TAPERED CONE SECTIONS FOR MODEL ROCKETS

So you want to make a tapered cone section, but you don't know the first thing about how to make the flat pattern?  Let's see if this helps a little.

First, you need to know 3 things:
The diameter at the large end (equal to the diameter of the large body tube).  (D₁)
The diameter at the small end (equal to the diameter of the small body tube, if there is one).  (D₂)
The length of the tapered cone. (L)

So, let's start with the easy part first - the true length of the tapered cone  (L_t).  If you image a section cut through the tapered cone, you know the length of both sides of a right triangle and you can solve for the hypotenuse. 

L_t²=L²+(D₁/2-D₂/2)²
L_t=  SQUARE ROOT ( L² + (D₁/2 - D₂/2)²)

Since you know the diameters D₁ and D₂, you can calculate the arc lengths of your flat pattern.

(Note: p = 3.1415927)
A₁= p * D₁ 
A₂= p * D₂

For the flat pattern, you need to find the radius for both of your arc lengths.  The difference between the two radii will be L_t.

To find the radius of the large arc length, use the formula:
R₁ = (A₁ * L_t) / (A₁ - A₂)

Next, find the radius of the small arc length:

R₂ = R₁ - L_t

OK, you're almost finished.  You only need a few more pieces of information.  Since you know the large radius for the large arc (R₁), you can calculate the circumference.

Circ₁ = 2 * p * R₁

To determine the angle of your flat pattern:

Angle₁ = (A₁ / Circ₁) * 360

It's time to draw:

Draw two concentric circles - one with a radius of R₁ and one with a radius of R₂.

Draw a horizontal line through the center of the two concentric circles.

Draw a second line through the center of the two circles at the angle of Angle₁ relative to the horizontal line.

The part of the two concentric circles between the two lines is your tapered cone section flat pattern.

When you cut it out, I would suggest that you leave a small tab at one end to help you glue the tapered cone together.

Have fun!!!