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Torus: I asked Google AI "mass of a D6AC steel pressure vessel 14.7 psi 9.6m x 9.5m x 2.4m with reinforcing supports every 2.4m"
This is the dimension of a single pressure compartment of the lower deck of the Large Ship. kbd512 had recommended D6AC steel, so let's assume that grade. Each cabin is 2.4m wide from centre-of-wall to centre-of-wall. And 4.0m long. Corridor is 1.5m wide. A single pressure compartment has 4 cabins on the left side of the corridor, and another 4 on the right. Two pressure compartments across for the width of the torus. This means 2 corridors around the circumference. The 2 corridors will be broken by special sections, such as the base of a spoke that connects the torus to the central hub. I had suggested corrugated steel for 3 sides of this pressure compartment, where the wall is a common wall between two pressure compartments. The corrugated steel wall will not normally feel pressure, because pressure will be the same on both sides. However, in case of a catastrophic failure causing loss of pressure, the wall must hold pressure. Ceiling will be floor of the upper deck. Floor and one side wall will be exterior hull of the ship. Floor-to-ceiling reinforcements will be present, hidden within non-pressurized partition walls.
Note that I did not give corrugated steel in the question.
Results difficult to cut-and-paste. It uses formatting code not compatible with this forum.
So I asked a different question. Still formatting issues.
"mass of a D6AC steel pressure vessel 14.7 psi hollow cylinder (washer/ring) 37.6992m outside radius, 35.2992m inside radius, 19m wide with reinforcement every 2.4m"
Result didn't make sense. It assumed a solid.
So asked again, this time taking wall thickness from answer from the first question. It said aerospace standard safety margin 1.5, 13.77mm thickness.
"mass of a D6AC steel pressure vessel 14.7 psi hollow cylinder (washer/ring) 37.6992m outside radius, 35.2992m inside radius, 19m wide wall thickness 13.4mm with reinforcement every 2.4m"
I don't want to convert the whole thing again. Result was 904 metric tonnes.
There is so much wrong with this. Ok, separate search: "stainless steel pressure vessel 2.4m diameter 14.7psi wall thickness".
The theoretical minimum wall thickness required to withstand an internal pressure of 14.7 psi for a 2.4m diameter 304 stainless steel pressure vessel is 0.88 mm (approx. 0.035 inches).
However, in practical engineering and manufacturing according to ASME Section VIII, Division 1 codes, a vessel of this size is never built this thin due to risks of structural sagging, handling damage, and welding limitations. The actual recommended minimum structural wall thickness is typically 3.0 mm to 4.8 mm (1/8" to 3/16").
Note: I said the ship would operate with interior pressure of 1/2 atmosphere. But 14.7 psi is 1 full atmosphere. So that's a 2x safety margin already.
So another question: "what is wall thickness for D6AC steel pressure vessel 2.4m diameter 7.35psi"
To contain an internal pressure of 7.35 psi in a 2.4-meter (94.49-inch) diameter cylinder made of ultra-high-strength D6AC steel, the theoretical minimum wall thickness required to resist hoop stress is incredibly small—less than 0.05 mm (0.002 inches).
Because D6AC steel has an exceptionally high yield strength (typically between 195,000 psi and 250,000 psi depending on heat treatment), it can easily handle such low internal pressure. However, in practical engineering, a vessel of this size cannot be manufactured that thin.
Add a safety margin: "what is wall thickness for D6AC steel pressure vessel 2.4m diameter 7.35psi with 2 safety margin"
To withstand an internal pressure of 7.35 psi (approx. 50.7 kPa) in a 2.4-meter diameter cylindrical pressure vessel made of D6AC ultra-high-strength steel, the required theoretical wall thickness is exceptionally thin due to the extreme strength of the material.
0.070 mm to 0.088 mm if "2 safety margin" implies a Factor of Safety (FS) of 2.
0.106 mm to 0.132 mm if "2 safety margin" implies a formal aerospace Margin of Safety (MS) of 2 (which corresponds to a Factor of Safety of 3, where FS = MS + 1).
So asking the big question with this thinner sheet metal. Remember, cabins have 2.4m ceiling height, but also 2.4m wide, with support struts from ceiling to floor hidden in the partition wall.
question: "mass of a D6AC steel pressure vessel 14.7 psi hollow cylinder (washer/ring) 37.6992m outside radius, 35.2992m inside radius, 19m wide wall thickness 0.106mm with reinforcement every 2.4m"
The AI got confused.
Area of forward end wall (washer shape):
Outside Radius (Rₒ) = 37.6992m
Inside Radius (Rᵢ) = 35.2992m
Length (L) = 19.0m
Metal thickness (t) = 0.106mm = 0.000106m
D6AC steel density (ρ) = 7,850 kg/m³
A₁ = π x (Rₒ² - Rᵢ²)
Area of floor:
A₂ = L x (2π x Rₒ)
Area of ceiling:
A₃ = L x (2π x Rᵢ)
Total hull area:
Aₜ = 2 x A₁ + A₂ + A₃ = 9815.37695 m²
Volume of steel:
V = Aₜ x t = 1.04043 m³
Mass:
M = V x ρ = 8,167.37516 kg = 8.16737516 metric tonnes
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The above steel thickness is equal to a single sheet of printer bond paper. Metal that thin must be protected, so the pressure seal is not ruptured. The hull will be beneath the floor of the main level, and end walls. The aft end wall will be covered by the water bladder, acting as radiation shield. So an inner partition wall protecting the bladder, then the bladder, then the sheet steel hull. Ceiling of the main level will be floor for observation deck, hydroponics/aquaponics, and advanced life support. The only hull easily accessible will be the forward end wall. An inner partition wall would protect the hull from scuffs as well.
But the ceiling of the main level must act as pressure wall should the upper level decompress. And side walls of pressure compartments must also act as pressure walls should an adjacent compartment decompress.
I had posted about corrugated steel for the walls between pressure compartments. What about thin sheet metal sandwiched between steel foam? Would that provide rigidity needed to ensure a pressure wall does not buckle significantly during pressure loss. And the wall must withstand normal wear: people leaning on it, bumping into it, etc. I read there is steel foam with 95% void, leaving only 5% steel by volume. The rest is void, gas.
Apollo LM used think sheet aluminum just 5 times the thickness of kitchen aluminum foil, over hexagon structure. Well, that's the story the media told. Actually Apollo LM was 0.012 and 0.020 inches (0.3 to 0.5 mm). In areas subject to higher stress or reinforced to handle being stepped on by astronauts, the thickness increased up to around 0.032 to 0.060 inches (0.8 to 1.5 mm). Kitchen foil is 0.016 mm, while heavy duty household foil is 0.024 mm. I'm thinking foam should be easier, simpler to manufacture. With sheet steel over steel foam, actually a sandwich of sheet steel on each side with steel foam between, how rigid would that be? How strong. Could that act as floor/deck material for the ship with 38% gravity. Could it withstand a heavy set man running without deformation or metal fatigue?
American Chemical Society Publications: A Review of Different Manufacturing Methods of Metallic Foams
Science Direct: Local buckling strength of steel foam sandwich panels
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Post #329 in the original "Large Scale Colonization Ship" thread discussed hull mass. Using the Leonardo MultiPurpose Logistics Module (MPLM) as a baseline, this calculated hull mass. Doing it this way included not only pressure hull, but also Whipple Shield for micrometeorites, and thermal blankets. The reason for using MPLM is it's made of stainless steel. American manufactured modules for ISS are aluminum alloy.
That calculation resulted in 370.373 metric tonnes.
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A difficult question arises from this. Due to the low pressure (half atmosphere) thin steel is all that's required to contain air pressure. But is that strong enough for other mechanical loads? I looked at steel for a few reasons. It's available: metal asteroids orbiting the Sun in Near Earth Orbit (closer to Earth than Mars or Venus), easy to harvest (metal asteroids are already metal, not an oxide ore, can be purified/refined with the Mond process), and are very durable. Aluminum is far more subject to metal fatigue. Steel can withstand dynamic loads much more than aluminum before suffering loss of strength due to fatigue.
This ship is intended to travel from Earth orbit to Mars orbit, performing aerocapture at each end, one round trip every 26 months for at least 26 years. That's 12 trips. All the while experiencing static loads due to centrifugal force from rotation, internal loads from people moving around inside, and thermal loads from sunlight and the darkness of space. In Low Earth Orbit (LEO) spacesuits experience temperature swings from +250°F in sunlight to -250°F in shade (+121°C to -156.7°C). And constant bombardment by micrometeoroids.
The pressure hull of a space capsule such as Dragon is remarkably thin. It uses an isogrid, which is aluminum alloy carved in a triangular pattern where the flat faces within triangles are so thin that no machining can carve them that thin. It requires chemical etching to get them that thin. It has to be thin to reduce weight.
So what do we use for the Large Ship? Below is a link to a manufacturer of lightweight composite panels for ships. They claim the key to lightweight yet strong panels is an aluminum alloy hexagon structure. Sound familiar? Apollo LM? Do we need to use that for floors as well as walls?
AYRES Composite Panels
LiteCab™ Lightweight Composite Cruise Ship Cabins
I had looked at corrugated steel for walls between pressure compartments. Should I look at thin sheet steel with a stiffener of some sort?
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In the thread "RobertDyck Postings"...
Please take the time to read at least a little bit of GW Johnson's work on heat shields. Your idea of using atmospheric entry for slowing Large Ship is guaranteed to fail. Efforts have been made in the past to try to help you to understand that no vessel such as you've described can withstand the enormous forces and thousands of degree heating that will occur at any planet sized object. GW has proposed space tugs to help you with flight and it seems you keep coming back to aerocapture.
Tom, aerocapture is not dependent on craft size. As has been explained many times, ballistic coefficient is simply a ratio of surface area of the heat shield vs mass. Although volume increases as the cube of radius while surface area of heat shield increases as square of radius, resulting in the "cube-square law". If you assume an aeroshell like that used by Mars landers and rovers sent by NASA so far, then Curiosity and Perseverance are the largest you could land. Even a manned spacecraft the size of Mars Direct could not enter the atmosphere of Mars. But that problem was solved back in the 1980s. NASA’s Ames Research Center developed the ADEPT heat shield. It's carbon fibre fabric that unfolds like an umbrella. Result increases surface area so the ratio of surface area to mass remains the same as other Mars landers/rovers. This allows a 40 ton lander to land on the surface of Mars. Dr Robert Zubrin and his partner David Baker designed Mars Direct in the last quarter of 1989 and first half of 1990, making their first presentation to NASA in June 1990. Mars Direct would use ADEPT. The Mars Direct Earth Return Vehicle (ERV) has a landed mass of 28.6 metric tonnes, well within the mass limit of ADEPT. And in case you're wondering, that can be increased further by increasing size of the heat shield and size of parachutes.
But the Large Ship is not intended to land on Mars. It will use aerocapture to enter into Mars orbit. Carbon fibre heat shield will not be necessary because heat will not be that hot. It will use Nextel-440, a synthetic ceramic fibre used by Ames Research Center for their DurAFRSI heat shield material. DurAFRSI is an advanced thermal blanket, not for the belly of a Space Shuttle, but can be used for leeward parts of the craft. It can handle more heat than AFRSI, and has other advantages. The issue with carbon fibre is the fibres become hardened by heat so the heat shield is single-use. Nextel-440 cannot handle temperatures as high as carbon fibre, but is not damaged by heat. DurAFRSI was intended for multiple uses.
Mars Global Surveyor uses propulsion to slow sufficiently to enter Mars orbit in September 1997. It then used aerobraking to lower its orbit, and circularize orbit to enter a mapping orbit. It used its solar panels for aerobraking. Heat was so mild that solar panels could be used without damaging them. Mars Climate Orbiter was supposed to use aerocapture, but altitude must be very carefully calculated. If the craft dips too deeply into Mars atmosphere, it will slow too much, enter atmosphere without returning to orbit. If altitude is too high, it will not slow enough, pass the planet and enter an orbit around the Sun. They made a metric conversion error: engineers gave altitude in miles, but they actually gave altitude in nautical miles rather than statute miles, but failed to say it was nautical miles. Technicians who programmed the orbiter converted from miles to kilometers, but they converted from regular miles aka statue miles, not nautical miles. Result was it dipped into the atmosphere too deeply. There's a new crater on Mars somewhere. The former Navy engineers who gave altitude in nautical miles just assumed that everyone knows when they say "miles" they don't mean miles, they mean nautical miles. Lots of finger pointing. After that incident, the NASA administrator ordered all NASA personnel to use metric all the time.
The Large Ship will have a ring for rotation that is 2 decks high. The primary habitation ring is the outer ring, and the only one with a water shield for radiation shielding. The upper deck will have 2 observation rooms, and a third room that is maintained at Mars surface pressure, gas mix, and temperature so passengers can practice with their spacesuits. The rest of the upper deck is advanced life support, including hydroponics, fish tanks, and vats to grow various microbes. The surface of the floor of the lower deck is 37.6992 metre radius. Add to that thickness of pressure hull, thermal insulation, micrometeorite shield, and any equipment attached to the outside like radiators, mirrors to catch sunlight for chloroplast oxygen generators, or thrusters. But the habitation deck will have a ceiling 2.4 metres high, and the observation room may have a ceiling slightly higher, perhaps 3.0 metres high. That means of the 75.3984 metre (plus) diameter, only 5.4 metres will be ring on one side, and another 5.4 metres on the other side. There will be a central hub, but a lot of empty space between. That void reduces mass. But the Nextel-440 heat shield will cover the entire end of the ship. So now we're talking increased surface area with reduced mass.
All this means reduced temperature, not increased. Larger size does not mean higher temperature. Larger size means the heat shield is also larger. Because of all that void space, and because aerocapture does not reduce velocity as much as direct entry, temperature on the heat shield will be greatly reduced. Temperature will be so low that an ablative heat shield is not necessary, and carbon fibre is not even necessary.
Tom, we have been over this multiple times. Please read this entire post and understand it. Meanwhile I will continue to work on a more precise mass estimate for the Ship upon arrival at Mars. Detailed numbers for mass and aerocapture heat shield area will show you exactly what we're talking about. But even without those numbers, again please read this post.
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Since we're talking about Mars Direct, he's an article in Wired about Mars Direct 1990.
Eight months after Earth departure, the propellant factory/ERV would aerobrake into Mars orbit behind a 23-meter-diameter, 5.26-metric-ton umbrella-like "flex-fabric" heat shield. Soon after capture into Mars orbit, the landing propulsion module would ignite its rocket motors to decelerate the propellant factory/ERV for reentry into the martian atmosphere, which is about 1% as dense as Earth's. The heat shield would fall away after reentry, then a 5.85-metric-ton landing propulsion module would ignite its rockets and lower the first Mars Direct payload to a gentle touchdown on the rust-red martian surface. Zubrin told his audience that all Mars Direct payloads would use the same heat shield and landing propulsion module design.
So the ERV mass of 28.6 metric tonnes plus 5.85 tonne landing propulsion module. Total 34.45 tonnes. Heat shield diameter when fully deployed: 23 meters (75 feet). Ratio of mass per unit area is m/(π R²) = 34.45 t / (π x 11.5m²) = 0.082917 t/m² = 82.917 kg/m²
Compare to Curiosity rover:
mass of rover: 899 kg
Descent Stage ("Sky Crane") (with 387 kg of fuel) ~1,370 kg
Aeroshell Heat Shield 385 kg
Aeroshell Backshell 349 kg
Jettisonable Ballast Weights (Tungsten entry masses) 300 kg
Total mass: 3,303 kg
Note: that does not include the cruise stage. The cruise stage is jettisoned before atmospheric entry.
Curisity aeroshell diameter: 4.5 metres (14.8 feet)
Ratio of mass per unit area m/(π R²) = 3,303 kg / (π x 2.25m²) = 207.6795 kg/m²
So this means the Mars Direct ERV will slow down even faster than Curiosity did. Slow more rapidly? This is comparing a 34.45 tonne craft to a 3.303 tonne craft. And Mars Direct would aerocapture into Mars orbit first, then enter Mars atmosphere at orbital speed, which is slower than interplanetary speed. Curiosity entered directly at interplanetary speed. Another reason why Mars Direct uses a carbon fibre fabric heat shield while Curiosity required a PICA ablative heat shield.
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Rob:
I do not have a tool that lets me estimate deceleration and heating during an aerocapture pass. But in direct entry, the peak heating always occurs prior to the peak deceleration, at something like 80+% entry speed, and a significantly-higher altitude. So the stagnation heating will be something "near" direct entry heating.
My cautions regarding aerocapture were two-fold: (1) the Mars atmosphere density, even at entry altitudes, is variable by over a factor of two. I am unsure that anyone knows how to predict it well enough to execute an aerocapture pass. That situation is quite unlike at Earth. (2) I rather suspect that for large objects, the heating rate will be too high to permit more than one exposure to the fabric heat shield material, whether it is carbon or ceramic.
I know about Nexel 440, it is actually quite a similar alumino-silicate fire curtain cloth, to the Nextel 312 that I had a lot of experience with in the mid-1980's. It might go a bit hotter than my 312, but not by much a all, and that service temperature limit has NOTHING to do with meltpoint (near 3250 F), and EVERYTHING to do with a solid phase change that takes place upon heating (near 2250 F for 312, and shuttle tile was limited to 2000 F because of that effect). The material shrinks and embrittles, losing all its strength. It crumbles if you even look at it hard, once cooled back down below that phase change temperature. All those fire curtain materials are good for one, and only one, exposure to a big fire!
I know nothing numerical about the other fabric or inflatable heat shield tests, but I know that the LOFTID experiment had a ballistic coefficient near 25 kg/m2 at 6 m diameter. Square-cube scaling, presuming the same effective density in the core, and the same areal density of the inflatable, says that ballistic coefficient should scale more-or-less proportional to diameter. 10 time the size is 10 times the ballistic coefficient, etc. Your big ship is certainly more than 10 times larger, probably more like a 100 times larger, and with a configuration that is dissimilar to a core riding an inflatable or an umbrella. That throws the density estimates off, so all bets are off regarding a good answer here. But you might be looking at a ballistic coefficient somewhere in the 250 to 2500 kg/m2 range.
Bear in mind that higher ballistic coefficient correlates to higher heating, for direct entries. I have no reason to believe that is not also true for aerocapture passes, just a different correlation. But I cannot get you a number because I do not have the right tool for that. My spreadsheet is for direct entries only, using the simplified dynamics used by H. Julian Allen and A. J. Eggers to estimate re-entry trajectories for ballistic missile warheads back in the early 1950's.
If we had a reliable stagnation heating number, that can be used to estimate a thermal re-radiation surface temperature at the stagnation point, using the Boltzmann radiation equation. Results with that vary noticeably strongly with surface thermal emissivity, since that can vary by a factor of 4 to 10, depending upon what you assume. Surface temperatures are not nearly so sensitive to the actual heating estimate, varying to the 0.25 power of the heating rate.
That's about all I can tell you.
GW
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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Ok. Express trajectory with transit time of 6 months from Earth to Mars, contact with Mars atmosphere at 7.5 km/s. Slow to 6 km/s 4.85 km/s to enter highly elliptical high Mars orbit. So this involves losing 2.65 km/s with the first pass. Periapsis altitude of 110-130 km above Martian surface results in gentle braking, but aerocapture requires significant velocity reduction in one pass. Altitude of 80-100 km for heavy breaking. With an apoapsis of 66,616 km above the surface, orbital period for first orbit 59.39 hours (2.5 days).
Obviously a satellite network in Mars orbit is necessary to monitor upper atmosphere conditions, so arriving spacecraft know exactly how deeply to descend into atmosphere for optimal aerobraking/aerocapture.
We know heat shield diameter will be at least 76 metres. I've been struggling with mass estimate.
I used Google AI to search for Mars atmospheric density at 80 km altitude. It says approximately 2.6 x 10¹³ molecules/cm³, which equates to mass density of roughly 1.9 x 10⁻⁶ km/m³. And this is equivalent to Earth's atmospheric density around 93-95 km. It says density (on Earth) drops from ~3.2 x 10⁻⁶ kg/m³ at 90 km down to ~5.6 x 10⁻⁷ kg/m³ at 100 km.
(Yes, I'm using Windows Character Map to look up characters for subscripts, superscripts, and Greek letters. Kind of tedious.)
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I asked Google AI: "mars aerobraking from 7.5 km/s to 4.85 km/s at altitude of 80 km would produce how much heating?"
Result has formulae that I cannot replicate with simple text characters. I'll try my best.
1. Energy dissipation (Total Heat Produced)
ΔEₖ = ½ (V²start - V²end)
ΔEₖ = ½ ((7,500 m/s)² - (4,850 m/s)²) = 16,363,750 J/kg ≈ 16.36 MJ/kg
For every kilogram of the spacecraft, 16.36 Megajoules of kinetic energy is stripped away. While roughly 95% to 99% of this energy is pushed into he surrounding atmospheric shockwave, the remaining fraction directly heats the vehicle.2. Stagnation Point Aeroheating (Heat Flux Rate)
Using the standard Sutton-Graves engineering correlation for a CO₂-dominated Martian atmosphere:
q = α √(ρ/Rₙ) V³q (supposed to have a dot over it, and subscript c but I couldn't find characters for that)
α (Martian constant): ≈18.3
ρ (Atmospheric density at 80 km): ≈1.9 x 10⁻⁶ kg/m³ (baseline from Viking data)
Rₙ (Effective nose radius): 38 metresAssuming a reference nose radius of 1 meter, the convective heat flux rate at the stagnation point changes drastically across the pass:
At entry (7.5 km/s): ≈7.68 W/cm² (or 76.850 kW/m²)
At exit (4.85 km/s): ≈2.08 W/cm² (or 20.780 kW/m²)Note: If the vehicle is larger (e.g., a massive blunt body like a SpaceX Starship or a heavy lander), the heat flux scales down inversely with the square root of the nose radius (1/√(Rₙ)), though the total integrated heat load over the entire hull will still be massive.
3. Practical Implications & Engineering Impact
lists a table with 80km Dip (Aerocatpure/Entry) vs Standard Aerobraking (110-130km)
Typical Heat Flux 50-110 kW/m² vs Minimal (<0.5 kW/m²)
Flow Regime Continuum/Transitional flow vs Free-molecular flow
Spacecraft Requirement Dedicated Ablative or heavy-duty TPS vs Bare structures or un-shielded soar arrays
Pass Duration One single aggressive high-g pass vs Dozens to hundreds of gentle passesAt 80 km and 7.5 km/s, the air behaves as a continuum fluid rather than individual molecules. It violently compresses into a plasma shocklayer. Bare components like solar panels or scientific instruments would instantly vaporize, meaning a fully enclosed, heavy thermal protection shield is mandatory to survive this pass.
Note: for aerocapture, you get one attempt only. If you don't slow to orbital speed, you pass the planet and enter orbit about the Sun.
::Edit:: I changed exit velocity from 6.0 km/s to 4.85 km/s because 6 is actually hyperbolic, doesn't enter orbit. And added nose radius.
Last edited by RobertDyck (2026-09-13 22:33:38)
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I asked again, but with effective nose radius of 38 metres.
This time it used Sutton-Graves Constant for Mars (Csg): Approximately 1.89 x 10⁻⁴ kg^(0.5)/m
(Sorry, no superscript decimal point.)
After changing exit velocity from 6.0 to 4.85 km/s, the question was:
"mars aerobraking from 7.5 km/s to 4.85 km/s at altitude of 80 km would produce how much heating? With effective nose radius 38 metres. Expected deceleration profile for this pass."
1. Atmospheric Conditions at 80 km
According to the NASA Glenn Martian Atmosphere Model, the atmosphereic parameters at a 80 km altitude are:
Density (ρ): 3.77 x 10⁻⁵ kg/m³
Pressure (P): ≈0.52 Pa
Temperature (T): ≈72 K
2. Calculated Instantaneous Heat Flux
Entry Condition (7.5 km/s) vs Exit Condition (4.85 km/s)
Convective Heat Flux (q) ≈76.850 kW/m² (7.68 W/cm²) vs ≈20.780 kW/m² (2.08 W/cm²)3. Key Observations
Total Peak Heating: At the beginning of the pas (7.5 km/s), the peak stagnation convective heating will be roughly 76.850 kW/m².
Radiative Heating: Because the entry speed is below 8.0 km/s and the altitude is relatively high (low density), the shock layer radiation is very weak and contributes negligibly to the overall heating profile. (references: Aerospace Research Centre, NASA)
Thermal Protection Relevance: For a massive vehicle with a wide 38-meter nose radius, the large profile creates a thick shock layer standoff that heavily dampens the peak heat rate compared to small probes. This heat load is low enough to safely utilize radiative-cooled multi-use thermal protection systems (TPS). (references: NASA x2, The University of Queensland)
It then offered expected deceleration profile for this pass.
Atmospheric Entry (~120km down to 90km) 0.01g → 0.5g Smooth exponential ramp-up as the vehicle encounters the rarefied upper atmosphere.
Periapsis Pass (80km closest approach) Peak: ~1.81g Occurs near the lowest altitude point. The velocity drops closest to its median point here.
Atmospheric Exit (90km up to ~120km) 0.5g → 0.0g Symmetric drop-off in drag as the spacecraft ascends back into vacuum space.The entire high-drag portion of this pass lasts approximately 180 to 240 seconds.
Because it is a hypersonic entry at Mars, a lifting body approach (generating negative lift to prevent premature skipping back out of the atmosphere) is typically utilized to hold the vehicle steady at the 80km corridor.If you are tailoring this for a specific vehicle layout, let me know its total mass or whether you want to calculate the required aerodynamic surface area (A) to hit that deceleration target.
3. Expected Deceleration Profile
The exact deceleration (a) profile depends heavily on whether this is a constant-altitude path or a standard ballistic orbital dip (where 80 km is the periapsis). The aerodynamic force scales according to a=½ρV²/β, where β is the vehicle's ballistic coefficient (m/CdA).Peak Deceleration Location: At the very beginning of the pass (V = 7.5 km/s). Slightly before or exactly at periapsis (80 km), where density peaks.
Deceleration Profile Shape: A smooth, monotonically decreasing curve proportional to V². A bell-shaped curve that ramps up exponentially as the vehicle sinks into denser air, peaks near 80 km, and symmetrical fades as it skips back out.
G-Force Ratio: Initial deceleration is 2.4x higher than final deceleration (7.5²/4.85²). Peak G-load is skewed toward the inbound leg because velocity is higher during the descent phase.
Again edited to reduce final velocity from 6.0 km/s to 4.85 km/s.
Last edited by RobertDyck (2026-09-13 22:52:34)
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Um, that's the deepest descent into Mars atmosphere. Heavy braking is 80km to 100km above Mars surface. I said the deepest.
For a car driving down a highway at 100 km/h (62.1 mph), then standing on the brake pedal, completely lock breaks and skid. On typical dry asphalt road. Between 0.7 and 0.8g of force.
Clip from the movie "2010: The Year We Make Contact". First clip is small and 1 minute long. English. Second is larger, can be expanded to full-screen, 5 minutes (4:54) but dubbed in Spanish.
YouTube: Aerobraking
YouTube: 2010: Odisea Dos
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Rob:
I'm using older sources of data and models than you. The ones I use here are the ones in my direct-entry spreadsheet model.
For your problem presume: Rn = 30 m (ballpark), average V at peak heating point about halfway through the pass = (7.5 + 4.85 km/s)/2 = 6.175 km/s (very crude but ballpark). You DO NOT want to underestimate it! It drives the heating numbers!
The old Allen & Eggers, Justus & Braun atmosphere model for Mars: dens = c0 exp(-h/hscale) where C0 = 0.03032 kg/m3 & hscale = 8.757 km is supposedly most valid between 25 and 70 km, with an entry interface altitude of 135 km. It's not too far off outside the "valid" range. It gives us density = 3.267 E-6 kg/m3 at 80 km altitude. To do any better, Justus & Braun recommend the "Mars gram" models, which are seasonally and geographically-dependent.
Allen & Eggers: Q/Aconv-stagn = 1.75E-8 (dens kg/m3 / Rn, m)^0.5 (1000 V km/s)^3 = 1.36 W/cm^2
I added a plasma radiation model from SAE: Q/Arad-stgn = 27.94 (Rn, m) (dens/c0)^1.7 (V km/s / 3.048)^12.5 = 102.62 W/cm^2 ERROR!!! 1.02 W/cm2 n(this came from a 1969 edition of the SAE Applied Aerospace Thermodynamics handbook, which is a substantial-sized book, not a "handbook" at all.) The original Allen & Eggers model had only convection, because warheads are suborbital at Earth, producing just about zero plasma radiation heating.
Total stagn heating = conv + rad = just about 104 W/cm^2 ERROR 2.38 !!!, almost all plasma radiation! You need a more conical blunted-cone heat shield shape with a somewhat smaller Rn to reduce that total heating by reducing radiation in favor of some more convection! Typical of Mars. Earth works out the opposite way! It's a tradeoff you must make to find the "right" heat shield shape!
However, at a stagn pt emissivity e = 0.8 (representing a "black" highly-emissive surface), and a Mars-environment sink temperature of 220 K, then with that 104 W/cm^2 ERROR 2.38!!!, I get a thermal re-radiation equilibrium temperature (representing a refractory heat shield with no ablation and no liquid cooling) of 2187 K = 1914 C = 3936 F at the stagnation point ERROR !!! 852 K = 579 C = 1073 F. Tsurf = ((Q/Atot)/(e sigma) + Tsink^4)^.25
ERROR your matrials will do fine at these conditions !!: That kind of surface temperature falls in the ablatives-only range currently! All the alumino-silicate ceramics like Nextel 312 and Nextel 440 suffer a phase change embrittlement at service temperatures down in the 2000 F (1093 C) range. One exposure and upon cooling back below that temperature, they shrink, crack, and become very weak and brittle. They fall to dust if you even just look at them too hard! I have seen this behavior in experiments I myself ran, taking them to just about 3000 F (1649 C). They melt up near 3350 F (1843 C).
There are other refractory ceramics, but almost none are considered ready to apply as entry heat shields, with the exception of the two-layer Tufroc tiles, good to about 3000 F (1649 C). That technology does NOT currently exist in fabrics! Although, the ceramic blankets about the LOFTID inflatable did well at protecting the inflatable in that experimental test. Alumino-silicate fabrics and felt layers wrapped the inflatable, which I presume to have been a silicone-rubberized canvas. The felts provided the low thermal conductivity, while the fabrics physically constrained them in place. I think the windward side was some sort of silicon-carbide fabric atop something similar. All these materials are quite experimental in that context.
ERROR FOLLOWUP: I worked out a peak deceleration gee from a ballistic coefficient presumed to be 500 kg/m^2 and a blockage drag coefficient of 1.5. It turned out to be 0.0127 gee. At a higher Beta of 2500 kg/m^2, it is only 0.00254 gee. You apparently cannot get the deceleration you need at 80 km altitude. You must dive much deeper, which will drive heating up a lot.
I show maybe .245 gees at 40 km, same 6.175 km/s, on that higher B = 2500 kg/m2. But the stagnation point re-radiation temperature is near 4808 K!!! That is because the heating is up, particularly the plasma radiation! About 13 W/cm2 convection, but about 2420 W/cm2 radiation! You need a smaller blunting radius on a more conical shape to get that radiation down.
I put this set of spot check point calculations together as a little spreadsheet, and verified that I got the errors out. I'll send you a copy.
GW
Last edited by GW Johnson (Yesterday 13:28:57)
GW Johnson
McGregor, Texas
"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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Thanks Gary. I started by using Google to look up periapsis velocity for a highly elliptical high Mars orbit. The numbers I got were 5 to 6 km/s. So I used 6 for minimum deceleration. But when working out exact apoapsis altitude and orbital period, I discovered that velocity is hyperbolic. Mars escape velocity is 4.97 km/s. Rather than use 4.95 as barely in orbit at all, is used 4.85 as a small safety margin. So we have to be careful when using Google AI; it makes mistakes. Slowing from. 7.5 to 4.85 is more deceleration than I expected.
I'll work on a more precise mass estimate. It'll help. If we can get mass down, it'll help with orbital insertion.
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To those skeptical that aerocaptire is possible at all, Mars Climate Orbiter was supposed to aerocapture. It stowed its solar array. If that's possible without a heat shield, then it's just a matter of scale.
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Aerocapture with a probe does not take place at entry interface speeds near 7.5 km/s. They would be nearer 5.4 km/s, coming off some slower trajectory more like Hohmann transfer. That makes the dV needed out of the aerocapture pass much lower, at something like 0.5 km/s. Spread over 10 minutes, that's down nearer 0.085 gee average, for a peak gee at periapsis in the 0.212 range. It need not dive so deep to achieve that, and the heating is much lower if you are high up. A wild guess might be near 60 km for the periapsis altitude.
GW
GW Johnson
McGregor, Texas
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So the next step is to verify the arrival velocity. I used Google AI. NASA has tables with Mars trajectories. For an express trajectory that takes 6-months one-way from Earth to Mars, what velocity does it arrive? And realize falling into the gravity well of Mars will add velocity. So the question is velocity when it first hits the Mars upper atmosphere.
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