Monday, March 30, 2015

Rockets IV: Thermal rockets, nuclear and otherwise

See also parts IIIIII, V, and VI.

Here we talk about applying some sort of external heat source to your propellant so it expands a bunch and then shoots out of the rocket.  Technically chemical rockets are thermal rockets too but I'm trying not to be pedantic here.   There are lots of things you can use as your source of heat.  NASA has done a lot of studies with using a nuclear reactor to heat some propellant directly.  If you've got a big parabolic mirror you can focus sunlight on your engine and heat it that way.  If you've got a friend nearby with a big laser they can use it the same way.

The constraints for these sorts of rockets aren't the same as for the last two sorts of rockets.  You don't have a fixed ratio of energy to propellant that chemical rockets have so the ve isn't fixed that way.  Energy is a concern as with electric rockets but not as large a one since its much easier to turn an energy source into heat than it is to turn it into electricity.  There's a more pressing limit, though.  When things get too hot they tend to melt and you probably don't want this to happen to your rocket. In the other sort of rockets you can have the engine itself be a lower temperature than the propellant but since thermal rockets transfer heat from the engine to the propellant thermodynamics means that the engine has to be hotter than the propellant.

We all know that things expand as they get hot and it stands to reason that really hot gasses will probably leave the rocket faster giving you a higher  ve.  There's an equation for this, of course, which is ½Mmv2 = 3/2 RT where Mm is the molar mas of the atoms or molecules making up the gas, R is the Molar Gas Constant (8.314 J/K*mol), and T is the temperature of the gas.  So the ve we get is proportional to the square root of the temperature of the gas divided by the mass of the particles in it.  Lets say we can get our engine up to 3,200 K.  That's pretty hot but not undoable.  If we've got steam coming out like the Space Shuttle did this means that our ve is going to be 2100 m/s.  That's a lot less than the 4600 m/s the Shuttle got.  Now, we do get to store our propellant as nice dense water at room temperature which will save us a lot of design hassle.  However we haven't explained how we're going to be heating up the water and that's probably going to take a lot of mass.  Also, did I mention that when you're talking about ve 2100 is a lot less than 4600?  Clearly there's a big advantage in only having your propellant rather than your entire engine get hot.

But since our propellant isn't the result of a chemical reaction nothing says that we have to use a big, heavy molecule like H20.  What if we just use pure hydrogen, H2 with a molecular weight of 2 rather than 18.  In that case suddenly our ve goes up to 6300 m/s.  That's certainly much nicer!  And at that temperature some of the hydrogen molecules will split apart and for monatomic hydrogen with an even lower molecular weight.  Most of the designs I've looked at for normal nuclear thermal engines like MITEE say they ought to get their ve up past 9000 m/s but I'm not conversant in all the math there.

People have come up with various ways to effectively increase the temperature of the engine by doing things like making part of it transparent to try to get the same differential heating you can get in chemical rockets.  Maybe you put your propellant behind a quartz window and put some carbon in to make it absorb the incoming energy more than the quartz.  There's an interesting design with this and gaseous uranium hexafloride called the nuclear lightbulb that's only somewhat crazy.

I've glossed over the problem of engine weight.  They generally range around 10 to 100 N/kg which is much better than the .005 you'd see for an electric rocket but much worse than the 700 to 1500 N/kg you see for a chemical rocket.  So maybe good for a second stage in your rocket but not your first.

A note on the radiation.  If you've got a high powered nuclear reactor or engine your going to be generating lots of neutrons and xrays that the crew will have to be shielded from.  Lots of neutrons will end up hitting the propellant but this isn't really a problem since hydrogen and a neutron just make deuterium which is pretty innocuous.  And if you fire it in the air you won't be making anything horrible from the oxygen and nitrogen either.  But if you launch one of these babies from the ground those neutrons will play havoc with various minerals and you'll have a serious cleanup problem.  So don't do that, ok?

Another option is to have a nuclear electric rocket but when you need the extra thrust just run your propellant through the reactor and get the full 500 kW of thermal power rather than the mere 100 kW of electricity it provides to the electric drive.  And the  ve is lower so the thrust is higher for the same energy too, giving you a wider range of tradeoff between thrust and efficiency than even a VASMIR can.

That's it for thermal rockets.  Tune in later for me talking about rockets that aren't actually rockets.

Sunday, March 29, 2015

Rockets III: Electric

See also parts IIIIVV, and VI.

So besides burning stuff, how else can we make our rockets move?  Well, one probe that's been in the news a lot recently is Dawn which recently went into orbit around Ceres and showed us those two funny bright spots on it.  One of the nifty things about Dawn is that it uses an ion drive for propulsion.

Ion drives, just one sort of electric drive out there, work by using electric fields to accelerate atoms very quickly out the back of the rocket.  Since they decouple the energy used to accelerate the propellant from the propellant itself there really isn't any firm limit on how fast the propellant goes besides how much electrical power you have available to shove them.  A typical ion thruster might have a ve 42,000 m/s, almost 10 times higher than the best you can get from a chemical rocket.

Unfortunately that electrical power is a bit of a sticking point.  It has to come from somewhere and that somewhere is going to be relatively heavy compared to a chemical rocket with the same thrust.  For instance, the Space Shuttle engines had a combined thrust of 5,580 kN.  Remember that for a rocket power is half the thrust times the ve so the space shuttle is putting out 12.4 GW of power which is comparable to the biggest power stations in the world.  Since the Shuttle engines just had to put the hydrogen and oxygen together, burn them, and only let the hot gasses leave in one direction it was possible to make them fairly light at just 10 metric tons all together.  Just the turbines of an electric plant that can generate 12 GW would be much, much heavier than that.  And a typical Ion Drive with a v10 times higher and so requiring 120 GW for that thrust would be totally unfeasible.

All that means that ion drives tend to be low thrust.  When you're getting into orbit you need to accelerate quickly just to overcome gravity.  If your acceleration is at 9.8 m/sor less you won't be able to do anything at all.  But if you make it to orbit then there isn't nearly as much of a hurry.  If you're spending a week traveling to the moon like Apollo 11 you can probably afford to spend a day accelerating.  And if you're going to be taking multiple years getting to the asteroid belt like Dawn did then you can take a long time indeed to get up to cruising speed.

How fast will a typical ion engine accelerate?  Well, lets say we want to go from low Earth orbit to low Mars orbit and back without anything complicated like aerobraking, which should take about 20,000 m/s of Δv all told.  With a ion drive with a  ve of 42,000 m/s that means that we'll need 38% of our mass to be propellant.  That's pretty good for a trip like this.  Lets say we're willing to use another 38% on the engine mass, how fast can we go?  Well Dawn's engine (named NEXT) weighs 5kg, puts out .236 N of thrust, and takes in 6.9 kW of power.  If we calculate how much power that thrust/ve combo ought to give us it comes to 5.0 kW, so the rocket is 72% efficient which isn't that bad.  So if we took that 38% mass and filled it full of NEXTs the rocket would accelerate at .018 m/s2.  At that rate all our acceleration and deceleration would be over in 12 days, which is pretty small considering an efficient trajectory will take eight and a half months traveling each direction.

Sadly we do have to think about power.  For each kg of NEXTs we use we need 1.38 kW or power.  Space grade photovoltaics have a power to mass ratio of 77 W/kg so we'd need 18 kg of solar panels for every kg of thruster, increasing our acceleration/deceleration times by a factor of 19.  That would mean acceleration periods equal to half the normal trip time.

Can we do better?  Well, NASA has a nuclear generator for use in space that they've tested out some that gives 195 W/kg, which means only 7 kg of generator for every kg of thruster which means 3 months of acceleration which is still bad but less so.

Of course if you're willing to have a lower ve you can have more thrust at the cost of using more fuel.  And if you want to go to the outer system it might make sense to try to use a higher ve engine since your trip is going to take so long anyways that you can afford to spend longer getting up to speed.  There's actually one sort of electric thruster, VASIMR, that can alter its  ve in flight instead of having a fixed ve for the particular design.

I expect that a lot of future missions to places further than the moon are going to use these sort of rockets in one form or another.  We've put a lot of effort into making chemical rockets as efficient as possible but various sorts of electric rockets are fairly undeveloped and I hope that there's a lot of room for improvement.

Monday, March 23, 2015

Rockets II: Burning stuff

See also parts I, IIIIVV, and VI.

The most common sort of rocket and the ones we're all familiar with from seeing them on TV are the ones that work by burning stuff.  That is, they work by combining two different chemicals that react to produce the energy that propels the byproduct of the reaction out the back of the rocket.  Since the fuel that provides the energy and the propellant that is ejected for the momentum are the same thing this means that you're always using more or less the same amount of energy for the same amount of propellant.  This means that the ve, the velocity of the exhaust, is always going to be more or less constant depending on sort of chemicals you're using with some variation depending on inefficiencies in the engine.

Many chemical rockets use cryogenic fuels - substances that are normally gasses but which have been cooled down enough that they liquefy and can be put in reasonably sized fuel tanks.  Take the fuel used by the Space Shuttle, liquid hydrogen and liquid oxygen.  When you combine H2 and O2 to make H2O you liberate 232 kJ (kilojoules) of energy per mol of water.  A mol of water weights 18 grams.  Plug that into you your standard equation for kinetic energy (½mv2) and we find that if everything goes well we'll be getting steam coming out the back of the rocket at 5077 m/s.  If you go look up the Space Shuttle's main engines you'll see that their exhaust goes out at 4436 m/s in a vacuum.  Clearly there are a lot of sources of inefficiency that I'm not including, as you would expect.  Still, first principles give you a fairly decent ballpark estimate.

However they also list the ve for when they start firing at sea level as only 3590 m/s.  The atmosphere sort of gets in the way of stuff exiting out the back without interruption.  Oh well.

Out of the various chemical fuels you could put into a rocket hydrogen is the best in terms of ve but it's got some drawbacks.  For instance even after you liquefy it hydrogen isn't really very dense.  Also, it takes a lot of work to liquefy hydrogen in the first place.  Oxygen turns to a liquid at 90 degrees Kelvin which is admittedly rather chilly but still warmer than liquid nitrogen.  Hydrogen by contrast will only stay liquid below 20 K.  So you need big bulky tanks to store your liquid hydrogen propellant and even with lots of insulation some will boil off during the countdown and need to be continually replaced.  If you've ever watched a rocket launch and wondered what that gas was coming out of the rocket before liftoff or why it has those tubes connected, well, now you know.

Some rockets use other fuels.  You can combine liquid methane with oxygen for a ve of up to 3700 m/s.  Liquid methane is much denser than hydrogen and liquefies at a relatively reasonable 112 K.  Purified kerosene is even denser and doesn't have to be cooled at all but at the cost of a ve of only 3500 m/s.

There are also the hypergolic propellants.  When you mix your fuel together with, say, oxygen and methane you have to do something to ignite it.  Otherwise it will just build up in the combustion chamber and if it accidentally gets ignited after having built up it can explode.  Hypergolic propellant doesn't have to be mixed - it will ignite all by itself when you bring the two chemicals together.  Even better both halves are liquid at room temperature meaning you don't have any cooling or boiloff concerns at all!  Why do we bother with this liquid oxygen stuff then?  Well its ve is generally around 3300 m/s and more importantly it's toxic as all hell.  Still, if you've got something like a maneuvering thruster that's going to be turning on and off repeatedly it's hard to avoid using.

Oh, and finally there are solid rocket propellants.  They have the lowest ve of the bunch but they're pretty tough for rockets and since they aren't particularly toxic and don't have to be kept cold they tend to be cheaper than the other kind.  Because they don't mind being shaken a bit they're the sort of rocket that is used in most military weapons.

So there you have the basic types of chemical rockets.  I'll talk about electric rockets next post.

Saturday, March 21, 2015

Rockets I: Some basics

See also parts II, III, IV, V, and VI.

I've been on a bit of a space propulsion kick recently between getting a copy of High Frontier, rediscovering Atomic Rockets, doing an archive binge on Selenian Boondocks, and generally following all the excitement around SpaceX.  I thought I'd write up a few blog posts on what I think of as the interesting bits.  Be warned that there'll be a bit of math involved but I'll try to keep it from getting out of hand.

So, lets say you want to go to space today.  Maybe you even want to head out to the Moon or Mars or Ceres.  When you travel on the Earth in a car or plane or boat the hard part is energy you spend is going to be in used to overcome the resistance of whatever medium you're traveling in.  You get up to some maximum speed and have to exert your motor constantly to stay at that speed.  When you want to stop you simply stop applying force and maybe apply a brake as well, neither of which require fuel.

Space travel isn't like that.  Once you leave the atmosphere you can use your engine once and then pretty much coast as long as you want.  Of course with no atmosphere or ground to you also need to use your engine again if you want to change direction or stop.  So in theory if you want to go from point A to point B and you're really patient you can just turn your engine very briefly and then slowly coast to where you want to go until you turn it on again to stop.  And if you want to get there faster you'll just have to burner it longer as you start and stop.

Well, that would be how things would work if were out in the middle of perfectly empty space.  But as it turns out most of the interesting stuff near by is orbiting around other things like the Sun or the Earth and if you want to get to where you're going you have to worry about orbital mechanics.  I'm not going to get into those (if you want to learn more you should really try playing Kerbal Space Program) but the important point is that there's a minimum speed you need to be going to leave one orbit and go to a different one.  If you're in orbit around Earth at a height of 200 km and the place you want to go is also in orbit around Earth at 200 km then great, you can get there with a super short burn and patience.  But if you want to go to a different orbit then you need to change your velocity by a certain amount called a Δv.  Here's a handy chart that can tell you how big that amount is for various destinations you might want to go to.

To travel rockets invariably expel propellant out their back and since for every action there is an equal and opposite reaction this accelerates the rocket forward.  How large a change in velocity a rocket achieves after a burn is governed by something called the rocket equation that follows.

Where Δv is the change in velocity, ve is the velocity that the propellant is expelled at, m0 is the "wet" mass of the rocket that includes all the propellant being used, and m1 is the "dry" mass of the rocket after the propellant has been used.  So if 63% of a rocket's starting mass is propellant its final velocity will be the same as the velocity at which it was ejecting its propellant.  So ideally if you want to have a lot of Δv you also want to have a very high propellant velocity too.  From the prospective of the rocket equation you want that velocity to be as high as possible, in fact.

Sadly there's another limit here that rears its head.  If you throw enough propellant to accelerate your rocket by a certain amount you've imparted a momentum of mpropellant * ve.  But the energy it takes to throw that propellant is going to be ½ mpropellant * ve2.  Divide one by the other and it turns out that for each bit of Δv you generate you have to pay energy proportional to your ve.  Or in other words the more mass efficient your rocket is the less energy efficient it is.

Sunday, March 15, 2015

Links for February/March

So I was sort of busy the last two weekends with Intercon and PAX being back to back.  Hence this is a bit late.

We got a lot of snow.  Seriously.  Enough that people considered Extreme measures.  We might be going over the all time winter record this weekend if we get just a bit more, we'll see.

This kickstarter (oh look, I guess it failed in the time since I found it) strikes me as an excellent idea in principle but not one that's going to be successful as a Kickstarter.  The idea is that for the serves that provide us our internet one of the biggest costs is the electricity consumed by the data center.  And the biggest drain on electricity isn't what the servers consume but what's required to power the air conditioning for the data center.  But if you spread out all those servers and put them in homes in places where they aren't running the AC all the time then the cooling cost basically disappears.  Then the owner of the server just reimburses the host for the electricity used and everyone is happy.  There are a bunch of problems with that starting with the fact that it violates the terms of the agreements most of us have with our ISPs.  I sort of suspect that Google could make this work with Google Fiber customers but I don't see it working as a Kickstarter.  And as expected it flopped.

You might know that I work on a hospital delivery robot.  Well, here's an excellent article in Wired about one of our competitors.  I'm actually pretty happy for the publicity on the concept of delivery robots - especially since QC Bot is much smarter than Aethon's Tug.

You know that comet we have a probe orbiting?  It's starting to heat up, producing pretty pictures.

The FAA has finally created some rules for commercial drones.  They're not perfect but I'm glad they actually exist now.

A while ago a group called Mars One got a whole bunch of people to sign up for a one way trip to Mars.  Recently some people at MIT did some analysis (PDF) of their exact plans.  This was mostly spun as the Mars One plans being unfeasible but the problems brought up aren't all that hard to solve.  So I have more respect for Mars One than I had previously but I still think they'll never get off the ground.

I've been a longtime user of Lenovo's Thinkpad line of laptops and generally happy with them.  Sadly some recent Lenovo laptops (not the Thinkpad brand) have come with some crapware that accidentally let third parties pretend to be trusted sites like your bank.  Which is really very bad!  What I've always done is to just get a Thinkpad with the cheapest available hard drive them buy my own SSD separately and use that.  Buying upgrades from a third party is usually much cheaper than buying them from the laptop manufacturer and hard drives are very easy to replace.  I still get my laptop subsidized by all the people paying Lenovo to put their ads in but I don't have to deal with the ads.  This might be harder for you if you use Windows and have to pay money for your operating system.

Nifty furniture that assembles itself.

This is an excellent idea.  Putting two camera eyes on a robot, giving a person a VR headset that shows what the robot sees, and having the direction of the cameras track the person's head movements.

My goodness Google's crazy plan to provide the world with Internet broadcast from weather balloons is going forward.

We're trying to make our SARS-2 tests better than we should

Ok, that's a somewhat provocative title but I think it's basically accurate.  During this pandemic the US in particular has had a pr...