# Fabrication Layout Development of Half Cone by using Geometrical & Numerical Method with Example

In this Post we will learn fabrication layout development of half cone or truncated Cone by using both Geometrical and Numerical method also we will see practical example for use of numerical method.

Half cone development is most useful in fabrication of Pressure Vessels, Heat Exchanger, storage Tank and some other vessel fabrication which are widely used for reducing section of vessel or Discharge of material from bottom outlet by utilizing gravity effect of the earth.
So in this Post we will discuss all the terms related to development of half cone lay outing on to the plates and cutting out the cutting profile of required size from the plate and Rolling of this blank plate on rolling machine or on point press and formed in to Desired shapes.
Whenever we use development calculation for any shapes it necessary to develop the layout using mean dimensions so that our required shape could be made in perfect size. If we are not use mean dimension in calculation of layout then it has variation in sizes after pressing. ## Geometrical or Graphical Method for Half Cone Layout: Steps for Geometrical Development of Half Cone:

1. Draw the Elevation & half bottom view of cone as shown in figure 1.1.

2. Divide the base circle in many no of equal parts as per required accuracy of the development such as shown in figure 1.1. let’s take seven no of parts such as shown in figure 1.1

3. Project vertical line from circle points(1,2,3,4,5,6,7) to base line of cone such as shown in figure 1.1.

4. Connect all this points (1,2,3,4,5,6,7 )with vortex( A) of the cone as shown in figure 1.1.

5. Draw the arc from A-1 and A-D & mark the point (1,2,3,4,5,6,7,6,5,4,3,2,1) on that arc ( A-1) equal to distance (1-2,2-3,3-4,4-5,5-6,6-7) measure on base circle divided parts and connect all outer profile of this to get required profile.

6. Cut out the required development profile by using gas cutting and by other means and sent for further fabrication Works.

By using above steps we can layout half cone by graphical or geometrical method.

## Numerical method for Half or Truncated Cone Layout:  Let,
D and D1 = Large & Small Diameter of Cone respectively.
r and r1= large & Small radius of cone.
H=Height of the Cone.
R= Large Development Radius of the cone plate.
e= Small development radius of the cone.
α= Included angle of Cone.
β= Development Angle of the cone.

So,

r1 = D1 / 2 ;

b = ( D – D1 ) / 2 ;

tan α = b / H ; ——————- calculate α from here & use it in other equation;

c = √(H2+b2);

e= r1 / sinα ; ————————– small development radius;

R= c + e ; ———————– large Development radius;

β= ( r / R ) * 360 ; ———— Development Angle ;

Large Cord Length = 2*R* sin( β/2 );

Small Cord length = 2*e* sin( β/2 ); If our cone size does not fit in to our available plate size then we have to make our cone in more than one part & more than one level of height for maximum utilization of our plate and locating welding joint in systematic manner or to avoid falling of weld joint then we want make slight changes in our above formulae as given below and layout cone as per revised size.

Let,
N= no of part to be fabricate;

β= ( r / R ) * (360 / N ) ; ———— Development Angle ;

and use above revised angle in below formulas.

Large Cord Length = 2*R* sin( β/2 );

Small Cord length = 2*e* sin( β/2 ); If we are planning to develop our cone more than one part then we can use above layout for maximum utilization plate by arranging cone blank plate as per above.
So this calculation is very helpful for developing of cone.

And Finally we want share link of our Android Application for calculating Half and full cone layout by numerical method in faster way. we had made this tool for use of this concept in your mobile for minimize your daily fabrication work.

Example for Half Cone Layout using Numerical Method:

Develop the layout for the cone having top diameter 250 mm and bottom Diameter 500 mm and height of cone 800 mm. r1 = D1 / 2 ; r1 = 250 / 2 = 125 ;

r = 500 / 2 = 250 mm ;

b = (D – D1 ) / 2 ; b = ( 500 – 250 ) / 2 =125 mm;

tan α = b / H ; tan α = 125 / 800 =0.156 α = 8.88 degree;

c = √(H2+b2); c = √(8002+1252) = 809.7 mm;

e= r1 / sinα ; e= 125 / sin(8.88) = 809 mm. ;

R= c + e ; R= 809.7 + 809 = 1618.7 mm ;

β= ( r / R ) * 360 ; β= ( 250 / 1618.7 ) * 360 = 55.60 degree.

Large Cord Length = 2*R* sin ( β/2 ) = 2*1618.7*sin(55.60/2) = 1509.8 mm.

Small Cord length = 2*e* sin ( β/2 ) = 2*809*sin(55.60/2) = 754.6 mm. from all above calculated values we can layout half cone.

please share this post and application for those who are in field of fabrication and also give your suggestion making new tools ease of fabrication methods.