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Old 2nd October 2012, 08:24 PM   #31
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Join Date: Mar 2008
methinks thou hast made yon tpyo....
If you meant Phi = 1.5 the Fr(1.5,p) is:
Fr(1.5,0.5) = 1.03
Fr(1.5,1.0) = 1.38
Fr(1.5,1.5) = 1.96
Fr(1.5,2.0) = 2.78
Fr(1.5,2.5) = 3.83
Fr(1.5,3.0) = 5.11
Fr(1.5,3.5) = 6.63

OTOH if you want a fixed value of Fr = 1.5:
Fr = 1.5, p = 0.5 => Phi = 3.267
Fr = 1.5, p = 1.0 => Phi = 1.634

OK, it wasn't a tpyo, and your numbers are bang on.
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Old 3rd October 2012, 10:57 AM   #32
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Terry, i am fairly convinced i have the ticks on the horizontal axis correct. The numbers are in a nice even descending order, and the values i pick off of your chart and compare with the commercial chart match up. Also just using the log lines on your chart and the commercial chart the values match up (hint, use your original chart with lots of log lines).

With that said the numbers you calculated are all over the map. To make the calculated numbers match the tick marks, some marks have to go to the left and some to the right. Some are off so far i would have to move them 1/2 to 3/4 of the way over to the next tick mark.

Here are my notes when i used your calculated values.

1.1 should move to the left 1/4 line width
1.2 is right on
1.3 has to be moved at least 1 line width to the left
1.4 has to move to the right 90% of the way to 1.5
1.5 must move to the right 3 line widths
1.6 two values do not agree, must move to the right 1/2 for one and 3/4 the way to 1.7 for the other.
1.7 must move to the right 3/4 of the way to 1.8
1.8 must move to the right 2 line widths
1.9 ok

These are an example of some of the worst. Try selecting them on a commercial chart.

Fr(1.5,3.5) = 6.63, should be 6
Phi = 1.4, p = 5.0 => Fr = 10.17, commercial says Fr 8.75, your chart says Fr 9.

Phi = 1.6, p = 3.0 => Fr = 6.08, the two Phi 1.6 do not compare in position.
Phi = 1.6, p = 3.5 => Fr = 7.95

So at this point i am believing your chart, but not so much your calculations. Are you using different formulas for the chart and hand calculations?
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File Type: jpg dowell 1-2 layer well marked 10 layers.JPG (218.3 KB, 39 views)
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Old 3rd October 2012, 07:42 PM   #33
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I put some tick marks on the vertical axis. They compare reasonably well with the commercial chart. Sometimes right on, sometimes off about .5 of a number, like 1.45 instead of 1.5, depending on which layer i am comparing. If i knew for sure what chart was right i would tweek the tick marks if needed. But in the real world that differance does not mean much.
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Old 6th October 2012, 06:13 PM   #34
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Latest version of Dowell chart. The tick marks Phi from .3 to 1 are .1, .5, .9
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Old 6th October 2012, 09:00 PM   #35
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Quote:
Originally Posted by powerbob View Post
Terry, i am fairly convinced i have the ticks on the horizontal axis correct. The numbers are in a nice even descending order, and the values i pick off of your chart and compare with the commercial chart match up. Also just using the log lines on your chart and the commercial chart the values match up (hint, use your original chart with lots of log lines).

With that said the numbers you calculated are all over the map. To make the calculated numbers match the tick marks, some marks have to go to the left and some to the right. Some are off so far i would have to move them 1/2 to 3/4 of the way over to the next tick mark.

[snip]
These are an example of some of the worst. Try selecting them on a commercial chart.

Fr(1.5,3.5) = 6.63, should be 6
Phi = 1.4, p = 5.0 => Fr = 10.17, commercial says Fr 8.75, your chart says Fr 9.

Phi = 1.6, p = 3.0 => Fr = 6.08, the two Phi 1.6 do not compare in position.
Phi = 1.6, p = 3.5 => Fr = 7.95

So at this point i am believing your chart, but not so much your calculations. Are you using different formulas for the chart and hand calculations?
I am of course using the same function to calculate individual values and generate the charts, in the same MathCAD worksheet. I gave you the expression a few posts back.
so:
Fr(1.4,5.0) = 10.17 is indeed correct (I just checked it).
its also the value given in Snelling fig. 11.14

yet you manage to read the result as 9 from the graph of the same function.
ergo the problem does not lie with the function....

Likewise I checked the Phi = 1.6, p = (3.0,3.5) and snelling also gives Fr = 6,8
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Old 6th October 2012, 10:40 PM   #36
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Terry, check this one to.
Phi = 1.6, p = 3.5 => Fr = 7.95 as the 2 Phi 1.6 plotted values do not match up to the same point.

But more importantly we are going around in circles. Check your original chart with all the decades to the commercial chart in my last post and with Snelling. There are plenty of log lines that intersect with layers for both Fr and Phi. Using the log lines we can eliminate the tick marks as a source of error. I have compared every layer between your graph and the commercial graph using the log lines and they are almost identical. Now i need the results from Snelling.

Also if you have the technology, post Snelling’s chart as large as you can. So i can see what is going on.
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Old 7th October 2012, 02:02 AM   #37
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Terry, i might be on to something.

I went over everything again and found something of interest. When i tried your table below for Phi 1.5, the .5 and 1 layer were right on, but all other layers were noticeably off. I kept playing with locations for Phi and i was surprised that i was able to find a location were all of the numbers worked out.

Phi 1.5, P 0.5 = Fr 1.03
Phi 1.5, P 1.0 = Fr 1.38
Phi 1.5, P 1.5 = Fr 1.96
Phi 1.5, P 2.0 = Fr 2.78
Phi 1.5, P 2.5 = Fr 3.83
Phi 1.5, P 3.0 = Fr 5.11
Phi 1.5, P 3.5 = Fr 6.63

So now i would like to start over with the tick marks but i think what i need is a chart like you made above but for a Phi of 1.1 and 1.9. so i can try to look for scaling factors to calculate the other positions.

Phi 1.1, P 1.0 = Fr
Phi 1.1, P 1.5 = Fr
Phi 1.1, P 2.0 = Fr
Phi 1.1, P 2.5 = Fr
Phi 1.1, P 3.0 = Fr
Phi 1.1, P 3.5 = Fr
Phi 1.1, P 4.0 = Fr
Phi 1.1, P 4.5 = Fr
Phi 1.1, P 5.0 = Fr
Phi 1.1, P 6.0 = Fr

Phi 1.9, P 0.5 = Fr
Phi 1.9, P 1.0 = Fr
Phi 1.9, P 1.5 = Fr
Phi 1.9, P 2.0 = Fr
Phi 1.9, P 2.5 = Fr
Phi 1.9, P 3.0 = Fr

And 2 more entry’s for Phi 1.5

Phi 1.5, P 4.0 = Fr
Phi 1.5, P 4.5 = Fr

Thanks
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Old 7th October 2012, 05:45 AM   #38
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Powerbob,

I had a crack at adding the marks once, and ballsed it up completely. that annoyed me enough to replicate the whole damn chart, so I had the actual function and hence didn't need the marks.

once you crack it, I imagine the generic solution becomes immediately apparent. good on you for persevering, and I'm interested to see how it works out.
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Old 7th October 2012, 05:49 AM   #39
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Powerbob,

Phi 1.1, P 0.5 = Fr 1.01
Phi 1.1, P 1.0 = Fr 1.12
Phi 1.1, P 1.5 = Fr 1.32
Phi 1.1, P 2.0 = Fr 1.58
Phi 1.1, P 2.5 = Fr 1.93
Phi 1.1, P 3.0 = Fr 2.35
Phi 1.1, P 3.5 = Fr 2.85
Phi 1.1, P 4.0 = Fr 3.43
Phi 1.1, P 4.5 = Fr 4.08
Phi 1.1, P 5.0 = Fr 4.81
Phi 1.1, P 6.0 = Fr 6.50

Phi 1.9, P 0.5 = Fr 1.07
Phi 1.9, P 1.0 = Fr 1.78
Phi 1.9, P 1.5 = Fr 2.97
Phi 1.9, P 2.0 = Fr 4.63
Phi 1.9, P 2.5 = Fr 6.77
Phi 1.9, P 3.0 = Fr 9.39
Phi 1.9, P 3.5 = Fr 12.48
Phi 1.9, P 4.0 = Fr 16.04
Phi 1.9, P 4.5 = Fr 20.08
Phi 1.9, P 5.0 = Fr 24.59
Phi 1.9, P 6.0 = Fr 35.05

HTH
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Old 7th October 2012, 06:35 AM   #40
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Location: South Sweden
Hehe, you guys

I am still reading and fighting with your small attachment , Terry... Will do a Matlab script for it...
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