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The Nealon Equation |
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y = (A*sin(B*x+C) + D*sin(E*x+F) + G*sin(H*x+I) + J*sin(K*x+L)) * (M + N*x + O*x^2 + P*x^3 + Q*x^4) * atan(R*x) * atan(S*(BL-x)) |
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Gibson Les Paul |
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y = (A*sin(B*x+C)+D*sin(E*x+F)+G*sin(H*x+I)+J*sin(K*x+L))*(M+N*x+O*x^2+P*x^3+Q*x^4)*atan(R*x)*atan(S*(17.275-x)) |
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The two curves from the graphs put together. |
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The drawing is of a 1959 flame top. |
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y = (A*sin(B*x+C)+D*sin(E*x+F)+G*sin(H*x+I)+J*sin(K*x+L))*(M+N*x+O*x^2+P*x^3+Q*x^4)*(3-atan(R*x))*atan(S*(3.59-x)) |
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Cutaway A modified equation is required for the cutaway. The first arctan term is subtracted from 3. |
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Now the body twice, one mirror image of the other and the cutaway. All of this is done with the curves produced by the mathematical equation. I suppose it also could be done with the point series of data taken from the instrument, but what’s the fun in that? |
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Length around the perimeter of the bass side of the Les Paul. |
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Les Paul Body Outline |
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A |
0.3661125 |
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B |
-0.6542102 |
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C |
-3.428853 |
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D |
0.04257652 |
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E |
-1.426924 |
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F |
0.9901923 |
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G |
4.458389 |
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H |
0.07430593 |
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I |
1.892568 |
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J |
1.918956 |
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K |
0.3106034 |
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L |
-2.663953 |
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M |
0.3029042 |
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N |
0.2545602 |
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O |
-0.0215465 |
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P |
-0.0007298772 |
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Q |
8.45777E-05 |
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R |
24.62258 |
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S |
23.2647 |
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BL |
17.275 |
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A B C D E F G H I J K L M N O P Q R S BL |
0.3661125 -0.6542102 -3.428853 0.04257652 -1.426924 0.9901923 4.458389 0.07430593 1.892568 1.918956 0.3106034 -2.663953 0.3029042 0.2545602 -0.0215465 -0.0007298772 8.45777E-05 24.62258 23.2647 17.275 |
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A = 0.3661125 |
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B = -0.6542102 |
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C = -3.428853 |
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D = 0.04257652 |
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E = -1.426924 |
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F = 0.9901923 |
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G = 4.458389 |
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H = 0.07430593 |
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I = 1.892568 |
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J = 1.918956 |
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K = 0.3106034 |
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L = -2.663953 |
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M = 0.3029042 |
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N = 0.2545602 |
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O = -0.0215465 |
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P = -0.0007298772 |
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Q = 8.45777E-05 |
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R = 24.62258 |
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S = 23.2647 |
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BL = 17.275 |
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Les Paul Cutaway |
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A |
0.002098982 |
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B |
-6.793013 |
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C |
1.691257 |
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D |
3.204554 |
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E |
-0.8213864 |
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F |
1.118254 |
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G |
2.366427 |
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H |
-0.2342140 |
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I |
0.29424849 |
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J |
4.349017 |
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K |
-0.7233598 |
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L |
4.076135 |
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M |
5.072948 |
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N |
-11.91285 |
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O |
12.03647 |
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P |
-5.864441 |
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Q |
1.146872 |
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R |
16.64988 |
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S |
98.20209 |
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BL |
3.59 |
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A B C D E F G H I J K L M N O P Q R S BL |
0.002098982 -6.793013 1.691257 3.204554 -0.8213864 1.118254 2.366427 -0.2342140 0.29424849 4.349017 -0.7233598 4.076135 5.072948 -11.91285 12.03647 -5.864441 1.146872 16.64988 98.20209 3.59 |
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A = 0.002098982 |
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B = -6.793013 |
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C = 1.691257 |
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D = 3.204554 |
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E = -0.8213864 |
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F = 1.118254 |
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G = 2.366427 |
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H = -0.2342140 |
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I = 0.29424849 |
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J = 4.349017 |
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K = -0.7233598 |
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L = 4.076135 |
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M = 5.072948 |
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N = -11.91285 |
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O = 12.03647 |
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P = -5.864441 |
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Q = 1.146872 |
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R = 16.64988 |
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S = 98.20209 |
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BL = 3.59 |
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