**Relation between Taper Angle and Amount of Yarn on a Beam**

**Rofiquzzaman Raju**

Fabric Technologist,

B.J.Group, Mawna, Gazipur

**Email:**rtextile.finance@gmail.com

Relation between Taper Angle and Amount of Yarn on a Beam:

Relation between Taper Angle and Amount of Yarn on a Beam:

Let,

s = Traverse length.

L = Axial

d = Empty beam dia.

D = Full beam dia.

**dm = (D+d)/2 = mean dia.**

Where,

X = Tape distance

α = Taper angle

v = Volume of yarn stored on

**beam**.

Let, s > x so as to maintain stability

∏D

^{2}L ∏d^{2}L**V**=

**………. - ………….**

4 4

∏L

=

**……..**(D^{2}– d^{2})
4

D+d D-d

= ∏L (

**…….**) (**……..**)
2 2

From figure, it is clear that

D+d D-d

dm =

**…….**&

**……….**= x tan α

2 2

So, v = π L dm (x tanα)

V > π L dm S tan α if, x > s

V < π L dm S tan α if, x < s

So, V ∞ S tan α if α = 90° then V = α

So unlimited amount of yarns can be wound if flange stays perpendicular to beam barrel. Practically this is impossible. But this type of package permit’s to wind high amount of yarn.