How to Develop a Cone - Cone Development
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How to develop a cone or how to create a flat pattern of a cone can be achieved in a few easy geometrical steps. The geometrical method shown below does however have inaccuracy, so at the end of this hub I have included a mathematical formula to help produce an accurate conical development.
First of all you should draw your cone in elevation and plan as shown in Figure 1.
Divide your plan view up into equal segments. I have broken the plan view shown up into twelve (12) equal segments. (The accuracy of the development will increase with the number of segments that you break the plan view of the cone into.)
For twelve (12) equal divisions break the plan view up by drawing lines through the centre line at 30, 60 90 and 180 degrees.
We will use these divisions in a couple of steps but first we must lay out the initial overall cone development.
In Figure 2 I have shown the use of a drawing compass to get the true length of the cone side. You could use any computer aided drafting (CAD) method to obtain this length.
With Figure 3 as an example (shown below), take this true length of the cone side and scribe a full circle.
This is now your main development.
Now as in Figure 4 below, draw a horizontal line from the centre of this circle to intersect the outside diameter.
We now go back to our cone plan view and take one of the equal divisions we made earlier, as shown in Figure 5. You can do this using your compass or CAD program.
With this equal division on your compass and starting back at the horizontal line on your main development scribe the equal number of division. In my example I will scribe twelve (12) equal arcs along the circumference of the main development as shown in Figure 6.
Now finish this off by drawing a line from the last arc to the centre of the main development as shown in Figure 7.
An finally draw lines from every arc back to the center of the main development as shown in Figure 8. We can disregard the top half of the main development as the equal divisions form your full cone development.
Note: If this cone was to be cut out of steel these lines from the circumference to the center are actually called press lines.
You can check your work by printing out the development. Cut around the outline of the development and lightly folding each press line down. Join the two outside straight edges with sticky tape and there you have your cone!
Finally I promised a mathematical formula to help produce a more accurate cone development. The inaccuracy occurs when you use a compass to break your cone base circle up into equal segments. You can check this buy measuring one of your arc lengths and multiplying this by the number of divisions. Compare this result with the formula for the circumference of a circle which equals Pi times by diameter. You will notice the calculated result is longer.
Now to help produce your accurate cone development use this formula:
Angle = (D1 x 360) / D2
Where:
- Angle = the included angle between the outside lines of the main development
- D1 = the diameter is of the base of the cone (see diagram below)
- D2 = the diameter is of the developed cone, which you get from the elevation of your cone (see diagram below)
To use this formula, scribe your main development radius then draw your horizontal line. Then use the formula to calculate the included angle of the outside lines, grab a protractor (or use AutoCAD) and measure/draw this included angle out from the horizontal line.
The formula described in diagram...
Hope this helps, please drop me a comment if anything needs clarifying and I will certainly update this hub. Thanks!
Other drafting articles that you may like...
How to draw fast in AutoCAD, shows you how to improve your drafting productivity over time (by changing the way you enter commands) even with updates of AutoCAD where you get lost in the new user interface.
How to develop a Pyramid, follow similar easy steps on how to develop a flat pattern of a pyramid.
How to develop a Cylinder, follow easy steps to develop a flat pattern of a cylinder.
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THANKS FOR GIVING USEFULL TIPS
No worries mate, thanks Manoj Bala.
Hi there..
i am having problems physically drawing the development of a cone. it keeps coming up short, like you have mentioned.. i have had a read through this infomation, and i see that the equation at the bottom keeps coming up with the same answer. 360. it doesnt matter what numbers you put in there. it still comes out with 360..
the circumference of a circle is worked out by :
pi x diameter = c
so the equation ACTUALLY looks like this :
( PI x D ) X 360
angle = -----------------
PI x D
so therefore you cancel out the PI x D on the top and bottom
and you are left with angle = 360..
can you please help me out here. i have asked many people about this and no one can give me an answer. my email is cambo@live.co.za if you would rather reach me there.
thank you.
Thanks cameron for your comment, I've tried to clarify the formula above with better descriptions, a diagram of the formula and a worked example. Hope this helps.
Phi ? rather than pi?
Thanks for that techteddy, have updated with the correction of pi rather than Phi.
This is very useful, but nomenclature 'D' use for twice time in same formula instead of that you use two different name i.e. 'D' & 'd' this is very easy to understand for any person.
Thanks,
imple is (D/d)*360!! why you add pi to both the sides?
Thanks.
Now am following same method.
Its too big.Can you teach simple method., also MITRE BEND.
many thanks once agin.
-PK.
it was neat hub .and i have a doubt pls help me to find the angle for developing a cone in sheet of thickness is (say for ex:5 mm) and top id 230 mm and bottom id is 560mm and my mail id is kamal_august@yahoo.co.in .please explain me
Kannan, you need to tell me the height of the cone from the 230mm id to the 560mm id, then you can calculate the angle of the cone and the development with respect to the 5mm thickness of plate.
Thank you So much Dear Leonjane, Very Wonderful and Elaborated Definition, These Explanation Like a Mother feeds Food to the small child,Thanks
yawa mong tanan
Very nice post man. I went through everything, actually developed an Excel spreadsheet to spit out the numbers, and sure enough....It works! Tried it in autocad using calculated numbers and makes great templates. Printed a few different ones on paper, works perfectly! Thanks for the information again!
Thanks Josh, glad this helped you! And cool that you made a spreadsheet from this.
Dear Sir,
This is very useful, can u pl. explain how to do the development of Cone, one side flat i.e. one quadrant of smaller and bigger Dia is vertically in one line.
Thanking you,
Ajay Patel
Thank you for your needful help..........
Thanks guys, i'll try to answer your question Ajay in future hubs.
sir please mail me cone developement excel sheet id kurubararaja@yahoo.in.
it is very use full for lerners
i like you.
dear sir,
I am dheeraj redkar plz explain full detail of cone development strating to blank plate
point (1) which of the diameter cutting layout
(2) which formula equal part
ex. 500dia & 60 height plz explain which cutting layout use plz help me this is my id dhirajredkar@yahoo.com
thanks
Thanks Santosh I have simplified the formula.
thanks so much for good information
Please explain me how to develope a cone.
Top dia 12 inch,bottom dia 2" and slant height 10 inch.
Waiting for your valuable reply
regards/ranjith
HOW TO DEVELOP ECCENTRIC CONE
thanks alooooooot
how to development frustum cone
THANKS FOR GIVING USEFULL TIPS.
sir, how to make pattern for eccentric cone please send to mail for me, my id rexyputhussery@gmail.com
Man , i am grateful to you , in a word your cone development was the best and the easiest way to describe , you have given so simple method , which is just fabulous and your angle mathematical was simply the best to find the true development , my all development are giving me the right length since i've been using your method .
thank you very much and all the best :)
mastach sir....
pan mala kahich samajal nahi...
Thanks.
I WANT TO CROSS CHECK THE ACCURACY OF THIS ONE
AND BACK TO U
Thanks PKR let me know how you go!
Dear SIr,
I want to calculate the plate size of cone.Is any formula to make a cone development.Pls let me know.
Waren E 2 years ago
Neat hub on drafting,I use AutoCad mostly,thanks for sharing LeonJane!