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

The relation between Taper Angle and Amount of Yarn on a Beam is discussed below:

Let,
s = Traverse length.
L = Axial
d = Empty beam dia.
D = Full beam dia. ### Relation between Taper Angle and Amount of Yarn on a Beam is:

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

…….∏D2L       ∏d2L
V = ………. –  ………….
……….4…………….4

…..∏L
= ……..  (D2 – d2)
……4

………….D+d       D-d
= ∏L  (………) (……….)
…………….2          . 2

From the 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 the flange stays perpendicular to the beam barrel. Practically this is impossible. But this type of package permit’s wind a high amount of yarn.

You may like also: Relation between Yarn Dia and Yarn Count

```Author of this Article:
Rofiquzzaman Raju
Fabric Technologist,
B.J.Group, Mawna, Gazipur
Email: [email protected]```

Sharing is caring!