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Because the existing winches are the starting point for this essay, it is tried to stay as
close as possible to the existing dimensions. The measurements to follow are therefore taken
from Bemastung und Takelung of F.L. Middendorf. What should we do without him!
The lower yard drum measures: length 75 cm, small diameter 27 cm, and large diameter 38 cm.
For b counts:
tan b = (t - s) / 2 . (y - x)
For p:
p = s - 2 . a
With these equations it should be possible to determine the angle b
for the coning and the smallest and largest diameter of the drum for
every position of the discs s and t.
This drawing above shows the following magnitudes:
The total circumference of the drum (O) must equal the length
of the brace: L.
For v counts:
v = d . tan b
For every next radius counts:
The total drum circumference, measured over the wire, is called O.
One can say that O always has to be equal or greater then the brace length
L. Otherwise it could happen that drum can not stow all the wire.
To work out exactly how many windings (x) the drum contains, one can state:
So far the theory!
Now
it is known what length of wire has to fit on the drum of the winch. The proportional
differences in length between port- and starboard side are also known. The next step is to
design a drum on which both quantities will fit.
However, there are 3 shafts (with 3 pairs of drums), which are driven simultaneously.
When the dimensions of the first set of drums is settled, the two remaining pairs are
related to this one, because they have to brace around the yards in the same amount of revolutions.
The lower topsail yard measures: length 65 cm, small diameter 22 cm, and large diameter 35 cm.
The upper topsail yard measures: length 65 cm, small diameter 20 cm, and large diameter 35 cm.
For the bars (ribs) on the drum we take 3 cm.
The diameters of the drums are measured on the outside of the bars, this out of practical
point of view.
The drawing represents a cross-section of a drum. The characters s and t represent
the moveable discs, their diameter includes the bars. The characters p and q represent
the smallest and the largest diameter of the ends of the drum. These are of interest,
because with those values one works, when fine-tuning the winch.
Value x is the distance from the foreside of the drum to the heart line of disc s.
Value y is the distance from the foreside of the drum to the heart line of disc t.
The coning is given by b and at last, the length of the
bars is presented by z.
From this equation the conclusion can be extracted that if the discs s and t are moved
in the same direction, over the same distance, only the total diameter of the drum will
change. If, however, only one of the discs is moved, or both in different ways, the
diameter as well as the coning will change.
Next the diameter p has to be determined to serve, together with value b,
as input for the calculation of the total circumference of the drum etc.
When the difference in radius of s and p is given by a, then the
difference between their diameters is 2 * a.
In the same logic for
q and p, the difference is 2 * k.
For a:
a = x . tan b
Þ
p = s - 2 . (x . tan b)
For q:
q = p + 2 . k
For k:
k = z . sin b
Þ
q = p + 2 . (z . sin b)
The circumference of a circle is 2pr.
The radius of the drum increases after every revolution
with v.
For the circumference of the smallest radius counts:
r = r + d
The radius of the drum is increased with the diameter of the
steel wire, because the circumference of the drum is measured on the
outside of the wire, not on the empty bars.
r1 = r + d . tan b + d
r2 = r1 + d. tan b + d
rx = rx-1 + d . tan b + d
O = 2pr + 2pr1 +
2pr2 + 2pr3 +
2pr4 + ....+ 2prx
Þ
O = 2p(r + r1 + r2 + r3 +
r4 +....+ rx)
If x represents the number of windings on the drum, then 2prx
is the circumference of the last and so the greatest winding on the drum. Of this last winding
perhaps only a fraction is used, to know:
O - L / 2prx
x = x - 1 + O - L / 2prx
If you are still reading this site at this point, you have shown some dogged persistence.
