Pt. 3. Blade Edge Angles.
As I wrote in Pt. 1, most discussions of blade edge angles focus on the bite angle: as the bite angle increases, the blade bites more deeply into the ice. I believe it’s more intuitive to focus on the included angle, as this corresponds to the cutting angle of a tool (such as a knife blade): the smaller the included angle, the sharper the tool. For a knife blade, the included angle is typically 40 deg or less, depending on the application. For tools designed for chopping, such as a cleaver or axe, the included angle is typically larger, since a more robust edge is needed. For a skate blade, the included angle is relatively large, on the order of 80 deg. Since the sum of the included angle and the bite angle is equal to 90 deg, the included angle decreases as the bite angle increases. Hence, the scenario is consistent: as the bite angle increases, the included angle decreases, and the tool (skate blade) becomes sharper and cuts deeper into the ice.
Shown below are values of the blade edge angles as a function of blade thickness and radius of hollow.
In Table 3, the blade thickness is fixed, and the blade edge angles are shown as functions of the radius of hollow. For a fixed blade thickness, as the radius of hollow decreases, the included angle decreases and the bite angle increases.
In Table 4, the radius of hollow is fixed, and the blade edge angles are shown as functions of the blade thickness. For a fixed radius of hollow, as the blade thickness decreases, the included angle increases and the bite angle decreases; this is the basis for the recommendation to sharpen (thinner) dance blades to a smaller radius of hollow than (thicker) freestyle blades. For example, consider a freestyle blade with a thickness t = 0.150 inch and a dance blade with a thickness t = 0.100 inch. If they are both sharpened to a 7/16 inch radius of hollow, then the blade edge angles are:
included angle: 80.13 (t = 0.150 inch ); 83.44 deg (t = 0.100 inch)
bite angle: 9.87 (t = 0.150 inch ); 6.56 deg (t = 0.100 inch).
On the basis of blade edge angles, the dance blade is less sharp than the freestyle blade, for the same radius of hollow.
If you wish the dance blade to have approximately the same blade edge angles as the freestyle blade, you need a radius of hollow of approximately 5/16 inch:
included angle: 80.79 deg (t = 0.100 inch)
bite angle: 9.21 deg (t = 0.100 inch).
Table 3. Blade Edge Angles as a Function of Radius of Hollow for Fixed Blade Width.
t: blade thickness (decimal inch)
r: radius of hollow (fractional inch)
α: blade edge included angle (deg)
β: blade edge bite angle (deg)
__t______r_____α_______β_
0.100 5/16 80.79 9.21
0.100 3/8 82.34 7.66
0.100 7/16 83.44 6.56
0.100 1/2 84.26 5.74
0.100 9/16 84.90 5.10
0.100 5/8 85.41 4.59
0.100 3/4 86.18 3.82
0.100 1 87.13 2.87
0.125 5/16 78.46 11.54
0.125 3/8 80.41 9.59
0.125 7/16 81.79 8.21
0.125 1/2 82.82 7.18
0.125 9/16 83.62 6.38
0.125 5/8 84.26 5.74
0.125 3/4 85.22 4.78
0.125 1 86.42 3.58
0.150 5/16 76.11 13.89
0.150 3/8 78.46 11.54
0.150 7/16 80.13 9.87
0.150 1/2 81.37 8.63
0.150 9/16 82.34 7.66
0.150 5/8 83.11 6.89
0.150 3/4 84.26 5.74
0.150 1 85.70 4.30
0.175 5/16 73.74 16.26
0.175 3/8 76.51 13.49
0.175 7/16 78.46 11.54
0.175 1/2 79.92 10.08
0.175 9/16 81.05 8.95
0.175 5/8 81.95 8.05
0.175 3/4 83.30 6.70
0.175 1 84.98 5.02
0.200 5/16 71.34 18.66
0.200 3/8 74.53 15.47
0.200 7/16 76.79 13.21
0.200 1/2 78.46 11.54
0.200 9/16 79.76 10.24
0.200 5/8 80.79 9.21
0.200 3/4 82.34 7.66
0.200 1 84.26 5.74
Table 4. Blade Edge Angles as a Function of Blade Width for Fixed Radius of Hollow.
r: radius of hollow (fractional inch)
t: blade thickness (decimal inch)
α: blade edge included angle (deg)
β: blade edge bite angle (deg)
__r______t_____α_____β__
5/16 0.100 80.79 9.21
5/16 0.125 78.46 11.54
5/16 0.150 76.11 13.89
5/16 0.175 73.74 16.26
5/16 0.200 71.34 18.66
3/8 0.100 82.34 7.66
3/8 0.125 80.41 9.59
3/8 0.150 78.46 11.54
3/8 0.175 76.51 13.49
3/8 0.200 74.53 15.47
7/16 0.100 83.44 6.56
7/16 0.125 81.79 8.21
7/16 0.150 80.13 9.87
7/16 0.175 78.46 11.54
7/16 0.200 76.79 13.21
1/2 0.100 84.26 5.74
1/2 0.125 82.82 7.18
1/2 0.150 81.37 8.63
1/2 0.175 79.92 10.08
1/2 0.200 78.46 11.54
9/16 0.100 84.90 5.10
9/16 0.125 83.62 6.38
9/16 0.150 82.34 7.66
9/16 0.175 81.05 8.95
9/16 0.200 79.76 10.24
5/8 0.100 85.41 4.59
5/8 0.125 84.26 5.74
5/8 0.150 83.11 6.89
5/8 0.175 81.95 8.05
5/8 0.200 80.79 9.21
3/4 0.100 86.18 3.82
3/4 0.125 85.22 4.78
3/4 0.150 84.26 5.74
3/4 0.175 83.30 6.70
3/4 0.200 82.34 7.66
1 0.100 87.13 2.87
1 0.125 86.42 3.58
1 0.150 85.70 4.30
1 0.175 84.98 5.02
1 0.200 84.26 5.74