Calculate the "knee" of line

P

pltom55

New Member
Joined
Oct 6, 2014
Messages
27
So I need to figure out how to get the "knee" value which in my case would be the load.
I can tell its going to be about 6.2 by just hovering over it, but is there a faster way of slicing up the sample into multiple slopes and looking for a slope that's above a certain value?

QXCP7


Thanks
 

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<colgroup><col><col></colgroup><tbody>[TR]
[TD]Here is one sample of data

Compressive extension[/TD]
[TD]Load[/TD]
[/TR]
[TR]
[TD](mm)[/TD]
[TD](N)[/TD]
[/TR]
[TR]
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[TD="align: right"]0.12341[/TD]
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[TR]
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[TR]
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[TR]
[TD="align: right"]-0.00005[/TD]
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[TR]
[TD="align: right"]0.00001[/TD]
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[TR]
[TD="align: right"]0.00011[/TD]
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[TD="align: right"]0.94513[/TD]
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[/TR]
[TR]
[TD="align: right"]0.94664[/TD]
[TD="align: right"]5.31371[/TD]
[/TR]
[TR]
[TD="align: right"]0.94813[/TD]
[TD="align: right"]5.32197[/TD]
[/TR]
[TR]
[TD="align: right"]0.94962[/TD]
[TD="align: right"]5.33075[/TD]
[/TR]
[TR]
[TD="align: right"]0.95115[/TD]
[TD="align: right"]5.34031[/TD]
[/TR]
[TR]
[TD="align: right"]0.95273[/TD]
[TD="align: right"]5.34899[/TD]
[/TR]
[TR]
[TD="align: right"]0.95439[/TD]
[TD="align: right"]5.3578[/TD]
[/TR]
[TR]
[TD="align: right"]0.95614[/TD]
[TD="align: right"]5.36855[/TD]
[/TR]
[TR]
[TD="align: right"]0.95795[/TD]
[TD="align: right"]5.38097[/TD]
[/TR]
[TR]
[TD="align: right"]0.95976[/TD]
[TD="align: right"]5.39282[/TD]
[/TR]
[TR]
[TD="align: right"]0.96153[/TD]
[TD="align: right"]5.4035[/TD]
[/TR]
[TR]
[TD="align: right"]0.96325[/TD]
[TD="align: right"]5.41271[/TD]
[/TR]
[TR]
[TD="align: right"]0.9649[/TD]
[TD="align: right"]5.42126[/TD]
[/TR]
[TR]
[TD="align: right"]0.96649[/TD]
[TD="align: right"]5.43163[/TD]
[/TR]
[TR]
[TD="align: right"]0.96802[/TD]
[TD="align: right"]5.44041[/TD]
[/TR]
[TR]
[TD="align: right"]0.96951[/TD]
[TD="align: right"]5.448[/TD]
[/TR]
[TR]
[TD="align: right"]0.97098[/TD]
[TD="align: right"]5.45574[/TD]
[/TR]
[TR]
[TD="align: right"]0.97244[/TD]
[TD="align: right"]5.46311[/TD]
[/TR]
[TR]
[TD="align: right"]0.97391[/TD]
[TD="align: right"]5.47076[/TD]
[/TR]
[TR]
[TD="align: right"]0.97542[/TD]
[TD="align: right"]5.47942[/TD]
[/TR]
[TR]
[TD="align: right"]0.97698[/TD]
[TD="align: right"]5.48874[/TD]
[/TR]
[TR]
[TD="align: right"]0.97859[/TD]
[TD="align: right"]5.49846[/TD]
[/TR]
[TR]
[TD="align: right"]0.98025[/TD]
[TD="align: right"]5.50926[/TD]
[/TR]
[TR]
[TD="align: right"]0.982[/TD]
[TD="align: right"]5.51999[/TD]
[/TR]
[TR]
[TD="align: right"]0.98386[/TD]
[TD="align: right"]5.5316[/TD]
[/TR]
[TR]
[TD="align: right"]0.98585[/TD]
[TD="align: right"]5.54215[/TD]
[/TR]
[TR]
[TD="align: right"]0.98794[/TD]
[TD="align: right"]5.55313[/TD]
[/TR]
[TR]
[TD="align: right"]0.99005[/TD]
[TD="align: right"]5.56619[/TD]
[/TR]
[TR]
[TD="align: right"]0.99207[/TD]
[TD="align: right"]5.57743[/TD]
[/TR]
[TR]
[TD="align: right"]0.99395[/TD]
[TD="align: right"]5.58838[/TD]
[/TR]
[TR]
[TD="align: right"]0.99566[/TD]
[TD="align: right"]5.59965[/TD]
[/TR]
[TR]
[TD="align: right"]0.99721[/TD]
[TD="align: right"]5.60858[/TD]
[/TR]
[TR]
[TD="align: right"]0.99866[/TD]
[TD="align: right"]5.61772[/TD]
[/TR]
[TR]
[TD="align: right"]1.00007[/TD]
[TD="align: right"]5.62642[/TD]
[/TR]
[TR]
[TD="align: right"]1.00149[/TD]
[TD="align: right"]5.63444[/TD]
[/TR]
[TR]
[TD="align: right"]1.00296[/TD]
[TD="align: right"]5.64127[/TD]
[/TR]
[TR]
[TD="align: right"]1.00447[/TD]
[TD="align: right"]5.64909[/TD]
[/TR]
[TR]
[TD="align: right"]1.00605[/TD]
[TD="align: right"]5.65836[/TD]
[/TR]
[TR]
[TD="align: right"]1.00767[/TD]
[TD="align: right"]5.67011[/TD]
[/TR]
[TR]
[TD="align: right"]1.00937[/TD]
[TD="align: right"]5.68029[/TD]
[/TR]
[TR]
[TD="align: right"]1.01112[/TD]
[TD="align: right"]5.68954[/TD]
[/TR]
[TR]
[TD="align: right"]1.01294[/TD]
[TD="align: right"]5.69847[/TD]
[/TR]
[TR]
[TD="align: right"]1.01478[/TD]
[TD="align: right"]5.70792[/TD]
[/TR]
[TR]
[TD="align: right"]1.0166[/TD]
[TD="align: right"]5.71792[/TD]
[/TR]
[TR]
[TD="align: right"]1.01837[/TD]
[TD="align: right"]5.72789[/TD]
[/TR]
[TR]
[TD="align: right"]1.02007[/TD]
[TD="align: right"]5.73803[/TD]
[/TR]
[TR]
[TD="align: right"]1.02168[/TD]
[TD="align: right"]5.74825[/TD]
[/TR]
[TR]
[TD="align: right"]1.0232[/TD]
[TD="align: right"]5.75832[/TD]
[/TR]
[TR]
[TD="align: right"]1.02464[/TD]
[TD="align: right"]5.76611[/TD]
[/TR]
[TR]
[TD="align: right"]1.02604[/TD]
[TD="align: right"]5.77457[/TD]
[/TR]
[TR]
[TD="align: right"]1.02741[/TD]
[TD="align: right"]5.78326[/TD]
[/TR]
[TR]
[TD="align: right"]1.02877[/TD]
[TD="align: right"]5.7925[/TD]
[/TR]
[TR]
[TD="align: right"]1.03017[/TD]
[TD="align: right"]5.80177[/TD]
[/TR]
[TR]
[TD="align: right"]1.03163[/TD]
[TD="align: right"]5.81207[/TD]
[/TR]
[TR]
[TD="align: right"]1.03318[/TD]
[TD="align: right"]5.81896[/TD]
[/TR]
[TR]
[TD="align: right"]1.03486[/TD]
[TD="align: right"]5.82877[/TD]
[/TR]
[TR]
[TD="align: right"]1.03666[/TD]
[TD="align: right"]5.83879[/TD]
[/TR]
[TR]
[TD="align: right"]1.03857[/TD]
[TD="align: right"]5.85061[/TD]
[/TR]
[TR]
[TD="align: right"]1.0406[/TD]
[TD="align: right"]5.8639[/TD]
[/TR]
[TR]
[TD="align: right"]1.04269[/TD]
[TD="align: right"]5.87868[/TD]
[/TR]
[TR]
[TD="align: right"]1.04482[/TD]
[TD="align: right"]5.89203[/TD]
[/TR]
[TR]
[TD="align: right"]1.04691[/TD]
[TD="align: right"]5.90285[/TD]
[/TR]
[TR]
[TD="align: right"]1.04888[/TD]
[TD="align: right"]5.91268[/TD]
[/TR]
[TR]
[TD="align: right"]1.05071[/TD]
[TD="align: right"]5.92181[/TD]
[/TR]
[TR]
[TD="align: right"]1.05239[/TD]
[TD="align: right"]5.93012[/TD]
[/TR]
[TR]
[TD="align: right"]1.05395[/TD]
[TD="align: right"]5.93874[/TD]
[/TR]
[TR]
[TD="align: right"]1.05542[/TD]
[TD="align: right"]5.94612[/TD]
[/TR]
[TR]
[TD="align: right"]1.05685[/TD]
[TD="align: right"]5.95326[/TD]
[/TR]
[TR]
[TD="align: right"]1.05825[/TD]
[TD="align: right"]5.96097[/TD]
[/TR]
[TR]
[TD="align: right"]1.05966[/TD]
[TD="align: right"]5.97006[/TD]
[/TR]
[TR]
[TD="align: right"]1.0611[/TD]
[TD="align: right"]5.98041[/TD]
[/TR]
[TR]
[TD="align: right"]1.06261[/TD]
[TD="align: right"]5.99078[/TD]
[/TR]
[TR]
[TD="align: right"]1.0642[/TD]
[TD="align: right"]6.00058[/TD]
[/TR]
[TR]
[TD="align: right"]1.06588[/TD]
[TD="align: right"]6.01009[/TD]
[/TR]
[TR]
[TD="align: right"]1.06763[/TD]
[TD="align: right"]6.01995[/TD]
[/TR]
[TR]
[TD="align: right"]1.06943[/TD]
[TD="align: right"]6.03083[/TD]
[/TR]
[TR]
[TD="align: right"]1.07125[/TD]
[TD="align: right"]6.04338[/TD]
[/TR]
[TR]
[TD="align: right"]1.07303[/TD]
[TD="align: right"]6.05423[/TD]
[/TR]
[TR]
[TD="align: right"]1.07474[/TD]
[TD="align: right"]6.06325[/TD]
[/TR]
[TR]
[TD="align: right"]1.07637[/TD]
[TD="align: right"]6.07259[/TD]
[/TR]
[TR]
[TD="align: right"]1.07795[/TD]
[TD="align: right"]6.08134[/TD]
[/TR]
[TR]
[TD="align: right"]1.07949[/TD]
[TD="align: right"]6.08978[/TD]
[/TR]
[TR]
[TD="align: right"]1.08101[/TD]
[TD="align: right"]6.09757[/TD]
[/TR]
[TR]
[TD="align: right"]1.0825[/TD]
[TD="align: right"]6.10601[/TD]
[/TR]
[TR]
[TD="align: right"]1.084[/TD]
[TD="align: right"]6.11432[/TD]
[/TR]
[TR]
[TD="align: right"]1.08551[/TD]
[TD="align: right"]6.12325[/TD]
[/TR]
[TR]
[TD="align: right"]1.08709[/TD]
[TD="align: right"]6.13193[/TD]
[/TR]
[TR]
[TD="align: right"]1.08874[/TD]
[TD="align: right"]6.14094[/TD]
[/TR]
[TR]
[TD="align: right"]1.09045[/TD]
[TD="align: right"]6.14975[/TD]
[/TR]
[TR]
[TD="align: right"]1.09224[/TD]
[TD="align: right"]6.16165[/TD]
[/TR]
[TR]
[TD="align: right"]1.09409[/TD]
[TD="align: right"]6.17445[/TD]
[/TR]
[TR]
[TD="align: right"]1.096[/TD]
[TD="align: right"]6.1856[/TD]
[/TR]
[TR]
[TD="align: right"]1.09794[/TD]
[TD="align: right"]6.19715[/TD]
[/TR]
[TR]
[TD="align: right"]1.09986[/TD]
[TD="align: right"]6.20992[/TD]
[/TR]
[TR]
[TD="align: right"]1.10173[/TD]
[TD="align: right"]6.2214[/TD]
[/TR]
[TR]
[TD="align: right"]1.1035[/TD]
[TD="align: right"]6.23313[/TD]
[/TR]
[TR]
[TD="align: right"]1.10519[/TD]
[TD="align: right"]6.2437[/TD]
[/TR]
[TR]
[TD="align: right"]1.10677[/TD]
[TD="align: right"]6.25477[/TD]
[/TR]
[TR]
[TD="align: right"]1.1083[/TD]
[TD="align: right"]6.28596[/TD]
[/TR]
[TR]
[TD="align: right"]1.10981[/TD]
[TD="align: right"]6.37194[/TD]
[/TR]
[TR]
[TD="align: right"]1.11132[/TD]
[TD="align: right"]6.5248[/TD]
[/TR]
[TR]
[TD="align: right"]1.11286[/TD]
[TD="align: right"]6.7355[/TD]
[/TR]
[TR]
[TD="align: right"]1.11442[/TD]
[TD="align: right"]6.98878[/TD]
[/TR]
[TR]
[TD="align: right"]1.11458[/TD]
[TD="align: right"]7.01581[/TD]
[/TR]
</tbody>[/TABLE]
 
Upvote 0
pltom55,
Assuming your data starts in Row 2 of columns A & B...I assume Row 1 to be a header.
This code will find the 'knee' based on whatever slope change you specify. In this example I used '1.5' which is 50% more than the adjacent segment, which yielded 'N = 6.25477'. You can tweak the % to suit your needs.
Perpa

Code: 
Sub FindTheKnee()
Dim L_slope, R_slope
Dim rw, LastRow As Long
    LastRow = ActiveSheet.Cells(Rows.Count, "A").End(xlUp).Row
    For rw = 2 To LastRow
        L_slope = (Cells(rw + 1, "B") - Cells(rw, "B")) / (Cells(rw + 1, "A") - Cells(rw, "A"))
        R_slope = (Cells(rw + 2, "B") - Cells(rw + 1, "B")) / (Cells(rw + 2, "A") - Cells(rw + 1, "A"))
        
        If R_slope > L_slope * 1.5 Then    'R_slope >50% more than L_slope, change to suit
            MsgBox "Knee at N = " & Cells(rw + 1, "B") & Chr(10) & "Left Slope = " & L_slope & Chr(10) & "Right Slope = " & R_slope
            Exit Sub
        End If
    Next rw
End Sub
 
Upvote 0
pltom55,
I inadvertantly used the inverse slope in my previous post. I believe the following is a more accurate solution:
Using an average slope of 5 rows of data each side of the 'knee' using these formulae:

Code: 
L_slope = (Cells(rw + 5, "A") - Cells(rw, "A")) / (Cells(rw + 5, "B") - Cells(rw, "B"))

R_slope = (Cells(rw + 10, "A") - Cells(rw + 5, "A")) / (Cells(rw + 10, "B") - Cells(rw + 5, "B"))
Gives this solution:
N = 6.23313
>50% change in slope
L_slope = .053673
R_slope = .174171
I hope this is helpful.
Perpa
 
Upvote 0
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