# 17.4: Appendix D- The Shear Angle β Non-Cavitating

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

 hb/hi=1 φ 32o 37o 42o 47o 52o α δ 15 15o 40.892 40.152 39.169 38.012 36.727 18o 39.024 38.380 37.483 36.402 35.184 21o 37.355 36.781 35.947 34.924 33.756 24o 35.847 35.321 34.534 33.552 32.423 27o 34.468 33.975 33.220 32.269 31.166 30o 33.196 32.723 31.989 31.058 29.973 30 15o 37.967 36.937 35.707 34.334 32.854 18o 36.187 35.250 34.100 32.795 31.372 21o 34.564 33.696 32.606 31.353 29.974 24o 33.072 32.255 31.209 29.994 28.648 27o 31.690 30.907 29.893 28.705 27.382 30o 30.401 29.640 28.646 27.476 26.166 45 15o 33.389 32.254 30.936 29.481 27.919 18o 31.792 30.726 29.467 28.061 26.539 21o 30.326 29.310 28.092 26.720 25.224 24o 28.969 27.984 26.793 25.442 23.963 27o 27.700 26.733 25.557 24.218 22.745 30o 26.503 25.543 24.373 23.036 21.562 60 15o 28.220 26.928 25.482 23.917 22.253 18o 26.813 25.569 24.160 22.623 20.978 21o 25.500 24.287 22.901 21.379 19.742 24o 24.264 23.067 21.692 20.174 18.535 27o 23.091 21.897 20.522 18.999 17.350 30o 21.967 20.767 19.382 17.845 16.177

The shear angle β as a function of the blade angle α, the angle of internal friction φ, the soil/interface friction angle δ, for the non-cavitating cutting process, for hb/hi=1.

 hb/hi=2 φ 32o 37o 42o 47o 52o α δ 15o 15o 41.128 40.402 39.427 38.273 36.986 18o 39.239 38.609 37.720 36.643 35.424 21o 37.554 36.993 36.167 35.147 33.979 24o 36.030 35.517 34.738 33.760 32.630 27o 34.638 34.158 33.410 32.462 31.358 30o 33.354 32.893 32.167 31.238 30.152 30o 15o 39.129 37.939 36.562 35.056 33.457 18o 37.223 36.144 34.859 33.429 31.894 21o 35.458 34.468 33.258 31.891 30.408 24o 33.820 32.899 31.748 30.432 28.992 27o 32.293 31.425 30.320 29.043 27.637 30o 30.864 30.035 28.965 27.718 26.336 45o 15o 33.483 32.334 30.991 29.508 27.918 18o 31.743 30.679 29.408 27.985 26.444 21o 30.142 29.141 27.925 26.547 25.043 24o 28.660 27.704 26.527 25.182 23.705 27o 27.278 26.353 25.202 23.879 22.420 30 o 25.982 25.074 23.939 22.630 21.179 60o 15o 27.692 26.533 25.186 23.694 22.085 18o 26.156 25.057 23.759 22.307 20.729 21o 24.744 23.683 22.418 20.991 19.432 24o 23.432 22.394 21.147 19.733 18.180 27o 22.203 21.173 19.932 18.520 16.965 30o 21.039 20.008 18.763 17.344 15.776

The shear angle β as a function of the blade angle α, the angle of internal friction φ, the soil/interface friction angle δ, for the non-cavitating cutting process, for hb/hi=2.

 hb/hi=3 φ 32o 37o 42o 47o 52o α δ 15o 15o 42.346 41.502 40.418 39.164 37.786 18o 40.414 39.674 38.681 37.507 36.198 21o 38.673 38.010 37.086 35.973 34.718 24o 37.087 36.481 35.609 34.542 33.328 27o 35.631 35.064 34.230 33.197 32.013 30 o 34.283 33.742 32.934 31.926 30.763 30o 15o 40.176 38.793 37.257 35.619 33.909 18o 38.242 36.978 35.537 33.977 32.331 21o 36.421 35.258 33.900 32.407 30.817 24o 34.711 33.631 32.341 30.906 29.364 27o 33.103 32.090 30.858 29.470 27.968 30o 31.590 30.631 29.444 28.095 26.625 45o 15o 35.406 33.895 32.248 30.509 28.703 18o 33.548 32.142 30.578 28.907 27.156 21o 31.788 30.472 28.981 27.368 25.665 24o 30.126 28.885 27.455 25.891 24.230 27o 28.557 27.376 25.996 24.474 22.845 30o 27.075 25.941 24.600 23.111 21.509 60o 15o 28.252 26.972 25.516 23.930 22.241 18o 26.613 25.406 24.010 22.472 20.823 21o 25.094 23.940 22.588 21.086 19.464 24o 23.677 22.560 21.238 19.760 18.156 27o 22.348 21.253 19.950 18.485 16.890 30o 21.092 20.008 18.713 17.254 15.600

The shear angle β as a function of the blade angle α, the angle of internal friction φ, the soil/interface friction angle δ, for the non-cavitating cutting process, for hb/hi=3.

17.4: Appendix D- The Shear Angle β Non-Cavitating is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.