This Nestler Progress does not exist physically. Inspired by FanHsiu's findings about the Hemmi 120 it assembles ideas from Faber 1/98 and Nestler 36, Darmstadt Faber 1/54 and Nestler 21 as well as from Thornton 121 and Hemmi 120 into a new system for sliderule scales which fits onto a standard wooden Nestler or Faber body.
A, B, CI, C, D as well as Sin and Tan are used as usual on the System Rietz, but the latter divided in deci degs. The Sin and Tan side of the Slide features a CI scale, so that it is also convenient to work with the flipped slide. Contrary to the Darmstadt system chain calculations with Sin and Tan are possible. Small angles are handled by the C scale by means of 180/PI = 57.3, marked with rho on C
e.g. 1*sin(4 deg): Move rho on C to 10 on D. At 4 on C: 0.0698 on D. This very slide setting can also be used to transfer arbitrary angles in degree on C to rad on D
e.g. 5/tan(4 deg): Move 4 on C to 5 on D. At rho on C: 71.7 on D. Please note that as on typical ST scales the same method is used for sin and tan.
Cos of all angels < 5.5 deg is approx. 1.The Sinh scales allow to calculate Cosh by means of Cosh(x) = sqrt(1+Sinh(x)^2) using scale A. E.g. Cosh(1.3)= 1.97: Set cursor to 1.3 on Sh2. At A: 2.89. Add 1 in the head: 3.89. Move cursor to 3.89 on A. On D 1.97. It also allows to calculate Tanh by the Gudermanian approach Tanh(x) = sin(tan^-1(Sinh(x)). The slide needs to be flipped for this. For Sh2 a value transfer is needed since there is no T2 scale. E.g. Tanh(1.3)= 0.862: Set cursor to 1.3 on Sh2. At D: 1.699. Move cursor to 1.699 on CI. Read 59.5 deg on CoTan (red!). Move cursor to 59.5 on Sin. Read 0.862 on D. For further details on this Gudermanian approach refer to FanHsius work on the Hemmi 120 on the sliderule group.
LL2 and LL3 are used as typically and arranged as on Faber 98 and Nestler 36. LL1 is simulated by C scale by means of Differential LogLog Approach of Thornton 121 and 131. E.g. 1.03^10: Set 1 on C to 0.985 on left scale extension of D. Each tick towards left represents 0.01 more as correction mark. For 1.03 three ticks to the left being the same as 0.985 on left scale extension. At 3 on C read 1.344 on LL2, as 3 on C stands now for 1.03 on LL1. LL0 can be simulated as well but please note that only very minor corrections between left index of D and first tick of left extension scales are needed. For further details please refer to the Thornton Differential manual.
An L scale is provided on the bevelled edge but cannot be simulated properly with a cursor reading right now; it is however included in the markings on side and/or on central hairline (switch on/off by check boxes in the top).
For K there was the question of importance compared to L. Since L at least for teaching purposes is considered more important than K, K had been skipped. For calculating x^3 in high precision: Please use C CI and D instead. For calculating the third root, please either use LL2 and LL3 or the approach e.g. explained in Pickworth for the Mannheim scale layout.
Mechanical and civil engineers may have asked for a variant with one section of cosh (chain line!) and K instead of Sh1 and Sh2. This layout however would not be suitable for electrical engineers. If a K scale is seen as crucial for their practical use, then the L scale should be replaced by K. L as a function can be replaced by LL2 and LL3 setting the index of C to 10 on LL3 and using LL2 and LL3 in the range between 1.1 and 10 only.
Using Sh1 and Sh2 instead of two lengths of tanh as on Hemmi 120 has the disadvantage that value transfers to CI are needed for Sh2, but the advantage that Cosh which is of some importance for civil and mechanical engineering can be calculated quite easily and that the untypical second length of Tanh is avoided. From a teaching perspective the additional CI also simplifies the use of the CoTan if seen directly in conjunction. That may also be an important reason for DI on US-American slide rules.