30 April 2010, Ludhiana - The following
unedited text has
been submitted to Knitting Industry by Sunil Kumar Puri, Executive
Director of
Sportking Institute of Fashion Technology, Ludhiana, India. Sunil has
over 30
years experience in the knitting industry, is a qualified professional
in Total
Quality Management, Kaizen and Lean Production and runs his own knitting
machinery sales company, Techknit Overseas Pvt. Ltd. The paper attempts
to
explain ‘Sweater Geometry’ for
fully-fashioned knitwear, to explain the size chart and give in depth
knowledge
to the reader about the hidden measurements which are needed to make a
good
sweater.
“The fully Fashioned Sweaters can be classified in five
different shapes, Set-in Sleeve, Straight, Raglan, Saddle Shoulder and
Classic.
Examples of these styles are given in pictures given below. The beauty
of the garment lies in the
accurate fitting of the union points of front back and sleeve. The
common
mistake is that most of the times, as these panels knitted and not
woven, the
loops compensate for the deficiencies of the shapes of front, back and
sleeves.
The garment may measure accurately but the expert eye will always know
that
because of the inaccuracy of panels, the stitches or knit loops do get
distorted and are not aligned any more. A very nicely made garment when
placed
on a table shall have all the courses and wales in straight lines, which
at
times becomes very difficult to achieve and the arms of the sweater
shall
extend at the same angle as that of the shoulder slope. The sleeves
shall not
puff out at the shoulder joint nor shall they cave in. Therefore the
most
important measurement in a sweater is the slope of the arm hole as the
angle so
created shall be the angle of the sleeve joint as well. Surprisingly the
shoulder slope is not given the due respect by the knitters that it
demands.
The calculations of
knitting specifications are based on combination of simple mathematics
and the
Pythagoras theorem of Geometry. In most of the cases the dimensions
given by
the customer are as given under in two different sets, the first one
where the
sleeve length is given as under sleeve length this practice is more
common in
UK and the other in which the sleeve length is given for the upper part
of the
sleeve.
But in both the cases the measurement of the actual length
of the sleeve up to the part where it has to join the body is not given.
Also
the side length of the body where the sleeve has to join the body is
rarely
provided by the buyer. By simple
calculations and by applying the Pythagoras theorem we can make all the
calculations precisely and accurately. If we look at the picture 1A
which
represents the table 1A we can draw that whereas the measurement for the
under
sleeve is provided it does not tell us what length has to be knitted to
achieve
the under arm length. Similarly it does
not tell us how much of the sleeve head ( crown or cap) has to be
knitted so
that it does not just fits in the joint of the front and back properly
but also
maintains the angle of slope of the shoulder. Slight variation will lead
to the
change in the angle of the sleeve with the horizontal plane that starts
from
the back neck of the garment. If at this point the sleeve cap is larger
than
required it will make the angle steeper than that of the shoulder and
may also
result in a protruding bulge at the joint of shoulder. The opposite of
this
will give opposite results i.e., the angle will become shorter than that
of the
shoulder slope giving wing like shape to the sleeve and the sleeve joint
may
also show a caved-in effect at the joint.
Before we go further we must understand the basic principles
of the Pythagoras theorem as well as elementary trigonometry.
The values of Sin ǿ and Cos ǿ can be easily obtained by
using a scientific calculator or trigonometric tables. What we learn
from this
is that if we know any two values the third can be calculated using
simple
calculations i.e., if we know the hypotenuse and the adjacent we can
find the
value of the opposite, and if we know the hypotenuse and the opposite we
can
calculate the adjacent and if we know the values of the adjacent and the
opposite we can calculate the hypotenuse. Also by using simple
trigonometric
functions if we know the value of either of the hypotenuse, the adjacent
or the
opposite and any of the angle other than the right angle we can find the
value
of all other arms of the triangle or if we know the value of any two
sides of
the triangle we can not only find the value of the third one but also
the angle
of the triangle.
Angle of Shoulder Slope
As discussed earlier to knit a good sweater “the arms of the
sweater shall be at the same angle as that of the shoulder slope”. It
therefore
becomes necessary to ascertain the angle of the Shoulder Slope.
Normally the buyer provides shoulder drop as
a measurement for all sizes. At times this measurement is same as
mentioned by
the customer. If we keep the drop as same for all sizes the angle of
shoulder
drop will vary for all the sizes.
In cut and sew garments there is no problem but the three
basic fully fashioned garments i.e., Raglan, Saddle Shoulder and Classic
style
the shoulder slope angle has to be maintained and therefore it is
necessary to
understand how to obtain the shoulder slope angle and the angle that
regulates
the measurement of the sleeve cap or crown and its width.
The triangle GCH represents the angle of the shoulder slope.
If we know the value of the Shoulder drop i.e., GC we can easily deduce
the
value of the adjacent i.e., GH. GH = (Shoulder width-Neck Width)/2. We
also
know the value of the opposite i.e., GC. The angle between GHC can be
easily
calculated using simple trigonometric formulas.
The simple way to find the Angle would be Opposite /Adjacent = Tanf.
Angle of the Arm Hole
The arm hole of a sweater is measured from point to point
i.e., from the point where under sleeve and the over sleeve join the
main body,
i.e., A and C in the figure 5. The Arm AC hole is the hypotenuse of the
triangle ABC formed by the Arm Hole, where AB is the adjacent and the BC
is the
opposite. It is not important to know the valve of the angle CAB alone.
It is
also important to know the value of the opposite the distance between B
and C.
Knowing this value we will know where on the side body the sleeve has to
be
attached. By knowing this value we can measure the side length of the
garment.
This point will be = (Total length of the garment – the shoulder drop –
the
opposite of the Arm Hole) and needless to mention that seam margin has
to be
added to it, as it has to be added for all other seam margins. So as per
the
figure 5applying the Pythagoras theorem a²
+ b² = c², BC=√ (AC²- AB²)
And the angle of the Arm Hole with the base of the garment
or the back of the neck of the garment can be calculated using the
scientific
calculator as described before. The angle of the Arm hole and the
opposite in
the case will be:
BC = √ (21² - 5²) = √416 = 20.39 or let us say 20.4
The angle CAB will be sin⁻¹ 20.4/21 i.e., inverse of the
sine of Opposite/Hypotenuse = 76.27 or say 76°
The side length of the Garment = 60 – 2 – 20.4 = 37.6
Defining the Angle of the Arm
Once the Angle of the Arm hole is obtained it is important
to know the angle of the Arm or the angle of ACE. This angle will
provide us
calculations for the crown as well as the sleeve width at the point of
the
joint with the main body of the garment.
For this we need to ascertain the value of the angle ACE.
The figure above
shows the triangle ACE as well as triangle ABC to understand the value
of the
angle between ACE we need to study the Rectangle ABCD so we enlarge the
area of
the rectangle ABCD in figure 6B
Let us presume the angle CAB is β and ABCD being a rectangle
the angle DCA will also be angle β. This is also the angle of the arm
Hole
which we have calculated as 76°
in our earlier calculation. The angle
between DCE is also equal to the Angle between GHC (angle of Shoulder
Slope and
calculated as 12 in our earlier calculation. The Angle ACE = Angle ACD β
-
Angle DCE α = 76°-12°=64°
Calculations of the Sleeve Width and
the Sleeve Cap
Once we know the value of the angle between ACE we can also
not just obtain the value of the crown and the width of the sleeve, we
can also
cross check the width of the sleeve as provided by the customer. At
times the sleeve width provided by the
customer is little over or under the exact value which often falls in
the
tolerance range set by the customer or the industry standards. The other
reason
why the sweater still will be sew-able is that the knitted panels adjust
to
such irregularities to quite an extent because of the nature of the loop
structure which can rob and get robbed by the next loops. The idea here
is to
set a target which is accurate, if we have an accurate target and if our
aim is
accurate our result will be too close to the target considering there
can be
some special causes which may deter us from getting the desired results.
But if
our target is hazy, our aim is not right the special causes may play
havoc with
our results. And we may not be able to drive at the root cause of the
problem. If our calculations are right
and if still don’t get the desired results it certainly mean presence of
special causes, but if our calculations are challengeable the results
may point
towards presence of special causes which may not be there and
unnecessary time
effort and money may be spent on trying to apprehend a nonexistent
ghost.
If we refer to figure 7, if we know the angle between ECA
and if we know the value of AC i.e., the Arm Hole, we can reconfirm the
width
of the sleeve as well as we can ascertain the value of CE the crown or
Cap of
the sleeve.
For the width the equation to be used can be any of the
three equations described in figure 2. But we will use the equation
Opposite /
Hypotenuse = Sin f
, AE/AC= Sinf or AE= AC* Sin f. Here the width of the
sleeve according to mathematical and trigonometric calculations will
be.
The sin of angle 64°
= 0.8987940
The product of sine of 64°
and Arm Hole = 18.874 or let us say 18.9 CM.
The width according to the measurements supplied by the
customer say 18 which may be a bit too short and shall be replaced by
let us
say 19 cm. The variation may be within the tolerance and thus a supplier
may
get his garment approved barely even if his measurement is more
accurate. A
garment with exact muscle measurement may not look good at all.
Therefore
understanding of these calculations can save a lot of tense moments
during the
inspections conducted by the customer and especially by the third party.
The
customer may see your point of view but the third party inspector has to
stick
to the rules and may reject the shipment which was a perfect shipment.
Similarly the crown of the sleeve which is also responsible
for maintaining the angle of the shoulder slope throughout the length of
the
sleeve can also be calculated as:
Adjacent / Hypotenuse = Cos f
EC / AC = Cos f or EC = AC * Cos 64° or EC= 21 *0.4383 = 9.2
The Exact Length of the sleeve where
it joins the main body at lower Arm Hole point.
By calculating the Opposite of the Arm Hole we were able to
ascertain the length where the sleeve shall join the lower point of the
Arm
Hole, but the exact sleeve length where it shall join the main body has
to be
ascertained and the total sleeve length is not the answer. The Total
Sleeve
length – The crown of the sleeve which also matches with the width of
the
sleeve shall be the measurement of the sleeve length where the sleeve
shall
join with the Main Body. But if the customer has provided us the under
sleeve
length as a standard measurement, the following calculation has to be
made.
Please refer to Figure 8 given below. If we know the value of underarm
Length, and
we know the value of maximum width of the sleeve as calculated earlier,
and the
cuff width which is 7.5 then we know the value of AF as AE – cuff width =
18.87- 7.5 = 11.37. The value of the line between K and F can be
calculated
using Pythagoras theorem as SQRT of (44*44-11.37*11.37) = 42.5. This
means we
have to knit 42.5 Cm of sleeve length to knit to the joining point of
the
sleeve with the body and the increment of the sleeve width will
compensate of
the balance 1.5 Cm, of course some margin for the seat of the sleeve as
well as
seam margin has o be kept in mind.
Conclusions
Using these simple calculations which shall not take more
than five minutes and if an excel sheet is prepared for different styles
using
the necessary formulas the correct measurements required to knit a
perfect
garment becomes a child’s play. An
understanding of these calculations also helps the knitter to point out
the
corrections needed if any in the measurement sheets supplied by the
customer.
These calculations not only will save a lot of time effort and money but
will
also give more confidence to the knitter.”
To comment on this
article or submit your article to be considered for publication, please
email editor@knittingindustry.com.
.gif)
