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Here is a method for drawing a logarithmic spiral.

To draw a logarithmic spiral, follow these steps:
1.  Draw a line.  One of the ends of this line will be the center of the spiral.
2.  Make a 360° circular array of the line with one of the endpoints as the center and choose the option to rotate the object so they will all be oriented radially from the center point.  The number of lines in this array will determine the angle between the tangent and the radial line of the spiral.  For starters use 20 lines to make a spiral like the one shown in the pictures below.  The angle of the spiral will be equal to one half of the angle between adjacent radial lines.  With 20 equally spaced lines the angle between two adjacent lines will be 360/20 = 18°  So the angle of this spiral is 9°.  If drawing by hand use a protractor to draw marks where the radial lines extend and then draw lines through these points from the center.
3  Draw a polyline beginning at the outer end of one of the lines and use the perpendicular object snap setting to pick the spot on the next line around and continue this for as long as you like (you will never reach the center point).  Zoom in as needed.  If drawing the spiral by hand, use a 90° corner (sheet of paper, cd case, drafting triangle, etc...) to draw a perpendicular line to the next radial line.  Align one edge along the next radial line to extend the spiral to and move along this line until the other edge intersects the previous line at its end where it touches the radial line and draw a line segment to the radial line.
4.  Smooth out the polyline using fit (Autocad).  Using "fit" will prevent moving any of the vertex points.

Step 2
Make a line and then a polar array using an endpoint as the center.

Step 3
Use Perpendicular Snap Setting.

Step 4
Smooth the curve with either spline or fit.

Here is a method for drawing an Archimedean spiral.


1.  Draw a polar array of radial lines.

2.  Draw equally spaced concentric circles

3.  Starting at the outer edge, draw a line from an intersection point diagonally across to the next intersection where the next radial line crosses the next smaller circle.  Continue until you reach the center.

4.  Smooth the line and remove the "spider-web".