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This topic became available in 2025 as Gemini and NewMars studied the behavior of a system designed to capture air ahead of a rising projectile. The study was going well until it came time to model the behavior of the gas as it interacts with a cold pipe.
As a quick summary:
We are studying the interaction of air at STP (Standard Temperature and Pressure) with a tube made of metal such as iron.
The tube has a volume of 3 cubic meters, a mass of 1000 kilograms, a diameter of 1 meter.
The main tube is subdivided into smaller tubes of 4 cm ID, 5 cm OD.
The tube system is cooled to 100 Kelvin.
The velocity of the tube is given as 11 km/s.
In initial studies that did not take cooling into account, the air capture system collected just under a metric ton of air.
It is expected that the quantity of air collected will increase as cooling is taken into account.
In Post #3 of this series, Gemini provides a starting Python program to model the cooling problem.
This kind of problem would be a natural fit for a CFD program such as OpenFOAM, but Gemini thinks Python can do the job, so we will see how far we can get.
Thank you for considering this approach to dealing with what is turning out to be a ** very ** interesting aspect of physics. I am thinking of setting up this new study as it's own topic in our forum, in hopes it will have educational value. Before I create the topic, do you think it would be correct to call the new topic "Thermodynamics Study" or do you have a suggestion for a better title?
***
Gemini's reply:"Thermodynamics Study" is an excellent and accurate title for your new forum topic. It precisely describes the core physics you are investigating—the transfer of heat and energy within a system. This title is both professional and clear, making it easy for others to understand the subject matter.
Alternative Titles
If you want a title that is more specific to your project, you could consider these alternatives:"Air Capture: Thermal Energy Transfer"
"Gas-Pipe Thermal Dynamics"
"Simulating Heat Transfer in Hypersonic Air Capture"
However, "Thermodynamics Study" is a broad and classic term that is perfectly suitable for this kind of detailed physics investigation. It's concise and well-understood by engineers and scientists.
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This post is reserved for an index to posts that may be contributed by NewMars members.
Index:
Post #3: Opening Python program to begin study of a scenario of gas entering a pipe at 11 km/s.
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In this post we provide the code for a Python program to study a physics problem.
We are imagining a pipe with a closed end moving toward a volume of air on Earth at STP.
We imagine the pipe is traveling at 11 km/s and that it has a temperature of 100 Kelvin.
# 20250828ThermodynamicsStudyV01
import math
# --- Constants ---
TIME_STEP_S = 0.01 # s
SIMULATION_DURATION_S = 1.0 # s
INITIAL_PIPE_TEMP_K = 100.0 # K
INITIAL_GAS_TEMP_K = 288.0 # K (Ambient temp)
PIPE_MASS_KG = 1000.0 # kg
PIPE_VOLUME_M3 = 15.0 # m^3
PROJECTILE_VELOCITY_MPS = 11000.0 # m/s
PROJECTILE_DIAMETER_M = 1.0 # m
AIR_DENSITY_KG_M3 = 1.225 # kg/m^3 (Sea level)
SPECIFIC_HEAT_AIR_J_KG_K = 1005.0 # J/(kg*K)
SPECIFIC_HEAT_PIPE_J_KG_K = 450.0 # J/(kg*K)
PIPE_ID_M = 0.04 # m
PIPE_OD_M = 0.05 # m
PIPE_DENSITY_KG_M3 = 7850.0 # kg/m^3
HEAT_TRANSFER_COEFFICIENT = 50.0 # W/(m^2*K)
# --- Calculations for Pipe Geometry ---
pipe_cross_sectional_area = math.pi * ((PIPE_OD_M / 2)**2 - (PIPE_ID_M / 2)**2)
pipe_length_for_mass = PIPE_MASS_KG / (pipe_cross_sectional_area * PIPE_DENSITY_KG_M3)
pipe_internal_volume_single = math.pi * (PIPE_ID_M / 2)**2 * pipe_length_for_mass
number_of_pipes = PIPE_VOLUME_M3 / pipe_internal_volume_single if pipe_internal_volume_single > 0 else 0
total_cooling_surface_area_sqm = number_of_pipes * math.pi * PIPE_ID_M * pipe_length_for_mass
print(f"--- Thermal Model Test ---")
print(f"Number of Pipes: {number_of_pipes:.0f}")
print(f"Total Cooling Surface Area: {total_cooling_surface_area_sqm:.2f} m^2")
print(f"Initial Pipe Temp: {INITIAL_PIPE_TEMP_K:.2f} K")
print(f"Initial Gas Temp: {INITIAL_GAS_TEMP_K:.2f} K")
print("--------------------------")
# --- Simulation Variables ---
gas_temperature_K = INITIAL_GAS_TEMP_K
pipe_temperature_K = INITIAL_PIPE_TEMP_K
collected_air_mass = 0.0
total_gas_energy = 0.0
cross_sectional_area_capture = math.pi * (PROJECTILE_DIAMETER_M / 2)**2
# --- Simulation Loop ---
for time_step in range(int(SIMULATION_DURATION_S / TIME_STEP_S)):
# 1. Mass and Energy of incoming air
mass_collected_in_step = AIR_DENSITY_KG_M3 * cross_sectional_area_capture * PROJECTILE_VELOCITY_MPS * TIME_STEP_S
kinetic_energy_in_step = 0.5 * mass_collected_in_step * PROJECTILE_VELOCITY_MPS**2
# 2. Update Gas Energy with new air
total_gas_energy = (collected_air_mass * SPECIFIC_HEAT_AIR_J_KG_K * gas_temperature_K) + kinetic_energy_in_step
collected_air_mass += mass_collected_in_step
if collected_air_mass > 0:
gas_temperature_K = total_gas_energy / (collected_air_mass * SPECIFIC_HEAT_AIR_J_KG_K)
# 3. Calculate Heat Flow
temp_diff = gas_temperature_K - pipe_temperature_K
heat_transferred_this_step = HEAT_TRANSFER_COEFFICIENT * total_cooling_surface_area_sqm * temp_diff * TIME_STEP_S
# 4. Update Temperatures based on Heat Flow
if total_gas_energy > 0:
gas_temperature_K -= heat_transferred_this_step / (collected_air_mass * SPECIFIC_HEAT_AIR_J_KG_K)
pipe_temperature_K += heat_transferred_this_step / (PIPE_MASS_KG * SPECIFIC_HEAT_PIPE_J_KG_K)
print(f"Time: {time_step * TIME_STEP_S:.2f}s | Gas Temp: {gas_temperature_K:.2f} K | Pipe Temp: {pipe_temperature_K:.2f} K | Mass: {collected_air_mass:.2f} kg")If anyone runs this program this topic is available for comments. Since I have no way of knowing ahead of time how this is going to turn out, if there is someone in the active membership who has knowledge in this area, you are welcome to pitch in.
If there is a forum reader who would like to participate, see the Recruiting topic for procedure.
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TH, at that speed (>Mach 30) the air would be shock heated into a plasma as it enters the tube. W.r.t to the tube, the air is moving at 11km/s. That is a kinetic energy of 60.5MJ/kg, all of which is converted into a combination of pressure and thermal energy, as the air accelerates to the velocity of the tube. Your tube will probably melt and frontal pressure will blow it apart. Did Gemini pick that up?
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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For Calliban re #4
Thank you for your interest in this inquiry! I will ask Gemini about plasma in our next interaction. If you have time, please look at this set of results. The computation assumes a set of conditions that are listed in the source code in Post #3. However, the listing may be self-explanatory.
We are admitting air into a cold tube and we can see that the tube is heating as energy is transferred to the walls of the container. We had found earlier that the pressure inside the container equals the incoming air pressure after about one ton of air is collected. That is not shown in the chart below. What ** is ** shown is that the tubes are heating rapidly to the melting point of the material, so we would have to close the doors before then.
My hope in adding cooling to the simulation was to capture more air on the way up. This little study program appears to be showing that the amount of air captured will indeed increase.
python3 20250828ThermodynamicsStudyV01.py
--- Thermal Model Test ---
Number of Pipes: 66
Total Cooling Surface Area: 1500.00 m^2
Initial Pipe Temp: 100.00 K
Initial Gas Temp: 288.00 K
--------------------------
Time: 0.00s | Gas Temp: 59775.22 K | Pipe Temp: 200.17 K | Mass: 105.83 kg
Time: 0.01s | Gas Temp: 59776.32 K | Pipe Temp: 299.81 K | Mass: 211.66 kg
Time: 0.02s | Gas Temp: 59777.09 K | Pipe Temp: 399.17 K | Mass: 317.50 kg
Time: 0.03s | Gas Temp: 59777.71 K | Pipe Temp: 498.31 K | Mass: 423.33 kg
Time: 0.04s | Gas Temp: 59778.25 K | Pipe Temp: 597.25 K | Mass: 529.16 kg
Time: 0.05s | Gas Temp: 59778.74 K | Pipe Temp: 696.00 K | Mass: 634.99 kg
Time: 0.06s | Gas Temp: 59779.20 K | Pipe Temp: 794.57 K | Mass: 740.83 kg
Time: 0.07s | Gas Temp: 59779.64 K | Pipe Temp: 892.97 K | Mass: 846.66 kg
Time: 0.08s | Gas Temp: 59780.06 K | Pipe Temp: 991.19 K | Mass: 952.49 kg
Time: 0.09s | Gas Temp: 59780.47 K | Pipe Temp: 1089.24 K | Mass: 1058.32 kg
Time: 0.10s | Gas Temp: 59780.87 K | Pipe Temp: 1187.12 K | Mass: 1164.16 kg
Time: 0.11s | Gas Temp: 59781.27 K | Pipe Temp: 1284.84 K | Mass: 1269.99 kg
Time: 0.12s | Gas Temp: 59781.65 K | Pipe Temp: 1382.39 K | Mass: 1375.82 kg
Time: 0.13s | Gas Temp: 59782.03 K | Pipe Temp: 1479.77 K | Mass: 1481.65 kg
Time: 0.14s | Gas Temp: 59782.41 K | Pipe Temp: 1576.99 K | Mass: 1587.49 kg
Time: 0.15s | Gas Temp: 59782.79 K | Pipe Temp: 1674.04 K | Mass: 1693.32 kg << 1643 Kelvin steel alloy melting point see Google below
Time: 0.16s | Gas Temp: 59783.16 K | Pipe Temp: 1770.93 K | Mass: 1799.15 kg
Time: 0.17s | Gas Temp: 59783.52 K | Pipe Temp: 1867.65 K | Mass: 1904.98 kg
Time: 0.18s | Gas Temp: 59783.89 K | Pipe Temp: 1964.21 K | Mass: 2010.82 kg
Time: 0.19s | Gas Temp: 59784.25 K | Pipe Temp: 2060.62 K | Mass: 2116.65 kg
Time: 0.20s | Gas Temp: 59784.61 K | Pipe Temp: 2156.85 K | Mass: 2222.48 kg
Time: 0.21s | Gas Temp: 59784.97 K | Pipe Temp: 2252.93 K | Mass: 2328.31 kg
Time: 0.22s | Gas Temp: 59785.33 K | Pipe Temp: 2348.85 K | Mass: 2434.15 kg
Time: 0.23s | Gas Temp: 59785.69 K | Pipe Temp: 2444.60 K | Mass: 2539.98 kg
Time: 0.24s | Gas Temp: 59786.04 K | Pipe Temp: 2540.20 K | Mass: 2645.81 kg
Time: 0.25s | Gas Temp: 59786.39 K | Pipe Temp: 2635.64 K | Mass: 2751.64 kg
Time: 0.26s | Gas Temp: 59786.75 K | Pipe Temp: 2730.91 K | Mass: 2857.47 kg
Time: 0.27s | Gas Temp: 59787.10 K | Pipe Temp: 2826.03 K | Mass: 2963.31 kg
Time: 0.28s | Gas Temp: 59787.45 K | Pipe Temp: 2920.99 K | Mass: 3069.14 kg
Time: 0.29s | Gas Temp: 59787.80 K | Pipe Temp: 3015.79 K | Mass: 3174.97 kg
Time: 0.30s | Gas Temp: 59788.14 K | Pipe Temp: 3110.43 K | Mass: 3280.80 kg
Time: 0.31s | Gas Temp: 59788.49 K | Pipe Temp: 3204.92 K | Mass: 3386.64 kg
Time: 0.32s | Gas Temp: 59788.84 K | Pipe Temp: 3299.24 K | Mass: 3492.47 kg
Time: 0.33s | Gas Temp: 59789.18 K | Pipe Temp: 3393.41 K | Mass: 3598.30 kg
Time: 0.34s | Gas Temp: 59789.53 K | Pipe Temp: 3487.43 K | Mass: 3704.13 kg
Time: 0.35s | Gas Temp: 59789.87 K | Pipe Temp: 3581.28 K | Mass: 3809.97 kg
Time: 0.36s | Gas Temp: 59790.22 K | Pipe Temp: 3674.98 K | Mass: 3915.80 kg
Time: 0.37s | Gas Temp: 59790.56 K | Pipe Temp: 3768.52 K | Mass: 4021.63 kg
Time: 0.38s | Gas Temp: 59790.90 K | Pipe Temp: 3861.91 K | Mass: 4127.46 kg
Time: 0.39s | Gas Temp: 59791.24 K | Pipe Temp: 3955.14 K | Mass: 4233.30 kg
Time: 0.40s | Gas Temp: 59791.58 K | Pipe Temp: 4048.22 K | Mass: 4339.13 kg
Time: 0.41s | Gas Temp: 59791.92 K | Pipe Temp: 4141.14 K | Mass: 4444.96 kg
Time: 0.42s | Gas Temp: 59792.26 K | Pipe Temp: 4233.91 K | Mass: 4550.79 kg
Time: 0.43s | Gas Temp: 59792.60 K | Pipe Temp: 4326.52 K | Mass: 4656.63 kg
Time: 0.44s | Gas Temp: 59792.94 K | Pipe Temp: 4418.98 K | Mass: 4762.46 kg
Time: 0.45s | Gas Temp: 59793.28 K | Pipe Temp: 4511.28 K | Mass: 4868.29 kg
Time: 0.46s | Gas Temp: 59793.61 K | Pipe Temp: 4603.44 K | Mass: 4974.12 kg
Time: 0.47s | Gas Temp: 59793.95 K | Pipe Temp: 4695.43 K | Mass: 5079.96 kg
Time: 0.48s | Gas Temp: 59794.29 K | Pipe Temp: 4787.28 K | Mass: 5185.79 kg
Time: 0.49s | Gas Temp: 59794.62 K | Pipe Temp: 4878.97 K | Mass: 5291.62 kg
Time: 0.50s | Gas Temp: 59794.96 K | Pipe Temp: 4970.51 K | Mass: 5397.45 kg
Time: 0.51s | Gas Temp: 59795.29 K | Pipe Temp: 5061.90 K | Mass: 5503.28 kg
Time: 0.52s | Gas Temp: 59795.63 K | Pipe Temp: 5153.13 K | Mass: 5609.12 kg
Time: 0.53s | Gas Temp: 59795.96 K | Pipe Temp: 5244.21 K | Mass: 5714.95 kg
Time: 0.54s | Gas Temp: 59796.29 K | Pipe Temp: 5335.15 K | Mass: 5820.78 kg
Time: 0.55s | Gas Temp: 59796.63 K | Pipe Temp: 5425.93 K | Mass: 5926.61 kg
Time: 0.56s | Gas Temp: 59796.96 K | Pipe Temp: 5516.56 K | Mass: 6032.45 kg
Time: 0.57s | Gas Temp: 59797.29 K | Pipe Temp: 5607.04 K | Mass: 6138.28 kg
Time: 0.58s | Gas Temp: 59797.62 K | Pipe Temp: 5697.36 K | Mass: 6244.11 kg
Time: 0.59s | Gas Temp: 59797.95 K | Pipe Temp: 5787.54 K | Mass: 6349.94 kg
Time: 0.60s | Gas Temp: 59798.28 K | Pipe Temp: 5877.57 K | Mass: 6455.78 kg
Time: 0.61s | Gas Temp: 59798.61 K | Pipe Temp: 5967.45 K | Mass: 6561.61 kg
Time: 0.62s | Gas Temp: 59798.94 K | Pipe Temp: 6057.18 K | Mass: 6667.44 kg
Time: 0.63s | Gas Temp: 59799.27 K | Pipe Temp: 6146.76 K | Mass: 6773.27 kg
Time: 0.64s | Gas Temp: 59799.60 K | Pipe Temp: 6236.19 K | Mass: 6879.11 kg
Time: 0.65s | Gas Temp: 59799.93 K | Pipe Temp: 6325.47 K | Mass: 6984.94 kg
Time: 0.66s | Gas Temp: 59800.26 K | Pipe Temp: 6414.61 K | Mass: 7090.77 kg
Time: 0.67s | Gas Temp: 59800.58 K | Pipe Temp: 6503.59 K | Mass: 7196.60 kg
Time: 0.68s | Gas Temp: 59800.91 K | Pipe Temp: 6592.43 K | Mass: 7302.44 kg
Time: 0.69s | Gas Temp: 59801.24 K | Pipe Temp: 6681.12 K | Mass: 7408.27 kg
Time: 0.70s | Gas Temp: 59801.56 K | Pipe Temp: 6769.66 K | Mass: 7514.10 kg
Time: 0.71s | Gas Temp: 59801.89 K | Pipe Temp: 6858.06 K | Mass: 7619.93 kg
Time: 0.72s | Gas Temp: 59802.21 K | Pipe Temp: 6946.31 K | Mass: 7725.77 kg
Time: 0.73s | Gas Temp: 59802.54 K | Pipe Temp: 7034.41 K | Mass: 7831.60 kg
Time: 0.74s | Gas Temp: 59802.86 K | Pipe Temp: 7122.37 K | Mass: 7937.43 kg
Time: 0.75s | Gas Temp: 59803.19 K | Pipe Temp: 7210.17 K | Mass: 8043.26 kg
Time: 0.76s | Gas Temp: 59803.51 K | Pipe Temp: 7297.84 K | Mass: 8149.09 kg
Time: 0.77s | Gas Temp: 59803.83 K | Pipe Temp: 7385.36 K | Mass: 8254.93 kg
Time: 0.78s | Gas Temp: 59804.16 K | Pipe Temp: 7472.73 K | Mass: 8360.76 kg
Time: 0.79s | Gas Temp: 59804.48 K | Pipe Temp: 7559.96 K | Mass: 8466.59 kg
Time: 0.80s | Gas Temp: 59804.80 K | Pipe Temp: 7647.04 K | Mass: 8572.42 kg
Time: 0.81s | Gas Temp: 59805.12 K | Pipe Temp: 7733.98 K | Mass: 8678.26 kg
Time: 0.82s | Gas Temp: 59805.45 K | Pipe Temp: 7820.77 K | Mass: 8784.09 kg
Time: 0.83s | Gas Temp: 59805.77 K | Pipe Temp: 7907.42 K | Mass: 8889.92 kg
Time: 0.84s | Gas Temp: 59806.09 K | Pipe Temp: 7993.92 K | Mass: 8995.75 kg
Time: 0.85s | Gas Temp: 59806.41 K | Pipe Temp: 8080.28 K | Mass: 9101.59 kg
Time: 0.86s | Gas Temp: 59806.73 K | Pipe Temp: 8166.50 K | Mass: 9207.42 kg
Time: 0.87s | Gas Temp: 59807.05 K | Pipe Temp: 8252.58 K | Mass: 9313.25 kg
Time: 0.88s | Gas Temp: 59807.37 K | Pipe Temp: 8338.51 K | Mass: 9419.08 kg
Time: 0.89s | Gas Temp: 59807.68 K | Pipe Temp: 8424.30 K | Mass: 9524.92 kg
Time: 0.90s | Gas Temp: 59808.00 K | Pipe Temp: 8509.94 K | Mass: 9630.75 kg
Time: 0.91s | Gas Temp: 59808.32 K | Pipe Temp: 8595.45 K | Mass: 9736.58 kg
Time: 0.92s | Gas Temp: 59808.64 K | Pipe Temp: 8680.81 K | Mass: 9842.41 kg
Time: 0.93s | Gas Temp: 59808.96 K | Pipe Temp: 8766.03 K | Mass: 9948.25 kg
Time: 0.94s | Gas Temp: 59809.27 K | Pipe Temp: 8851.11 K | Mass: 10054.08 kg
Time: 0.95s | Gas Temp: 59809.59 K | Pipe Temp: 8936.04 K | Mass: 10159.91 kg
Time: 0.96s | Gas Temp: 59809.90 K | Pipe Temp: 9020.84 K | Mass: 10265.74 kg
Time: 0.97s | Gas Temp: 59810.22 K | Pipe Temp: 9105.49 K | Mass: 10371.58 kg
Time: 0.98s | Gas Temp: 59810.54 K | Pipe Temp: 9190.01 K | Mass: 10477.41 kg
Time: 0.99s | Gas Temp: 59810.85 K | Pipe Temp: 9274.38 K | Mass: 10583.24 kg
Per Google:
There is no single "best possible alloy" of steel, as "best" depends on the application, but typical steel alloys have a melting range between approximately 1370°C and 1530°C, which is about 1643 K to 1803 K. The specific melting point varies significantly based on the different alloying elements like carbon, nickel, manganese, and chromium, which can raise or lower the temperature at which the steel transitions from solid to liquid.
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Gas temperature is nearly 60,000K. The gas will be ionised plasma at this temperature. That is a direct result of shock heating. Your tube temperature reaches 9000K in <1s. I don't see how this could work as a method for gathering propellant from the atmosphere.
One thing I find interesting. The specific heat of air between 100K and 60,000K, averages at 1KJ/kg.K. Roughly what it is under standard conditions.
Last edited by Calliban (2025-08-28 10:47:51)
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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For Calliban re #6
This entire topic is intended as a learning opportunity for NewMars members and for readers who are not members.
I'd like to point out that the SABRE engine (as I understand it) was designed to capture air and cool it using hydrogen gas as the coolant.This had to take place using metal fins for heat exchange. The engine was (apparently) tested with some success on the ground. I don't know much more than that.
One detail of this study should be explained for our readers...
The study is of performance of a gas gun, such as designed and tested by Dr. John Hunter. This forum contains a number of posts about Dr. Hunter, and if anyone is interested it should be easy to find.
Dr. Hunter's design envisioned a launch in the 5-7 km/s range. I am interested in exploring the potential for a more ambitious use of the technology, which is why I've chosen 11 km/s as the exit velocity.
The current study is run at 11 km/s, which is why the problem is so difficult.
Indeed, the end result may well be confirmation that the air capture idea cannot be put into practice in the Real Universe, at this velocity.
That is why the idea of doing the air capture at a lower velocity is interesting.
One more note for our readers.... this study is being done to evaluate the potential of capture of air for sale on orbit. This has nothing to do with propulsion. The value of oxygen and nitrogen on orbit is measured in Falcon 9 rates per kilogram.
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Using a light gas gun to accelerate payloads to Earth escape velocity is an innovative approach. Barrel wear would be a problem at such speeds. I wonder if the barrel can be lined with a sacrificial shell that is discarded after each shot?
"Plan and prepare for every possibility, and you will never act. It is nobler to have courage as we stumble into half the things we fear than to analyse every possible obstacle and begin nothing. Great things are achieved by embracing great dangers."
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This post is a follow up to Calliban's observation that the interactions of matter at 11 km/s are going to enter the plasma state. Today I asked Gemini to begin to explore this aspect of physics. Here is our discussion, rendered in BBCode for the forum.
User: Hello Again! A couple of days local time have passed since our last session.
In working with you on this problem, we started with a very simple question, and our studies have provided some encouragement, but now we are facing the problem at a deeper level. I am grateful you are there to share in this exploration. May I enlist you in study of what happens to an individual molecule when it encounters a wall (steel in our hypothetical pipe) that is approaching at 11 km/s. If my calculator is correct, that would be 11 millimeters in one microsecond. Our engineer has predicted that an encounter between a molecule of nitrogen and a steel wall at this velocity would cause the electric forces of the respective molecules to be overcome. Let's focus on this aspect of the situation. Can you find any studies that might have been done on this interaction? It seems likely to me (as I think about it) that many studies must have been done because of military activity over the centuries, and because of the challenges of space flight and high speed air flight today.
Gemini: I can help you investigate the interaction of a nitrogen molecule with a steel wall at such high velocities. Your engineer is correct that at a relative velocity of 11 km/s, the kinetic energy of the incoming molecules is so high that it will overcome the typical electrical forces that hold a molecule together. This phenomenon has been extensively studied, particularly in the context of hypervelocity impacts, reentry physics, and plasma dynamics.
Physics of Hypervelocity Impacts
When a gas molecule like nitrogen (N2) hits a solid surface at 11 km/s (1.1 x 10^4 m/s), the collision is an inelastic process where the molecule's kinetic energy is converted into other forms of energy. Here's a breakdown of what happens:
Kinetic Energy Calculation: The kinetic energy (KE) of a single nitrogen molecule can be calculated using the formula KE = 0.5 * m * v^2. The mass (m) of a nitrogen molecule is approximately 4.65 x 10^-26 kg.
KE = 0.5 * (4.65 x 10^-26 kg) * (1.1 x 10^4 m/s)^2 ~= 2.82 x 10^-18 JBond Dissociation: To break the triple bond of a nitrogen molecule, the energy required is about 9.8 eV or 1.57 x 10^-18 J. Our calculated kinetic energy (2.82 x 10^-18 J) is more than enough to dissociate the nitrogen molecule into two separate nitrogen atoms.
Ionization: Ionizing a nitrogen atom (stripping an electron) requires 14.5 eV or 2.32 x 10^-18 J. Our calculated kinetic energy is also sufficient to cause ionization, creating a charged particle and a free electron (N+ + e-). This is the plasma state your engineer mentioned.
Heating the Wall: The remaining energy from the collision will be transferred as heat to the wall. This energy transfer will cause a sharp, localized increase in the wall's temperature. Over time, as more molecules collide with the wall, this heating will propagate and increase the overall temperature of the pipe.
The Phenomenon of Sputtering
At these extreme velocities, a phenomenon called sputtering occurs. Sputtering is the process where atoms are ejected from a solid material due to the bombardment of the material by energetic particles. In our scenario, the hypervelocity nitrogen molecules hitting the steel pipe will not only heat it, but will also have enough energy to knock iron and other atoms off the pipe's surface. This would be a form of material loss and would generate additional friction and heat.
Relevant Studies
While specific military documents are not publicly available, the physics of these interactions has been extensively studied in publicly accessible research.
NASA Hypervelocity Impact Studies: NASA has done a lot of research on micrometeoroid and orbital debris impacts on spacecraft, which are essentially hypervelocity impacts. These studies focus on the resulting damage and the physics of plasma formation.
Aerospace Engineering Research: High-speed atmospheric reentry and hypersonic flight require a deep understanding of how air molecules interact with vehicle surfaces. A major focus of this research is predicting the heat flux and drag, which are direct consequences of the kinetic to thermal energy conversion you're asking about. The shock layer in front of a hypersonic vehicle is a region of intensely hot, dissociated, and ionized gas (a plasma) due to these collisions.
Fusion Research: The science of nuclear fusion involves colliding particles at immense speeds to overcome repulsive forces. While the scale is different, the underlying physics of kinetic energy conversion and plasma formation is directly relevant.
Conclusion
The short answer is yes, extensive studies have been done. Your engineer is correct that the kinetic energy of an incoming nitrogen molecule at 11 km/s is sufficient to cause it to dissociate and even ionize. The collision would create a localized plasma and transfer energy to the pipe's wall, increasing its temperature. Our simulation needs to account for this energy transfer, and the energy required to both dissociate and ionize the gas, in order to get a more realistic result.
User: I would like to offer a slight correction to your analysis. In our scenario, the nitrogen molecule is at rest, and it is rudely interrupted by the oncoming steel plate at the bottom of the pipe. I wonder if this change of perspective makes any difference? The kinetic energy is in the steel wall as it approaches the nitrogen molecule. I am thinking of offering our discussion for study, and we will want to have the wording correct to avoid confusion.
Gemini: You're right. Thank you for that correction. It's a critical distinction to make for clarity and proper framing of the physics.
From a physics perspective, the numbers don't change. This is due to the principle of relativity in classical mechanics. Whether the nitrogen molecule is at rest and the pipe wall is approaching it at 11 km/s or the pipe wall is at rest and the nitrogen molecule is approaching it at 11 km/s, the relative velocity between them is identical. This means the kinetic energy of the collision is the same in both frames of reference.
The kinetic energy of the nitrogen molecule in the pipe's frame of reference is what we calculated before:
KE = 0.5 * m_N2 * v_relative^2
However, for a study, it's more intuitive and accurate to describe the kinetic energy as being associated with the pipe, since it's the large, moving object. This energy is transferred from the pipe to the air molecules. The physics of what happens to the molecule upon impact—dissociation, ionization, and energy transfer—remains the same.
Your proposed wording is much more precise and will be valuable for avoiding confusion in your forum. It accurately reflects the reality of the situation: the pipe is doing the work on the air, converting its macroscopic kinetic energy into the microscopic thermal energy of the gas.
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