🚀 go-pugleaf

In article <4b6p20$bm7@scotsman.ed.ac.uk>, ajc@reaxp01.roe.ac.uk says...
>
>In article <4b6nep$gu3@ixnews2.ix.netcom.com>,
>Alan \"Uncle Al\" Schwartz  <uncleal0@ix.netcom.com> wrote:
>>The radiometer is under a light vacuum.  Heating of the black side of 
>>each vane launches mass convection currents with sufficient orthogonal 
>>component to drive the vanes.
>
>        what is the fine detail behind the phrase `convection currents'?
>
>        i guess that the dark side of the vane is heated by radiation
>        and so any air molecule that collides with the vane is heated
>        slightly and then leaves with more energy that it arrived (on 
>        average).  this gives a net loss of momentum to leaving 
molecules
>        and so the vane moves in the opposite direction.
>
>        (you could think of the process as molecules being held on the
>        surface, heated, and released like the gas flying out of a
>        rocket.)
>
>        alternatively, if the mean free path of molecules is less than
>        the size of the vane, then these heated molecules remain to the
>        dark side of the vane for a few collisions, giving a locally
>        increased pressure.  (i'm automatically suspicious about this 
because
>        it's talking about gas that's not in thermal equilibrium).
>
>        i think these are two separate processes and i don't know which
>        dominates, or if `convection currents' implies some other 
process -
>        any comments?
>
>        andrew
>
>-- 
>           work phone/fax: 0131 668 8356, office: 0131 668 8357
>    institute for astronomy, royal observatory, blackford hill, 
edinburgh
>                     http://www.roe.ac.uk/ajcwww


Well, all of the previous comments are excellent in this post and the 
others addressing the question.  Let me take the phenomena one level down 
in detail to show where the force originates in each of the two kinds of 
radiometer.

The first kind of radiometer is a reflective one.  It requires a very 
good vacuum and is not normally sold as a science toy so I doubt this is 
the kind the teacher has.  But lets consider it any way.  Normally, to 
maximize the effect, one has a black surface on one side and a highly 
reflective surface on the other.  White paint meerly decreases the 
effeciency of the effect but in space would work fine.

Now the energy imparted by a photon colliding with the black side of the 
surface and being absorbed is one times its momentum.  This is given by 
its relativistic mass times velocity, or, U = mc  where U is momentum and 
c is the speed of light.  Using the intensity of the light, and the 
surface area of the absorber (and the effeciency of absorption if you 
want to get into details, but then you would need to add the radiation 
and the problem gets ugly.  It essentially all cancels in the end, so 
don't worry.  I think, though, that the blackbody emissions end up 
completely canceling the thrust of the absorbed energy since energy in 
must equal energy out)

Considering the reflective side, though, we find that the incident energy 
strikes and reflects which yields a 2U momentum transfer.  The absorbed 
energy, since reflectors are not perfect, again heats the material, and 
is again emitted.  A good reflector is synonomous with "poor absorber", 
and with "poor emitter" in radiation theory.  One is the other.  So the 
small amount of energy absorbed by the reflective side is again cancelled 
by its emissions.

Because Black is synonamous with "good emitter" and "good absorber", it 
turns out that everything balances.  The black side absorbs and emits the 
light with which it interacts, and the shiny side does the same.  No net 
thrust yet.

But, the shiny side had those pesky photons that dumped 2U momentum and 
if we want to be picky, the inefficiency of absorption on the Black side 
did as well.  However, the amount of energy reflected from the shiny side 
is clearly far greater, and so that is the origin of the momentum 
transfer that gets the radiometer spinning.  


Convective radiometer:

All of the absorptive and reflective forces are indeed still going on and 
contribute a thrust on this radiometer as well.  You just reduce the 
effeciency of the white paint as compared to the reflective surface.  It 
doesn't turn out to matter much that the reflection is diffuse, but such 
a reflector intrinsically absorbs more of the incident light diminishing 
the effect.

Now, in this radiometer, we have another factor to consider, namely a 
little gas.  It turns out that even if you had a perfect vacuum when they 
made the normal radiometers, helium can penetrate through it so no glass 
container is completely empty.  In fact, gas can even migrate down 
through the structure of a 12 foot bar of stainless steel which is why 
when machining parts for high vacuum applicaions, the cut squares out of 
plate steel, and then turn the squares round if they want a round flange. 
 That is another story.

So, we have this white surface and this black surface and it is pretty 
clear which one is absorbing more of the photons, the black surface.  
This absorption of energy heats the surface of the vane and so we see 
that the heating is originating to a greater degree on the black side of 
the vane.  Since your real vane is not a perfect conductor of heat, there 
develops a temperature gradient from one side or surface of the vane to 
the other with the black side being hotter.  

Now what do we mean when we say something is hot or that it has a given 
temperature?  What we are really doing is using a convenient way to 
communicate how well a surface can transfer kinetic energy.  Temperature 
is *defined* as the average kinetic energy of the atoms in the material.

	Kinetic Energy = 1/2 mv^2  where m is mass and v velocity

So, what we really did was to set up a situation where the atoms on one 
side of the plate are moving at a speed greater than the other side of 
the vane.  Thus, in the end, what we really find is that an atom of the 
surrounding gas that comes near the black side is going to get smacked by 
the oscilatting surface atoms like a home run slugger while the atoms on 
the white side of the vane are going to be tapped by your eigth and 
ninthe graders.  Since the atoms on the black side are moving faster on 
average, they will send the atoms flying away from the surface on 
average, faster.  Take your same old mv momentum transfer equations and 
you have the answer.

This is why the radiometer spins.  Now when you look at the velocity of 
the particles it will be on the order of 1000 meters per second for 
helium if I remember right, don't quote me on that one, and around 330 
m/s (1100 ft/s) for air.  What the rarefaction of the vessel does is it 
allow the molecules to increase their mean free path for collisions with 
other molecules.  Put another way, it allows the molecules to transfer 
the heat from the vane to a position out in the gas that is farther from 
the vane.  I doubt, but they might actually reduce it to where the next 
collision is with the glass wall itself, perhaps someone knows that fine 
point.

By gettin the molecules farther away, you distribute the momentum better 
throughout the volume.  What this means is that you do not cause a steep 
pressure gradient right in front of the vane trying to get rid of the 
energy but instead throw it a ways out into the gas.  From the standpoint 
of propulsion, this actually works against you since the higher the 
pressure that builds up, the greater the PA thrust.  But if you consider 
the other side of the vane, the leading side, then you see why they do 
it.  Any air in front of the vane must be pushed out of the way and flow 
around the vane.  This is aerodynamic drag and a flat vane like that 
while about the best shape you could have for the radiometric propulsion 
effect, is about the worst shape you could have for reducing aerodynamic 
resistance to motion.

Because aerodynamic drag (been a long time so correct me if I am wrong) 
is proportional to the square of the velocity, and the energy required to 
push it is then proportional to the cube of the velocity.  Now, we are 
building a radiometer here and not a race car, and energy comes at a 
premium.  So this cubic factor doesn't cut the mustard.

Therefore, they get all of the air out that they can.

As cited in other posts, one spins one way and the other the other so it 
is easy to tell which you have, but if blind, I would still wager the 
latter since the odds the school paid for one that probably costs 100 
times more than the other is low.  Besides, the first radiometer would 
need to come with a cryo vac to keep pumping the helium out or a special 
coating on the glass, who knows.

If I made any technical goofs, let me know which they were, I did not 
reread this closely.  Thanks.


This is one more in a long list of things we do indeed understand where 
there were no attractive force mechanisms found.  The white side was not 
"attracted" to the light.

Later, Ross
	There exist in nature, no attractive forces.
	And gravitation is a differential push.