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#276 2020-10-07 11:12:08

kbd512
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Registered: 2015-01-02
Posts: 7,414

Re: Mission to Venus

tahanson43206,

The atmospheric pressure at the altitude that these blimps would operate at is essentially the same as Earth Sea Level, except that the nearly pure CO2 Venetian atmosphere would provide more buoyancy for an easier-to-come-by gas such as O2 or O2/N2 mix.

The lift coefficient for 1,000 cubic feet of Helium lifting gas, according to the K-Type Airship Pilot's Manual, is given as follows:

L = CP * (1325/Ta) - (185/Tg)

If no significant heating of the lifting gas, then L = 1140 * (CP/Ta)

USN K-Type Airship Pilot's Manual

More info on lifting gases:

Sitting on Cloud Nine: Airship Lift and Altitude Control

Based upon the numbers provided in the link above, 945m^3 for lifting 1,000kg using Helium, at sea level, agrees quite well with what Calliban stated.  However, 1m^3 of CO2 is 1.98kg/m^3 at STP, so 1kg of hot O2/N2 (air) would provide 70% as much lifting force as Helium at STP conditions, but without the hassles of light gases.  If we could figure out how to use steam effectively on Venus, then we could potentially generate more lifting force at Venus "sea level" (50km in altitude) than we can at Earth sea level using Hydrogen gas.  If we were dead set on using Hydrogen, then we would get substantially more lifting force on Venus.

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#277 2020-10-07 17:33:17

tahanson43206
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Registered: 2018-04-27
Posts: 17,039

Re: Mission to Venus

For kbd512 re #276

Thank you for your detailed and helpful follow up regarding balloon operation in the Atmosphere of Venus

SearchTerm:VenusBalloon Specifications by kbd512 http://newmars.com/forums/viewtopic.php … 27#p172927

i'm setting this post for a reply after I've had a chance to go back and look at the Science article about the recent Analog yarn featuring Venus.

The author imagined a wide variety of balloon habitats, from small family sized ones to much larger community ones funded by corporations.

The author took pains (pun recognized but pushing on anyway) to show the presence of sulphuric acid, and offered practices that his characters used to deal with it.  The author made clear that the residents who were living on the edge financially were likely to be scarred with acid burns due to deterioration of their habitat suits and resulting leaks.

One speculative aspect of the yarn was the hypothesis that life might have found a way to gain a modest foothold in the complex atmosphere of Venus.

All that said, the aspect of the writing that stays with me is the imagination of the beauty of the cloud layers, with sunlight streaming down through a great variety of conditions.  The author used the rapid movement of the atmosphere to provide for changes of scene the residents would experience.

My brief report about the subject is here: http://newmars.com/forums/viewtopic.php … 02#p171702

(th)

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#278 2020-10-08 08:02:30

tahanson43206
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Posts: 17,039

Re: Mission to Venus

This is a follow up to a post by kbd512 (#276 )

In that post kbd512 showed how much lift might be expected for balloons in the atmosphere of Venus.

Design of a habitat suitable for a small group to be floated in the atmosphere of Venus should be within the existing capability of the people of Earth.

Design of a habitat suitable for a large community may be outside the existing capability on Earth, but there are no laws of physics (that I am aware of) that would preclude creating of such an artifact.

One consideration that seems reasonable (to me at least) is that any community structure should be composed of loosely bound independently suspended elements.   These could be networked with light weight webbing, capable of gently managing the constant flexing that would be a characteristic of the environment, and therefore of the structure suspended within.

SearchTerm:Todo Image Venus Community Balloons holding habitats linked by web of lightweight components

In the September/October 2020 issue of Analog, Derik Kunsken provided a Science Fact article about the research he had done before writing his recently published three part series on Venus, entitled "The House of Styx".

The science article is six pages long, printed in fairly dense font, so I'll just excerpt a single paragraph:

The cloud layer from 55 km to 56 km would e a sweet spot for colonists. This altitude has a temperature of about 25 degrees C and a pressure of about half an atmosphere.  That's about the same pressure as the summit of Mount Kilimamjaro (5,895 m). Interestingly for colonists, our atmosphere (78% nitrogen, 21% oxygen) is lighter than CO2 -- so a balloon of Earth-composition air would not only be breathable, but buoyant.  A lot of space exploration plans have looked at how habitats floating in the clouds of Venus could work.

A reasonable concern colonists might have is the constant risk of losing buoyancy and falling into the abyss.  But that is not different from the concern any person out on the open water in a boat might have, with the notable difference that on Earth, a person who loses the buoyancy of a ship can still hope to float.  That option would not be available on Venus.

Derik Kunsken provided a variety of safety devices for colonists in his story, and gave the possibility of free flight a careful study.  I note that a critical capability of small, powerful jet engines was a part of Kunsken's vision, but those were not needed most of the time, since the vigorous movement of the atmosphere of Venus is likely to provide plenty of updrafts for free flyers to catch for positive elevation.

(th)

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#279 2020-10-08 08:18:04

Calliban
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From: Northern England, UK
Registered: 2019-08-18
Posts: 3,408

Re: Mission to Venus

I would suggest a flattened (oblate) spheroid geometry for a habitat.  The habitat is non-pressurised, so we are talking about using the buoyant force of trapped air acting on the upper surface of the habitat to support mass that will somehow hang from it.  The most mass efficient structural solution is the one that avoids large unsupported spans.  The roof would be a triangulated steel lattice work.  Glass plates would cover the steel structure on the outside and plastic tensile sheet would transfer buoyant force to the steel frame on the inside.

The habitation decks would be cantilevered steel structures that would hang from the roof frame at regular intervals using basalt fibres.  The cantilevers would be braced together allowing them to transfer load during replacement of basalt fibre rope supports.  A modular structure allows individual structural elements to be replaced as a result of wear or fatigue.

The habitat will contain a flexible bladder, allow outside atmospheric gas to expand in and out, as pressure changes.  Buoyancy could be trimmed by regulating temperature of the air within the habitat.

Most of the structural strength will be be provided by basalt fibres.  Basalt is a material that can be mined from the Venusian surface by grabbing loose rocks.  Glass is silicon dioxide with other inclusions to moderate melting point.  Polymers can be produced from atmospheric CO2 and hydrogen derived from sulphuric acid.  Iron can be produced by reducing iron oxides in surface materials.

A spheroid habitat 1km in diameter a 500m in height would have total lift of about 200,000 tonnes for a median deck area of 785,000m2.  This means that mass per unit deck area, including structure, must be no greater than 250kg/m2.  A floating habitat would have to pay careful attention to weight of individual components and the distribution of weight.

Last edited by Calliban (2020-10-08 08:31:19)


"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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#280 2020-10-08 11:17:48

tahanson43206
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Posts: 17,039

Re: Mission to Venus

For Calliban re #279

Nice!  SearchTerm:Venus Oblate Spheroid habitat http://newmars.com/forums/viewtopic.php … 40#p172940

Management of mass distribution in the habitat you've described reminds me of the similar problem RobertDyck will be facing, when he gets around to thinking of the dynamics of rotation of his Large Ship concept.  His vessel is going to be subject to constant movement of personnel and materials inside (and outside) the structure, which is going to be rotating once every 20 seconds.

The problems to be solved are so similar, I can envision a collaboration between the teams working on the designs.

***

There is a probe "opportunity" at Venus that catches my attention ... it would be a balloon that rides above the tops of the clouds, and moves with the fierce winds that circle the planet every four days.

Such a probe would have to use Hydrogen for lift, if it is even possible.  While there wouldn't be much to see in the optical spectrum when looking down at the clouds (I could be wrong of course), such a probe could provide a platform for sensors able to work at the slower pace afforded by location in the atmosphere.

***
Please continue developing your concept of the large habitat. 

(th)

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#281 2020-10-08 13:35:20

tahanson43206
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Registered: 2018-04-27
Posts: 17,039

Re: Mission to Venus

For kbd512 re topic (following up on 276 with variation) ...

I'm trying to get fall chores done, and I keep thinking of discussions in this forum ...

Here's the latest .... solar powered aircraft are a (reasonably) well established technology on Earth.  We've had one complete round-the-world flight with a single passenger aircraft, and we've seen a number of demonstrations of solar powered flight in test cases for possible commercial application, as well as possible military ones.

The recent discussion of conditions in the upper atmosphere of Mars leads me to wonder if a solar powered aircraft could operate in the clear air above the tops of the uppermost cloud layer.  Because of the wind conditions in which such a vehicle would operate it might not be able to stay in sunlight, but (I at least) don't know enough about wind patterns at that altitude to know if an automated craft could navigate successfully so as to stay in sunlight.

(th)

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#282 2020-10-08 18:56:05

GW Johnson
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From: McGregor, Texas USA
Registered: 2011-12-04
Posts: 5,455
Website

Re: Mission to Venus

For a dirigible or blimp,  the lift gas is in pressure equilibrium with the surrounding atmosphere.  Unless energy is expended otherwise,  it will also be in temperature equilibrium with the surrounding atmosphere.  What that means is the density of the lift gas and the surrounding atmosphere are both proportional to their respective molecular weights,  assuming both are far from their liquifaction points,  so that ideal gas behavior may be assumed.  That is because rho = P/RT = P MW / Runiv T.

Venus's atmosphere is mostly carbon dioxide,  molecular weight 44.1.  Oxygen is O2,  just about MW = 32.  Water is H2O with a molecular weight of just about 18.  Hydrogen is H2,  just about MW = 2.  Helium just about 4.  And so forth.

The buoyancy force of an airship depends upon a density difference,  times the displaced volume of lifting gas in the airship.  This has been understood since the time of Archimedes.  For equilibrium flight,  the lift force must balance the total weight.  The lift is the buoyancy force.  The total weight is the weight of the airship structure, its crew,  its payload,  its fuel,  etc. 

The bigger the density difference between Venus's atmosphere and the lifting gas,  the more buoyancy force you get from every unit volume of lifting gas.

It really isn't hard to bound any proposed design by some rather simple calculations.

But don't forget and underestimate the weight of your airship structure.  Any such vehicle riding the high winds of Venus at high altitude,  must survive the turbulence fluctuations (storms,  etc) of that wind,  which are also very large. Such induce very large forces,  which must be resisted successfully,  or your airship breaks up.  Into itty bitty pieces. As did the Shenandoah,  the Macon,  the Akron,  and several others whose names I no longer remember.

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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#283 2020-10-08 20:09:46

kbd512
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Registered: 2015-01-02
Posts: 7,414

Re: Mission to Venus

tahanson43206,

There are hybrid airship / aircraft type vehicles that could feasibly operate for extended duration using solar power, but a light aircraft with the handling qualities of a light aircraft would be a different proposition altogether.  Solar Impulse 2 is not a good example of the type of aircraft suitable for use at Venus.  It's far too delicate to survive there and so under-powered for its size as to be uncontrollable.  Voyager / Global Flyer / Solar Impulse 2 were all retired after a single circumnavigational flight because all of those aircraft were so lightly constructed that they were not considered structurally sound afterwards.  If electrically powered, any of those machines would be capable of flying, no doubt about that, but they could never turn around and fly into the wind, which is likely to be important for landing in the event of a missed approach.

When they flew Solar Impulse around the world, they were completely at the mercy of the jet stream.  Eventually you'd have to land somewhere, such as a floating platform, or be snatched out of the air using a soft robotic gripping arm of some kind.  Solar Impulse 2 wouldn't have enough reserve power or thrust to merely make a go-around for another attempt at landing, as a function of the jet stream speeds on Venus.  That's a bit of a problem.  Recall that Solar Impulse 2 weighed just 2,300kg, yet it had a 236 foot wingspan and 87mph top speed.  The jet stream on Venus moves at over 200mph.

If you recall, the "soft" (kevlar fabric manipulated using pneumatic or hydraulic pressure) robotic arm was a feature of my airborne aircraft carrier concept.  The carrier would have multiple flexible fabric "arms", operated in a similar way to a specialized refueling probe, and attach itself to the target aircraft using suction cups to "trap" the micro fighters to return them to an internal hangar bay.  That was intended to negate the requirement for extremely precise attachment of a rigid boom or hook that might severely damage both aircraft in the process, and also permitted engine startup and shutdown outside the carrier while the micro fighter was still "captured" by the arm.  This is a real product of the company named Festo Robotics.  Instead of wheel chocks and chains, you'd have soft shackles and ropes for tying down aircraft on Venus.  In addition to aerospace technology, a lot of the newer sailing technology would apply.

Anyway, there's a specific type of electric aircraft I had in mind, named "Transwing", that uses 4 electric motors mounted like conventional aircraft engines on pivoting wings to enable vertical and conventional flight like a fixed wing aircraft.  This is a more practical substitute for a pure helicopter and a pure fixed wing light aircraft.

Pterodynamics Transwing

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#284 2020-10-09 04:55:37

tahanson43206
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Registered: 2018-04-27
Posts: 17,039

Re: Mission to Venus

For GW Johnson re #282

Thank you for your review of design requirements for a vehicle that would float in the atmosphere of Venus!

SearchTerm:VenusBalloon Design Physics
SearchTerm:BalloonVenus

For kbd512 re #283

Thank you for review of the electrically powered aircraft for Venus idea.  I'll look at the Transwing link later today.

As a small note of adjustment of expectations for anyone who might come across this topic later ... a probe inserted into the upper atmosphere of Venus would be on a one-time mission.  It would eventually sink and experience dissolution, as has every other probe sent to Venus.

The air turbulence predicted by GW Johnson may not be survivable by any vehicle for more than a few Earth days.

On the other hand, the vehicle imagined by Calliban  might have the flexibility required.   This is an engineering problem, and with time and enough trials of various ideas, I am confident it can and will be solved. Oblate Spheroid habitat

It is difficult to see any economic reward for investment along these lines, so the exercise would be motivated by scientific inquiry and by generosity of spirit.

Fortunately, the human race has demonstrated both of these qualities over the eons.

The probes flying to Mars right now are pure examples of both.

Edit#1 ... In case this conversation should inspire further creative thinking by NewMars forum contributors, here is a Google snippet set that appears to show candidates for the exterior of probes (or potentially habitats) in the atmosphere of Venus:

For 90% to 100% sulfuric acid, a good choice would be 316L stainless steel. Since it is a molybdenum bearing grade, it has improved resistance to velocity enhanced corrosion or impingement in valves.Apr 8, 2011

Re: What material would work best for 98% Sulfuric acid ...www.chemicalprocessing.com › experts › corrosion › show
Feedback
About Featured Snippets
People also ask
What material can withstand sulfuric acid?
PTFE
PTFE/ Teflon

The only material that can withstand all concentrations of sulfuric acid at the temperatures that can be created during the dilution of sulfuric acid is PTFE (Teflon) or other fluoropolymers such as PFA.

Concentrated Sulfuric Acid - Inyo Processinyoprocess.com › selecting
Search for: What material can withstand sulfuric acid?

Recently kbd512 reminded forum readers of the possibility a buoyant aircraft carrier might be feasible in the context of Venus exploration.  This would solve the significant problem of loss of sunlight for a solar powered aircraft.  Such an aircraft would not be limited in power to what it could collect on its surfaces, but instead it could collect whatever it can while pulling energy from onboard battery packs.   Design for the turbulent weather in the Venus atmosphere would demand currently unavailable performance by flight systems.

This should be just the sort of challenge that would intrigue the current generation of aerospace engineers, world wide.

(th)

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#285 2020-10-09 16:21:42

SpaceNut
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From: New Hampshire
Registered: 2004-07-22
Posts: 28,825

Re: Mission to Venus

I do not believe that we float airplane like blimp structures here on earth due to the mass of metals and that is why we are using fabrics with reinforcing's ribs that make up the holding structures from metals to limit overall mass. Lest we for get any crew that goes to venus will want to return and that means a metal rocket being hung under the blimp balloon structure to make that possible.

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#286 2020-10-09 17:38:28

tahanson43206
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Registered: 2018-04-27
Posts: 17,039

Re: Mission to Venus

For SpaceNut re #285

My post was about unmanned vehicles.  However, your post here caused me to remember an "invention" of many years ago, that should be suitable for the Venus situation.

If you go back many decades, you'll find active development of the idea of rotating cables timed to arrive at a specific point on the Earth to pick up a load, before lifting that load to orbit.

That idea has not been developed on Earth, beyond great numbers of paper studies.  However, the special circumstances of Venus might turn out to be better for development of the idea.   At present, and for a while to come, Venus' skies are not cluttered with countless satellites and debris items, so a rotating cable might work on Venus.

This technology would address the problem you (rightly) posed, of how to retrieve personnel who might be deployed to a dirigible (or similar device) floating in the upper atmosphere of Venus.

The other option is to simply fly to the balloon from orbit, collect passengers in a brief stall maneuver, and return to orbit.

My sense of the situation is that hanging a rocket on the balloon would be an unnecessary encumbrance, since it would only be needed in an emergency or for regularly scheduled crew rotation.

(th)

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#287 2020-10-09 17:53:21

SpaceNut
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From: New Hampshire
Registered: 2004-07-22
Posts: 28,825

Re: Mission to Venus

This the unmanned Venus express orbiter mission but I can see how the topics placement can be both manned and unmanned in nature.
Not sure that I remember the cable thing....

Searching in the unmanned folder did turn up a few more venus related topics...

Venus Exploration, What are the future missions?

Russian Venus mission to be launched around 2024


That said why not do a solid reducing or shrinking ring in orbit that gets smaller and stays at equal distance from the planets surface by using the solar and fuels to maintain that distance as we visit it.

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#288 2020-10-11 05:00:26

kbd512
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Registered: 2015-01-02
Posts: 7,414

Re: Mission to Venus

tahanson43206,

There's every bit as much turbulence in Earth's atmosphere as Venus, yet military airships that persist over targets in Earth's jet stream for days to months very seldom experience structural failures.  To GW's point, we're talking about next level reliability here, meaning persisting for ten or more years in the jet stream.  That was the stated endurance goal of Lockheed-Martin's airship program prior to funding being pulled.  An airship that can persist indefinitely will be much more heavily constructed than the units in common use here on Earth, therefore larger to lift a given payload.  LM's airship hull design goals for a durable long duration airship were a reduction in envelope material weight from 400g/m^2 to 100g/m^2.

It turns out that NASA already designed a long duration high altitude balloon intended to resist sulfuric acid:

Prototype design and testing of a Venus long duration, high altitude balloon

I'm guessing that its 173g/m^2 is not indicative of a durable design.

The key technologies here are:

1. Durable fluoropolymer coatings.  PTFE-PFA appears to be ideal for this application.
2. Lightweight envelope fibers.  Vectran is the current standard fiber reinforcement for airship envelopes, but CNT is likely better.
3. LM says power system reliability and Helium loss is what presently limits high altitude airship mission duration, which dictates the development of a lightweight and efficient atmospheric Helium separation system.  Concentration of Helium in Earth's atmosphere is 5ppm, but Venus is 12ppm.  This is the greatest "unknown" for me.  I know that air separation requires tremendous amounts of energy input and the equipment is not lightweight, but we need to know the numbers.
4. Robotic-inflight repair of the envelope to prevent significant penetration of sulfuric acid.
5. Lightweight 10,000psi Helium storage spheres.  Current CFRP technology dictates about 8.25kg of storage vessel mass for each kilo of Helium stored at 10,000psi, based upon the Toyota Mirai's H2 storage tanks.  Each cubic meter of He storage can accommodate about 85kg at room temperature.

LM High Altitude Airship Design / Program Explanation:

Higher ground: Stratospheric airships special report

Notes:

Each 1,000 cubic feet of Helium would provide 103.85 pounds of buoyancy in a nearly pure CO2 atmosphere at 50km in altitude (STP conditions, more or less), so a 5M/ft^3 airship would provide 519,272 pounds of lifting force.  This is 10 times the size of LM's HALE-D prototype airship, and 800K/ft^3 smaller than the full scale ISIS airship.  HALE-D's sea level gross weight is 3,000 pounds.

Full size HALE (5.8M/ft^3) structural mass breakdown and envelope fabrication materials / methods:

HALE Airship - Manufacture, Flight and Operation Presentation by John Pattinson, Projects Manager Lindstrand Technologies Ltd

Edit:

High Altitude Long Endurance Air Vehicle Analysis of Alternatives and Technology Requirements Development

Last edited by kbd512 (2020-10-11 05:11:08)

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#289 2020-10-11 05:59:34

tahanson43206
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Registered: 2018-04-27
Posts: 17,039

Re: Mission to Venus

For kbd512 re #288

SearchTerm:Airship Venus Earth Military Long Endurance

http://newmars.com/forums/viewtopic.php … 20#p173020

Thanks for pulling together all these links, and for putting them into context!

The 2008 paper from JPL with which you led off the post opens with a reminder of the Soviet mission to float two balloons for two days.

That was quite an achievement!   I was surprised to not find solar cells included in the 2008 redesign, but perhaps the trades simply aren't there to make the extra mass worth while, and in any case the expected lifetime of the mission was a minimum of two weeks.

Helium was chosen as the lifting gas, and issues of leakage were addressed.

(th)

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#290 2020-10-12 11:25:35

kbd512
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Registered: 2015-01-02
Posts: 7,414

Re: Mission to Venus

tahanson43206,

I'm not sure that the lifting gas issue has been addressed, but I would love to know what the loss rate is so that a mission could be planned with that knowledge in mind, such as the onboard air separation plant has to separate #kg of Helium from the atmosphere in such and such time frame in order to replenish losses.

The thin film solar of today is nothing like what was available back in 2008, which was more suitable for powering cell phones than aircraft.  It took a good 10 years to develop a practical product, but now we have multiple commercial providers to choose from.  A civilian with cash in hand can now purchase what only NASA and DARPA had back in those days.  That's what NASA and DARPA do best- bleeding edge technology development.  Both aircraft and airships have PV now as a result (they actually put these on new-built light aircraft skins to provide AC and battery trickle charging on the ground), our soldiers don't require tons of primary batteries or noisy generators that give away their positions in the field merely to power their radios, and missions to Venus or Mars can now feasibly be PV powered, at least in part.

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#291 2020-10-19 01:24:34

kbd512
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Registered: 2015-01-02
Posts: 7,414

Re: Mission to Venus

tahanson43206,

I was thinking about a valid reason to store a tank of molten Silicon or Boron for the Venus and Mars missions, mostly because I want to see a technology demonstrator mission using this form of heat energy storage, and then it occurred to me that this is a good way to use process heat for reducing H2SO4 to H2O and SO3, then SO2 and O.  H2SO4 should completely decompose to water and Sulfur Trioxide by around 400C and by using a Cu-Fe catalyst, it should be possible to obtain O2 by around 700C.  We could use electrical resistance heating from onboard wind turbines to liquefy a tank of Silicon or Boron, then use that thermal power store to break down Sulfuric Acid as part of a single-pass process that sucks in H2SO4 vapor from the clouds and spits out distilled water and one of the breathing gas constituents at the other end.  Doing this might negate the significant power requirements associated with compressing and electrolyzing CO2 at 800C to 850C in a reverse SOFC, which has the potential for catalyst degradation from Carbon plate-out.  If energy efficiency and system durability is important, then running an intake pump at near atmospheric pressure and collecting H2SO4 at least appears to be a reasonably good way to do that.

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#292 2020-10-19 18:33:12

SpaceNut
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From: New Hampshire
Registered: 2004-07-22
Posts: 28,825

Re: Mission to Venus

Venus surface temperature of 465 °C and pressure of 92 bar

https://en.wikipedia.org/wiki/Molten_salt_reactor

https://www.sciencedirect.com/science/a … 5319314855

But at where we are looking to fly the mission is more earth balmy temperatures and pressure.

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#293 2020-10-19 19:01:10

tahanson43206
Moderator
Registered: 2018-04-27
Posts: 17,039

Re: Mission to Venus

For kbd512 re #290

Your idea seems (to me at least) worth pursuing a bit further ... 

SpaceNut ... it sounds as though you agree?   If I read #290 correctly, the facility would be floating at the point where air pressure is close to Earth sealevel.  What I'm not clear on (yet) is how the facility will capture wind flows if it is floating with the wind, but (hopefully) kbd512 will develop the idea a bit more.

(th)

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#294 2020-10-19 19:14:04

SpaceNut
Administrator
From: New Hampshire
Registered: 2004-07-22
Posts: 28,825

Re: Mission to Venus

We need to reach downward towards the surface to capture heat from the pressure and temperature of the venus surface.

File:Molten_Salt_Reactor.svg

We would be using part of this diagram for the molten salt reactor

UF2RN.png

Venus-Atmosphere-and-Temperature.jpg

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#295 2021-06-11 14:39:03

Mars_B4_Moon
Member
Registered: 2006-03-23
Posts: 9,175

Re: Mission to Venus

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