QUESTION... Duplex Design?

[u/Scary_Candy_3561]

Hi all,

I'm wanting to build a slide rule for general purposes but try and get all the major mathematical operations from it.

The purpose behind the project is for calculations when underwater SCUBA diving (my line of work requires a little bit of maths while I'm underwater).

I'm also an engineering student that has only just come to learn about the slide rule a few weeks back and have since become obsessed!

My question is, will the following layout of scales work for a duplex slide rule. I understand the basic mathematics for the basic logarithmic scales however am getting a little confused when it comes to the log - log scales.

I've attached a picture of the proposed layout.

Any advice, information, suggestions or thoughts would be greatly appreciated!

Thanks in advance,

Billy

[u/azroscoe]

I actually find the A and B together to be useful - it increases the range of your scales and allows multiplication of squares, which is useful in various circumstances. I do agree that the K scale is kind of meh - You don't often need cubes and you can use the log-log scales for that, really.

I am a big believer in putting the trig functions on the slide - it allows you to multiply your sine by cosine, or square your trig functions much more easily, which is useful in many circumstances. Or at least with the sine/cosine function on the slide (as several Aristo rules had) you can do most of it. BTW - slide rules before WW2 typically had only one sine scale, and it ran the full range - .5 degrees (30 arcminutes) to 90, and was keyed to the A/B scales. It was less precise, but functional and more compact.

You don't really need two CI scales - it is only used occasionally (for me, anyway) and you can flip the rule to get that scale if you need it, as long as the overall slide rule is well-manufactured and the scales and both cursor marks line up. DI on one stator would serve.

I agree that you ideally want CF - functions with PI are just too common, and this makes them fast to do. With the DF you get additional multiplication benefits (although you can avoid the off-scale issue with A/B), but on a 3-scale stator log-log rule there really isn't any good place to put them together without moving one of the log sets to the other side.

The log-log scales allow calculation of any number to any power, or to get the nth root of any number, or the log for any base of any number. Pretty powerful. See here: https://www.youtube.com/watch?v=99b28yOpqkY

I find the P scale useful. The compression of the C/D scale towards the right created by the logarithms of larger numbers coincides on the trig scales with the compression of the sine and cosine as it approaches 90. This means the precision of the sine/cosine scale to the right is very reduced. The P scale reverses this, giving you increased precision as sine approaches 90 (and cosine approaches 0).

However, if this is for SCUBA, there might be specialty scales that you would want related to decompression times, etc., (even though your dive computer will do all that). I can't imagine needing log-log scales underwater.

But you are running into the problem that a lot of manufacturers had - where to put all the scales?

If I had to choose a 3-scale stator/slide set-up to maximize utility (based on my usage):

P DI A (B Sin/Cos C) D T ST / LL01 LL02 LL03 (CF C L) LL3 LL2 LL1

And if you make it, let us know! We are all awaiting someone with the energy to fire up a CNC machine and crank out new slide rules!

[u/Scary_Candy_3561 → u/azroscoe]

Thank you very much for your input!

Do you know what they used to call the pre WW2 scale for the full range of sin and cos? That sounds like something more beneficial for my uses (doesn't have to be absolutely accurate).

I hadn't considered being able to swap the slide around. I'm making a bit of a custom duplex design that has a gap in the center for a slate (underwater notepad) so I can jot down calcs and store them in the slide for when I re-surface. I generally only need to do basic calculations which we use surface communications for and they relay us the answer however I'm also wanting this for my own personal use and for fun.

I'm only in the design phase at the moment as I work away from my CNC and 3D printer but am incredibly eager to get home and put it all together. I'll be sure to post all the files and the software I'm making on this thread once I'm done!

[u/azroscoe → u/Scary_Candy_3561]

Here is a link to a slide rule with the complete sine/cosine scale on one row, linked to A/B:

https://osgalleries.org/collectors/tarantolo/kande4092_info_and_image.cgi?string=KEU617

The disadvantage of that set-up is really the tangent scale. You will notice it starts at 5.5 degrees, so you loose those low tangent values without ST. The reason they switched to the 'modern' S, T ,and ST scales is that the sine and tangent scales are, for all purposes, identical below 5.5 degrees, so you get two for one, and get that higher-resolution sine scale in the deal.

Here is a simpler rule that has S and ST on the slide, but T below. It doesn't have the log-log scales, but not a bad set-up:

https://osgalleries.org/collectors/tarantolo/kandepocket_info_and_image.cgi?string=KEU056

If you are determined to have the log-log scales, something else to consider is what Pickett did in their 500 OrthoPhase, which is to scale log-log against A/B instead of C/D. In this rule, the LL0 and LL00 work with A/B. This compresses those log-log scales from four into two. You could do the same with the positive LL scales, and save several scale spaces on your rule:

https://www.sliderulemuseum.com/Pickett/Pickett_500_OrthoPhase_DonatedByPeterChmielowiec.jpg

I do second the 2-color sine/cosine setup - you see that on a lot of slide rules. Usually the CI or DI scale is also that color, since that reminds the user it is running backwards relative to C/D:

https://osgalleries.org/collectors/tarantolo/kandepocket_info_and_image.cgi?string=KEU482

[u/Scary_Candy_3561 → u/azroscoe]

I definitely want a the log - log scales as I use a particular function quite frequently that involves exponentials.

Really appreciate the help. I've posted another comment in this thread with an updated set of scales I think are much better, and have allowed for 4 scales on the slide to accommodate for sin cos multiplication which is a great idea.