Yarn Spinning Related Mathematical Formulas

 

Grams per Meter	0.5905 / Ne
Grams per Yard	0.54 / Ne
Tex	den x .11 = 1000/Nm = Mic/25.4
Ne	Nm/1.693
DRAFT	(feed weight in g/m) / (delivery weight in g/m)
DRAFT	Tex (feed)/Tex(delivery)
DRAFT	delivery roll surface speed/feed roll surface speed
No. of hanks delivered by m/c	(Length delivered in m/min)/1.605grams per meter = 0.5905/Ne

Carding

Production in kgs / hr	( L x 1.0936 x 60 x effy ) / (hank (Ne) x 36 x 840 x 2.2045) Here, L – delivery speed in m/min effy- efficiency Ne – English count ( number of 840 yards in one pound) 840 – constant 2.2045- to convert from lbs to kilograms
Production in kgs / hr	(L x Ktex x 60 x effy) / ( 1000 ) L – delivery speed in m/min Ktex- sliver count in Ktex (kilotex) effy – efficiency 1000- to convert to kilograms from grams
Production in kgs / 8 hrs	(0.2836 x L x effy) / (Ne) L – delivery speed in m/min effy – efficiency Ne – English count
Production / 8 hrs	(Hank x Nd) /( Ne x 2.2045) Hank = no of hank (840 yards)delivered by the machine Nd = no of deliveries Ne = hank of the material
Total draft in card	(feed weight in g/m) / (sliver weight in g/m)

Drawframe

Break draft	surface speed of 2nd roller / surface speed of back roller
Main draft	surface speed of 1st roller / surface speed of 2nd( middle) roller
Total draft	surface speed of delivery roller / surface of feed roller
Production in kgs / 8 hrs	(0.2836 x L x effy x Nd) / (Ne) L – delivery speed in m/min effy – efficiency Ne – english count Nd – No of deliveries
Production in kgs / hr	(FRD x FRrpm x 3.14 x 60 x effy x Nd) / (Ne x 840 x 36 x 2.2045) FRD – front roller dia in inches FRrpm – front roller rpm effy – efficiency Ne – Sliver hank Nd – number of deliveries

Speedframe & Ring Frame

Twist / Inch (TPI)	Spindle speed / FRS FRS – front roller surface speed in inches/mi
FRS = FRrpm x 3.14 x FRD	FRS – Front roller surface speed FRD – front roller diameter
T.P.I	T.M. x sqrt(count or hank) T.M. – Twist multiplier sqrt – square root
Production in kgs / 8 hrs	(7.2 x SS x effy) / (TPI x Ne x 1000) SS – spindle speed
Spindle speed	m/min x TPI x 39.37
Hank delivered	spindle speed / ( tpi x 62.89)
Ring traveller speed in m/sec	(spindle speed x ring dia in mm x 3.14) / (60 x 1000)

Winding

Production in kgs / 8 hrs	(0.2836 x L x effy x Nd) / (Ne) L – delivery speed in m/min effy – efficiency Ne – english count Nd – No of deliveries.
Production in kgs / hr	( L x 1.0936 x 60 x effy ) / (hank (Ne) x 36 x 840 x 2.2045) L – delivery speed in m/min effy- efficiency Ne – English count ( number of 840 yards in one pound) 840 – constant 2.2045- to convert from lbs to kilograms