What if there's no iPod, iPad or internet...

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What if there's no iPod, iPad or internet...

Postby heidtwd@att.net » Thu Dec 15, 2011 2:13 pm

As unlikely and disturbing as this might sound, one must prepare for the worst. The worst in this case turns out to be pretty convenient for those of us that keep programmable calculators close at hand including in the toolbox.

My calculators of choice have always been Hewlett - Packard and I have come to really appreciate the virtues of RPN as my personal faculties fade.

Writing a little program to save in the calculator was much less of a chore than making the calculation of the AMP v2 geometry - and that wasn't too tough. Given that the AMP v2 business is accomplished by the caliper measuring the change in length of the base of an isoceles triangle and that the difference is 152.40 mm for a change of 90 degrees, following provides the unique solution of leg lengths that make this work.

Where:
A = the change in base length
a = the angle opposite A
OA = the desired obtuse angle
C = the length of one of the equal legs
The solution for the leg lengths at an obtuse angle = 90 degrees is had by
A = 2C x sine (a/2)

At an obtuse angle setting of 90 degrees, a = 45 degrees. Therefore at an obtuse angle of 180 degrees, a = 135 degrees. Given these two known conditions, the lengths of A and C can be calculated as follows.
2C x sine (45/2) + 152.40 = 2C x sine (135/2)
C = 140.799 mm
A at obtuse angle of 90 degrees = 2 x 140.799 x sine (45/2) = 107.763 mm

Solving for A for a given obtuse angle is then
A = 2C x sine ((OA-45)/2) - 107.763

Solving for the obtuse angle for a given A is
OA = 2 x (arcsine ((A + 107.763)/281.598) + 22.5)

A simple program for the venerable HP 10C is then
fLBLA
45
-
RCL02
X
RCL01
-
fLBLB
RCL01
+
RCL02
/
gsin-1
22.5
+
2
X
To calculate A, enter the obtuse angle, press enter, and press f LBL A
To calculate the Obtuse angle, enter A, press enter, and press f LBL B

After all this, the good news was that the result corresponded to the APP!

Bill
Last edited by heidtwd@att.net on Sun Jan 08, 2012 8:01 am, edited 1 time in total.
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Re: What if there's no iPod, iPad or internet...

Postby rwest » Thu Dec 15, 2011 6:06 pm

Bill,

Nice work, good to know there are smart people posting.

The original AMP actually came with a bunch of formulas(8) to put into an HP-32s and a laminated cheat sheet to show you which one to use.

The app is easier though.

-Rutager
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Re: What if there's no iPod, iPad or internet...

Postby spudman@wybatap.com » Sat Jan 07, 2012 8:00 pm

Nice Job. I had not thought about using the delta in length and angle to fill in the missing leg lengths.

Now to write a little program for windows. Could probably do a spreadsheet. Any interest in that? I wonder if I did one if it could be posted on the BCT site?

Bob Roos
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Re: What if there's no iPod, iPad or internet...

Postby mathewanna403@gmail.com » Tue Aug 28, 2018 2:41 am

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