Re: Standard notation for slide rule moves?


Andreas Poschinger
 

Hi Steve and all,

a principal problem which I have with my effort estimations is how to
wheight a slide setting  with and without cursor and how to weight a
cursor setting alone and how to weight a reading. As long as I do not
know this, my idea would be to sum up all of them, so that later
different weight sets can be applied, and a summurized effort can be
calculated.

With respect of slide setting with and without cursor, for me it is a
large different whether there is a tick mark and maybe whether it is
major though eventually everthing is a matter of exercise.

I need a lot time for fine settings.

If I used the example D:3 < C:7.31, I'd clearly work without cursor and
save some 2 seconds.

If I used the example D:3.43 < C:7, I'd also work without cursor and
maybe save some 1 seconds, while in both examples most likely winning
accuracy.

If I used the example D:3.43 <|< C:7.31 I'd work with cursor because
there is the risk that I do not remember both numbers in full length...

I'd say I'd not use the cursor for up to two times two counting numbers.
But that of course is quite personal.

With respect to this example
D:3 <|< C:7        // optional D:3 < C:7
C:5 <|< CI:pi      // (@|=D:2.14)
B:6 <| = D:16.48
and if we assume we use the cursor always I would still rewrite it in

D:3 <|< C:7; C:5 <| (=D:2.14) // 3/7*5=2.14
|< CI:pi; B6 <|= D:16.48 // 2.14*pi*sqrt(6) = 16.48

I think I have two reasons. The first is that every line consists of a basic recipe involving one slide setting only. The second is, that I trace the intermediate results, not in exact number but in magnitude, so that I know 3/7*5 is about a 2, and after multipling with pi and sqrt(6) it should be bigger than 12, so that I know where the decimal point needs to go.

The lines can get quite long for complicated basic recipes such as the famous Darmstadt recipe with result on CI or the virtual H scale. E.g. with the catheti of a rectangular triangle given, what is the angle phi and what is the hypothenusis h by virtual H scale:

D:3 < C:1; D:4 <|= (C:1.33), T2red:36.92, B:1.78; B:(1+1.78) <|= D:5 // 4/3=1.33, phi=arccot(1.33), h=3*sqrt((1.33)^2+1)

In English:

C:1 to D:3; Cursor to D:4; (read 4/3=C:1.33), read phi=arccot(1.33)=T2red:36.92, read 1.33^2=B:1.78
Add one in your head 1.78+1=2.78; Cursor to B:2.78; read h=3*sqrt(2.78) = D:5

Please note, that this recipe only needs one slide setting followed by two cursor settings, and it outperforms all other recipes not involving an H scale if red T scales exist for the needed magnitudes. The little strange thing is that 1 must be added to 1.78 in the head, so that again it is important to know that it is 1.78 and e.g. not 0.178.

If I'd needed to break it down due to line length restriction or for teaching purposes I'd write:

D:3 < C:1; D:4 <|= (C:1.33), T2red:36.92, B:1.78 // 4/3=1.33, phi=arccot(1.33), 1.33^2=1.78
; B:2.78 <|= D:5 // h=3*sqrt(1+1.78)



The first column I always reserve for a slide setting, so I keep it empty in the second line. In the Faber recipes it is written like you did. They use a leading dot to indicate that no slide setting is needed.

Usually when having the hypothenuses a multiplication or divition may follow, so that it is good to have it on D, while for the angle an addition or substraction may follow, if using these calculations for complex number calculations.

Best regards
Andreas

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