Developing a pattern for a cone with a pitch using radial line development

What's important to remember with radial line development is all tapers (slants) must remain constant. (Left).

 

First step, draw an elevation view of the cone (this can be any measurements) for this tutorial we used 12" as a base and 5" as a top dia. And a height of 15"

Once you draw your your elevation view then you draw in your pitch deg.(Any pitch will work) see Fig.1  The next step would be to add a profile of the fitting to the base.We need to divide the cone up into equal areas and to do this we need to see the base in a true form and the only way to see the base of the cone in true form is perpendicular to its plane.
Next we need to determine where the apex is. We find this by extending both planes (Slants) upward until they intersect. This is very important, the apex is what we use for the radial lines.
 

 

 

 

 

 

 

 

 

 

 

Now we divide our profile into equal areas. Once this is done we can extend those reference marks to the base of the cone see 1, 2, 3, 4, 5, 6, 7.

Draw a line from those reference marks up through the apex. (Doing this we divided the cone into equal areas)

Draw horizontal lines where your reference marks meet with line A, project these lines to the side as shown this makes lines 2, 3, 4, 5, 6 all true length (line 1, 7 are already true length).

Note:

Projecting these lines would be the same as turning the fitting until they become in view perpendicular to the plane.

 

 

 

 

 

 

 

Above we covered all the necessary steps to obtain your pattern (shaded gray area)

- Drawing an elevation view, includes the pitch.
- Determining the Apex.
- Drawing a profile, Dividing the profile into equal areas,
- Determining where our radial lines will be.

 

 

 

 

 

 

The red lines represent the radial lines, these lines represent the true length sections from your elevation drawing. (Don't forget to draw the top radial line [A] that represents the top of the fitting

Take your trammel points and place one end on the Apex, take the other end and line it up with the reference points on the taper(Slant) side of the fitting(Determined in Fig.3) Draw each arch around (Shown in red).

 

 

 

 

 

 

 

 

 

Once the radial lines are drawn the next step is to mark your length of the base (total circumference), which would be Base Dia. x 3.141. This can be done anywhere on the radial line that represents the base of your fitting, makes no difference where you start to layout your pattern.

Now divide the circumference length into the same equal areas as you did on the profile in Fig.3 and make a reference mark for each. On the profile in Fig.3 we numbered them 1 through 7 on the base, do the same here in Fig.6 being careful to watch the placement of the numbers.(In Fig.3 No.1 on the base represents the short side of the slant and No.7 the long side of the slant.)

Once you have the base circumference divided and marked. Draw a line from each of these marks up to the Apex.

 

 

 

 

 

 

 

 

 

 

The last step you need to do is connect each true length line to the next. This pattern does not include allowance for seams or hems.

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