Quote from: TinselKoala on September 25, 2012, 05:12:26 PM
In case anyone really doubted it, Mondrasek's data show a linear relationship between the independent variable (the water added to the weight reservoir) and the two dependent variables (the Zed drop in response to the added weight, and the rise of the head level in the input tube in response).

Thanks TK!  I had made the graphs and looked myself, but I did not have time/patience to annotate and present like you have.

Did you look at graphs of the delta in the incremental distances of the ZED lift and also the Input Tube rise for each data point yet?  Weird stuff there.  I'm not sure what is going on.  Just build issues?  Measurement issue?  Or is it correct due to the changing internal pressures in the ZED?

BTW, do NOT graph those two previously mentioned delta data sets against each other.  Weirder stuff there!  But I only did it for fun and have no idea if it has an relevance at all.

Thanks again!

M.

Quote from: mondrasek on September 25, 2012, 05:21:32 PM

Thanks TK!  I had made the graphs and looked myself, but I did not have time/patience to annotate and present like you have.

You are welcome, I am a graphing whiz so it only took me a couple of minutes to do it, right in your spreadsheet. Using, of course, Office Libre, the free software that comes with Ubuntu Linux installs.

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Did you look at graphs of the delta in the incremental distances of the ZED lift and also the Input Tube rise for each data point yet?  Weird stuff there.  I'm not sure what is going on.  Just build issues?  Measurement issue?  Or is it correct due to the changing internal pressures in the ZED?

No, I didn't. Just eyeballing the graphs, though, it looks perfectly linear with a bit of noise, so I would expect the deltas to look the same when broken out. I am assuming your millimeter measurements are from your digital dial indicator so are fairly accurate, and ditto the water weights that you are pouring in. To get a real handle on the error range we need more runs. If you can manage to do, say, ten runs just like that last one, it will be possible to determine the standard deviation of your data and so get a handle on just how small your random errors are likely to be. I would bet, right offhand, that the "weird stuff" you are seeing in the deltas is probably noise, and will turn out to be linear when the error is taken into account. Still, it does look like the system starts of slowly; there may be a bit of a curve right there at the start of lift. Small tapers, irregularities, bumps.... all would be seen as "nonlinearities" at some scale in the graph, but are considered systematic noise (as opposed to random noise like variations in the "100 grams" for example).

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BTW, do NOT graph those two previously mentioned delta data sets against each other.  Weirder stuff there!  But I only did it for fun and have no idea if it has an relevance at all.

Thanks again!

M.

I dunno either. The next step, I guess, would be to compute the transfer efficiency. Presumably if you started as before, but simply poured in the whole 1200 mL water at once, the thing would settle at the same zed sink and input head rise values. So you could figure out the input and output work, going backwards, considering the Zed the input and the water level in the tube the output.

But now that I realise that we are dealing with an "automatic bollard" where the weight is supported not by the input water totally, but almost entirely by the precharge.... I'm not sure at all how to analyze the system any more. You might just be tossing an apple, enough to move some heavy object that is already just about to move anyway.

@mondrasek: How did you manage to measure the water height in the input tube to the hundredth of a millimeter? I find that....er..... slightly improbable.

Anyhow... maybe you have a microscope and can read the meniscus in the tube to finer than a human hair's width. That's good, my eyeballs can't manage that. 
1 mm = about 0.040 inch, so one hundredth of a mm is .... well, call it a shade less than half a thousandth of an inch.

Regardless of the uncanny precision, I think your numbers are likely to be accurate enough, since there isn't a perceptible deviation from linearity and the noise, even in the single data set, seems quite small.

Here is the graph that shows the slope of the regression line, in other words, the ratio of input to output travel. I'm not sure how useful even this is, though, since there is a great spring (the precharge) pushing up on your Riser/AddedWater combo.

Quote from: TinselKoala on September 25, 2012, 11:40:46 PM
@mondrasek: How did you manage to measure the water height in the input tube to the hundredth of a millimeter? I find that....er..... slightly improbable.

I was surprised you didn't jump on that as your first point of business before doing any graphs!  I put a piece of masking tape on the input water tube so that I could mark the meniscus to the best of my "eyeball" ability with a fine sharpie at each step.  At the end the tape was removed and placed on the edge of my workbench.  Then the distance from the initial "zero" mark to each of the step marks was measured with digital vernier calipers that read to 0.01 mm.  So the recorded values are correct and have that precision, but there are at least two "eyeball" and other errors introduced to each. 

M.