The Nealon Equation

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))

Nealon Resonator

Calculated curve

Graphed in Logger Pro

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*(20.1-x))

Front (lauan) and back (copper) of another thin body Nealon Resonator.

Back (Honduran mahogany) of a non-resonator instrument with the same shape.

Back of the instrument shown above.

This outline is created by plotting +y(x) and –y(x) in Graph and removing the axes.

Total length  =  29.91 inches

L

x

Length of the side around the perimeter.

 

Nealon Resonator

A

.1957769

B

-.9361852

C

-3.203335

D

 .4075888

E

.8057877

F

5.039549

G

4.322408

H

.09507775

I

3.699719

J

2.170954

K

.3080430

L

-3.177518

M

-.6046287

N

-.06450537

O

.04824956

P

-.00597517

Q

 .0001856246

R

16.00042

S

8.550479

BL

20.1

 

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

BL

.1957769

-.9361852

-3.203335

 .4075888

.8057877

5.039549

4.322408

.09507775

3.699719

2.170954

.3080430

-3.177518

-.6046287

-.06450537

.04824956

-.00597517

 .0001856246

16.00042

8.550479

20.1 

 

A = .1957769

B = -.9361852

C = -3.203335

D = .4075888

E = .8057877

F = 5.039549

G = 4.322408

H = .09507775

I = 3.699719

J = 2.170954

K = .3080430

L = -3.177518

M = -.6046287

N = -.06450537

O = .04824956

P = -.00597517

Q = .0001856246

R = 16.00042

S = 8.550479

BL = 20.1