274 NICHOLAS'S SEAMANSHIP AND NAUTICAL KNOWLEDGE
Construction.—Make AB and AC both equal to 4 unit-tons. Draw
ED parallel to the derrick and DC parallel to the fall. Join AD.
Then AD is the diagonal of the parallelogram ABDC and represents
the resultant of the two loads acting on the cargo gin, namely, the 4-ton
weight and the 4-ton power exerted by the winch to balance the weight.
The resultant AD is equal to 1\ tons as measured from the scale.
Second.—Consider the stress at A due to the resultant AD and the
tension on the span along A Y to keep the derrick in position.
Construction—Draw DE parallel to the span and EF parallel to
AD. Then AD and AF represent in magnitude and direction two
forces acting at A, and the diagonal AE of the parallelogram ADEF
represents the thrust on the derrick (8| tons) and AF or DE the tension
on the span (2J tons). Thus two parallelograms are required to solve
the problem.
Third.—It may be required to find the stress on the leading block
at X. We would then make XG and XH equal to 4 tons which is the
weight being lifted, and complete the parallelogram XGKH. The
diagonal XK represents the stress on the block X (5| tons), and is the
resultant of the two forces XG and XH acting at X. The angle GXH
would need to be known to construct this parallelogram.
Fourth —The stress on the span block may be found in a similar
way by making YM and YL each equal to DE, which represents the
tension on the span (2J tons). Complete the parallelogram YMNL.
The diagonal YN represents the stress on the span block at Y (3£ tons).
It is the resultant of the two forces YL and YM acting at Y.
No allowance has been made in the foregoing examples for the weight
of tackle and the derrick, but it will be understood that upending the
derrick increases the thrust at the heel and reduces the tension on the
span, also that a derrick swings easier when the heel is stepped vertically
below the point where the span is secured to the mast, that is where X
is exactly below Y.
Another Example.—When the lifting fall is turned into a purchase
the thrust on the derrick is reduced by an amount depending upon the
power gained by the purchase, because the pull on the hauling part to
hold the weight is thereby reduced.
Given the length of a derrick 25 feet; heel to span block on the mast
20 feet; length of span 18 feet; the angle the fall makes at the heel blosk
leading to the winch is _92 degrees; weight to be lifted 10 tons; lifting