# New mount for stirling motors and satalite dish solar and the liquid piston tracker - Page 2

 register ::  Login Password  :: Lost Password?
 Please Register and login to reply and use other advanced options Posted by dow on March 21, 2010, 3:42 pm  As you know, I have been interested in solar stuff, mainly heliostats, for decades. My bank account has suffered too! But saving the world is more important than money!? Yes. If a symmetrical bowl is used, the cooking pot will usually have to be at the end of some sort of arm that reaches into the bowl. That doesn't sound too difficult to do. The calculation of the depth of the bowl turned out to be truly horrible. I found myself facing an integral that I had no idea how to evaluate - and I'm a former math teacher! After asking a few people, and hunting through tables of integrals, all without success, I resorted to the brute-force-and-ignorance approach. I wrote a little computer program that made the machine loop around a few thousand times, evaluating the integral numerically by adding many terms. This kind of approach can produce an answer that is as accurate as is needed, but is never absolutely precise. That's how I came up with the result that the depth of the bowl should be 1.8478 times the focal length. Later, using that result, I calculated the radius of the rim of the bowl. It came out to approximately 2.718 times the focal length. When I saw that number, I was startled, because I recognized it as the value of "e", the base of natural logarithms! So now the question is, is this just a coincidence, or would a precise evaluation of the integral lead to the conclusion that the radius of the rim is precisely e times the focal length? My guess is the latter, but I'm not sure. If the radius of the rim is precisely e*F, then the depth of the bowl must be (e^2)/4 times the focal length. That ratio works out to 1.847264..., i.e. a few parts in ten thousand less than my computer program's result. It's quite plausible that the program was in error by that much. For practical purposes such as yours, an error that small will not be significant, but it is theoretically interesting. Get rich soon!                                  dow Posted by Morris Dovey on March 21, 2010, 4:00 pm  On 3/21/2010 10:42 AM, dow wrote: Hmm - Is the problem to match the area "under" the latus rectum to the area between the latus rectum and the rim? This is just too neat to be just a coincidence! Wow! "Interesting" is a _huge_ understatement! Not sure about riches for anyone, but if you can figure out a proof I'm willing to call it the "DOW's Lemma"... :) -- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/ Posted by dow on March 21, 2010, 6:11 pm  The problem is to find the condition that leads the torque that is exerted in one direction by the weight of the part of the bowl that is above the focus being equalled by the torque, in the opposite direction, that is produced by the weight of the part of the bowl that is below the focus. (Imagine the bowl being somewhat tilted, so the weights don't pass through the focal point.) So it isn't just the area of the bowl that has to be integrated, it's the product of the areas of a whole lot of little elements comprising the bowl and their distances above or below the focus. I find it hard to believe that this hasn't been investigated before. If the "e" thing is correct, there must surely be people who already know it. I'm going to continue asking around. I don't know how rich you are, but you are one of he few people I know of who manages to make a living from solar. That's an achievement!                             dow Posted by Morris Dovey on March 22, 2010, 1:16 am On 3/21/2010 1:11 PM, dow wrote: I was considering the special case where "center of mass" of the bowl coincides with its focal point. As I picture it, that center of mass should be independent of bowl orientation - which means that we can orient the bowl however we find convenient. It would seem to me that if the bowl is made up of uniform material, a differential amount of that mass can be represented by a differential area times the thickness of the bowl material, times the density of the material:     dm = dA * thickness * density and a convenient dA might be a ring-shaped "slice" of the bowl orthogonal to the line passing through vertex and focus of the parabola, and that each dA is a function (only) of the displacement of the slice from the vertex... Agreed, but I haven't seen it either. Do stick with the problem - it probably won't make you a pile of money, but it might be fun to be the first to publish! It's exciting for me just to see e pop up in this context. :) In almost all the ways that really matter to me, I'm wealthy beyond calculation - but if you're talking about just money, the R&D for panel and engine development has eaten up just about everything not needed for operating overhead. I have no regrets - there were problems that weren't being well-addressed, and I believed that I could produce solutions and deliver benefits that far outweighed the costs. I still see it that way. -- Morris Dovey DeSoto Solar DeSoto, Iowa USA http://www.iedu.com/DeSoto/ Posted by dow on March 22, 2010, 1:30 am  That's pretty much how I went about it, with one difference. If the material in the ring is not parallel with the axis, for example if the radius of the ring is increasing with increasing distance above the focus (which will be the case in this bowl), then the mass of the ring will be greater than it would be if the radius were constant. So another factor has to be included, besides the ones you've mentioned. You're a happy man. That's infinitely more important than money.                                dow This Thread Bookmark this thread:               Subject Author Date   New mount for stirling motors and satalite dish solar and the liquid piston tracker brian white 03-19-2010 please rate this thread Page 2 of 4   first < 1 2 3 > last Please Register and login to reply and use other advanced options Related Posts SubjectPosted InDate Solar in Florida Electricity from Sun 2004-10-10 solar forum Heating with Sun 2004-05-10 Solar cell modules Electricity from Sun 2004-04-18 Latest Posts