# A Study on Shape-Dependent Settling of Single Particles with Equal Volume Using Surface Resolved Simulations

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## Abstract

**:**

## 1. Introduction

## 2. Mathematical Modeling

#### 2.1. Drag Coefficient

#### 2.2. Shape Parameter

#### 2.3. Particle Representation

#### 2.4. Drag Correlations for Non-Spherical Particles

## 3. Numerical and Statistical Methods

#### 3.1. Particle Generation

#### 3.2. Statistical Tools

## 4. Numerical Experiments

#### 4.1. Preparation

#### 4.2. Simulation Setup

#### 4.3. Validation

## 5. Results and Discussion

#### 5.1. Examination of Simulation Data

#### 5.1.1. Data Processing

#### 5.1.2. Shape Classes and Influence of Shape Parameters

#### 5.1.3. Analysis of Exceptions

#### 5.2. Regression Analysis

#### 5.2.1. Polynomial Regression Regarding the Drag Coefficient

#### 5.2.2. Polynomial Regression Regarding Terminal Settling Velocity

## 6. Conclusions

## Author Contributions

## Funding

`CAPES`) [

`DAAD/CAPES PROBRAL`88881.198766/2018-01; CAPES-Finance Code 001]-Brazil.

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HLBM | homogenized lattice Boltzmann method |

LBM | lattice Boltzmann method |

Roman | |

${a}_{\mathrm{I}}$ | intermediate half-axis |

${a}_{\mathrm{L}}$ | longest half-axis |

${a}_{\mathrm{S}}$ | shortest half-axis |

A | projected particle surface in direction of motion |

${A}_{\mathrm{p}}$ | particle surface |

${C}_{\mathrm{D}}$ | drag coefficient |

${C}_{\mathrm{D},\mathrm{BB}}$ | drag coefficient according to Bagheri and Bonadonna [52] |

${C}_{\mathrm{D},\mathrm{CG}}$ | drag coefficient according to Clift and Gauvin [17] |

${C}_{\mathrm{D},\mathrm{DM}}$ | drag coefficient according to Dioguardi and Mele [26] |

${C}_{\mathrm{D},\mathrm{G}}$ | drag coefficient according to Ganser [21] |

${C}_{\mathrm{D},\mathrm{HL}}$ | drag coefficient according to Haider and Levenspiel [28] |

${C}_{\mathrm{D},\mathrm{HS}}$ | drag coefficient according to Hölzer and Sommerfeld [23] |

${C}_{\mathrm{D},\mathrm{S}}$ | drag coefficient according to Stokes [15] |

${C}_{\mathrm{D},\mathrm{SN}}$ | drag coefficient according to Schiller and Naumann [16] |

${d}_{\mathrm{Cook}}$ | Cook’s distance [71] |

${d}_{\mathrm{eq}}$ | diameter of a volume equivalent sphere |

E | elongation |

${\mathit{F}}_{\mathrm{f}}$ | force acting on the fluid |

${\mathit{F}}_{\mathrm{p}}$ | force acting on the particle |

${\mathit{F}}^{\mathrm{BG}}$ | combined buoyancy and gravitational force |

${\mathit{F}}^{\mathrm{D}}$ | drag force |

${\mathit{F}}^{\mathrm{H}}$ | hydrodynamic force |

F | flatness |

${F}_{\mathrm{sample}}$ | score of an F-test |

g | gravitational acceleration |

${\mathit{J}}_{\mathrm{p}}$ | moment of inertia |

${K}_{\mathrm{N}}$ | drag correction factor for the Newton regime |

${K}_{\mathrm{S}}$ | drag correction factor for the Stokes regime |

${m}_{\mathrm{p}}$ | particle mass |

$\mathit{MI}$ | mutual information |

N | resolution related parameter (number of cells per ${d}_{\mathrm{eq}}$) |

p | pressure |

$\mathit{PI}$ | permutation importance |

r | residual |

${R}^{2}$ | coefficient of determination |

${R}_{a}^{2}$ | adjusted coefficient of determination |

$\mathrm{Re}$ | Reynolds number |

t | time |

${\mathbf{T}}_{\mathrm{p}}$ | torque |

${T}_{\mathrm{sample}}$ | score of a t-test |

${\mathit{u}}_{\mathrm{f}}$ | fluid velocity |

${u}_{\mathrm{max}}^{\mathrm{L}}$ | maximum lattice velocity in a simulation |

${u}_{\mathrm{ts}}$ | terminal settling velocity |

${u}_{\mathrm{ts},\mathrm{D}}$ | terminal settling velocity according to Dellino [25] |

${u}_{\mathrm{ts},\mathrm{HL}}$ | terminal settling velocity according to Haider and Levenspiel [28] |

${u}_{\mathrm{ts},\mathrm{S}}$ | terminal settling velocity according to Stokes [15] |

${\mathit{u}}_{\mathrm{p}}$ | particle velocity |

${V}_{\mathrm{p}}$ | particle volume |

$\mathit{VIF}$ | variance inflation factor |

Greek | |

$\delta t$ | temporal discretization parameter |

$\delta x$ | spatial discretization parameter |

${\kappa}_{\mathrm{con}}$ | convexity |

${\kappa}_{\mathrm{rnd}}$ | roundness |

${\lambda}_{\mathrm{CSF}}$ | Corey shape factor [18] |

${\lambda}_{\mathrm{H}}$ | Hofmann shape entropy [44] |

${\lambda}_{\mathrm{LR}}$ | Le Roux shape factor [46] |

$\nu $ | kinematic viscosity |

${\xi}_{1},{\xi}_{2}$ | exponents determining the shape of a superellipsoid |

${\rho}^{\prime}$ | ratio of particle to fluid density |

${\rho}_{\mathrm{f}}$ | fluid density |

${\rho}_{\mathrm{p}}$ | particle density |

$\tau $ | lattice relaxation time |

$\varphi $ | circularity |

$\psi $ | sphericity |

${\psi}_{\perp}$ | crosswise sphericity |

${\psi}_{\Vert}$ | lengthwise sphericity |

${\omega}_{\mathrm{p}}$ | particle angular velocity |

## Appendix A

ID | ${\mathit{a}}_{\mathbf{L}}$ in m | ${\mathit{a}}_{\mathit{I}}$ in m | ${\mathit{a}}_{\mathbf{S}}$ in m | ${\mathit{\xi}}_{1}$ | ${\mathit{\xi}}_{2}$ | E | F | ${\mathit{\rho}}_{\mathbf{p}}$ | ${\mathit{\kappa}}_{\mathbf{con}}$ | $\mathit{\psi}$ | ${\mathit{\psi}}_{\perp}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{u}}_{\mathbf{ts}}$ | Re | ${\mathit{C}}_{\mathbf{D}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | $1.47\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $1.03\times {10}^{-4}$ | $8.0$ | $8.0$ | $1.0$ | $0.7$ | 2360 | $0.99$ | $0.87$ | $0.96$ | $0.18$ | $3.52\times {10}^{-2}$ | $11.16$ | $4.57$ |

2 | $2.17\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $1.21\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.7$ | $0.8$ | 2360 | $0.95$ | $0.88$ | $0.77$ | $0.15$ | $3.54\times {10}^{-2}$ | $11.23$ | $4.5$ |

3 | $1.83\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $1.32\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.9$ | $0.8$ | 2560 | $0.96$ | $0.91$ | $0.83$ | $0.15$ | $4.10\times {10}^{-2}$ | $12.98$ | $3.87$ |

4 | $2.08\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.7$ | $0.9$ | 2660 | $0.95$ | $0.9$ | $0.83$ | $0.15$ | $4.24\times {10}^{-2}$ | $13.43$ | $3.85$ |

5 | $2.08\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.7$ | $0.9$ | 2760 | $0.95$ | $0.9$ | $0.83$ | $0.15$ | $4.43\times {10}^{-2}$ | $14.03$ | $3.74$ |

6 | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $1.37\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $0.9$ | 2460 | $0.95$ | $0.9$ | $0.86$ | $0.15$ | $3.94\times {10}^{-2}$ | $12.48$ | $3.92$ |

7 | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $1.37\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $0.9$ | 2560 | $0.95$ | $0.9$ | $0.86$ | $0.15$ | $4.14\times {10}^{-2}$ | $13.12$ | $3.79$ |

8 | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $1.37\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $0.9$ | 2660 | $0.95$ | $0.9$ | $0.86$ | $0.15$ | $4.33\times {10}^{-2}$ | $13.74$ | $3.68$ |

9 | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.7$ | $1.0$ | 2360 | $0.95$ | $0.9$ | $0.89$ | $0.15$ | $3.74\times {10}^{-2}$ | $11.86$ | $4.04$ |

10 | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.7$ | $1.0$ | 2460 | $0.95$ | $0.9$ | $0.89$ | $0.15$ | $3.95\times {10}^{-2}$ | $12.52$ | $3.9$ |

11 | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.7$ | $1.0$ | 2760 | $0.95$ | $0.9$ | $0.89$ | $0.15$ | $4.55\times {10}^{-2}$ | $14.41$ | $3.54$ |

12 | $1.84\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $1.0$ | 2360 | $0.96$ | $0.91$ | $0.93$ | $0.15$ | $3.81\times {10}^{-2}$ | $12.08$ | $3.89$ |

13 | $1.84\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $1.0$ | 2560 | $0.96$ | $0.91$ | $0.93$ | $0.15$ | $4.23\times {10}^{-2}$ | $13.41$ | $3.62$ |

14 | $1.84\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $1.0$ | 2660 | $0.96$ | $0.91$ | $0.93$ | $0.15$ | $4.44\times {10}^{-2}$ | $14.06$ | $3.51$ |

15 | $1.84\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $1.47\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.8$ | $1.0$ | 2760 | $0.96$ | $0.91$ | $0.93$ | $0.15$ | $4.63\times {10}^{-2}$ | $14.69$ | $3.41$ |

16 | $1.70\times {10}^{-4}$ | $1.53\times {10}^{-4}$ | $1.53\times {10}^{-4}$ | $2.0$ | $2.0$ | $0.9$ | $1.0$ | 2360 | $0.95$ | $0.92$ | $0.96$ | $0.15$ | $3.87\times {10}^{-2}$ | $12.28$ | $3.77$ |

17 | $2.92\times {10}^{-4}$ | $2.34\times {10}^{-4}$ | $1.17\times {10}^{-4}$ | $2.0$ | $1.0$ | $0.8$ | $0.5$ | 2760 | $0.91$ | $0.65$ | $0.39$ | $0.09$ | $3.24\times {10}^{-2}$ | $10.26$ | $7.16$ |

18 | $2.18\times {10}^{-4}$ | $2.18\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.6$ | 2760 | $0.97$ | $0.87$ | $0.84$ | $0.13$ | $4.91\times {10}^{-2}$ | $15.56$ | $3.57$ |

19 | $2.23\times {10}^{-4}$ | $2.00\times {10}^{-4}$ | $1.40\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.7$ | 2360 | $0.94$ | $0.87$ | $0.88$ | $0.13$ | $4.13\times {10}^{-2}$ | $13.09$ | $3.91$ |

20 | $2.23\times {10}^{-4}$ | $2.00\times {10}^{-4}$ | $1.40\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.7$ | 2460 | $0.94$ | $0.87$ | $0.88$ | $0.13$ | $4.35\times {10}^{-2}$ | $13.79$ | $3.78$ |

21 | $2.23\times {10}^{-4}$ | $2.00\times {10}^{-4}$ | $1.40\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.7$ | 2560 | $0.94$ | $0.87$ | $0.88$ | $0.13$ | $4.57\times {10}^{-2}$ | $14.47$ | $3.67$ |

22 | $2.23\times {10}^{-4}$ | $2.00\times {10}^{-4}$ | $1.40\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.7$ | 2660 | $0.94$ | $0.87$ | $0.89$ | $0.13$ | $4.78\times {10}^{-2}$ | $15.15$ | $3.56$ |

23 | $2.23\times {10}^{-4}$ | $2.00\times {10}^{-4}$ | $1.40\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.7$ | 2760 | $0.94$ | $0.87$ | $0.89$ | $0.13$ | $4.99\times {10}^{-2}$ | $15.83$ | $3.46$ |

24 | $2.07\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.45\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.7$ | 2460 | $0.96$ | $0.88$ | $0.9$ | $0.13$ | $4.40\times {10}^{-2}$ | $13.95$ | $3.7$ |

25 | $2.07\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.45\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.7$ | 2560 | $0.96$ | $0.88$ | $0.9$ | $0.13$ | $4.62\times {10}^{-2}$ | $14.65$ | $3.58$ |

26 | $2.07\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.45\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.7$ | 2660 | $0.96$ | $0.88$ | $0.9$ | $0.13$ | $4.84\times {10}^{-2}$ | $15.35$ | $3.47$ |

27 | $2.07\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.45\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.7$ | 2760 | $0.96$ | $0.88$ | $0.9$ | $0.13$ | $5.06\times {10}^{-2}$ | $16.04$ | $3.37$ |

28 | $2.13\times {10}^{-4}$ | $1.92\times {10}^{-4}$ | $1.53\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.8$ | 2460 | $0.94$ | $0.87$ | $0.85$ | $0.13$ | $4.44\times {10}^{-2}$ | $14.07$ | $3.63$ |

29 | $1.98\times {10}^{-4}$ | $1.98\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.8$ | 2360 | $0.97$ | $0.88$ | $1.03$ | $0.13$ | $4.31\times {10}^{-2}$ | $13.66$ | $3.59$ |

30 | $1.98\times {10}^{-4}$ | $1.98\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.8$ | 2460 | $0.97$ | $0.88$ | $1.03$ | $0.13$ | $4.54\times {10}^{-2}$ | $14.4$ | $3.46$ |

31 | $1.98\times {10}^{-4}$ | $1.98\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.8$ | 2560 | $0.97$ | $0.88$ | $1.03$ | $0.13$ | $4.78\times {10}^{-2}$ | $15.14$ | $3.35$ |

32 | $1.98\times {10}^{-4}$ | $1.98\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.8$ | 2760 | $0.97$ | $0.88$ | $1.03$ | $0.13$ | $5.23\times {10}^{-2}$ | $16.59$ | $3.15$ |

33 | $2.05\times {10}^{-4}$ | $1.84\times {10}^{-4}$ | $1.66\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $0.9$ | 2360 | $0.94$ | $0.87$ | $0.74$ | $0.12$ | $4.13\times {10}^{-2}$ | $13.1$ | $3.91$ |

34 | $1.91\times {10}^{-4}$ | $1.91\times {10}^{-4}$ | $1.72\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.9$ | 2360 | $0.97$ | $0.89$ | $1.06$ | $0.13$ | $4.27\times {10}^{-2}$ | $13.54$ | $3.65$ |

35 | $1.91\times {10}^{-4}$ | $1.91\times {10}^{-4}$ | $1.72\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.9$ | 2560 | $0.97$ | $0.89$ | $1.06$ | $0.13$ | $4.73\times {10}^{-2}$ | $15.0$ | $3.41$ |

36 | $1.91\times {10}^{-4}$ | $1.91\times {10}^{-4}$ | $1.72\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.9$ | 2660 | $0.97$ | $0.89$ | $1.06$ | $0.13$ | $4.96\times {10}^{-2}$ | $15.73$ | $3.3$ |

37 | $1.91\times {10}^{-4}$ | $1.91\times {10}^{-4}$ | $1.72\times {10}^{-4}$ | $1.0$ | $2.0$ | $1.0$ | $0.9$ | 2760 | $0.97$ | $0.89$ | $1.06$ | $0.13$ | $5.19\times {10}^{-2}$ | $16.44$ | $3.2$ |

38 | $1.98\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.0$ | $2.0$ | $0.9$ | $1.0$ | 2360 | $0.95$ | $0.87$ | $0.73$ | $0.12$ | $4.08\times {10}^{-2}$ | $12.95$ | $4.0$ |

39 | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $1.0$ | $1.0$ | $1.0$ | $1.0$ | 2360 | $1.0$ | $0.89$ | $0.87$ | $0.1$ | $3.66\times {10}^{-2}$ | $11.6$ | $4.22$ |

40 | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $1.0$ | $1.0$ | $1.0$ | $1.0$ | 2460 | $1.0$ | $0.89$ | $0.87$ | $0.1$ | $3.86\times {10}^{-2}$ | $12.24$ | $4.07$ |

41 | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $1.0$ | $1.0$ | $1.0$ | $1.0$ | 2560 | $1.0$ | $0.89$ | $0.87$ | $0.1$ | $4.06\times {10}^{-2}$ | $12.87$ | $3.93$ |

42 | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $1.0$ | $1.0$ | $1.0$ | $1.0$ | 2660 | $1.0$ | $0.89$ | $0.87$ | $0.1$ | $4.26\times {10}^{-2}$ | $13.49$ | $3.81$ |

43 | $2.31\times {10}^{-4}$ | $2.08\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.7$ | 2760 | $0.9$ | $0.85$ | $0.92$ | $0.12$ | $5.23\times {10}^{-2}$ | $16.57$ | $3.35$ |

44 | $2.61\times {10}^{-4}$ | $1.83\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.7$ | $0.8$ | 2360 | $0.89$ | $0.82$ | $0.68$ | $0.11$ | $4.03\times {10}^{-2}$ | $12.78$ | $4.35$ |

45 | $2.61\times {10}^{-4}$ | $1.83\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.7$ | $0.8$ | 2560 | $0.89$ | $0.82$ | $0.68$ | $0.11$ | $4.46\times {10}^{-2}$ | $14.14$ | $4.07$ |

46 | $2.61\times {10}^{-4}$ | $1.83\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.7$ | $0.8$ | 2660 | $0.89$ | $0.82$ | $0.68$ | $0.11$ | $4.67\times {10}^{-2}$ | $14.8$ | $3.95$ |

47 | $2.61\times {10}^{-4}$ | $1.83\times {10}^{-4}$ | $1.46\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.7$ | $0.8$ | 2760 | $0.89$ | $0.82$ | $0.67$ | $0.11$ | $4.87\times {10}^{-2}$ | $15.44$ | $4.05$ |

48 | $2.21\times {10}^{-4}$ | $1.99\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.8$ | 2360 | $0.89$ | $0.85$ | $1.0$ | $0.12$ | $4.26\times {10}^{-2}$ | $13.5$ | $3.9$ |

49 | $2.21\times {10}^{-4}$ | $1.99\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.8$ | 2460 | $0.89$ | $0.85$ | $1.0$ | $0.12$ | $4.49\times {10}^{-2}$ | $14.22$ | $3.77$ |

50 | $2.21\times {10}^{-4}$ | $1.99\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.8$ | 2560 | $0.89$ | $0.85$ | $1.0$ | $0.12$ | $4.71\times {10}^{-2}$ | $14.93$ | $3.65$ |

51 | $2.21\times {10}^{-4}$ | $1.99\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.8$ | 2660 | $0.89$ | $0.85$ | $0.73$ | $0.12$ | $4.93\times {10}^{-2}$ | $15.63$ | $3.56$ |

52 | $2.21\times {10}^{-4}$ | $1.99\times {10}^{-4}$ | $1.59\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.8$ | 2760 | $0.89$ | $0.85$ | $0.73$ | $0.12$ | $5.15\times {10}^{-2}$ | $16.31$ | $3.45$ |

53 | $2.06\times {10}^{-4}$ | $2.06\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $0.9$ | $2.0$ | $1.0$ | $0.8$ | 2560 | $0.89$ | $0.84$ | $1.03$ | $0.12$ | $4.90\times {10}^{-2}$ | $15.54$ | $3.4$ |

54 | $2.06\times {10}^{-4}$ | $2.06\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $0.9$ | $2.0$ | $1.0$ | $0.8$ | 2760 | $0.89$ | $0.84$ | $1.03$ | $0.12$ | $5.36\times {10}^{-2}$ | $17.0$ | $3.18$ |

55 | $2.30\times {10}^{-4}$ | $1.84\times {10}^{-4}$ | $1.66\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.8$ | $0.9$ | 2360 | $0.9$ | $0.83$ | $0.67$ | $0.12$ | $4.12\times {10}^{-2}$ | $13.05$ | $4.17$ |

56 | $2.30\times {10}^{-4}$ | $1.84\times {10}^{-4}$ | $1.66\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.8$ | $0.9$ | 2460 | $0.9$ | $0.83$ | $0.67$ | $0.12$ | $4.33\times {10}^{-2}$ | $13.74$ | $4.04$ |

57 | $2.30\times {10}^{-4}$ | $1.84\times {10}^{-4}$ | $1.66\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.8$ | $0.9$ | 2560 | $0.9$ | $0.83$ | $0.67$ | $0.12$ | $4.55\times {10}^{-2}$ | $14.42$ | $3.92$ |

58 | $2.30\times {10}^{-4}$ | $1.84\times {10}^{-4}$ | $1.66\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.8$ | $0.9$ | 2760 | $0.9$ | $0.83$ | $0.68$ | $0.12$ | $4.96\times {10}^{-2}$ | $15.73$ | $3.72$ |

59 | $2.13\times {10}^{-4}$ | $1.91\times {10}^{-4}$ | $1.72\times {10}^{-4}$ | $0.9$ | $2.0$ | $0.9$ | $0.9$ | 2460 | $0.9$ | $0.84$ | $0.7$ | $0.12$ | $4.43\times {10}^{-2}$ | $14.03$ | $3.87$ |

60 | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $1.22\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.6$ | 2360 | $0.91$ | $0.81$ | $1.11$ | $0.12$ | - | - | - |

ID | ${\mathit{a}}_{\mathbf{L}}$ in m | ${\mathit{a}}_{\mathit{I}}$ in m | ${\mathit{a}}_{\mathbf{S}}$ in m | ${\mathit{\xi}}_{1}$ | ${\mathit{\xi}}_{2}$ | E | F | ${\mathit{\rho}}_{\mathbf{p}}$ | ${\mathit{\kappa}}_{\mathbf{con}}$ | $\mathit{\psi}$ | ${\mathit{\psi}}_{\perp}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{u}}_{\mathbf{ts}}$ | Re | ${\mathit{C}}_{\mathbf{D}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

61 | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $1.22\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.6$ | 2460 | $0.91$ | $0.81$ | $1.11$ | $0.12$ | - | - | - |

62 | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $1.22\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.6$ | 2560 | $0.91$ | $0.81$ | $1.11$ | $0.12$ | - | - | - |

63 | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $1.22\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.6$ | 2660 | $0.91$ | $0.81$ | $1.11$ | $0.12$ | - | - | - |

64 | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $1.22\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.6$ | 2760 | $0.91$ | $0.81$ | $1.11$ | $0.12$ | - | - | - |

65 | $1.78\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.60\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.9$ | 2360 | $0.93$ | $0.82$ | $0.97$ | $0.13$ | $5.62\times {10}^{-2}$ | $17.83$ | $3.34$ |

66 | $1.78\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.60\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.9$ | 2460 | $0.93$ | $0.82$ | $0.98$ | $0.13$ | $5.93\times {10}^{-2}$ | $18.78$ | $3.23$ |

67 | $1.78\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.60\times {10}^{-4}$ | $0.87$ | $8.0$ | $1.0$ | $0.9$ | 2660 | $0.93$ | $0.82$ | $0.99$ | $0.13$ | $6.51\times {10}^{-2}$ | $20.63$ | $3.04$ |

68 | $2.51\times {10}^{-4}$ | $2.26\times {10}^{-4}$ | $1.36\times {10}^{-4}$ | $0.83$ | $2.0$ | $0.9$ | $0.6$ | 2660 | $0.84$ | $0.82$ | $0.85$ | $0.11$ | $4.99\times {10}^{-2}$ | $15.81$ | $3.65$ |

69 | $2.51\times {10}^{-4}$ | $2.26\times {10}^{-4}$ | $1.36\times {10}^{-4}$ | $0.83$ | $2.0$ | $0.9$ | $0.6$ | 2760 | $0.84$ | $0.82$ | $0.85$ | $0.11$ | $5.21\times {10}^{-2}$ | $16.5$ | $3.55$ |

70 | $2.38\times {10}^{-4}$ | $2.15\times {10}^{-4}$ | $1.50\times {10}^{-4}$ | $0.83$ | $2.0$ | $0.9$ | $0.7$ | 2760 | $0.84$ | $0.82$ | $0.95$ | $0.11$ | $5.37\times {10}^{-2}$ | $17.02$ | $3.33$ |

71 | $2.28\times {10}^{-4}$ | $2.05\times {10}^{-4}$ | $1.64\times {10}^{-4}$ | $0.83$ | $2.0$ | $0.9$ | $0.8$ | 2360 | $0.84$ | $0.82$ | $0.68$ | $0.11$ | $4.32\times {10}^{-2}$ | $13.7$ | $3.99$ |

72 | $2.28\times {10}^{-4}$ | $2.05\times {10}^{-4}$ | $1.64\times {10}^{-4}$ | $0.83$ | $2.0$ | $0.9$ | $0.8$ | 2560 | $0.84$ | $0.82$ | $0.69$ | $0.11$ | $4.78\times {10}^{-2}$ | $15.15$ | $3.72$ |

73 | $3.94\times {10}^{-4}$ | $2.36\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.6$ | $0.7$ | 2360 | $0.84$ | $0.77$ | $0.57$ | $0.08$ | $3.04\times {10}^{-2}$ | $9.64$ | $6.4$ |

74 | $3.94\times {10}^{-4}$ | $2.36\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.6$ | $0.7$ | 2560 | $0.84$ | $0.77$ | $0.57$ | $0.08$ | $3.37\times {10}^{-2}$ | $10.69$ | $5.97$ |

75 | $3.94\times {10}^{-4}$ | $2.36\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.6$ | $0.7$ | 2660 | $0.84$ | $0.77$ | $0.57$ | $0.08$ | $3.53\times {10}^{-2}$ | $11.18$ | $5.81$ |

76 | $3.94\times {10}^{-4}$ | $2.36\times {10}^{-4}$ | $1.65\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.6$ | $0.7$ | 2760 | $0.84$ | $0.77$ | $0.57$ | $0.08$ | $3.68\times {10}^{-2}$ | $11.67$ | $5.66$ |

77 | $3.40\times {10}^{-4}$ | $2.38\times {10}^{-4}$ | $1.90\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.7$ | $0.8$ | 2460 | $0.84$ | $0.78$ | $0.63$ | $0.08$ | $3.47\times {10}^{-2}$ | $10.99$ | $5.28$ |

78 | $3.40\times {10}^{-4}$ | $2.38\times {10}^{-4}$ | $1.90\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.7$ | $0.8$ | 2660 | $0.84$ | $0.78$ | $0.63$ | $0.08$ | $3.80\times {10}^{-2}$ | $12.06$ | $4.99$ |

79 | $3.62\times {10}^{-4}$ | $2.17\times {10}^{-4}$ | $1.95\times {10}^{-4}$ | $0.83$ | $1.0$ | $0.6$ | $0.9$ | 2460 | $0.85$ | $0.79$ | $0.67$ | $0.08$ | $3.47\times {10}^{-2}$ | $10.99$ | $5.29$ |

80 | $3.15\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $9.45\times {10}^{-5}$ | $0.8$ | $8.0$ | $0.6$ | $0.5$ | 2360 | $0.84$ | $0.78$ | $0.85$ | $0.12$ | - | - | - |

81 | $3.15\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $9.45\times {10}^{-5}$ | $0.8$ | $8.0$ | $0.6$ | $0.5$ | 2660 | $0.84$ | $0.78$ | $0.87$ | $0.12$ | $6.24\times {10}^{-2}$ | $19.77$ | $3.61$ |

82 | $3.15\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $9.45\times {10}^{-5}$ | $0.8$ | $8.0$ | $0.6$ | $0.5$ | 2760 | $0.84$ | $0.78$ | $0.86$ | $0.12$ | $6.52\times {10}^{-2}$ | $20.66$ | $3.51$ |

83 | $3.35\times {10}^{-4}$ | $1.67\times {10}^{-4}$ | $1.00\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.5$ | $0.6$ | 2760 | $0.84$ | $0.78$ | $0.73$ | $0.12$ | $6.00\times {10}^{-2}$ | $19.02$ | $4.14$ |

84 | $2.67\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.12\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.7$ | $0.6$ | 2360 | $0.84$ | $0.77$ | $1.02$ | $0.11$ | $5.48\times {10}^{-2}$ | $17.38$ | $3.83$ |

85 | $2.67\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.12\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.7$ | $0.6$ | 2460 | $0.84$ | $0.77$ | $0.69$ | $0.11$ | $5.77\times {10}^{-2}$ | $18.28$ | $3.72$ |

86 | $2.67\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.12\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.7$ | $0.6$ | 2560 | $0.84$ | $0.77$ | $0.68$ | $0.11$ | $6.05\times {10}^{-2}$ | $19.16$ | $3.61$ |

87 | $2.67\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.12\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.7$ | $0.6$ | 2660 | $0.84$ | $0.77$ | $0.68$ | $0.11$ | $6.31\times {10}^{-2}$ | $20.01$ | $3.53$ |

88 | $2.67\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.12\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.7$ | $0.6$ | 2760 | $0.84$ | $0.77$ | $0.69$ | $0.11$ | $6.57\times {10}^{-2}$ | $20.84$ | $3.45$ |

89 | $1.98\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.60\times {10}^{-4}$ | $0.8$ | $8.0$ | $0.9$ | $0.9$ | 2560 | $0.85$ | $0.77$ | $0.65$ | $0.11$ | $6.18\times {10}^{-2}$ | $19.59$ | $3.46$ |

90 | $4.02\times {10}^{-4}$ | $2.01\times {10}^{-4}$ | $1.00\times {10}^{-4}$ | $0.8$ | $2.0$ | $0.5$ | $0.5$ | 2460 | $0.85$ | $0.83$ | $0.68$ | $0.11$ | $3.92\times {10}^{-2}$ | $12.42$ | $5.36$ |

91 | $3.78\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $1.13\times {10}^{-4}$ | $0.8$ | $2.0$ | $0.5$ | $0.6$ | 2360 | $0.84$ | $0.83$ | $0.76$ | $0.11$ | $3.89\times {10}^{-2}$ | $12.33$ | $5.07$ |

92 | $3.78\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $1.13\times {10}^{-4}$ | $0.8$ | $2.0$ | $0.5$ | $0.6$ | 2460 | $0.84$ | $0.83$ | $0.76$ | $0.11$ | $4.08\times {10}^{-2}$ | $12.94$ | $4.94$ |

93 | $3.78\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $1.13\times {10}^{-4}$ | $0.8$ | $2.0$ | $0.5$ | $0.6$ | 2560 | $0.84$ | $0.83$ | $0.76$ | $0.11$ | $4.29\times {10}^{-2}$ | $13.6$ | $4.78$ |

94 | $3.78\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $1.13\times {10}^{-4}$ | $0.8$ | $2.0$ | $0.5$ | $0.6$ | 2660 | $0.84$ | $0.83$ | $0.76$ | $0.11$ | $4.49\times {10}^{-2}$ | $14.23$ | $4.65$ |

95 | $3.78\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $1.13\times {10}^{-4}$ | $0.8$ | $2.0$ | $0.5$ | $0.6$ | 2760 | $0.84$ | $0.83$ | $0.75$ | $0.11$ | $4.67\times {10}^{-2}$ | $14.81$ | $4.54$ |

96 | $3.63\times {10}^{-4}$ | $1.81\times {10}^{-4}$ | $9.07\times {10}^{-5}$ | $0.77$ | $8.0$ | $0.5$ | $0.5$ | 2360 | $0.85$ | $0.8$ | $0.85$ | $0.12$ | - | - | - |

97 | $4.08\times {10}^{-4}$ | $2.45\times {10}^{-4}$ | $1.72\times {10}^{-4}$ | $0.77$ | $1.0$ | $0.6$ | $0.7$ | 2760 | $0.78$ | $0.77$ | $0.59$ | $0.08$ | $3.78\times {10}^{-2}$ | $11.97$ | $5.55$ |

98 | $3.39\times {10}^{-4}$ | $2.37\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.77$ | $1.0$ | $0.7$ | $0.9$ | 2360 | $0.78$ | $0.76$ | $0.59$ | $0.08$ | $3.37\times {10}^{-2}$ | $10.67$ | $5.4$ |

99 | $3.39\times {10}^{-4}$ | $2.37\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.77$ | $1.0$ | $0.7$ | $0.9$ | 2660 | $0.78$ | $0.76$ | $0.58$ | $0.08$ | $3.88\times {10}^{-2}$ | $12.31$ | $4.96$ |

100 | $3.70\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $9.26\times {10}^{-5}$ | $0.73$ | $8.0$ | $0.5$ | $0.5$ | 2360 | $0.84$ | $0.8$ | $0.88$ | $0.11$ | - | - | - |

101 | $3.70\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $9.26\times {10}^{-5}$ | $0.73$ | $8.0$ | $0.5$ | $0.5$ | 2460 | $0.84$ | $0.8$ | $0.88$ | $0.11$ | - | - | - |

102 | $3.70\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $9.26\times {10}^{-5}$ | $0.73$ | $8.0$ | $0.5$ | $0.5$ | 2560 | $0.84$ | $0.8$ | $0.88$ | $0.11$ | - | - | - |

103 | $3.70\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $9.26\times {10}^{-5}$ | $0.73$ | $8.0$ | $0.5$ | $0.5$ | 2660 | $0.84$ | $0.8$ | $0.88$ | $0.11$ | - | - | - |

104 | $2.24\times {10}^{-4}$ | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $0.73$ | $8.0$ | $0.9$ | $0.7$ | 2360 | $0.78$ | $0.75$ | $0.66$ | $0.11$ | $6.02\times {10}^{-2}$ | $19.09$ | $3.53$ |

105 | $2.24\times {10}^{-4}$ | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $0.73$ | $8.0$ | $0.9$ | $0.7$ | 2460 | $0.78$ | $0.75$ | $0.67$ | $0.11$ | $6.33\times {10}^{-2}$ | $20.06$ | $3.44$ |

106 | $2.24\times {10}^{-4}$ | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $0.73$ | $8.0$ | $0.9$ | $0.7$ | 2560 | $0.78$ | $0.75$ | $0.68$ | $0.11$ | $6.63\times {10}^{-2}$ | $21.02$ | $3.35$ |

107 | $2.24\times {10}^{-4}$ | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $0.73$ | $8.0$ | $0.9$ | $0.7$ | 2660 | $0.78$ | $0.75$ | $0.66$ | $0.11$ | $6.92\times {10}^{-2}$ | $21.95$ | $3.27$ |

108 | $2.24\times {10}^{-4}$ | $2.01\times {10}^{-4}$ | $1.41\times {10}^{-4}$ | $0.73$ | $8.0$ | $0.9$ | $0.7$ | 2760 | $0.78$ | $0.75$ | $0.66$ | $0.11$ | $7.21\times {10}^{-2}$ | $22.86$ | $3.19$ |

109 | $3.70\times {10}^{-4}$ | $2.22\times {10}^{-4}$ | $1.11\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.6$ | $0.5$ | 2360 | $0.78$ | $0.8$ | $0.73$ | $0.1$ | $4.09\times {10}^{-2}$ | $12.96$ | $4.94$ |

110 | $3.70\times {10}^{-4}$ | $2.22\times {10}^{-4}$ | $1.11\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.6$ | $0.5$ | 2460 | $0.78$ | $0.8$ | $0.73$ | $0.1$ | $4.30\times {10}^{-2}$ | $13.63$ | $4.79$ |

111 | $3.70\times {10}^{-4}$ | $2.22\times {10}^{-4}$ | $1.11\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.6$ | $0.5$ | 2560 | $0.78$ | $0.8$ | $0.73$ | $0.1$ | $4.53\times {10}^{-2}$ | $14.37$ | $4.6$ |

112 | $3.70\times {10}^{-4}$ | $2.22\times {10}^{-4}$ | $1.11\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.6$ | $0.5$ | 2660 | $0.78$ | $0.8$ | $0.73$ | $0.1$ | $4.74\times {10}^{-2}$ | $15.03$ | $4.47$ |

113 | $3.70\times {10}^{-4}$ | $2.22\times {10}^{-4}$ | $1.11\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.6$ | $0.5$ | 2760 | $0.78$ | $0.8$ | $0.73$ | $0.1$ | $4.91\times {10}^{-2}$ | $15.56$ | $4.43$ |

114 | $3.74\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.5$ | $0.7$ | 2360 | $0.79$ | $0.8$ | $0.63$ | $0.1$ | $3.89\times {10}^{-2}$ | $12.33$ | $5.45$ |

115 | $3.74\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.5$ | $0.7$ | 2460 | $0.79$ | $0.8$ | $0.63$ | $0.1$ | $4.09\times {10}^{-2}$ | $12.97$ | $5.29$ |

116 | $3.74\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.5$ | $0.7$ | 2560 | $0.79$ | $0.8$ | $0.63$ | $0.1$ | $4.29\times {10}^{-2}$ | $13.6$ | $5.14$ |

117 | $3.74\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.5$ | $0.7$ | 2660 | $0.79$ | $0.8$ | $0.63$ | $0.1$ | $4.48\times {10}^{-2}$ | $14.21$ | $5.0$ |

118 | $3.74\times {10}^{-4}$ | $1.87\times {10}^{-4}$ | $1.31\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.5$ | $0.7$ | 2760 | $0.79$ | $0.8$ | $0.63$ | $0.1$ | $4.67\times {10}^{-2}$ | $14.82$ | $4.89$ |

119 | $3.58\times {10}^{-4}$ | $1.79\times {10}^{-4}$ | $1.43\times {10}^{-4}$ | $0.73$ | $2.0$ | $0.5$ | $0.8$ | 2560 | $0.79$ | $0.78$ | $0.58$ | $0.1$ | $4.27\times {10}^{-2}$ | $13.54$ | $5.18$ |

120 | $3.57\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.6$ | 2460 | $0.78$ | $0.76$ | $0.68$ | $0.11$ | $5.63\times {10}^{-2}$ | $17.86$ | $4.61$ |

ID | ${\mathit{a}}_{\mathbf{L}}$ in m | ${\mathit{a}}_{\mathit{I}}$ in m | ${\mathit{a}}_{\mathbf{S}}$ in m | ${\mathit{\xi}}_{1}$ | ${\mathit{\xi}}_{2}$ | E | F | ${\mathit{\rho}}_{\mathbf{p}}$ | ${\mathit{\kappa}}_{\mathbf{con}}$ | $\mathit{\psi}$ | ${\mathit{\psi}}_{\perp}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{u}}_{\mathbf{ts}}$ | Re | ${\mathit{C}}_{\mathbf{D}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

121 | $3.57\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.6$ | 2560 | $0.78$ | $0.76$ | $0.68$ | $0.11$ | $5.90\times {10}^{-2}$ | $18.71$ | $4.48$ |

122 | $3.57\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.6$ | 2660 | $0.78$ | $0.76$ | $0.68$ | $0.11$ | $6.16\times {10}^{-2}$ | $19.53$ | $4.39$ |

123 | $3.57\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.6$ | 2760 | $0.78$ | $0.76$ | $0.68$ | $0.11$ | $6.41\times {10}^{-2}$ | $20.33$ | $4.3$ |

124 | $3.39\times {10}^{-4}$ | $1.69\times {10}^{-4}$ | $1.19\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.7$ | 2360 | $0.79$ | $0.74$ | $0.61$ | $0.1$ | $5.34\times {10}^{-2}$ | $16.93$ | $4.79$ |

125 | $3.39\times {10}^{-4}$ | $1.69\times {10}^{-4}$ | $1.19\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.7$ | 2460 | $0.79$ | $0.74$ | $0.61$ | $0.1$ | $5.61\times {10}^{-2}$ | $17.79$ | $4.65$ |

126 | $3.39\times {10}^{-4}$ | $1.69\times {10}^{-4}$ | $1.19\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.7$ | 2560 | $0.79$ | $0.74$ | $0.61$ | $0.1$ | $5.87\times {10}^{-2}$ | $18.62$ | $4.54$ |

127 | $3.39\times {10}^{-4}$ | $1.69\times {10}^{-4}$ | $1.19\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.7$ | 2660 | $0.79$ | $0.74$ | $0.61$ | $0.1$ | $6.13\times {10}^{-2}$ | $19.42$ | $4.44$ |

128 | $3.39\times {10}^{-4}$ | $1.69\times {10}^{-4}$ | $1.19\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.5$ | $0.7$ | 2760 | $0.79$ | $0.74$ | $0.61$ | $0.1$ | $6.38\times {10}^{-2}$ | $20.22$ | $4.33$ |

129 | $2.37\times {10}^{-4}$ | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.8$ | $0.8$ | 2360 | $0.73$ | $0.7$ | $0.61$ | $0.1$ | $5.95\times {10}^{-2}$ | $18.86$ | $3.86$ |

130 | $2.37\times {10}^{-4}$ | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.8$ | $0.8$ | 2560 | $0.73$ | $0.7$ | $0.59$ | $0.1$ | $6.55\times {10}^{-2}$ | $20.75$ | $3.67$ |

131 | $2.37\times {10}^{-4}$ | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.8$ | $0.8$ | 2660 | $0.73$ | $0.7$ | $0.59$ | $0.1$ | $6.82\times {10}^{-2}$ | $21.63$ | $3.58$ |

132 | $2.37\times {10}^{-4}$ | $1.90\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $0.7$ | $8.0$ | $0.8$ | $0.8$ | 2760 | $0.73$ | $0.7$ | $0.59$ | $0.1$ | $7.11\times {10}^{-2}$ | $22.54$ | $3.49$ |

133 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $2.0$ | $0.5$ | $0.5$ | 2360 | $0.78$ | $0.82$ | $0.73$ | $0.1$ | $4.05\times {10}^{-2}$ | $12.83$ | $5.27$ |

134 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $2.0$ | $0.5$ | $0.5$ | 2460 | $0.78$ | $0.82$ | $0.73$ | $0.1$ | $4.24\times {10}^{-2}$ | $13.44$ | $5.15$ |

135 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $2.0$ | $0.5$ | $0.5$ | 2560 | $0.78$ | $0.82$ | $0.73$ | $0.1$ | $4.46\times {10}^{-2}$ | $14.14$ | $4.97$ |

136 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $1.07\times {10}^{-4}$ | $0.7$ | $2.0$ | $0.5$ | $0.5$ | 2660 | $0.78$ | $0.82$ | $0.73$ | $0.1$ | $4.64\times {10}^{-2}$ | $14.71$ | $4.88$ |

137 | $4.78\times {10}^{-4}$ | $2.87\times {10}^{-4}$ | $1.43\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.5$ | 2660 | $0.74$ | $0.73$ | $0.52$ | $0.07$ | $3.34\times {10}^{-2}$ | $10.58$ | $6.99$ |

138 | $4.78\times {10}^{-4}$ | $2.87\times {10}^{-4}$ | $1.43\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.5$ | 2760 | $0.74$ | $0.73$ | $0.52$ | $0.07$ | $3.49\times {10}^{-2}$ | $11.05$ | $6.81$ |

139 | $4.31\times {10}^{-4}$ | $3.02\times {10}^{-4}$ | $1.51\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.5$ | 2460 | $0.74$ | $0.73$ | $0.52$ | $0.07$ | $3.17\times {10}^{-2}$ | $10.04$ | $6.83$ |

140 | $4.31\times {10}^{-4}$ | $3.02\times {10}^{-4}$ | $1.51\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.5$ | 2660 | $0.74$ | $0.73$ | $0.52$ | $0.07$ | $3.48\times {10}^{-2}$ | $11.04$ | $6.43$ |

141 | $4.31\times {10}^{-4}$ | $3.02\times {10}^{-4}$ | $1.51\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.5$ | 2760 | $0.74$ | $0.73$ | $0.53$ | $0.07$ | $3.61\times {10}^{-2}$ | $11.44$ | $6.36$ |

142 | $3.94\times {10}^{-4}$ | $3.15\times {10}^{-4}$ | $1.58\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.5$ | 2360 | $0.73$ | $0.73$ | $0.54$ | $0.07$ | $3.09\times {10}^{-2}$ | $9.81$ | $6.67$ |

143 | $3.94\times {10}^{-4}$ | $3.15\times {10}^{-4}$ | $1.58\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.5$ | 2460 | $0.73$ | $0.73$ | $0.54$ | $0.07$ | $3.25\times {10}^{-2}$ | $10.29$ | $6.5$ |

144 | $3.94\times {10}^{-4}$ | $3.15\times {10}^{-4}$ | $1.58\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.5$ | 2560 | $0.73$ | $0.73$ | $0.54$ | $0.07$ | $3.42\times {10}^{-2}$ | $10.86$ | $6.26$ |

145 | $3.94\times {10}^{-4}$ | $3.15\times {10}^{-4}$ | $1.58\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.5$ | 2660 | $0.73$ | $0.73$ | $0.54$ | $0.07$ | $3.58\times {10}^{-2}$ | $11.35$ | $6.09$ |

146 | $4.50\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.62\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.6$ | 2360 | $0.74$ | $0.75$ | $0.57$ | $0.07$ | $3.08\times {10}^{-2}$ | $9.78$ | $6.72$ |

147 | $4.50\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.62\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.6$ | 2460 | $0.74$ | $0.75$ | $0.56$ | $0.07$ | $3.24\times {10}^{-2}$ | $10.27$ | $6.55$ |

148 | $4.50\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.62\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.6$ | 2560 | $0.74$ | $0.75$ | $0.56$ | $0.07$ | $3.40\times {10}^{-2}$ | $10.77$ | $6.36$ |

149 | $4.50\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.62\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.6$ | 2660 | $0.74$ | $0.75$ | $0.56$ | $0.07$ | $3.56\times {10}^{-2}$ | $11.3$ | $6.14$ |

150 | $4.50\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.62\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.6$ | 2760 | $0.74$ | $0.75$ | $0.57$ | $0.07$ | $3.70\times {10}^{-2}$ | $11.73$ | $6.05$ |

151 | $4.06\times {10}^{-4}$ | $2.84\times {10}^{-4}$ | $1.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.6$ | 2360 | $0.73$ | $0.74$ | $0.58$ | $0.07$ | $3.18\times {10}^{-2}$ | $10.09$ | $6.3$ |

152 | $4.06\times {10}^{-4}$ | $2.84\times {10}^{-4}$ | $1.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.6$ | 2460 | $0.73$ | $0.74$ | $0.58$ | $0.07$ | $3.36\times {10}^{-2}$ | $10.64$ | $6.09$ |

153 | $4.06\times {10}^{-4}$ | $2.84\times {10}^{-4}$ | $1.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.6$ | 2560 | $0.73$ | $0.74$ | $0.58$ | $0.07$ | $3.52\times {10}^{-2}$ | $11.17$ | $5.91$ |

154 | $4.06\times {10}^{-4}$ | $2.84\times {10}^{-4}$ | $1.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.6$ | 2660 | $0.73$ | $0.74$ | $0.58$ | $0.07$ | $3.69\times {10}^{-2}$ | $11.7$ | $5.74$ |

155 | $4.06\times {10}^{-4}$ | $2.84\times {10}^{-4}$ | $1.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.6$ | 2760 | $0.73$ | $0.74$ | $0.58$ | $0.07$ | $3.86\times {10}^{-2}$ | $12.22$ | $5.56$ |

156 | $4.08\times {10}^{-4}$ | $2.45\times {10}^{-4}$ | $1.96\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.8$ | 2360 | $0.74$ | $0.75$ | $0.6$ | $0.07$ | $3.29\times {10}^{-2}$ | $10.44$ | $5.9$ |

157 | $4.08\times {10}^{-4}$ | $2.45\times {10}^{-4}$ | $1.96\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.8$ | 2460 | $0.74$ | $0.75$ | $0.6$ | $0.07$ | $3.46\times {10}^{-2}$ | $10.97$ | $5.73$ |

158 | $4.08\times {10}^{-4}$ | $2.45\times {10}^{-4}$ | $1.96\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.8$ | 2560 | $0.74$ | $0.75$ | $0.59$ | $0.07$ | $3.63\times {10}^{-2}$ | $11.49$ | $5.57$ |

159 | $4.08\times {10}^{-4}$ | $2.45\times {10}^{-4}$ | $1.96\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.8$ | 2760 | $0.74$ | $0.75$ | $0.59$ | $0.07$ | $3.95\times {10}^{-2}$ | $12.51$ | $5.31$ |

160 | $3.45\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.03\times {10}^{-4}$ | $0.67$ | $8.0$ | $0.6$ | $0.5$ | 2360 | $0.73$ | $0.75$ | $0.7$ | $0.1$ | $5.85\times {10}^{-2}$ | $18.54$ | $4.3$ |

161 | $3.45\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.03\times {10}^{-4}$ | $0.67$ | $8.0$ | $0.6$ | $0.5$ | 2460 | $0.73$ | $0.75$ | $0.7$ | $0.1$ | $6.14\times {10}^{-2}$ | $19.46$ | $4.18$ |

162 | $3.45\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.03\times {10}^{-4}$ | $0.67$ | $8.0$ | $0.6$ | $0.5$ | 2560 | $0.73$ | $0.75$ | $0.7$ | $0.1$ | $6.43\times {10}^{-2}$ | $20.37$ | $4.08$ |

163 | $3.45\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.03\times {10}^{-4}$ | $0.67$ | $8.0$ | $0.6$ | $0.5$ | 2660 | $0.73$ | $0.75$ | $0.69$ | $0.1$ | $6.71\times {10}^{-2}$ | $21.26$ | $3.98$ |

164 | $3.45\times {10}^{-4}$ | $2.07\times {10}^{-4}$ | $1.03\times {10}^{-4}$ | $0.67$ | $8.0$ | $0.6$ | $0.5$ | 2760 | $0.73$ | $0.75$ | $0.7$ | $0.1$ | $6.99\times {10}^{-2}$ | $22.16$ | $3.89$ |

165 | $3.48\times {10}^{-4}$ | $1.74\times {10}^{-4}$ | $1.22\times {10}^{-4}$ | $0.67$ | $8.0$ | $0.5$ | $0.7$ | 2460 | $0.76$ | $0.73$ | $0.6$ | $0.1$ | $5.77\times {10}^{-2}$ | $18.29$ | $4.72$ |

166 | $3.09\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.6$ | $1.0$ | 2460 | $0.69$ | $0.69$ | $0.5$ | $0.08$ | $4.32\times {10}^{-2}$ | $13.69$ | $5.19$ |

167 | $3.09\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.6$ | $1.0$ | 2660 | $0.69$ | $0.69$ | $0.5$ | $0.08$ | $4.72\times {10}^{-2}$ | $14.96$ | $4.95$ |

168 | $2.79\times {10}^{-4}$ | $1.95\times {10}^{-4}$ | $1.95\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.7$ | $1.0$ | 2460 | $0.7$ | $0.69$ | $0.52$ | $0.08$ | $4.46\times {10}^{-2}$ | $14.15$ | $4.9$ |

169 | $2.79\times {10}^{-4}$ | $1.95\times {10}^{-4}$ | $1.95\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.7$ | $1.0$ | 2560 | $0.7$ | $0.69$ | $0.52$ | $0.08$ | $4.67\times {10}^{-2}$ | $14.82$ | $4.71$ |

170 | $2.55\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.8$ | $1.0$ | 2360 | $0.69$ | $0.7$ | $0.54$ | $0.08$ | $4.36\times {10}^{-2}$ | $13.81$ | $4.76$ |

171 | $2.55\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.8$ | $1.0$ | 2460 | $0.69$ | $0.7$ | $0.54$ | $0.08$ | $4.58\times {10}^{-2}$ | $14.53$ | $4.62$ |

172 | $2.55\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.8$ | $1.0$ | 2560 | $0.69$ | $0.7$ | $0.54$ | $0.08$ | $4.80\times {10}^{-2}$ | $15.23$ | $4.49$ |

173 | $2.55\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $2.04\times {10}^{-4}$ | $0.67$ | $2.0$ | $0.8$ | $1.0$ | 2660 | $0.69$ | $0.7$ | $0.54$ | $0.08$ | $5.02\times {10}^{-2}$ | $15.91$ | $4.37$ |

174 | $3.28\times {10}^{-4}$ | $3.28\times {10}^{-4}$ | $1.97\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $0.6$ | 2760 | $0.67$ | $0.73$ | $0.65$ | $0.07$ | $4.24\times {10}^{-2}$ | $13.45$ | $4.74$ |

175 | $2.98\times {10}^{-4}$ | $2.98\times {10}^{-4}$ | $2.39\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $0.8$ | 2560 | $0.68$ | $0.69$ | $0.78$ | $0.07$ | $4.17\times {10}^{-2}$ | $13.21$ | $4.35$ |

176 | $3.33\times {10}^{-4}$ | $2.66\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $0.9$ | 2360 | $0.69$ | $0.7$ | $0.55$ | $0.07$ | $3.45\times {10}^{-2}$ | $10.95$ | $5.51$ |

177 | $3.33\times {10}^{-4}$ | $2.66\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $0.9$ | 2460 | $0.69$ | $0.7$ | $0.55$ | $0.07$ | $3.64\times {10}^{-2}$ | $11.53$ | $5.36$ |

178 | $3.33\times {10}^{-4}$ | $2.66\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $0.9$ | 2560 | $0.69$ | $0.7$ | $0.54$ | $0.07$ | $3.81\times {10}^{-2}$ | $12.09$ | $5.19$ |

179 | $3.33\times {10}^{-4}$ | $2.66\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $0.9$ | 2660 | $0.69$ | $0.7$ | $0.55$ | $0.07$ | $3.99\times {10}^{-2}$ | $12.64$ | $5.06$ |

180 | $3.08\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $2.49\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $0.9$ | 2460 | $0.68$ | $0.69$ | $0.55$ | $0.07$ | $3.74\times {10}^{-2}$ | $11.85$ | $5.07$ |

ID | ${\mathit{a}}_{\mathbf{L}}$ in m | ${\mathit{a}}_{\mathit{I}}$ in m | ${\mathit{a}}_{\mathbf{S}}$ in m | ${\mathit{\xi}}_{1}$ | ${\mathit{\xi}}_{2}$ | E | F | ${\mathit{\rho}}_{\mathbf{p}}$ | ${\mathit{\kappa}}_{\mathbf{con}}$ | $\mathit{\psi}$ | ${\mathit{\psi}}_{\perp}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{u}}_{\mathbf{ts}}$ | Re | ${\mathit{C}}_{\mathbf{D}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

181 | $3.08\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $2.49\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $0.9$ | 2560 | $0.68$ | $0.69$ | $0.57$ | $0.07$ | $3.92\times {10}^{-2}$ | $12.42$ | $4.92$ |

182 | $3.08\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $2.49\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $0.9$ | 2660 | $0.68$ | $0.69$ | $0.56$ | $0.07$ | $4.09\times {10}^{-2}$ | $12.98$ | $4.8$ |

183 | $3.08\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $2.49\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $0.9$ | 2760 | $0.68$ | $0.69$ | $0.55$ | $0.07$ | $4.27\times {10}^{-2}$ | $13.52$ | $4.69$ |

184 | $2.87\times {10}^{-4}$ | $2.87\times {10}^{-4}$ | $2.58\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $0.9$ | 2360 | $0.68$ | $0.68$ | $0.72$ | $0.06$ | $3.69\times {10}^{-2}$ | $11.7$ | $4.82$ |

185 | $2.87\times {10}^{-4}$ | $2.87\times {10}^{-4}$ | $2.58\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $0.9$ | 2660 | $0.68$ | $0.68$ | $0.83$ | $0.06$ | $4.28\times {10}^{-2}$ | $13.58$ | $4.38$ |

186 | $2.87\times {10}^{-4}$ | $2.87\times {10}^{-4}$ | $2.58\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $0.9$ | 2760 | $0.68$ | $0.68$ | $0.83$ | $0.06$ | $4.47\times {10}^{-2}$ | $14.18$ | $4.25$ |

187 | $3.51\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.7$ | $1.0$ | 2360 | $0.69$ | $0.69$ | $0.53$ | $0.07$ | $3.32\times {10}^{-2}$ | $10.53$ | $5.97$ |

188 | $3.51\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.7$ | $1.0$ | 2460 | $0.69$ | $0.69$ | $0.53$ | $0.07$ | $3.50\times {10}^{-2}$ | $11.09$ | $5.79$ |

189 | $3.51\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.7$ | $1.0$ | 2560 | $0.69$ | $0.69$ | $0.53$ | $0.07$ | $3.67\times {10}^{-2}$ | $11.62$ | $5.63$ |

190 | $3.51\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $2.46\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.7$ | $1.0$ | 2660 | $0.69$ | $0.69$ | $0.52$ | $0.07$ | $3.83\times {10}^{-2}$ | $12.15$ | $5.48$ |

191 | $3.21\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $1.0$ | 2360 | $0.68$ | $0.68$ | $0.53$ | $0.07$ | $3.41\times {10}^{-2}$ | $10.82$ | $5.67$ |

192 | $3.21\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $1.0$ | 2460 | $0.68$ | $0.68$ | $0.53$ | $0.07$ | $3.59\times {10}^{-2}$ | $11.39$ | $5.48$ |

193 | $3.21\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $1.0$ | 2560 | $0.68$ | $0.68$ | $0.54$ | $0.07$ | $3.77\times {10}^{-2}$ | $11.95$ | $5.31$ |

194 | $3.21\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $1.0$ | 2660 | $0.68$ | $0.68$ | $0.53$ | $0.07$ | $3.94\times {10}^{-2}$ | $12.49$ | $5.16$ |

195 | $3.21\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $2.57\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.8$ | $1.0$ | 2760 | $0.68$ | $0.68$ | $0.54$ | $0.07$ | $4.11\times {10}^{-2}$ | $13.02$ | $5.06$ |

196 | $2.97\times {10}^{-4}$ | $2.67\times {10}^{-4}$ | $2.67\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $1.0$ | 2460 | $0.68$ | $0.68$ | $0.54$ | $0.06$ | $3.69\times {10}^{-2}$ | $11.69$ | $5.21$ |

197 | $2.97\times {10}^{-4}$ | $2.67\times {10}^{-4}$ | $2.67\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $1.0$ | 2660 | $0.68$ | $0.68$ | $0.56$ | $0.06$ | $4.04\times {10}^{-2}$ | $12.79$ | $4.95$ |

198 | $2.97\times {10}^{-4}$ | $2.67\times {10}^{-4}$ | $2.67\times {10}^{-4}$ | $0.67$ | $1.0$ | $0.9$ | $1.0$ | 2760 | $0.68$ | $0.68$ | $0.56$ | $0.06$ | $4.20\times {10}^{-2}$ | $13.33$ | $4.82$ |

199 | $2.77\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $1.0$ | 2460 | $0.69$ | $0.67$ | $0.89$ | $0.06$ | $3.83\times {10}^{-2}$ | $12.14$ | $4.81$ |

200 | $2.77\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $2.77\times {10}^{-4}$ | $0.67$ | $1.0$ | $1.0$ | $1.0$ | 2560 | $0.69$ | $0.67$ | $0.89$ | $0.06$ | $4.02\times {10}^{-2}$ | $12.75$ | $4.67$ |

E | ${\mathit{\rho}}_{\mathbf{p}}$ | $\mathit{\psi}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{\lambda}}_{\mathbf{H}}$ | Re | ${\mathit{C}}_{\mathbf{D}}$ | ${\mathit{u}}_{\mathbf{ts}}$ | |
---|---|---|---|---|---|---|---|---|

mean | $0.757$ | $2563.17$ | $0.786$ | $0.101$ | $-0.962$ | $14.380$ | $4.544$ | $0.045$ |

standard deviation | $0.166$ | $141.01$ | $0.072$ | $0.026$ | $0.038$ | $3.103$ | $0.970$ | $0.010$ |

## Appendix B

ID | ${\mathit{a}}_{\mathbf{L}}$ in m | ${\mathit{a}}_{\mathit{I}}$ in m | ${\mathit{a}}_{\mathbf{S}}$ in m | ${\mathit{\xi}}_{1}$ | ${\mathit{\xi}}_{2}$ | E | F | ${\mathit{\rho}}_{\mathbf{p}}$ | ${\mathit{\kappa}}_{\mathbf{con}}$ | $\mathit{\psi}$ | ${\mathit{\psi}}_{\perp}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{u}}_{\mathbf{ts}}$ | Re | ${\mathit{C}}_{\mathbf{D}}$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | $5.39\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.35\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $0.5$ | 2460 | $0.75$ | $0.75$ | $0.51$ | $0.07$ | $2.89\times {10}^{-2}$ | $9.17$ | $8.21$ |

2 | $4.78\times {10}^{-4}$ | $2.87\times {10}^{-4}$ | $1.43\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.5$ | 2460 | $0.74$ | $0.73$ | $0.52$ | $0.07$ | $3.06\times {10}^{-2}$ | $9.71$ | $7.33$ |

3 | $3.65\times {10}^{-4}$ | $3.28\times {10}^{-4}$ | $1.64\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $0.5$ | 2460 | $0.72$ | $0.73$ | $0.55$ | $0.07$ | $3.32\times {10}^{-2}$ | $10.54$ | $6.21$ |

4 | $3.40\times {10}^{-4}$ | $3.40\times {10}^{-4}$ | $1.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $0.5$ | 2460 | $0.72$ | $0.73$ | $0.56$ | $0.07$ | $3.40\times {10}^{-2}$ | $10.76$ | $5.96$ |

5 | $5.08\times {10}^{-4}$ | $2.54\times {10}^{-4}$ | $1.52\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $0.6$ | 2460 | $0.76$ | $0.77$ | $0.57$ | $0.08$ | $3.08\times {10}^{-2}$ | $9.75$ | $7.28$ |

6 | $3.71\times {10}^{-4}$ | $2.97\times {10}^{-4}$ | $1.78\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.6$ | 2460 | $0.72$ | $0.74$ | $0.59$ | $0.07$ | $3.45\times {10}^{-2}$ | $10.95$ | $5.75$ |

7 | $3.43\times {10}^{-4}$ | $3.09\times {10}^{-4}$ | $1.85\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $0.6$ | 2460 | $0.71$ | $0.74$ | $0.61$ | $0.07$ | $3.54\times {10}^{-2}$ | $11.22$ | $5.5$ |

8 | $3.20\times {10}^{-4}$ | $3.20\times {10}^{-4}$ | $1.92\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $0.6$ | 2460 | $0.71$ | $0.73$ | $0.64$ | $0.07$ | $3.60\times {10}^{-2}$ | $11.4$ | $5.31$ |

9 | $4.82\times {10}^{-4}$ | $2.41\times {10}^{-4}$ | $1.69\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $0.7$ | 2460 | $0.75$ | $0.77$ | $0.61$ | $0.08$ | $3.24\times {10}^{-2}$ | $10.28$ | $6.53$ |

10 | $4.27\times {10}^{-4}$ | $2.56\times {10}^{-4}$ | $1.79\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.7$ | 2460 | $0.73$ | $0.76$ | $0.62$ | $0.07$ | $3.40\times {10}^{-2}$ | $10.79$ | $5.92$ |

11 | $3.85\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $1.89\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.7$ | 2460 | $0.72$ | $0.75$ | $0.63$ | $0.07$ | $3.54\times {10}^{-2}$ | $11.22$ | $5.48$ |

12 | $3.53\times {10}^{-4}$ | $2.82\times {10}^{-4}$ | $1.97\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.7$ | 2460 | $0.71$ | $0.74$ | $0.65$ | $0.07$ | $3.64\times {10}^{-2}$ | $11.53$ | $5.19$ |

13 | $3.26\times {10}^{-4}$ | $2.93\times {10}^{-4}$ | $2.05\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $0.7$ | 2460 | $0.7$ | $0.73$ | $0.67$ | $0.07$ | $3.71\times {10}^{-2}$ | $11.77$ | $4.98$ |

14 | $3.04\times {10}^{-4}$ | $3.04\times {10}^{-4}$ | $2.13\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $0.7$ | 2460 | $0.7$ | $0.73$ | $0.69$ | $0.07$ | $3.76\times {10}^{-2}$ | $11.93$ | $4.85$ |

15 | $4.61\times {10}^{-4}$ | $2.31\times {10}^{-4}$ | $1.84\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $0.8$ | 2460 | $0.75$ | $0.77$ | $0.59$ | $0.08$ | $3.28\times {10}^{-2}$ | $10.4$ | $6.37$ |

16 | $3.69\times {10}^{-4}$ | $2.58\times {10}^{-4}$ | $2.06\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.8$ | 2460 | $0.72$ | $0.74$ | $0.61$ | $0.07$ | $3.61\times {10}^{-2}$ | $11.45$ | $5.27$ |

17 | $3.37\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $2.16\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $0.8$ | 2460 | $0.71$ | $0.74$ | $0.66$ | $0.07$ | $3.73\times {10}^{-2}$ | $11.83$ | $4.94$ |

18 | $3.12\times {10}^{-4}$ | $2.81\times {10}^{-4}$ | $2.24\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $0.8$ | 2460 | $0.7$ | $0.72$ | $0.69$ | $0.07$ | $3.83\times {10}^{-2}$ | $12.15$ | $4.67$ |

19 | $2.91\times {10}^{-4}$ | $2.91\times {10}^{-4}$ | $2.32\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $0.8$ | 2460 | $0.7$ | $0.72$ | $0.75$ | $0.07$ | $3.96\times {10}^{-2}$ | $12.56$ | $4.38$ |

20 | $4.43\times {10}^{-4}$ | $2.22\times {10}^{-4}$ | $2.00\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $0.9$ | 2460 | $0.75$ | $0.75$ | $0.55$ | $0.07$ | $3.23\times {10}^{-2}$ | $10.24$ | $6.59$ |

21 | $3.93\times {10}^{-4}$ | $2.36\times {10}^{-4}$ | $2.12\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $0.9$ | 2460 | $0.72$ | $0.74$ | $0.56$ | $0.07$ | $3.39\times {10}^{-2}$ | $10.76$ | $5.96$ |

22 | $3.54\times {10}^{-4}$ | $2.48\times {10}^{-4}$ | $2.23\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $0.9$ | 2460 | $0.72$ | $0.73$ | $0.57$ | $0.07$ | $3.53\times {10}^{-2}$ | $11.17$ | $5.53$ |

23 | $2.79\times {10}^{-4}$ | $2.79\times {10}^{-4}$ | $2.51\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $0.9$ | 2460 | $0.71$ | $0.71$ | $0.76$ | $0.07$ | $3.88\times {10}^{-2}$ | $12.31$ | $4.54$ |

24 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $1.0$ | 2460 | $0.75$ | $0.73$ | $0.53$ | $0.07$ | $3.22\times {10}^{-2}$ | $10.2$ | $6.62$ |

25 | $3.79\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $1.0$ | 2460 | $0.73$ | $0.72$ | $0.54$ | $0.07$ | $3.38\times {10}^{-2}$ | $10.7$ | $6.02$ |

26 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $1.0$ | 2360 | $0.75$ | $0.73$ | $0.53$ | $0.07$ | $3.06\times {10}^{-2}$ | $9.7$ | $6.83$ |

27 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $1.0$ | 2460 | $0.75$ | $0.73$ | $0.53$ | $0.07$ | $3.22\times {10}^{-2}$ | $10.2$ | $6.62$ |

28 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $1.0$ | 2560 | $0.75$ | $0.73$ | $0.53$ | $0.07$ | $3.37\times {10}^{-2}$ | $10.69$ | $6.44$ |

29 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $1.0$ | 2660 | $0.75$ | $0.73$ | $0.53$ | $0.07$ | $3.53\times {10}^{-2}$ | $11.18$ | $6.27$ |

30 | $4.28\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $2.14\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.5$ | $1.0$ | 2760 | $0.75$ | $0.73$ | $0.53$ | $0.07$ | $3.68\times {10}^{-2}$ | $11.66$ | $6.11$ |

31 | $3.79\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $1.0$ | 2360 | $0.73$ | $0.72$ | $0.53$ | $0.07$ | $3.21\times {10}^{-2}$ | $10.16$ | $6.23$ |

32 | $3.79\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $1.0$ | 2460 | $0.73$ | $0.72$ | $0.54$ | $0.07$ | - | - | - |

33 | $3.79\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $1.0$ | 2560 | $0.73$ | $0.72$ | $0.53$ | $0.07$ | $3.54\times {10}^{-2}$ | $11.21$ | $5.87$ |

34 | $3.79\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $1.0$ | 2660 | $0.73$ | $0.72$ | $0.53$ | $0.07$ | - | - | - |

35 | $3.79\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $2.28\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.6$ | $1.0$ | 2760 | $0.73$ | $0.72$ | $0.53$ | $0.07$ | - | - | - |

36 | $3.42\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $1.0$ | 2660 | $0.72$ | $0.71$ | $0.54$ | $0.07$ | - | - | - |

37 | $3.42\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $2.40\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.7$ | $1.0$ | 2760 | $0.72$ | $0.71$ | $0.55$ | $0.07$ | - | - | - |

38 | $3.13\times {10}^{-4}$ | $2.50\times {10}^{-4}$ | $2.50\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.8$ | $1.0$ | 2560 | $0.72$ | $0.71$ | $0.56$ | $0.07$ | $3.77\times {10}^{-2}$ | $11.94$ | $5.16$ |

39 | $2.89\times {10}^{-4}$ | $2.60\times {10}^{-4}$ | $2.60\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $1.0$ | 2360 | $0.72$ | $0.7$ | $0.56$ | $0.07$ | $3.50\times {10}^{-2}$ | $11.09$ | $5.23$ |

40 | $2.89\times {10}^{-4}$ | $2.60\times {10}^{-4}$ | $2.60\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $1.0$ | 2560 | $0.72$ | $0.7$ | $0.56$ | $0.07$ | - | - | - |

41 | $2.89\times {10}^{-4}$ | $2.60\times {10}^{-4}$ | $2.60\times {10}^{-4}$ | $0.7$ | $1.0$ | $0.9$ | $1.0$ | 2660 | $0.72$ | $0.7$ | $0.57$ | $0.07$ | - | - | - |

42 | $2.70\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $1.0$ | 2360 | $0.71$ | $0.69$ | $0.71$ | $0.07$ | - | - | - |

43 | $2.70\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $1.0$ | 2660 | $0.71$ | $0.69$ | $0.75$ | $0.07$ | $4.20\times {10}^{-2}$ | $13.32$ | $4.42$ |

44 | $2.70\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $2.70\times {10}^{-4}$ | $0.7$ | $1.0$ | $1.0$ | $1.0$ | 2760 | $0.71$ | $0.69$ | $0.76$ | $0.07$ | $4.39\times {10}^{-2}$ | $13.91$ | $4.29$ |

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**Figure 1.**Some examples of particle shapes considered via superellipsoids. Depicted (from left to right and top to bottom) are the particles with ID 5, 17, 28, 143, 166 and 200, according to Appendix A.

**Figure 3.**Voxel representation of the particle with the shortest half-axis length of $9.1\times {10}^{-5}$ $\mathrm{m}$ for $N=20$.

**Figure 4.**Coordinates of the center of mass of the particle, projected on a plane normal to the settling direction. Results printed for different grid spacings, for the particle with the shortest half-axis.

**Figure 5.**Plot of the angle for rotation around the y-axis over time during the settling. Results printed for different grid spacings, for the particle with the shortest half-axis.

**Figure 6.**Plot of the angle for rotation around the y-axis over time during the settling. Results printed for different grid spacings, for the particle with the longest half-axis.

**Figure 7.**Coordinates of the center of mass of the particle projected, on a plane normal to the settling direction. Results printed for different grid spacings, for the particle with the longest half-axis.

**Figure 9.**The particles considered in this study are plotted for a shape classification according to Zingg [5]. The four shape classes are 1: discs, 2: spheres, 3: blades and 4: rods.

**Figure 10.**The particles considered in this study are plotted for a shape classification according to Sneed and Folk [6]. They are also classified regarding the compactness, leading to the ten shape classes 1: compact, 2: compactly platy, 3: compactly bladed, 4: compactly elongated, 5: platy, 6: bladed, 7: elongated, 8: very platy, 9: very bladed and 10: very elongated.

**Figure 11.**The drag coefficient plotted against the Reynolds number, color with shape classification according to Zingg [5]. A spread is revealed, describable via the sphericity (marker style).

**Table 1.**Results of a chi-squared test for equal distribution of frequencies of different shape parameters.

Elongation | Flatness | Convexity | Sphericity | Density | |
---|---|---|---|---|---|

numberof bins | 6 | 6 | 6 | 5 | 5 |

p-value | $0.998$ | $0.995$ | $0.999$ | $1.000$ | $1.000$ |

**Table 2.**Absolute Values of the correlation coefficients according to Pearson [61] for the considered shape parameters.

${\mathit{a}}_{\mathbf{L}}$ | ${\mathit{a}}_{\mathit{I}}$ | ${\mathit{a}}_{\mathbf{S}}$ | ${\mathit{\xi}}_{1}$ | ${\mathit{\xi}}_{2}$ | ${\mathit{\rho}}_{\mathbf{p}}$ | E | F | ${\mathit{\kappa}}_{\mathbf{con}}$ | $\mathit{\psi}$ | ${\mathit{\psi}}_{\perp}$ | ${\mathit{\kappa}}_{\mathbf{rnd}}$ | ${\mathit{\lambda}}_{\mathbf{CSF}}$ | ${\mathit{\lambda}}_{\mathbf{H}}$ | ${\mathit{\lambda}}_{\mathbf{LR}}$ | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${a}_{\mathrm{L}}$ | $1.0$ | $0.55$ | $0.04$ | $0.41$ | $0.17$ | $0.03$ | $0.74$ | $0.51$ | $0.65$ | $0.52$ | $0.64$ | $0.68$ | $0.67$ | $0.73$ | $0.75$ |

${a}_{\mathrm{I}}$ | $0.55$ | $1.0$ | $0.57$ | $0.39$ | $0.47$ | $0.08$ | $0.13$ | $0.13$ | $0.63$ | $0.61$ | $0.47$ | $0.85$ | $0.05$ | $0.04$ | $0.02$ |

${a}_{\mathrm{S}}$ | $0.04$ | $0.57$ | $1.0$ | $0.18$ | $0.57$ | $0.03$ | $0.44$ | $0.72$ | $0.41$ | $0.45$ | $0.31$ | $0.61$ | $0.73$ | $0.64$ | $0.65$ |

${\xi}_{1}$ | $0.41$ | $0.39$ | $0.18$ | $1.0$ | $0.02$ | $0.08$ | $0.19$ | $0.15$ | $0.47$ | $0.44$ | $0.31$ | $0.57$ | $0.18$ | $0.21$ | $0.21$ |

${\xi}_{2}$ | $0.17$ | $0.47$ | $0.57$ | $0.02$ | $1.0$ | $0.03$ | $0.16$ | $0.36$ | $0.07$ | $0.05$ | $0.23$ | $0.34$ | $0.34$ | $0.32$ | $0.31$ |

${\rho}_{\mathrm{p}}$ | $0.03$ | $0.08$ | $0.03$ | $0.08$ | $0.03$ | $1.0$ | $0.02$ | $0.1$ | $0.03$ | $0.05$ | $0.04$ | $0.05$ | $0.08$ | $0.02$ | $0.03$ |

E | $0.74$ | $0.13$ | $0.44$ | $0.19$ | $0.16$ | $0.02$ | $1.0$ | $0.45$ | $0.33$ | $0.2$ | $0.47$ | $0.17$ | $0.72$ | $0.85$ | $0.84$ |

F | $0.51$ | $0.13$ | $0.72$ | $0.15$ | $0.36$ |