as steam within a steam drum, and release energy suddenly by opening valves. We could improve efficiency by mounting the rocket on a sabot that never leaves the barrel. At the end of the barrel, the sabot decelerates rapidly, by transfering energy into gas pistons. The steam in the barrel is then collapsed by spraying water mist into it. This would allow unused energy to be recovered as stored mechanical energy and as hot (almost boiling) water, which can be reused. The gun would eventually produce an excess of hot water.

tahanson43206 · 2023-06-27 13:04:35

For Calliban re #6

Please pursue your idea further....

I would be happy to offer your proposal to ChatGPT to see if the numbers it generates are at all close to yours.

I would like to point out the list of requested data items in the link I posted in #4

We can save time by organizing the question set carefully, so we don't waste ChatGPT's (or our) time.

When I left off the discussion earlier today, I had a picture in mind of an apparatus of 9 meters diameter and 2 kilometers long.

Of that, the bottom kilometer would be the reservoir where gas would be given the energy needed for the boost operation.

The top kilometer would be the place where acceleration occurs.

A detail that I did not ask ChatGPT is how to condition the lower chamber so that the desired acceleration occurs throughout the tube.

Because the needed acceleration must still be in effect at the conclusion of the upward run, I deduce that a greater pressure is needed at the start of the run, because the volume of the acceleration tube must be filled with hot gas.

As a first guess, I am presuming that pressure in the lower chamber must be precisely double whatever the desired pressure might be at the moment of egress.

ChatGPT came up with a figure of 2,000,000 newtons of pressure at the base of the sabot. I have no way of knowing if that is in the ball park or not.

(th)

tahanson43206 · 2023-06-27 13:19:10

For Calliban re topic and specifically water >> steam suggestion ...

If you're going to use water, then (it seems to me) you might as well use sea water .... there's plenty of it, and in any case, the launcher needs to be deployed in a location (probably on the equator) where the ocean is 2 kilometers deep.

The output of the launcher would be a geyser of sea water in the form of steam. That team would (I presume) quickly form a cloud, and that would presumably carry sea water around the world according to wind patterns at the time.

Unlike with naturally evaporated sea water, this material would include the salt, so the geyser would pump salt molecules into the atmosphere at a greater rate than usual. I'm unsure of what effect (if any) this would have as the material drifts along with air currents.

My understanding is that salt is carried with air that is in the vicinity of breakers that crash on the shoreline, and I've read (somewhere) that sea salt is often found some distance inland from a sea coast.

(th)

tahanson43206 · 2023-06-27 18:15:46

In this session with ChatGPT, I reduced the description of the launcher significantly, from Calliban's original specification. My intention is to attempt to produce a set of numbers that might be tested in the Real Universe.

To achieve this, I set the payload mass at 100 Kg.
The acceleration run length is reduced to 100 meters.
The diameter of the tube is 1 meter.
The acceleration time is left at 10 seconds.
The output velocity is left at 500 meters per second.
The working fluid is left as Carbon Dioxide gas

User
tahanson43206
User
Hello Again on 2023/06/27 at 20:03
ChatGPT
Hello! I'm glad to see you again. How can I assist you today?
User
In an earlier session today, we (you and I) thought about a variation of the familiar Dry Ice rocket. I've started a new session. I have a set of requests you made and data for most of them. I'd like to try pasting the list into the input window. Are you ready?
ChatGPT
Certainly! Please go ahead and paste the list of requests into the input window. I'll do my best to assist you with the information you provide.
User
Title: 2023/06/27 1 meter diameter variation on Dry Ice Launcher variation
Payload mass: The mass of the payload that needs to be accelerated, preferably in kilograms. 100 kg
Acceleration distance: The distance over which the payload needs to be accelerated, typically in meters. 100 meters
Exit velocity: The desired velocity of the payload at the end of the acceleration phase, typically in meters per second. 500 meters per second
Tube diameter: The diameter of the launch tube, typically in meters. 1 meter
Time of acceleration: The duration for which the acceleration is applied, typically in seconds. 10 seconds
Force on the base: The force required to achieve the desired acceleration, typically in Newtons. (unknown)
Desired propulsion method: Clarify if carbon dioxide gas or any other specific method is preferred for propulsion. carbon dioxide
Environmental considerations: Any specific environmental conditions or constraints to consider, such as temperature, atmospheric pressure, or presence of air resistance. Sea Level: Standard Temperature and Pressure outside the apparatus.
Please provide these details when you return so that we can continue the discussion and calculations accurately.
The experiment apparatus is based upon the principle of a Dry Ice launcher. Pressure builds inside the compression chamber until the cork gives way. The acceleration tube is 100 meters in length. The gas pressure chamber below the acceleration tube is also 100 meters in length and 1 meter in diameter.
The principle of operation is to build up gas pressure in the compression chamber sufficient to accelerate the payload of 100 kilograms to 500 meters per second in 10 seconds, when the acceleration distance is 100 meters.
Please compute the moles of gas needed in the pressure chamber, and the pressure needed to produce the desired result.

ChatGPT
To calculate the moles of gas needed in the pressure chamber and the required pressure, we can use the ideal gas law, which states:
PV = nRT
Where:
P = Pressure of the gas (in Pascal)
V = Volume of the gas (in cubic meters)
n = Number of moles of gas
R = Ideal gas constant (8.314 J/(mol·K))
T = Temperature of the gas (in Kelvin)
In this case, we need to determine the number of moles of gas (n) and the pressure (P) required to achieve the desired acceleration.
Given data:
Payload mass (m) = 100 kg
Acceleration distance (d) = 100 meters
Exit velocity (v) = 500 meters per second
Tube diameter (D) = 1 meter
Time of acceleration (t) = 10 seconds
Standard Temperature and Pressure (STP) conditions:
Temperature (T) = 273.15 Kelvin
Pressure (P) = 101325 Pascal (1 atm)
To calculate the number of moles of gas (n), we need to know the molecular weight (M) of carbon dioxide (CO2), which is approximately 44.01 g/mol.
n = m / M
n = 100 kg / (44.01 g/mol * 1000 g/kg)
Now we can calculate the pressure (P) required using the following equation:
P = (m * v) / (d * t * A)
Where A is the cross-sectional area of the tube.
A = π * (D/2)^2
Now we can substitute the values and calculate the pressure (P) required:
A = π * (1/2)^2
A = π/4
P = (100 kg * 500 m/s) / (100 m * 10 s * (π/4))
P = 20000 N / (10 π) ≈ 636.62 N/π
Please note that the pressure is in Newtons per square meter (Pascal), but I've provided the value in the simplified form above.
To convert the pressure to atm, you can divide the value by 101325 (1 atm in Pascal).
Now you have the required number of moles of gas and the pressure needed to produce the desired result. Let me know if there's anything else I can assist you with!
User
Thank you for helping with this inquiry! Catch you next time.
ChatGPT
You're welcome! I'm glad I could assist you. If you have any more questions in the future, feel free to ask. Have a great day, and I'll be here whenever you need me. Take care!
Regenerate response
Send a message
Free Research Preview. ChatGPT may produce inaccurate information about people, places, or facts. ChatGPT May 24 Version

If there is a member who has the time to check the calculations, I'd definitely be interested to know if I provided enough information to obtain a reasonable result. Often, in working with ChatGPT, I discover after the fact that I left something out. That might well have happened here.

(th)

tahanson43206 · 2023-06-27 18:27:27

In looking over Post #9, I am reasonably sure I set up the problem in a way that appears to have led to an incorrect result.

In thinking about the situation, I think that much of the details are irrelevant ... If the problem is recast as:

How much energy must be stored in a perfectly elastic spring to accelerate 100 kg to 500 m/s in 100 meters in 10 seconds, I might have gotten a more useful answer. Gas in a chamber is comparable to a perfectly elastic spring, in that the molecules repel each other with electrostatic force.

(th)

tahanson43206 · 2023-06-27 19:07:01

Taking a step back, I simplified the problem to be solved to just computing the energy needed for acceleration of 100 kg to 500 m/s.

New chatHide sidebar
tahanson43206
Hello Again at 20:53 on 2023/06/27
ChatGPT
Hello! It's nice to see you again. How can I assist you today?
You and I've been working on a problem of simple physics. I'm attempting to simplify the problem description to try to avoid causing confusion. Are you ready for another go?
ChatGPT
Absolutely! I'm here to help you with your physics problem. Please go ahead and provide me with the simplified problem description, and I'll do my best to assist you.
We want to accelerate a mass of 100 kilograms to 500 meters per second over a distance of 100 meters in 10 seconds. We propose to use an ideal spring to perform the acceleration. How much energy must we add to the spring to achieve the desired result?
ChatGPT
To determine the amount of energy needed to achieve the desired acceleration using an ideal spring, we can utilize the principles of work and energy. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, we need to calculate the work done by the ideal spring to accelerate the mass. The work done by the spring will be equal to the change in kinetic energy of the mass.
The change in kinetic energy (ΔKE) can be calculated using the formula:
ΔKE = 0.5 * m * (vf^2 - vi^2)
Where: ΔKE = Change in kinetic energy m = Mass of the object (100 kg) vf = Final velocity (500 m/s) vi = Initial velocity (0 m/s, assuming the mass starts from rest)
Since the object starts from rest, the initial kinetic energy is zero. Therefore, the change in kinetic energy simplifies to:
ΔKE = 0.5 * m * vf^2
Substituting the given values:
ΔKE = 0.5 * 100 kg * (500 m/s)^2
Calculating the expression:
ΔKE = 0.5 * 100 kg * 250,000 m^2/s^2
ΔKE = 12,500,000 joules
Hence, the amount of energy that needs to be added to the spring to achieve the desired result is 12,500,000 joules.
Thank you! Catch you next time!
ChatGPT
You're welcome! I'm glad I could help. If you have any more questions in the future, don't hesitate to ask. See you next time, and have a great day!
Regenerate response
Free Research Preview. ChatGPT may produce inaccurate information about people, places, or facts. ChatGPT May 24 Version

If a member has a spare couple of minutes, please double check that result. It looks reasonable to me, but that's a long way from confirmation. The next step (if this one checks out) is to ask what pressure is needed in a volume of gas to deliver that spring performance.

(th)

tahanson43206 · 2023-06-27 21:01:16

In the session reported below, I worked with ChatGPT to consider a cylinder filled with dry ice. We then changed to a cylinder half filled with dry ice, and applied thermal energy to free the molecules. I had not realized that the temperature of the gas after sublimation would be the same as before, but that makes sense. However, the pressure inside the cylinder will increase from sea level to (approximately) 1,156,371.15 Pascal. How that compares to the requirements of the problem to be solved is not clear (to me for sure). The original problem was set up as acceleration of 100 kg to 500 meters per second in 100 meters, and ChatGPT estimated 12,500,000 joules would be needed.

In working the problem of dry ice sublimation, the 12,500,000 figure seems to have been lost along the way.

tahanson43206
Hello again at 21:55 on 2023/06/27
ChatGPT
Hello! Welcome back. How can I assist you today?
You and I've been working on a simple physics problem. I've broken the problem into pieces. In our previous session you calculated 12,500,000 joules to be stored. I will now define the size and shape of the storage device, the material to be contained, and ask you to compute properties of the system. The storage device is a cylinder 100 meters long and 1 meter in diameter. The cylinder is sealed except for a value through which gas may be admitted. The initial condition of the cylinder is filled with carbon dioxide at standard temperature and pressure. Please compute the number of moles of carbon dioxide gas in the cylinder before we add gas. The please add gas until we have stored 12,500,000 joules of energy in the cylinder. Please compute the number of moles of carbon dioxide in the cylinder after we add gas, the pressure against the end of the cylinder and the temperature of the gas.
ChatGPT
To calculate the number of moles of carbon dioxide gas in the cylinder before adding gas, we can use the ideal gas law, which states:
PV = nRT
Where: P = Pressure V = Volume n = Number of moles R = Ideal gas constant T = Temperature
Since the cylinder is sealed and filled with carbon dioxide at standard temperature and pressure (STP), we can assume the initial pressure and temperature are 1 atmosphere and 273.15 Kelvin, respectively.
Given that the cylinder has a diameter of 1 meter and a length of 100 meters, we can calculate its volume as follows:
V = πr^2h
Where: r = radius = 0.5 meters h = height = 100 meters
V = π(0.5^2)(100) = 78.54 cubic meters
Substituting the values into the ideal gas law equation, we can solve for the number of moles:
(1 atm)(78.54 m^3) = n(0.0821 L·atm/mol·K)(273.15 K)
n = (1 atm)(78.54 m^3) / [(0.0821 L·atm/mol·K)(273.15 K)] n ≈ 3034.34 moles
Therefore, there are approximately 3034.34 moles of carbon dioxide gas in the cylinder before adding any additional gas.
To store 12,500,000 joules of energy in the cylinder, we need to increase the pressure and temperature of the gas. However, to determine the exact values, we need additional information. Could you please provide the details of how the energy is being added to the system?
Thank you for computing the moles of gas before we start adding molecules. We will use a compressor to pump carbon dioxide into the cylinder. Please note that we are attempting to get a feeling for what this system might look like, so if you discover it cannot exist in reality, that is an outcome we can accept.
ChatGPT
Understood. Let's proceed with the information provided.
To store 12,500,000 joules of energy in the cylinder, we will add additional carbon dioxide gas using a compressor. However, without specific information about the compression process, we can make some assumptions to approximate the system's behavior.
Assuming an isothermal compression process, where the temperature remains constant throughout, we can use the ideal gas law to determine the final pressure and number of moles of carbon dioxide gas.
The ideal gas law equation is given by:
PV = nRT
Since the cylinder's volume remains constant, we can rewrite the equation as:
P_initial * V = P_final * V = n * R * T
Initially, the cylinder's volume is 78.54 cubic meters, and we know that the initial pressure and temperature are both at standard conditions (1 atmosphere and 273.15 Kelvin). Let's denote the final pressure as P_final.
1 atm * 78.54 m^3 = P_final * 78.54 m^3 = n * 0.0821 L·atm/mol·K * 273.15 K
Simplifying the equation:
P_final = (1 atm * 78.54 m^3) / (78.54 m^3) ≈ 1 atm
Thus, the final pressure after adding the carbon dioxide gas will be approximately 1 atmosphere.
To calculate the number of moles of carbon dioxide gas in the cylinder after adding gas, we need to determine the change in energy. However, since we don't have information about the compression process or the efficiency of the compressor, we cannot directly determine the change in energy or the resulting moles of gas.
If you can provide more details about the compression process, such as the compression ratio or any other relevant information, I can help you further analyze the system.
Let's change the scenario. Our goal is to add 12,500,000 joules to the cylinder. That sum was computed previously, to meet a requirement. We are now investigating how to store that much energy in the cylinder, including whether it is possible at all. Let's change the scenario to pack the cylinder with dry ice. In that case, please compute the number of moles of gas that will be present. then add energy to the dry ice so that it changes phase to become a gas. The energy will be added by apply electric current to resistance wires around the walls of the cylinder. For the purposes of computation, please assume thermal energy flows without hindrance from the electric wires into the cylinder. At the end of the heating process, we will have a cylinder filled with carbon dioxide gas at some temperature you will be able to determine. Please report the temperature of the gas, and the pressure on one end of the cylinder.
ChatGPT
Understood. We'll consider a new scenario where the cylinder is packed with dry ice to store 12,500,000 joules of energy, and then the dry ice undergoes a phase change to become a gas (carbon dioxide) by adding energy through electric current.
To compute the number of moles of gas present when the cylinder is filled with dry ice, we need to determine the mass of dry ice and convert it to moles. Dry ice is solid carbon dioxide (CO2) at a temperature of -78.5 degrees Celsius.
The molar mass of carbon dioxide (CO2) is approximately 44.01 grams/mol.
Let's assume the mass of dry ice required to store 12,500,000 joules of energy is M grams. We can calculate the number of moles (n) using the formula:
n = M / molar mass
Now, to determine the mass of dry ice, we'll need to calculate the energy required to convert it to a gas. The heat of sublimation for carbon dioxide (CO2) is approximately 25.2 kJ/mol. We can use this value to calculate the mass of dry ice (M) as follows:
Energy = n * heat of sublimation
12,500,000 J = n * (25.2 kJ/mol * 1000 J/kJ)
Simplifying:
12,500,000 J = n * (25,200 J/mol)
n = 12,500,000 J / (25,200 J/mol)
n ≈ 496.03 moles
Therefore, to store 12,500,000 joules of energy, you would need approximately 496.03 moles of dry ice (solid carbon dioxide) in the cylinder.
Next, by applying electric current to the resistance wires around the cylinder, we will add energy to the dry ice, causing it to change phase from a solid to a gas. Assuming efficient transfer of thermal energy, we can assume the dry ice will absorb the energy without any losses.
To determine the resulting temperature and pressure of the carbon dioxide gas, we need additional information about the specific heat capacity of the dry ice and the properties of the cylinder (volume, surface area, etc.).
If you have any additional information or specific values for the specific heat capacity or cylinder properties, please provide them, and I'll be able to assist you further in calculating the temperature and pressure of the resulting gas.
Thanks for finding the number of moles of carbon dioxide in the cylinder packed with dry ice.
ChatGPT
You're welcome! I'm glad I could help you determine the number of moles of carbon dioxide in the cylinder packed with dry ice. If you have any more questions or need further assistance, feel free to ask!
Can you find the specific heat capacity of dry ice? Perhaps it would help you to know that the expression "dry ice" refers to carbon dioxide in the frozen state. The cylinder is 100 meters long and a meter in diameter.
ChatGPT
Certainly! The specific heat capacity of dry ice, which refers to solid carbon dioxide, is approximately 2.08 J/g·K. This value represents the amount of heat energy required to raise the temperature of one gram of dry ice by one Kelvin (or one degree Celsius).
With this information, we can proceed with the calculation to determine the temperature and pressure of the resulting carbon dioxide gas after adding energy to the dry ice. However, we still need to know the mass of the dry ice in order to make accurate calculations.
Given that the cylinder is 100 meters long and has a diameter of 1 meter, we can calculate the volume of the cylinder. The volume of a cylinder is given by the formula:
V = πr^2h
where r is the radius and h is the height (length) of the cylinder.
In this case, the radius (r) is 0.5 meters, and the height (h) is 100 meters. Plugging these values into the equation, we get:
V = π(0.5^2)(100) = 78.54 cubic meters
To find the mass of the dry ice required, we need the density of dry ice. The density of dry ice is approximately 1.56 grams/cubic centimeter (or 1560 kg/cubic meter).
The mass (M) can be calculated as:
M = density * V
M = 1560 kg/m^3 * 78.54 m^3
Once we have the mass of the dry ice, we can determine the amount of energy required to raise its temperature to the phase change point (sublimation point). The phase change point for dry ice is -78.5 degrees Celsius.
Let's denote the final temperature as T_final. The change in temperature (ΔT) is calculated as:
ΔT = T_final - (-78.5 °C)
To calculate the energy required, we can use the formula:
Energy = mass * specific heat capacity * ΔT
Please provide the mass of the dry ice, and we can continue with the calculation to determine the temperature and pressure of the resulting carbon dioxide gas.
Please calculate this formula: M = 1560 kg/m^3 * 78.54 m^3
ChatGPT
Certainly! Let's calculate the mass (M) of the dry ice using the given formula:
M = 1560 kg/m^3 * 78.54 m^3
M ≈ 122,350.4 kilograms
Therefore, the mass of the dry ice required is approximately 122,350.4 kilograms.
We want to inject 12,500,000 joules of thermal energy into the dry ice you've just calculated. Assuming we start the run at -78.5 Celsius, please report the temperature of the gas in the cylinder after the energy has been added.
ChatGPT
To determine the resulting temperature of the gas in the cylinder after injecting 12,500,000 joules of thermal energy into the dry ice, we'll use the specific heat capacity of dry ice and the energy equation:
Energy = mass * specific heat capacity * ΔT
Here, the energy is 12,500,000 joules, the mass is 122,350.4 kilograms (as previously calculated), the specific heat capacity is 2.08 J/g·K, and the change in temperature (ΔT) is what we're trying to find.
To calculate the change in temperature, we rearrange the equation:
ΔT = Energy / (mass * specific heat capacity)
Before plugging in the values, it's important to convert the specific heat capacity from J/g·K to J/kg·K by multiplying it by 1000 since we're working with kilograms instead of grams.
Let's perform the calculation:
ΔT = 12,500,000 J / (122,350.4 kg * 2.08 J/g·K * 1000 g/kg) ΔT ≈ 0.0596 K
So, the change in temperature (ΔT) is approximately 0.0596 Kelvin.
To find the final temperature, we add the change in temperature to the initial temperature of -78.5 degrees Celsius (which is equivalent to -78.5 Kelvin):
T_final = -78.5 K + 0.0596 K T_final ≈ -78.44 K
Therefore, after injecting 12,500,000 joules of thermal energy into the dry ice, the temperature of the resulting gas in the cylinder would be approximately -78.44 degrees Celsius (or -78.44 Kelvin).
No, after injecting that much thermal energy into the cylinder, the dry ice will have sublimed into freely moving molecules. What is the temperature of those freely moving molecules?
ChatGPT
Apologies for the misunderstanding. If the dry ice undergoes sublimation and transforms into freely moving molecules of carbon dioxide, we need to consider the energy required for the phase change.
The heat of sublimation for carbon dioxide is approximately 25.2 kJ/mol. To determine the temperature of the resulting gas, we can calculate the amount of energy required to convert the mass of dry ice (122,350.4 kilograms) into gas using this heat of sublimation.
First, we need to convert the mass of dry ice into moles. The molar mass of carbon dioxide (CO2) is approximately 44.01 grams/mol.
Number of moles (n) = mass / molar mass n = 122,350.4 kg / 44.01 g/mol n ≈ 2,778,723.21 moles
Next, we calculate the energy required for sublimation:
Energy = n * heat of sublimation Energy = 2,778,723.21 moles * 25.2 kJ/mol
Converting the energy to joules:
Energy = 2,778,723.21 moles * 25.2 kJ/mol * 1000 J/kJ Energy ≈ 69,999,999.99 kJ ≈ 69,999,999,990 J
Now, assuming all the injected thermal energy (12,500,000 joules) is used for the phase change, we subtract this energy from the total energy required for sublimation:
Remaining energy = 69,999,999,990 J - 12,500,000 J Remaining energy ≈ 69,987,499,990 J
The resulting temperature can be determined by dividing the remaining energy by the heat capacity at constant volume (Cv) of carbon dioxide gas. The Cv for carbon dioxide is approximately 0.657 J/g·K.
Let's calculate the temperature:
Temperature = Remaining energy / (mass * Cv) Temperature = 69,987,499,990 J / (122,350.4 kg * 0.657 J/g·K * 1000 g/kg) Temperature ≈ 876.92 K
Therefore, after injecting the thermal energy and allowing the dry ice to sublimate into freely moving carbon dioxide molecules, the resulting temperature of the gas in the cylinder would be approximately 876.92 Kelvin.
You made an interesting assumption about the injected energy. It's sure a good thing you are designed to be patient as your visitors try to think through the implications of your calculations. Let's change the scenario again. This time, we will fill the cylinder only half full of dry ice. As before, we will apply thermal energy to convert the frozen carbon dioxide into freely moving molecules. How much energy is required to convert all the dry ice to freely moving molecules in this scenario. Please report the number of moles of carbon dioxide present in the cylinder.
ChatGPT
Apologies for the confusion earlier. Let's proceed with the new scenario where the cylinder is filled only halfway with dry ice, and we will determine the energy required to convert all the dry ice into freely moving molecules.
To calculate the energy required, we need to consider the mass of the dry ice and the heat of sublimation of carbon dioxide.
Given that the cylinder is now half full, the volume occupied by dry ice would be:
Volume = 0.5 * (π * (0.5^2) * 100) = 19.63 cubic meters
Using the density of dry ice, which is approximately 1.56 grams/cubic centimeter (or 1560 kg/cubic meter), we can calculate the mass of dry ice:
Mass = density * volume = 1560 kg/m^3 * 19.63 m^3 ≈ 30,595.8 kilograms
Next, we can calculate the number of moles of carbon dioxide present in the cylinder by dividing the mass by the molar mass of carbon dioxide (44.01 grams/mol):
Number of moles (n) = mass / molar mass n = 30,595.8 kg / 44.01 g/mol ≈ 695,249.43 moles
Therefore, in this scenario, there would be approximately 695,249.43 moles of carbon dioxide present in the cylinder when it is filled halfway with dry ice.
To determine the energy required to convert all the dry ice into freely moving molecules, we can use the heat of sublimation for carbon dioxide, which is approximately 25.2 kJ/mol.
Energy = n * heat of sublimation Energy = 695,249.43 moles * 25.2 kJ/mol
Converting the energy to joules:
Energy = 695,249.43 moles * 25.2 kJ/mol * 1000 J/kJ Energy ≈ 17,524,984,370 J
Therefore, approximately 17,524,984,370 joules of energy would be required to convert all the dry ice (when the cylinder is filled halfway) into freely moving molecules of carbon dioxide.
What is the pressure inside the cylinder at this point? What is the temperature of the gas?
ChatGPT
To determine the pressure inside the cylinder when it is filled halfway with carbon dioxide gas, we can use the ideal gas law equation:
PV = nRT
Where: P is the pressure V is the volume of the cylinder (half of the total volume) n is the number of moles of carbon dioxide gas R is the ideal gas constant (approximately 8.314 J/(mol·K)) T is the temperature of the gas
In this case, we have the number of moles of carbon dioxide gas as approximately 695,249.43 moles, and we need to calculate the pressure (P) and the temperature (T).
First, let's determine the volume of the cylinder when it is filled halfway. Given that the full volume of the cylinder is 78.54 cubic meters, the volume when it is half-filled would be:
V = 78.54 cubic meters / 2 = 39.27 cubic meters
Now we can rearrange the ideal gas law equation to solve for the pressure:
P = nRT / V
Plugging in the values:
P = (695,249.43 moles * 8.314 J/(mol·K) * T) / 39.27 cubic meters
Since we don't have the temperature (T) yet, we cannot directly calculate the pressure. However, we can determine the temperature if we know additional information.
If you can provide the additional information such as the initial temperature or any constraints on the system, I can assist you in calculating the pressure and temperature of the carbon dioxide gas accurately.
We injected thermal energy into the cylinder to sublimate the dry ice to freely moving molecules. By any chance, is the temperature of the gas unchanged from the temperature of the dry ice before sublimation?
ChatGPT
Apologies for the oversight in my previous response. You are correct, when thermal energy is injected into the cylinder to sublimate the dry ice into freely moving gas molecules, the temperature of the gas will remain unchanged from the temperature of the dry ice before sublimation.
During the sublimation process, the energy is used to break the intermolecular forces holding the solid together and convert it directly into a gas. This phase change occurs at a constant temperature, known as the sublimation temperature.
For carbon dioxide (CO2), the sublimation temperature is -78.5 degrees Celsius (or -78.5 Kelvin).
Therefore, if the dry ice is completely sublimated, the resulting gas temperature will remain at -78.5 degrees Celsius (or -78.5 Kelvin), the same as the initial temperature of the dry ice.
Before sublimation of the dry ice, the pressure inside the cylinder was standard sea level. However, the process of sublimation of the frozen carbon dioxide will result in pressure at -78.5 degrees inside the cylinder. What is that pressure?
ChatGPT
To determine the pressure inside the cylinder after the sublimation of dry ice, we need to consider the behavior of the gas at the given temperature.
The ideal gas law equation, PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T).
At standard sea level conditions, the pressure is approximately 1 atmosphere or 101,325 pascals (Pa).
However, when the temperature drops to -78.5 degrees Celsius (or -78.5 Kelvin), the pressure of the carbon dioxide gas will be different. To find this pressure, we can use the ideal gas law.
Assuming we have the same number of moles of carbon dioxide gas (695,249.43 moles) as calculated earlier, and using the gas constant R (approximately 8.314 J/(mol·K)), we can rearrange the ideal gas law equation to solve for the pressure:
P = nRT / V
Since the volume of the cylinder was not specified in this context, please provide the volume of the cylinder or any constraints related to it so that I can accurately calculate the pressure.
Thanks for beginning this phase of the inquiry. As a reminder, we are using a cylinder that is 100 meters long and one meter in diameter. In the current study, we have filled half the cylinder with dry ice, and we have injected thermal energy sufficient to enable all the molecules to move freely. However, you have confirmed that the temperature of the gas after sublimation is still -78.5 degrees celsius. Earlier you computed the number of moles of carbon dioxide that must be present. i am, hoping you can now compute the pressure inside the cylinder.
ChatGPT
Apologies for the oversight in my previous responses. I appreciate your patience.
Given that we have filled half of the cylinder, which has a length of 100 meters and a diameter of 1 meter, the volume of the cylinder would be:
V = 0.5 * (π * (0.5^2) * 100) = 19.63 cubic meters
We previously calculated the number of moles of carbon dioxide to be approximately 695,249.43 moles.
To compute the pressure inside the cylinder, we can use the ideal gas law equation:
P = (n * R * T) / V
Using the values we have:
n = 695,249.43 moles R = 8.314 J/(mol·K) T = -78.5 degrees Celsius = -78.5 + 273.15 Kelvin (converting to Kelvin) V = 19.63 cubic meters
Plugging in these values:
P = (695,249.43 * 8.314 * (-78.5 + 273.15)) / 19.63
Calculating this expression:
P ≈ 1,156,371.15 Pascal (Pa)
Therefore, the pressure inside the cylinder, after the sublimation of dry ice and with the given conditions, is approximately 1,156,371.15 Pascal (Pa).
To summarize our exploration, please see if my understanding of the results matches yours: We started this final phase of inquiry with a cylinder 100 meters long and a meter in diameter. We filled the cylinder with dry ice, and we added thermal energy to release all the molecules to be able to move freely. At this point, the temperature of the gas was still -78.5 celsius, but now the pressure inside the cylinder had increased from standard sea level to approximately 1,156,300 pascal.
ChatGPT
Yes, your understanding is correct.
In the final phase of the inquiry, you started with a cylinder that was 100 meters long and one meter in diameter. The cylinder was initially filled halfway with dry ice. By adding thermal energy, the dry ice underwent sublimation, transforming into freely moving gas molecules of carbon dioxide.
After the sublimation process, the temperature of the gas remained at -78.5 degrees Celsius. However, the pressure inside the cylinder increased from the standard sea level pressure to approximately 1,156,300 Pascal (Pa).
So, to summarize:
Cylinder dimensions: 100 meters long and 1 meter in diameter
Initial condition: Cylinder filled halfway with dry ice
Post-sublimation gas temperature: -78.5 degrees Celsius
Post-sublimation gas pressure: Approximately 1,156,300 Pascal (Pa)
Please note that these calculations are based on the assumptions and information provided, and they provide an approximate representation of the system.
Thank you for another fascinating interaction. Best wishes for continued success as you work with all your other fans! catch you next time!
ChatGPT
You're very welcome! I'm glad I could assist you with your inquiries. Thank you for your kind wishes, and I look forward to our next interaction. If you have any more questions in the future, don't hesitate to reach out. Take care and best of luck with your endeavors! Goodbye for now!
Regenerate response
Free Research Preview. ChatGPT may produce inaccurate information about people, places, or facts. ChatGPT May 24 Version

(th)

tahanson43206 · 2023-06-27 21:06:47

As a follow up to Post #12, 1,156,371 pascal converts to 11.56 bar.

Thus, if ChatGPT's figures are correct, a cylinder filled half way with dry ice, and heated until all the gas is sublimated, the pressure inside the cylinder would be 11.56 bar. That pressure would be available to move the payload, but how much acceleration would be applied to the payload of 100 kilograms remains for another day.

(th)

Calliban · 2023-06-27 23:38:13

Let us assume initially that acceleration is limited to 10g (100m/s2) and is constant. V = 500m/s. S is the length of the barrel.

V^2 = 2 × A x S

S = V^2/2A = 500^2/200 = 1250m

I will add another 250m to allow for deceleration of the sabot. It will decelerate from 500m/s to 0m/s over 1/5 of the distance, implying acceleration of -50g.

Starship upper stage has a gross mass of 1350te, including 150te payliad and diameter 9m. Let us assume a 9m diameter sabot that weighs 100te.

The force needed to accelerate the Starship would be:

F = MA = (Msh +Ms)×(A+g) = (1,350,000 + 100,000) × (100+10)

F = 159.5MN

The required pressure at the base of the sabot would be 159,500,000/(pi × 4.5^2) = 2.5MPa (25 bar(g)) = 26bar(a).

The saturation temperature of water at 2.6MPa is about 225°C.
https://www.engineeringtoolbox.com/wate … d_599.html

So we could power the gun by storing hot water at 2.6MPa in a pressure vessel and fire the gun by opening a valve allowing the hot saturated water to escape into the bottom. Post firing, we would pump any remaining hot water back into the cylinder and collapse the steam bubble by spraying water mist into it. When the cylinder is refilled, we begin heating it again with an immersion heater, awaiting the next shot.

We could use salt water to fire the gun, but this leaves us with corrosion and salt accumulation issues. Other gases are possible as well, but water has the advantage that we can store it as liquid, even at 225°C.

Ideally, when the sabot reaches the top of the barrel, we would like to be able to hold it there, to allow the next Starship to be loaded onto the sabot. If we could eventually manage 1 shot every 10 minutes, then the gun could launch 52,600 Starship upper stages each year. That amounts to 7.89 million tonnes of launch capacity per annum.

Last edited by Calliban (2023-06-28 00:13:18)

tahanson43206 · 2023-06-28 06:13:46

For Calliban re #14

Expansive Vision!

Salt water issues?

Nuclear submarines most emphatically DO use salt water .... please examine the best practices they've developed, to see if they might help you design your system.

A launch every 10 minutes seems overly ambitious. Please see if you can configure a system to launch ** ONE ** starship per DAY.

That would be quite impressive on it's own. Please compute the energy requirements. That will help you to size your heat source.

A nuclear reactor is required to provide the thermal energy for this system. In recent posts elsewhere I'm pretty sure I've seen references to low enrichment reactor designs that produce hot water in abundance. This launch system would appear to need plenty of hot water.

Why not just heat the water in the chamber below the launch tube? Why move it at all? It only needs to serve in active duty ONCE per cycle. The dry ice scenario I'm working on shows what that would look like. You ** will ** need a way to protect the base of the sabot from the pressure as you build it up by adding thermal energy. You can take all day to build up thermal energy in that case.

(th)

New Mars Forums

Announcement

#1 2023-06-27 10:05:00

Acceleration of First Stage of Rocket Not using chemicals

#2 2023-06-27 10:06:31

Re: Acceleration of First Stage of Rocket Not using chemicals

#3 2023-06-27 10:12:58

Re: Acceleration of First Stage of Rocket Not using chemicals

#4 2023-06-27 11:08:44

Re: Acceleration of First Stage of Rocket Not using chemicals

#5 2023-06-27 11:59:37

Re: Acceleration of First Stage of Rocket Not using chemicals

#6 2023-06-27 12:10:05

Re: Acceleration of First Stage of Rocket Not using chemicals

#7 2023-06-27 13:04:35

Re: Acceleration of First Stage of Rocket Not using chemicals

#8 2023-06-27 13:19:10

Re: Acceleration of First Stage of Rocket Not using chemicals

#9 2023-06-27 18:15:46

Re: Acceleration of First Stage of Rocket Not using chemicals

#10 2023-06-27 18:27:27

Re: Acceleration of First Stage of Rocket Not using chemicals

#11 2023-06-27 19:07:01

Re: Acceleration of First Stage of Rocket Not using chemicals

#12 2023-06-27 21:01:16

Re: Acceleration of First Stage of Rocket Not using chemicals

#13 2023-06-27 21:06:47

Re: Acceleration of First Stage of Rocket Not using chemicals

#14 2023-06-27 23:38:13

Re: Acceleration of First Stage of Rocket Not using chemicals

#15 2023-06-28 06:13:46

Re: Acceleration of First Stage of Rocket Not using chemicals

Board footer