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Re: Pellet oven linearity

johnsojc — Sun Jul 29, 2007 7:37 pm

Author: johnsojc

Posted: Sun Jul 29, 2007 7:37 pm

I think starting with sin^2 as the best guess at the curve is valid. The sine of what is the question. Since all the published info on actual data shows the curve varies linearly with the amount we can exclude it (maybe) from being the variable in any sine term. That leaves time and temp as candidates as the variable in a sine function.

We would need to determine why the peak is offset from peaking at 90. There are two simple ways to do this: scale the value of what you are taking the sine or pick an arbitrary point after which you start subtracting any increase over that point's value (or even a combination of the two).

Since the beginning of the curve of real data does not rise as rapidly as a pure sin^2 curve, it must be modified by some combination of the amount and possibly the time and/or temp. Using just the amount or some scaled value of the amount alone does not reproduce the curve so some other factor must be in play.

Then there are the limits. Oven 4 has the irritating habit of "shorting out" if the product of the time and temp are over a certain value giving an output of 0. All the ovens have certain points where increasing the amount, the time, or the temp have no further effect on the output.

This is a very complex problem of modeling a "real" world system and I'm not sure it is even possible to come up with a viable model just using the output values as a guide.

Re: Pellet oven linearity

belford — Sun Jul 29, 2007 3:27 pm

Author: belford

Posted: Sun Jul 29, 2007 3:27 pm

I'm sure I knew that about sin^2, twenty years ago.

Re: Pellet oven linearity

belford — Sun Jul 29, 2007 3:25 pm

Author: belford

Posted: Sun Jul 29, 2007 3:25 pm

As for a cubic, my graphing software says

ax3+bx2+cx+d

d=-0.0056, c=-0.0643, b=0.0261, a=-0.0002574

And that also fits well when rounded, although not quite as well.

Re: Pellet oven linearity

Christian Walther — Sun Jul 29, 2007 3:19 pm

Author: Christian Walther

Posted: Sun Jul 29, 2007 3:19 pm

1 - cos and sin^2 are the same thing, up to scaling. Specifically, 1 - cos(x) = 2 sin^2(x/2). Proof is left as an exercise to the reader .

Re: Pellet oven linearity

belford — Sun Jul 29, 2007 2:59 pm

Author: belford

Posted: Sun Jul 29, 2007 2:59 pm

It fits a sine (not sin^2) very well, up to that peak. My coefficient-twiddling got me to

17.8 * (1-cos(x*pi/6)

Round that to the nearest integer and it hits nearly every data point up until 66. (The 1-cos() is just a trick to get a sine curve that starts at zero and rises to a peak.)

Re: Pellet oven linearity

Christian Walther — Fri Jul 27, 2007 4:49 pm

Author: Christian Walther

Posted: Fri Jul 27, 2007 4:49 pm

That curve looks more like a cubic polynomial than a sin² to me. Notice how it's not symmetric around the peak, but steeper around 81 than around 41. Try fitting a scaled version of -2x³ + 3x² to it (maybe 35*(-2(x/66)³ + 3(x/66)²)).

Re: Pellet oven linearity

johnsojc — Fri Jul 27, 2007 12:14 am

Author: johnsojc

Posted: Fri Jul 27, 2007 12:14 am

OK, here is the 100 point curve for oven 4.
Time 20 (1hour), Amount 81, Time 1-100

For contrast, here is the curve for sin^2(A)

As you can see, if you squeeze the sine squared curve over so it peaks at 66 instead of 90, the curves are very similar. Something seems to be modifying the curve slightly, probably another factor related to the amount.

Re: Pellet oven linearity

johnsojc — Thu Jul 26, 2007 6:09 pm

Author: johnsojc

Posted: Thu Jul 26, 2007 6:09 pm

And, as long as we are being precise, any data reported has to specify whether the settings are using the 0-50 scale or the 0-100 scale. There are 100 positions on each slider (not counting 0 ). 0-50 scale readings should include 0.5 settings, i.e 0.5-1.0-1.5-2.0, etc, corresponding to 1-2-3-4 on the 0-100 scale.

Off topic comment: Why do people use 0-50? Because the correct Bahro formula is 40-30-20 for white light pellets which, when properly set on the sliders, is the 40th mark, the 30th mark, and the 20th mark on the sliders. There are 50 marks on each slider. (the kicker is there is a valid setting between each mark that makes a total of 100 possible settings.)
New for this version of Er'cana, 0-50 on the time scale is 0-5 hrs of real time. That makes one of the 100 settings on the time slider increment the bake time by 3 minutes (half marks). Each small mark adds 6 minutes.

Re: Pellet oven linearity

Kestryll — Thu Jul 26, 2007 5:58 pm

Author: Kestryll

Posted: Thu Jul 26, 2007 5:58 pm

johnsojc wrote:

Kestryll wrote:
Something else I'd like clarified from the ones doing the max burn-out tests. Are ya'll numbering the ovens based on the control room, or is 1-4 just the order in which you were testing them?

I think it would make sense if everyone was on the same page about which oven is which. I use the numbering based on which numbered push button in the control room activates which oven.

That's what I was assuming, and hoping. Just wanted to make sure.

Re: Pellet oven linearity

johnsojc — Thu Jul 26, 2007 5:52 pm

Author: johnsojc

Posted: Thu Jul 26, 2007 5:52 pm

Kestryll wrote:

Something else I'd like clarified from the ones doing the max burn-out tests. Are ya'll numbering the ovens based on the control room, or is 1-4 just the order in which you were testing them?

I think it would make sense if everyone was on the same page about which oven is which. I use the numbering based on which numbered push button in the control room activates which oven.

As you enter the oven/mixer room (the door with the power switch) coming from the control room via the vats and face the elevator push button, the oven directly to your left is #4, the far one on the left is #3, #2 is directly to your right, and #1 is the far one the right.

pellet
dispenser
room

(door w/rockfall)
Mixer 3 Mixer 1
Mixer 4 Mixer 2
(door w/ switch)

vats

Control
Room

Re: Pellet oven linearity

Kestryll — Thu Jul 26, 2007 5:22 pm

Author: Kestryll

Posted: Thu Jul 26, 2007 5:22 pm

Dovahn wrote:

I'm experimenting on just one avatar as well. I've figured it so I get three tests a day, but it's basically the same...

I've tested the pressure (or the middle slider) and I'm not sure it's pressure. I think a key piece to our understanding is learning what it actually is. My current theory is that it's the balance between two ingredients, which cook somewhat differently. (I should run tests with it at 0, then at 50, as that would be working with the pure versions of each). Of course, I could be wrong.

Since I also like to get scores greater than zero... I try to set the ovens at something will will give scores over 900 and play from there. I've started working with that middle slider, just having trouble deciding where to start.

So, if the middle slider is more like balance, rather than pressure(It does look more like a scale, and I do believe it's been refered to as weight, I just see Pressure a lot... hehe), would setting the middle slider to a value at the mid-point grant a more even distribution of scores, or how does it affect the point value?

So, if 30 is the mid-point value, and I set the oven at the max burn-out value, like oven 1 has a posted value of 35/20, would I want the middle slider at the midpoint(27.5 for oven 1), or do I set it higher or lower than 30? i.e. Does a higher than 30 give more weight to time, or temperature?

Have I lost ya yet?

Something else I'd like clarified from the ones doing the max burn-out tests. Are ya'll numbering the ovens based on the control room, or is 1-4 just the order in which you were testing them?

Keep up the good work everyone!

Re: Pellet oven linearity

johnsojc — Thu Jul 26, 2007 12:44 pm

Author: johnsojc

Posted: Thu Jul 26, 2007 12:44 pm

belford wrote:

Is that 100-point pellet data on line somewhere? I'd love to see it.

One reason I started this thread was to get some momentum for Uru science done the way real science is done. Post your data, show your error bars, explain your reasoning, speculate how you might be wrong.

I can put it up somewhere when I get home tonight. I'm not sure how useful it is. I may have picked an amount setting that was at or beyond the limit where the curve for change in amount starts to flatten out. I have a suspiciously flat area at the top of the curve for temp change. I need to run another curve varying the amount for the same time and temp. I picked a peak value based on what I could see on the FPI chart for O4T20. It appeared that the peak was at amount=81 so I used that value. My reasoning was that measuring output at a setting that gives a max value would minimize my errors due to rounding or truncation. I would have loved to run the peak for the 4 hour oven but that would have been two weeks of constant baking and RL is really too busy at the moment for me to spend this much time running tests.

Re: Pellet oven linearity

Dovahn — Thu Jul 26, 2007 11:17 am

Author: Dovahn

Posted: Thu Jul 26, 2007 11:17 am

I'm experimenting on just one avatar as well. I've figured it so I get three tests a day, but it's basically the same...

I've tested the pressure (or the middle slider) and I'm not sure it's pressure. I think a key piece to our understanding is learning what it actually is. My current theory is that it's the balance between two ingredients, which cook somewhat differently. (I should run tests with it at 0, then at 50, as that would be working with the pure versions of each). Of course, I could be wrong.

Dovahn

Re: Pellet oven linearity

Kestryll — Thu Jul 26, 2007 5:40 am

Author: Kestryll

Posted: Thu Jul 26, 2007 5:40 am

You know... I see a lot of people testing the Time and Temperature settings... Unless I missed it somewhere, has anyone tested the Pressure yet?

I'm only one person with limited time and only one avvy in there. It'll take awhile to come up with any real results from testing any of these settings. Doesn't quite stop me from testing, but it's still a pain when you're only getting two batches a day...

Re: Pellet oven linearity

belford — Thu Jul 26, 2007 4:31 am

Author: belford

Posted: Thu Jul 26, 2007 4:31 am

Is that 100-point pellet data on line somewhere? I'd love to see it.

One reason I started this thread was to get some momentum for Uru science done the way real science is done. Post your data, show your error bars, explain your reasoning, speculate how you might be wrong.