Posted by Curbie on March 24, 2009, 10:09 pm
Two things jump through my foggy recollection of Striling cycles and
solar concentration, here is what is confusing me:
1) Gas law is Gas law. P = (nRT) ÷ V Whether your moving a solid (a
piston) or liquid (water) you still have to heat the volume of gas to
the desired pressure, for each cycle, to the work.
2) Volume of heat from a parabola is a function of the area of the
collector and temperature of heat is a function of the "Concentration
Ratio" (geometric or ideal) of the collector aperture area / receiver
aperture area. I don't see how you create the volume of heat or
temperatures cited to heat the gas to pressurize enough cycles to
create 1hp (or anything like it)?
More math cheese:
8' x 4' = 32 Ft^2
250 BTU per Ft^2 (on a reasonably clear day)
32 (Ft^2) x 250 (BTU) = 8000 BTU per hour
Plug the 8000 BTU per hour into gas law and chop the pressure into any
bore, stroke, and frequency per hour combination you like and I can't
find the Hp.
I have a spread sheet on gas law into Hp if or interested, maybe it's
all goofed up and you point out my mistake, won't be the first time.
Posted by Morris Dovey on March 24, 2009, 11:22 pm
Here's another way to come at the problem (different units): figure
1kW/m^2 for total input. The trough uses a 4x8 sheet of mirror, but the
trough width is noticably less due to curving the mirror sheet.
Still, we end up with more than 2 m^2 of capture area which should
provide 2kW of input power. We're going to have losses at the focal tube
and losses due to Carnot cycle efficiency limitations. In the best of
all possible worlds [ :) ] the efficiency losses will be close to 26%
(at 70F/1450F head temperatures).
Those 26% efficiency losses drop our 2kW to 1.48kW, and I'm hoping
(because I don't yet have enough experience to predict) that the losses
at the focal tube leave enough to get at least 746W out as mechanical
Not factored into any of this is heat re-cycled by the fluidyne's
regenerator, possible water jacket cooling of the cold head to improve
Carnot efficiency, or collection efficiency boost resulting from tricky
(artsy-fartsy) sun side insulation and/or reflector shielding of the
In summary - I think there /should/ be enough juice to squeeze out
somewhere /around/ a horsepower - less if I do a shoddy job - and maybe
more if I can both design and build well - which is certainly still in
question, since I'm not an ME or physicist, and I don't have any
thermodynamics or heat transfer background. :P
I have a Stirling cycle web page (let me know if you spot errors) at
that tries to describe the Stirling cycle in both prose and formulas. I
used those formulas (formulae?) to build a software simulator - which
still doesn't account for everything it should, but does seem to agree
more or less with what I've been able to measure.
DeSoto, Iowa USA
Posted by Curbie on March 25, 2009, 12:00 am
I'll take a hard look at all in post a little later tonight and from
this your perspective and see if if I can't find your focus. NCIS now.
Posted by Curbie on March 25, 2009, 6:27 am
Your Stirling cycle web page looks fine which confuses me all the
more. Where did you consider gas law in your post? I don't know spit
about the metric system except that two liters is about the size of a
coke bottle, they didn't teach it when I went to school in the
After reading, and re-reading your post I'm still at a loss over the
same two questions I'll re-word slightly:
1) Whether your moving a solid or liquid you still have to produce
enough VOLUME of heat to heat the of gas to the desired pressure, for
EACH cycle, to do the designed work.
2) VOLUME of heat from a parabola is a function of the area of the
collector and TEMPERATURE of heat is a function of the "Concentration
I got into my solar concentrator spread-sheet and set-up a 2m^2
concentrator and adjusted the receiver area for a temperature of
1440F, I got a geometric "Concentration Ratio" of 127 to 1 and
requiring a receiver AREA of 6.5 Inches^2 or 403mm^2. Since you are
talking about a parabolic tough 4x8 feet, I think your talking about a
48" long receiver that has a total receiver AREA of 6.5 Inches^2?
I based my spread sheet on
I think submitted by an engineering student as his master's thesis. I
bring this up only because I know you've done software simulation and
you might be looking to cross-check for results. I like this Newton
manuscript because he proved all his calculations with answers which
is great for the metrically-challenged (me).
http://eosweb.larc.nasa.gov/sse/RETScreen/ is NASA site where you give
it your latitude and longitude and they give you a pile of data
including "Daily solar radiation".
You have heat volume and peak temperature calculations which are over
my head, but I'm easily confused.
Posted by Morris Dovey on March 25, 2009, 11:31 am
I have the same problem with metric - but this is the first problem of
its kind that I've tackled, so I converted familiar units to metric and
forged ahead in the hope that most of the physics/engineering experts
from whom I might need to beg help would be more comfortable with that
The approach I took in my post was "follow the power". I can guesstimate
the input power, and can identify losses at the focal tube and losses
within the engine because of the Carnot cycle efficiency limitations.
I know that there will be other losses since the mirror won't be a
perfect reflector, the focal tube won't be a perfect absorber, air
viscosity increases with temperature to prevent perfect flow, etc ad
nausea. I doubt that I'll ever be able to isolate and individually
quantify all of the loss mechanisms. My choices were to either shrug and
continue or declare myself incompetent and quit. I shrugged.
At this stage in /my/ development, there isn't a design output
requirement. I'm coming at this as a learning experience (which allows
me to re-invent wheels as necessary) to discover, given a particular
engine configuration, just how much work the thing can be tweaked to
I think  is true. From the energy perspective, if I increase the
energy level of the gas by 1kW, I should be able to see 1kW worth of
effect - and if I then reduce the energy level by 1kW, I should be able
to see 1kW worth of effect in the other direction. Carnot tells me that
this isn't quite so, and that my effects will be dependent on the
temperature extremes - and provides a formula for how much of my input
power can result in actual output power: (1 - Tc/Th, temps in K).
Since I have (a guesstimate of) the input power, and values for the
temperature extremes, I can approximate the maximum (ideal) output power
directly, without needing to involve pressure and volume variables.
What this tells me is that if I can manipulate the Th and Tc values so
as to produce a Carnot cycle efficiency of 74.6% (and if my engine were
"ideal"), an input of 1kW would result in a 746W (1 hp) output.
The big question is: "Just how far from 'ideal' will the engine be?" The
only way I know to get an answer is to build it and see how well it does. :)
The actual width will be close to 88" and the target area will be 3/8",
for a ratio closer to 88/0.375 or 234:1. 3/8" * 48 = 18 in^2. (I plan to
wear welding goggles.)
One of the nice things about the simulator is that I can enter all my
information in familiar units and do a front-end conversion to metric,
then display results in both units.
I'm very conscious that the simulator (so far) only simulates an ideal
engine. The only thing I hoped for in writing it was a tool that allowed
a "sanity check" on actual results. As I learn more about the real-world
operation of these things, I may be able to make the simulator more
I appreciate the links. I've saved 'em for when I've had more sleep.
I suspect that you aren't - and I think this stuff does take a bit of
time to internalize. All the calculations I have on the web page were
either lifted directly or derived from a handful of university web sites
and wikipedia articles - and I've had a good bit of help from some of
the folks who hang out on alt.solar.thermal.
If it weren't for the Internet I'd still be saying: "I wonder if..."
DeSoto, Iowa USA