Need help on armor sloping...

[Oddball_E8]

well im doing some mods (weeeell... im modding other peoples mods since they are all different and more often that not incompatible) for OFP. and i was just wondering how much armor (in mm) you get for each degree of sloping... in a very primitive way... so how much armor is 45mm at 30degrees slope compared to 45mm at 0degrees?

btw. i am going to try to make some scenarios based on scenarios for CMBB

[Schoerner]

Take this one: effective thickness = thickness/cos(PHI)

PHI...angle in degree between the horizontal and normal vector of the sloped plate

your example:

45mm/cos(30°)= ~52mm

The trigonometrical functions are no linear functions. Therefore it's not possible to say something like 'additional x mm of effective thickness per 1 degree sloping'

[ July 22, 2003, 09:02 PM: Message edited by: Schoerner ]

[Schoerner]

double post

[ July 22, 2003, 08:55 PM: Message edited by: Schoerner ]

[Oddball_E8]

i dont get it...

in the example... do i divide 45 by 30?

then again its probarbly just because of my half baked crap education... sweden has one of the best education systems in the world and i completely missed out on it... go figure...

but seriously im no good at math terminology... so give me an exact formula for the example and i can figure out the rest...

[Björn Eriksson]

Actually, that is the exact formula. You're gonna need an advanced calculator though. I'll take it in swedish instead, it's alot easier to explain

Om du kör Windows, starta Kalkylatorn. Gå sedan in på "Visa" och välj "Avancerad".

Om du vill få ut 45mm/cos(30°) så trycker du först in "45" sedan "/", sedan "30" sedan knappen "cos" (en av de rosa knapparna). Tryck enter efter det.

Jag kommer inte ihåg exakt vad cos innebär längre, men det behöver man inte veta

Hoppas du förstår något

[ July 23, 2003, 04:36 AM: Message edited by: Björn Eriksson ]

[Oddball_E8]

Tackar, tackar... precis va jag behövde... kan ju inte sånt... har bara gått handelsprogrammet ;o)

[MikeyD]

Simple way to do it:

Cut a 30mm strip of paper (or whatever armor thickness you're looking into), put it on the table, turn it 30 degrees (or whatever angle you're looking into), and measure the paper straight across with a ruler for the 'effective thickness'.

You can tell I'd do ANYTHING to avoid using math (yup, I'm an American )

[Michael Emrys]

Doing the math is simple if you have a calculator that handles trig functions. Of course, you have to know which trig functions to use, and it's been forty years since I took trigonometry in school. So it's nice having some guys around who remember.

Michael

[Doodlebug]

Hmmm. Don't remember much maths from school. I wonder if Pythagoras would help?

Pythagoras! Run and fetch my calculator

[Michael Emrys]

Originally posted by Doodlebug:

Pythagoras! Run and fetch my calculator

Pythagoras: "Arf!"

Translation: "Fetch it yourself, you lazy sod!"

Michael

[Lady Roxanne]

20 deg 25 deg 30 deg 35 deg 40 deg 45 deg 50 deg 55 deg 60 deg

10mm 11 12 12 13 14 15 17 19 22

15mm 16 17 19 20 21 23 25 28 32

20mm 22 23 25 26 28 30 34 37 43

25mm 27 29 31 33 35 38 42 47 54

30mm 32 35 37 40 42 46 50 56 65

35mm 38 41 43 46 49 53 59 65 75

40mm 43 46 50 53 56 61 67 75 86

45mm 49 52 56 59 63 68 76 84 96

50mm 54 58 62 66 71 76 84 94 108

55mm 59 64 68 73 78 84 92 103 118

60mm 65 70 74 79 85 91 101 112 129

65mm 70 75 81 86 92 99 109 122 140

70mm 76 81 87 92 99 106 118 131 151

75mm 81 87 93 99 106 114 126 140 161

80mm 86 93 99 106 113 122 134 150 172

85mm 92 99 105 112 120 129 143 159 183

90mm 97 104 112 119 127 137 151 168 193

95mm 103 110 118 125 134 144 160 178 204

100mm 108 116 124 132 141 152 168 187 215

105mm 113 122 130 139 148 160 176 196 226

110mm 119 128 136 145 155 167 185 206 237

115mm 124 133 143 152 162 175 193 215 247

120mm 130 139 149 158 169 182 202 224 258

130mm 140 151 161 172 183 198 218 243 280

140mm 151 162 174 185 197 213 235 262 301

150mm 162 174 186 198 212 228 252 281 323

EDIT: Hmmmm....not too helpful with the spacing all messed up. The first number to the right of the plate thickness is the effective thickness at 20 degrees. Each number further to the right is the plate thickness at 5 degrees more, on up to 60 degrees.

[ July 23, 2003, 11:55 PM: Message edited by: CrankyKris ]

[Michael Emrys]

Yeah, trying to do columns on the board is a heartbreak. Sometimes you can kind of get them to even out by getting creative with the spacebar, but I doubt that you want to spend that much time with it.

Michael

[Mouse]

Don't ask me where all the white space comes from... but it's a simple table.

<TABLE>

<TR>

<TD></TD><TD>20 deg</TD><TD>25 deg</TD><TD>30 deg</TD><TD>35 deg</TD><TD>40 deg</TD><TD>45 deg</TD><TD>50 deg</TD><TD>55 deg</TD><TD>60 deg</TD>

</TR><TR>

<TD>10mm</TD><TD>11</TD><TD>12</TD><TD>12</TD><TD>13</TD><TD>14</TD><TD>15</TD><TD>17</TD><TD>19</TD><TD>22</TD></TD><TR><TD>15mm</TD><TD>16</TD><TD>17</TD><TD>19</TD><TD>20</TD><TD>21</TD><TD>23</TD><TD>25</TD><TD>28</TD><TD>32</TD>

</TR><TR>

<TD>20mm</TD><TD>22</TD><TD>23</TD><TD>25</TD><TD>26</TD><TD>28</TD><TD>30</TD><TD>34</TD><TD>37</TD><TD>43</TD>

</TR><TR>

<TD>25mm</TD><TD>27</TD><TD>29</TD><TD>31</TD><TD>33</TD><TD>35</TD><TD>38</TD><TD>42</TD><TD>47</TD><TD>54</TD>

</TR><TR>

<TD>30mm</TD><TD>32</TD><TD>35</TD><TD>37</TD><TD>40</TD><TD>42</TD><TD>46</TD><TD>50</TD><TD>56</TD><TD>65</TD>

</TR><TR>

<TD>35mm</TD><TD>38</TD><TD>41</TD><TD>43</TD><TD>46</TD><TD>49</TD><TD>53</TD><TD>59</TD><TD>65</TD><TD>75</TD>

</TR><TR>

<TD>40mm</TD><TD>43</TD><TD>46</TD><TD>50</TD><TD>53</TD><TD>56</TD><TD>61</TD><TD>67</TD><TD>75</TD><TD>86</TD>

</TR><TR>

<TD>45mm</TD><TD>49</TD><TD>52</TD><TD>56</TD><TD>59</TD><TD>63</TD><TD>68</TD><TD>76</TD><TD>84</TD><TD>96</TD>

</TR><TR>

<TD>50mm</TD><TD>54</TD><TD>58</TD><TD>62</TD><TD>66</TD><TD>71</TD><TD>76</TD><TD>84</TD><TD>94</TD><TD>108</TD>

</TR><TR>

<TD>55mm</TD><TD>59</TD><TD>64</TD><TD>68</TD><TD>73</TD><TD>78</TD><TD>84</TD><TD>92</TD><TD>103</TD><TD>118</TD>

</TR><TR>

<TD>60mm</TD><TD>65</TD><TD>70</TD><TD>74</TD><TD>79</TD><TD>85</TD><TD>91</TD><TD>101</TD><TD>112</TD><TD>129</TD>

</TR><TR>

<TD>65mm</TD><TD>70</TD><TD>75</TD><TD>81</TD><TD>86</TD><TD>92</TD><TD>99</TD><TD>109</TD><TD>122</TD><TD>140</TD>

</TR><TR>

<TD>70mm</TD><TD>76</TD><TD>81</TD><TD>87</TD><TD>92</TD><TD>99</TD><TD>106</TD><TD>118</TD><TD>131</TD><TD>151</TD>

</TR><TR>

<TD>75mm</TD><TD>81</TD><TD>87</TD><TD>93</TD><TD>99</TD><TD>106</TD><TD>114</TD><TD>126</TD><TD>140</TD><TD>161</TD>

</TR><TR>

<TD>80mm</TD><TD>86</TD><TD>93</TD><TD>99</TD><TD>106</TD><TD>113</TD><TD>122</TD><TD>134</TD><TD>150</TD><TD>172</TD>

</TR><TR>

<TD>85mm</TD><TD>92</TD><TD>99</TD><TD>105</TD><TD>112</TD><TD>120</TD><TD>129</TD><TD>143</TD><TD>159</TD><TD>183</TD>

</TR><TR>

<TD>90mm</TD><TD>97</TD><TD>104</TD><TD>112</TD><TD>119</TD><TD>127</TD><TD>137</TD><TD>151</TD><TD>168</TD><TD>193</TD>

</TR><TR>

<TD>95mm</TD><TD>103</TD><TD>110</TD><TD>118</TD><TD>125</TD><TD>134</TD><TD>144</TD><TD>160</TD><TD>178</TD><TD>204</TD>

</TR><TR>

<TD>100mm</TD><TD>108</TD><TD>116</TD><TD>124</TD><TD>132</TD><TD>141</TD><TD>152</TD><TD>168</TD><TD>187</TD><TD>215</TD>

</TR><TR>

<TD>105mm</TD><TD>113</TD><TD>122</TD><TD>130</TD><TD>139</TD><TD>148</TD><TD>160</TD><TD>176</TD><TD>196</TD><TD>226</TD>

</TR><TR>

<TD>110mm</TD><TD>119</TD><TD>128</TD><TD>136</TD><TD>145</TD><TD>155</TD><TD>167</TD><TD>185</TD><TD>206</TD><TD>237</TD>

</TR><TR>

<TD>115mm</TD><TD>124</TD><TD>133</TD><TD>143</TD><TD>152</TD><TD>162</TD><TD>175</TD><TD>193</TD><TD>215</TD><TD>247</TD>

</TR><TR>

<TD>120mm</TD><TD>130</TD><TD>139</TD><TD>149</TD><TD>158</TD><TD>169</TD><TD>182</TD><TD>202</TD><TD>224</TD><TD>258</TD>

</TR><TR>

<TD>130mm</TD><TD>140</TD><TD>151</TD><TD>161</TD><TD>172</TD><TD>183</TD><TD>198</TD><TD>218</TD><TD>243</TD><TD>280</TD>

</TR><TR>

<TD>140mm</TD><TD>151</TD><TD>162</TD><TD>174</TD><TD>185</TD><TD>197</TD><TD>213</TD><TD>235</TD><TD>262</TD><TD>301</TD>

</TR><TR>

<TD>150mm</TD><TD>162</TD><TD>174</TD><TD>186</TD><TD>198</TD><TD>212</TD><TD>228</TD><TD>252</TD><TD>281</TD><TD>323</TD>

</TR>

</TABLE>

[ July 24, 2003, 09:05 AM: Message edited by: Mouse ]

[Gryphon]

Someone once told me this:

Maths won't help all that much. You can mess around with cosines if you like, and indeed that's a pretty good way to do things for HEAT rounds and modern long-rod penetrators. For WW2 vintage AP (yes, yes, and APC, APCBC, APHE, APCR, APCNR and APDS) rounds you will probably do better to use the table I include here(text formatting permitting), which is what was used by the US and UK at the time:

slope multiplier

10º 1.01

15º 1.03

20º 1.08

25º 1.15

30º 1.25

35º 1.37

40º 1.52

45º 1.69

50º 1.89

55º 2.13

60º 2.5

This is adapted from PRO document WO 185/118, "DDG/FV(D) Armour plate experiments". The values are read from an American armour basis curve, which it was suggested be adopted as an agreed standard as it did not differ greatly from that previously used in Britain.

I hope it's obvious enough how to use the table. To find, say, the equivalent of 45mm of armour sloped at 60 degrees (as on the glacis of a T-34) multiply the plate thickness by the multiplier for 60 degrees -- so, 45 x 2.5 = 113mm.

This adheres to the WW2 Anglo-American convention of citing the angle from the vertical, not the WW2 German and modern NATO convention of angle from the horizontal.

Notice that the benefits of slope get better than a plain cosine rule would indicate as slope increases; using a cosine rule, the T-34 glacis would be worth only 90mm.

The document I took the figures from also contains the following cautions about using armour basis curves:

"It is considered, however, that the facts are too complex to be represented even approximately by any single armour basis curve, and, as illustrated in figures I to V, the armour basis curve varies widely according to the type of projectile and plate attacked."

"...in the case of the 6pdr the armour basis curve is wrong by 7% and in the case of the 2pdr wrong by 28%."

The "too complex" facts include armour and projectile quality and hardness, the effects of piercing caps, and a whole bunch of stuff that I believe CM:BO probably deals with rather better than was possible even for research establishments during WW2.

I can't remember who it was again, but using cos obviously doesn't work.

Regards,

Gryph

[MikeyD]

Yeh, someone probably figured out that table by cutting out a strip of paper, placing on the table at each of those angles and measuring with a ruler!

Don't laugh. It would work!

[Michael Emrys]

Originally posted by MikeyD:

Yeh, someone probably figured out that table by cutting out a strip of paper, placing on the table at each of those angles and measuring with a ruler!

Don't laugh. It would work!

It would work to the extent of giving the same figures that you would get by doing the math using cosines. But as stated, actual penetration is determined by more factors than just armor basis, which is what you are measuring.

Michael

[MikeyD]

Hey, if you're factoring in penetration we're all doomed! CMBB accounts for more variablity than we can list here, including 'shatter gap' and projectile hardness, face-hardened versus homogeneous armor, armor quality (Brunell hardness numbers?). The permutations are almost unlimited, you'd need a computer to figure it out... oh yeh, that's right. We all DO have computers!

[Oddball_E8]

Holy COW! this is getting out of hand!

thanx you guys but Björn Eriksson explained it to me in swedish (yes thats what it looks like, and no, it doesnt sound like the swedish chef in the muppet show). Unfortunately since i answered in swedish most of you might not have understtod that Björns explanation was quite satisfying and no further explenation was needed.

*edited because for some reason half the message dissapeared*

ps. sorry for any spelling errors due to my extreme tiredness at the moment. ds.

[ July 24, 2003, 04:22 PM: Message edited by: Oddball_E8 ]

[rexford]

Originally posted by MikeyD:

Yeh, someone probably figured out that table by cutting out a strip of paper, placing on the table at each of those angles and measuring with a ruler!

Don't laugh. It would work!

When actual firing tests are conducted, the effect of slope is found to be much larger than the "thickness/cosine(slope angle)" equation predicts.

The above formula gives the straight line horizontal distance through a sloped plate. Projectiles penetrate by first being slid so the nose points upwards, then they penetrate going downward. The energy they lose going through all of that results in an increase in effective thickness.

We did a mathematical study of how slope effect differs with plate thickness and projecile diameter.

When 2 pdr AP hits 40mm at 40 degrees the effective vertical thickness is about 64mm, a 1.6 slope multiplier.

When 17 pdr AP hits 40mm at 40 degrees the effective vertical thickness is about 56mm, a 1.4 slope multiplier.

2 pdr AP is a smaller round and 40mm/40 degree plate is better able to change the rounds' flight path than the heavier 17 pdr (2.38 pounds vs 17 pounds projectile weight), so 2 pdr AP has larger slope multipliers.

When 17 pdr AP hits 80mm at 40 degrees the vertical resistance is about 64mm, a 1.6 slope multiplier.

The U.S. and British curves are rough estimates while we found the true relationship, which is a function of angle and the "plate thickness/projectile diameter" ratio.

[ July 24, 2003, 06:13 PM: Message edited by: rexford ]

[Michael Emrys]

Originally posted by MikeyD:

...armor quality (Brunell [sic] hardness numbers?).

Armor quality is also effected by alloying and flaws in the manufacture. Even the way the armor is mounted can effect its ability to resist penetration. As you say, the possibilities are endless.

Michael

[ July 24, 2003, 07:10 PM: Message edited by: Michael Emrys ]