IMPROVEMENTS IN THE CONSTRUCTION OF PROPELLING SCREWS to be as follows:
Year: 1884

page_text: I ALBERT DUROY DE BRUIGNAC of Versailles (Seine et Oise) France, Civil
Engineer do hereby declare the nature of said invention for "IMPROVEMENTS IN
THE CONSTRUCTION OF PROPELLING SCREWS to be as follows:-
"
This invention relates to improvements in screw propellers. A screw is generally
described as a helicoidal surface generated by the motion of a line resting upon a
helical directrix and upon its axis. Heretofore screw propellers generally used for
maritine purposes have had a straight generatrix which was constantly perpen-
dicular to the axis of the directrix the latter being a helix of uniform pitch
Hence, these surfaces have had a uniform pitch, that is to say, a section made in
such a surface by a cylinder concentrical with the helical directrix produced another
helix with uniform pitch, such pitch being similar to that of the helical directrix.
This section may be also termed a helical directrix. The above screw propellers
may be considered as formed by the juxtaposition of a number of helices (supposed
to have an appreciable thickness) all having a uniform and similar pitch. This
mode of generation is that which applies to the screw propeller forming the object of
this invention. The characterstic feature of this invention consists in constructing
the blade of a screw propeller by the juxtaposition of helices, which, although
having individually a uniform pitch, have nevertheless a different pitch as com-
pared with one another; whereas in most screws heretofore employed, as already
stated, the similarly juxtaposed helices which could be conceived have had all the.
same pitch. The pitches of the different helices do not vary indifferently, the
pitch of each helix being designed according to the propulsion which it is desired
to obtain from the surface of such helix Each screw has generally a pitch slightly
increasing in a ratio. hereinafter described. Each element in the construction of
such screws is determined according to a diagram of the relative motions of the
blades and of the water.
This diagram is drawn according to geometrical methods on the assumption
firstly that the blades move in water which had been previously still, secondly that
the reaction between the blades and the water is perpendicular to the surface of the
blade, and thirdly that the particles of water act as if they were isolated from one
another and had a suitable weight and resistance.
The formulae and principles hereinafter set forth are deducted firstly from
the diagram and secondly algebraically from one another, and thirdly some of the
said formulae and principles are obtained with the aid of the general rules of
mechanics.

page_text: One of the important features of this invention is the peculiar shapes of blades
which result from the application of the formulae and principles hereinafter
described; the formulae serve obviously to determine the shape of the blade with
precision but similar blades to the above may be constructed according to other
formulae, by altering the methods of comparison.
By the shape of the blades is meant not only the contour thereof, but the form
of the surface of any portion of the said blades which results from its mode of
generation, as the contour of one and the same blade may be completely altered
within given limits.
In order to render the above mentioned formulae thoroughly clear some previous
definitions will be necessary I term the generating line which, when the screw
rotates, first strikes the water, the initial edge. Vm represents the speed of the
motion, that is to say the speed of the movement of the screw propellor parallel
to its axis, or the speed of the vessel which is propelled by the said screw.
Vp represents the velocity of propulsion, that is to say, the velocity which the
blade imparts to the water parallel to the axis of the propeller and in a contrary
direction to the motion so as to determine the resistance which causes the pro-
pulsion. n represents the number of revolutions of the screw per second, a the
angle described by the blude; distance in metres measured upon the circumference
having a radius equal to the unit, between the original position of the inital edge
and another given position of this edge. W1 = 2 Fn the angular velocity of the
blades; r radius of the blade generally; that is the distance from one point of the
blades to the axis; r. initial radius that is to say the radius from the extremity of
which the blades commence to become propulsive; a is the angle of the blades
determined by a plane tangential to the said blades and a plane perpendicular
upon the axis; a, is the initial angle of the blades corresponding to r All
sections of the blades are determined by a cylinder having à circular basis con-
centrical with the screw, and a helix having either a uniform or slightly increasing
pitch. The sections are named indifferently, either directrix by analogy with
blades heretofore employed, or trajectories because one and the same particle of
water is displaced upon the blade by sensibly following a " section As &
rule, only the geometrical form of the blade shall be considered, leaving the
determination of the thicknesses required for the purpose of solidity to that part
which refers to its construction.
"
The coordinates selected are the axis of rotation, the initial edge and a plane
perpendicular to the axis and passing upon the said edge. One blade only will be
considered, all blades, whatever may be their number, being similar.
It is supposed that the screw always assumes the same velocity; as a screw
operates best only at the velocity for which it has been constructed.
The movement of translation of the screw is only considered as taking place in
water, but this invention is applicable to movements of translation taking place in
all kinds of fluids.
I
As the description, howsoever, brief of the theory of the following formulae
would occupy too much space I deem it sufficient to merely mention them and
accompany them with enough explanation to enable any one accustomed to the use
of formulae to employ these above mentioned easily and safely.
.
I have shewn in the accompanying drawings a geometrical diagram which,
although not indispensable for the application of the formulae, hereinafter set forth,
permits at a certain scale a graphic representation of the values derived from these
formulae to be obtained. This diagram is drawn for three directrices of the blade
at distances from the axis of respectively 1, 2 and 3 metres, and gives graphically
the angles and propelling speeds.
It is always useful in practise to draw such a diagram or a diagram analogous
thereto, not for the purpose of dispensing with the formulae, but to check with
sufficient approximation, the results obtained therefrom. It will be easily under-
stood that the principal formulae hereinafter set forth may be deducted from the
said diagram by means of simple geometrical considerations although this diagram.

page_text: is not indispensable for this purpose, a simple geometrical figure being sufficient to
establish these formulae.
The following description of the figures of the accompanying drawings will make
the diagram and the nature of the results obtained therefrom easily understood.
Figure 1 shews a geometrical diagram permitting a graphical representation of
the values derived from the above mentioned formulae in the case of the calculation
of a blade for maximum propulsion to be obtained.
Figure 2 shews the same diagram applicable to the case of a blade for constant
propulsion.
Figure 3 shews the application of said diagram in the case of an ordinary screw
having a uniform pitch.
Figure 4 is a schematic representation of a screw blade constructed, according to
this invention, for a maximum propulsion and provided with an inert arm.
:
Figure 5 is a schematic représentation of a portion of a screw similar to that
blade shewn in figure 4 and having eight blades comprised between two concentrical"
crowns and four inert arms.
Figure 6 is a schematic representation of a screw blade for constant propulsion
provided with an inert arm.
Figure 7 is a schematic representation of a screw blade for constant propulsion'
having the same superficial shape as the preceding one but more extended under
the same angles.
AA represent the projection of the initial edge at the commencement of the
motion A B₁, A. B₂ A B, are developed portions of directrices situated' at
distances of 1, 2 and 3 metres from the axis, belonging to a blade with uniform
pitch as heretofore constructed and the section of maximum propulsion of which is
situated at a distance of 1 metre from the axis.
A, B, A, B, A, B, are the developed position of the same portions of directrices
after the lapse of one second.
A C₁ A CAC, are representations of absolute developed movements of three
particles of water during the same time that is to say one second.
HC₁, HC, HC, are the propulsion speeds upon these three directrices parallel to'
the axis.
11
A₁₁¹ A B A, B," are analogous portions of the directrices for maximum
propulsion.
HC, HM, HM, are speeds of maximum propulsion.
111
A, B, A, B, A, B,111 are analogous portions of directrices for constant pro-
pulsion.
HC HP HP,-are speeds of constant propulsion.
OD pitch during 1" of the blade having uniform pitch OD
A D.
=
= 2 C I₁ A₁ A
N is a circumference, determining the equal speeds of propulsion perpendicularly
upon the blade.
Initial edge. The initial edge is a straight line and thus of the simplest form as
there is no advantage in having a curved edge. Besides, the process of construction
hereinafter described may be applied to any initial edge without altering the
principle, or generally speaking, the effects thereof. (2)
The aspect only of the "blades would be modified thereby but the mode of
generation of the blade could be easily recognised by determining "successive
directrices and examining the variation of their angles. Inert portion of the blade.
It is a well known fact that screw propellers heretofore constructed have had a very
weak propulsive action near the axis, and that this part moreover has caused an
injurious slip or recession of the water. There is at those points an amount of
power necessarily lost, as it is not possible when using such screws, to prevent at
the said points the water pushed by one blade from striking the preceding blade.
I prefer (without binding myself thereby) not to utilize, for the propulsion, a
portion of the blade situated near the axis and to give such a shape to that portion
that the same will not impede the movement and will act merely as an arm.

page_text: For that purpose it is sufficient to give to that portion the shape of an ordinary
screw with constant and uniform pitch for all the parts of the surface of the blade
the tangents to which have for their value at each section
(1)
V m
2 Trn
It will be obvious that if a blade thus formed is displaced with a translation
speed Vm and a rotation speed 2rn, it will traverse the fluid without exerting
any pressure upon it or being subjected to any pressure therefrom. I term angles
of movement a m, the angles the tangents of which have the value above stated.
I term inert blade, the above mentioned inert portion of a blade, and useful
blade the portion which is situated next to the former and which causes the
propulsion.
The inert blade or arm extends from the shaft to the extremity of ro described
as above.
In practice the inert blade has for purposes of solidity sections of elongated
lenticular shape, a shape which combines the necessary resistance with the facility
of translation in water. This inert blade may also be of divers thicknesses grooved
or notched whilst retaining its main inclination.
Generally speaking it is requisite to make the blade, in the direction of the
radius as long as the draught and other conditions of the vessel to which the blade
is applied, will allow. Starting from the extremity of the radius, a suitable length
is marked off for the useful blade and the rest of the blade extending to the shaft,
is the inert portion of the blade. The efficiency of a screw propeller increases with
the radius.
It will be easily understood that the propelling action of the blade depends upon
its angle. I shall indicate first what the angle must be at the initial edge in order
to obtain certain propulsions. (It must be understood that I do not refer to purely
geometrical lines but to small zones or surfaces having sufficient width to exert a
certain action) I shall state moreover what shape the blade should assume in
order to continue upon the remaining surface the propulsion effected at the
commencement.
In order that the blade at each point of the initial edge should produce a
maximum propulsion in the direction of the motion, and that each point should act
according to the conditions of movement of the ship, the angles along the initial
edge should be obtained from the formula
(3) YP
when a is known I have also
(3¹) V p=177
tg a
This formula in which Vp results from the angle, a is necessary for calculating.
the pressure exerted upon the water and the power produced. If from the.
peculiarities of the question the propulsive speed was first obtained, the angle and
the radius could be deducted therefrom by means of the formula

page_text: Figure 4 is a schematic representation of a blade of this kind provided with an
inert arm having a 1 m, 0 0 radius and based upon the following given quantities:
V m = 8, 0 0; n = 1, 5 3 m extreme radius.
From the quantities and the preceding formulae, the following angles are
calculated at divers points of the initial edge as also the corresponding propul-
sive speeds: for a radius of 1*,00 α = 65° 10′ V p
دو
1,50 a = 59° 45' Vp
"
"
"
2,00
"
"
=
2º,181
= 4,122
56° 29' Vp = 6,238
=
2,50 a = 54° 23' V p 8,442.
ሰሰ
540 KO VM
10 602
I take radii with 50° difference between one anothor, as it is sufficient to shew
the results; but the angles could be calculated as near in value to one another as
required.
The blade shewn in Figure 4 is at least 33% more powerful than blades hereto-
fore constructed with uniform pitch nearest in size to it that is to say that which
has likewise an angle of 65° 10 and a radius of 1". 00.
Figure 5 is a schematic representation of a portion of a screw similar to the
blade shewn in Figure 4 and having 8 blades comprised between two concentrical
crowns and four inert arms. This screw, by reason of the arrangement of eight
actuating blades instead of the four with which screws heretofore constructed were
provided has more than double the power of the latter.
The power mentioned is not valued superficially, it is calculated from the exact
formula that is to say for one point, by multiplying the pressure at that point by
its speed in the direction of the motion.
The pressure at one point is calculated by means of the propulsive speed at that
point and also by means of known experimental relations between the speed of a
fluid and the pressure exerted thereby. Starting from the initial edge, the
directrices of these blades are all helices with uniform pitch.
Particular cases. -1° Equal propulsion in the direction of the motion at any
point on the initial edge. When all the power obtainable is not required, and
when it is preferable to have a lesser propulsion permitting the motor power to be
economized it is natural to propose a blade which, constructed like the preceding
one upon a certain initial section, maintains upon its surface, without increasing it
the propulsive power of this initial section. I shall assume that the blade, as far
as this initial section, is an inert arm. In this case I determine by means of the
formulae (2) and (3) the angle and the propulsive speed at the extremity of the
inert portion of the blade that is to say for the radius r. at this point, (any
quantity may be employed between the limits when the formulae remain real)
For a greater radius than r, the initial angle is determined by the formula
°
when in the preceding equation r is replaced by K r..
=
When in such a section the angle is first obtained, the formula of Vp becomes
2rnty.a Vm
(4¹¹) V p
It may be observed that the formulae (4) and (411) are
1+ 193 a
absolutely general and answer for the section of any blade, on the condition that this
section should be a belix with uniform pitch and that these formulae should be
understood as applied to the quantities of this single section taken isolatedly, thus
forming a relation between the quantities of the same section.
With reference to the formulae (4¹) it applies specially to a blade having a
uniform propulsion, the initial section at r. of which is a section for maximum

page_text: propulsion. Figure 6 is a schematical representation of a blade constructed under
such conditions and provided with an inert arm of a length of 1* 50. The initial
section BH of the actuating portion of the blade (having a radius of 1" 50) is
similar to the section of same radius of the blade shewn in Figure 4 all the
remainder of the actuating portion of the blade has at all points the same 5
propulsive power than upon the section BH. Hereunder follows. the calculation
of the angles of this blade derived from the formula
In the various sections of this blade next to BH, the pitch is slightly increased.
This increase which cannot be shewn upon the figure does not reach, at the
extremity of the greatest section, one degree of increase upon the initial angle of
the section.
I have determined. by means of precise formulae the increase of the pitch and
the theoretical excentricity of the sections, and I have found that under practical
conditions that is to say for blades the angular aperture of which perpendicularly
upon the water does not exceed 45°, the excentricity was of no account, and the
increase of the pitch did not exceed one degree. That is the reason why I do not
give these formulae which are very complicated; in practice it is sufficient to
determine the increase of pitch at a glance according to the above mentioned
indications.
°
The blade shewn in Figure 6 has 12 p% more power than that of the ordinary
comparable blade above mentioned. This power is calculated exactly in the same
manner as the propulsive power hereinbefore mentioned, it is the quotient of the
propulsive power divided by the sum of the propulsive and resistance power.
resisting power of a blade is obtained at one point by multiplying the pressure at
that point by the velocity at that point.
The
The blade shewn in Figure 7 has the same general superficial form as that shewn
in Figure 6 but it is extended under the same angles parallel to the extreme limit
that the blade should not exceed, moreover its curvature is diminished in proximity
to the initial section (BH, Figure 6).
It will be easily understood that the useful power of this blade increases
proportionately to its surface; its productive power does not vary.
Equal propulsion perpendicularly upon the surface of a blade at any point of the
initial edge. When it is required, starting from a certain initial section (such
as BH Figure 6) to obtain a constant propulsion not in the direction of the
motion as in the preceding case but perpendicularly upon the surface of the blade,
the diagram still conducts to the following formulae in which Vp, and a, are the
quantities of the initial section selected (such as 59° 45′ and 4" 12 in the above
instance) and Vp, a the quantities of the points which it is required to
determine.
These formulae.are.
Six (a - am) =
V po COB a m
V
p =
cos a 2 x ra
V
Po cos a
COS
All the preceding formulae have been obtained by referring to the diagram and
also by calculation. According to the same principles and with the same diagram
other conditions may be realized when starting from the same initial section, such
as for instance to have unequal pressure in the direction of the motion at any
point of the initial edge, (the pressure and the propulsion are only simultaneously
constant when perpendicular on the blade) to have a constant productive power
upon the whole of the blade this case is that of screws with uniform pitch such
as heretofore constructed or to have a minimum propulsion and a maximum
productive power and such like. This last form is particularly important for

page_text: formula is complicated but can be easily obtained by empirically reducing the
angles of the blade of constant propulsion in parts where the productive power is
least.
From the above elaborate study of the principles herein expounded the following.
results are obtained that is to say; firstly, by means of the peculiar constructions
which form the object of this invention, a screw propeller can be manufactured for
application to any desired vessel, with a propelling power four times greater than
that of screw propellers heretofore constructed; secondly; for economical purposes
and the same speed being obtained in the motion of the vessel, an amount of
productive power can be obtained which is 33% greater than that of screw
propellers heretofore constructed; that is to say, a total economy of at least 10%
is effected.
HASELTINE, LAKE & Co.,
For the Applicant.

page_text: "
I, ALBERT DUROY DE BRUIGNAC, Versailles (Seine et Oise) France, Civil Engineer
.do hereby declare the nature of my invention for "IMPROVEMENTS IN THE CON-
STRUCTION OF PROPELLING SCREWS and in what manner the same is to be
performed, to be particularly described and ascertained in and by the following
statement:-
This invention relates to improvements in screw-propellers. A screw is generally
described as a helicoidal surface generated by the motion of a line resting upon a
helical directrix and upon its axis.
Heretofore screw-propellers generally used for maritime purposes have had a
straight generatrix which was constantly perpendicular to the axis of the directrix,
the latter being a helix of uniform pitch. Hence, these surfaces had a uniform
pitch, that is a say, a section made in such a surface by a cylinder concentrical
with the helical directrix produced another helix with uniform pitch, such pitch
being similar to that of the helical directrix. This section may be also termed a
helical directrix. The above screw-propellers may be therefore considered as
formed by the juxtaposition of a number of helices (supposed to have an appreciable
thickness) all having a uniformn and similar pitch. This mode of generation is that
which applies to the screw-propeller forming the object of this invention. The
characteristic feature of this invention consists in constructing the blades of a screw
propeller by the juxtaposition of helices which, although having individually a
uniform or nearly uniform pitch, have nevertheless a different pitch as compared
with one another; whereas in most screws heretofore employed, as already stated,
the similarly juxtaposed helices which could be conceived had all the same pitch.
The pitch for the different helices do not vary indifferently, the pitch of each helix
being designed according to the propulsion which it is desired to obtain from the
surface of such helix.
Each screw has generally a pitch slightly increasing in a ratio hereinafter
described. Each element in the construction of such screws is determined
according to a diagram of the relative motions of the blades and of the water.
This diagram is drawn according to geometrical methods on the assumption,
first, that the blades move in water which had been previously still, secondly, that
the reaction between the blades and the water is perpendicular to the surface of
the blade, and thirdly that the particles of water act as if they were isolated from
one another and had a suitable weight and resistance.
The formulae and principles hereinafter set forth are deducted firstly from the
diagram, or secondly algebraically from one another, and thirdly some with the aid
of the general rules of mechanics.
One of the important features of this invention is the peculiar shapes of blades
which result from the application of the formulae and principles bereinafter
described; the formulae serve obviously to determine the shape of the blade with
precision, but similar blades to the above may be constructed according to other
formulae by altering the methods of comparison.
By the shape of the blade is meant not only the contour thereof, but the form
of the surface of any portion of the said blade, which results from its mode of
generation, as the contour of one and the same blade may be completely altered
within given limits.

page_text: 11
In order to render the above mentioned formuláé thoroughly clear some previous
definitions will be necessary. I, term the generating line, which, when the screw
rotates, first strikes the water the initial edge. V m represents the speed of the
motion, that is to say the speed of the movement of the screw propeller parallel
to its axis or the speed of the vessel which is propelled by the said screw.
V p represents the velocity of propulsion, that is to say the velocity which the
blade imparts to the water parallel to the axis of the propeller and in a contrary
direction to the motion so as to determine the resistance of the water, which
causes the propulsion. 'n represents the number of revolutions of the screw per
second, a the angle described by the blade; that is the distance in metres measured
upon the circumference of a circle the radius of which is equal to the unit between
the original position of the initial edge and another given position of this edge.
wv₁ = 2n, the angular velocity of the blades; r radius of the blade generally,
that is the distance of a point on the blade from the axis; r, initial radius, that is
to say the radius from the extremity of which the blades commence to become
propulsive; a is the angle of the blades determined by a plane tangential to the
said blades and a plane perpendicular to the axis; a, is the initial angle of the
blades corresponding to ro All sections of the blades are determined by a cylinder
having a circular basis concentrical with the screw, that is a helix having either a
uniform or slightly increasing pitch. The sections are named indifferently, either
directrix, by analogy with blades heretofore employed, or trajectories because one
and the same particle of water is displaced upon the blade by sensibly following a
"section."
As a rule, only the geometrical form of the blade shall be considered, leaving
the determination of the thicknesses required for the purpose of solidity to that part
which refers to its construction. The coordinates selected are the axis of rotation,
the initial edge, and a plane perpendicular to the axis and passing through the said
edge. One blade only will be considered, all blades, whatever may be their number,
being similar. It is supposed that the screw always assumes the same velocity; as
a screw operates best only at the velocity for which it has been constructed. The
movement of translation of the screw is only considered as taking place in water,
but this invention is applicable to movements of translation taking place in any
fluid. As the description, however brief, of the theory of the following formulae
would occupy too much space I deem it sufficient to merely mention them and
accompany them with enough explanation to enable any one accustomed to the use
of formulae to employ the above mentioned easily and safely. I have shewn upon
the accompanying drawings a geometrical diagram which, although not indi-
spensable for the application of the formulae hereinafter set forth, permits, on a
certain scale, a graphic representation of the values derived from these formulae to
be obtained. This diagram is drawn for three directrices of the blade at distances
from the axis of respectively 1, 2 and 3 metres, and gives graphically the angles
and propelling velocities.
It is always useful in practice to draw such a diagram, or a diagram analogous
thereto, not for the purpose of dispensing with the formulae but to check, with
sufficient approximation, the results obtained therefrom. It will be easily under-
stood that the principal formulae hereinafter set forth may be deducted from
the said diagram by means of simple geometrical considerations, so that this
diagram is not indispensable for the said purpose, a simple geometrical figure
without a diagram being sufficient to establish these formulae. The following
description of the figures of the accompanying drawings will make the diagram
and the nature of the results obtained therefrom easily understood.
Figure 1 shews a geometrical diagram permitting a graphical representation of
the values derived from the above mentioned formulae in the case of the calculation
of a blade for maximum propulsion to be obtained.
Figure 2 shews the same diagram applicable to the case of a blade for constant
propulsion.

page_text: Figure 3 shews the application of said diagram in the case of an ordinary screw
having a uniform pitch.
Figure 4 is a diagram illustrating a screw-blade constructed, according to this
invention, for a maximum propulsion and provided with an inert arm.
Figure 5 is a diagram illustrating a portion of a screw similar to the blade
shewn in figure 4 and having eight blades comprised between two concentrical
crowns and four inert arms.
Figure 6 is a diagram illustrating a screw-blade for constant propulsion provided
with an inert arm.
Figure 7 is a diagram illustrating a screw-blade for constant propulsion having
the same superficial shape as the preceding one but more extended under the same
angles.
Figure 8 represents a perspective view of a screw constructed on the new system,
the shape and angles at each point corresponding to the case of maximum pro-
pulsion upon the initial edge.
Figure 9 represents an upper view of the blade.
Figure 10 is a perspective view of the screw corresponding to the case of equal
propulsion upon the initial edge.
Figure 11 shows this blade as seen from above.
A is the projection of the initial edge at the commencement of the motion.
-
A B₁, A B. - A B, are developed portions of directrices, situated at distances
of 1, 2 and 3 metres from the axis, belonging to a blade with uniform pitch as
heretofore constructed, and the section of maximum propulsion of which is situated
at a distance of 1 metre from the axis.
A₁ B₁A, B - A, B, are the developed positions of the same portions of
directrices after the lapse of one second.
A CA C, A C, are representations of absolute developed movements of
three particles of water during the same time, that is to say, one second.
-
HC, HC, H C, are the propulsion speeds upon these three directrices
parallel to the axis.
11
A₁ B₁ A, B,"
propulsion.
-
-
· A, B," are analogous portions of the directrices for maximum.
HC, HM, H M, are the speeds of maximum propulsion.
-
111
A₁ BA, BA, B are analogous portions of directrices for constant
propulsion.
-
-
=
H C₁, HP, HP, are speeds of constant propulsion.
OD pitch during 1" of the blade having uniform pitch OD 2 CI, A, A = A D.
N is a circumference deterinining the equal speeds of propulsion perpendicularly
upon the blade.
Initial edge. The initial edge is a straight line, and thus of the simplest form,
as there is no advantage in having a curved edge. Besides, the methods of con-
struction hereinafter described may be applied to any initial edge without altering
the principle nor, generally speaking, the effects thereof.
The aspect only of the blades would be modified thereby, but the mode of
generation of the blade could be easily recognized by determining successive
directrices and examining the variation of their angles.
Inert portion of the blade. It is a well known fact that screw propellers hereto-
fore constructed had a very weak propulsive action near the axis, and that this
part moreover caused an injurious recession of the water. There is at those points
an amount of power necessarily lost, as it is not possible when using such screws,
to prevent at the said points the water pushed by one blade from striking the
preceding blade.
I prefer (without binding myself thereby) not to utilize, for the propulsion, the
portion of the blade situated near the axis, but to give such a shape to that
portion that the same will not impede the movement and will act merely as
an arm,

page_text: For that purpose it is sufficient to give to that portion the shape of an ordinary
screw with a constant and uniform pitch, for all the parts of the surface of the
blade, the tangents to which have for their value at each section
V m
(1) 2 T 73
It will be obvious that if a blade thus formed is displaced with a translation
speed V m, and a rotation speed 2 rn, it will traverse the fluid without exerting
any pressure upon it or being subjected to any pressure therefrom. I term
angles of movement a m, the angles the tangents of which have the value above
stated.
I term inert blade, the above mentioned inert portion of a blade, and useful
blade the portion which is situated next to the former and which causes the
propulsion.
The inert blade or arm extends from the shaft to the extremity of r. described
as above.
In practice, the inert blade has for purposes of solidity sections of elongated
lenticular shape, a shape which combines the necessary resistance with the facility
of translation in water. This inert blade may also be of divers thicknesses, grooved
or notched, whilst retaining its main inclination.
Generally speaking, it is requisite to make the blade, in the direction of the
radius, as long as the draught of water and other conditions of the vessel to which
it is applied will allow. Starting from the extremity of the radius, a suitable
length is taken for the useful blade, and the rest of the blade, extending to the
shaft, is the inert portion of the blade. The efficiency of a screw propeller increases
with the radius.*
It will be easily understood that the propelling action of the blade depends upon
its angle. I shall indicate first what the angle must be at the initial edge in order
to obtain certain propulsions.
(It must be understood that I do not refer to purely geometrical lines but to
small zones or surfaces having sufficient width to exert a certain action.) I shall
state afterwards what shape the blade should assume in order to continue upon the
remaining surface the propulsion effected at the commencement.
In order that the blade at each point of the initial edge should produce a
maximum propulsion in the direction of the motion, and that each point should act
according to the conditions of movement of the ship, the angles along the initial
edge should be obtained from the formula.

page_text: Figure 4 is a diagrammatic representation of a blade of this kind provided
with an inert arm having 100 radius and based upon the following given
quantities:
Vm800: n = 1.5: 3m = extreme radius.
I take radii with 50° difference between one another, as it 18 sumcient to show
the results; but the angles could be calculated as near in value to one another as
required.
°
The blade shewn in Figure 4 is at least 33% more powerful than blades hereto-
fore constructed with uniform pitch nearest in size to it, that is to say that which
has likewise an angle of 65°,10' and a radius of 1*,00.
Figure 5 is a diagrammatic representation of a portion of a screw similar to the
blade shewn in figure 4 and having 8 blades comprised between two concentric
crowns and four inert arms. This screw, by reason of the arrangement of eight
actuating blades instead of the four with which screws heretofore constructed were
provided, has more than double the power of the latter.
The power mentioned is not valued superficially, it is calculated from the exact
formula, that is to say for one point, by multiplying the pressure at that point by
the speed in the direction of the motion.
The pressure at one point is calculated by means of the propulsive speed at that
point, and also by means of known experimental relations between the speed of a
fluid and the presure exerted thereby.
Starting from the initial edge, the directrices of these blades are all helices with
uniform pitch.
Particular cases--1st Equal propulsion in the direction of the motion at any
point on the initial edge. When all the power obtainable is not required, and
when it is preferable to have less propulsion, permitting the motive power to
be economized, it is natural to propose a blade which, constructed like the preceding
one upon a certain initial section, maintains upon its surface, without increasing it,
the propulsive power of this initial section. I shall assume that the blade, as far
as this initial section, is an inert arm. In-this case I determine by means of the
formulae (2) and (3) the angle and the propulsive speed at the extremity of the
inert portion of 'the blade, that is to say for the radius r, at this point. (Any
quantity may be employed between the limits when the formulae remain real) For
a greater radius than the initial angle is determined by the formula

page_text: De Drungmus improveme
With reference to the formulae (41) it applies specially to a blade having a,
constant propulsion, the initial section at r. of which is a section for maximum
propulsion..
1
Figure 6 is a diagram illustrating of a blade constructed under such conditions
and provided with an inert arm of a length of 1 50. The initial section BH of
the actuating portion of the blade (having a radius of 1 50) is similar to the
section of same radius of the blade shewn in Figure 4, the remainder of the
actuating portion of the blade has at all points the same propulsive power as upon
the section B H. Hereunder follows the calculation of the angles of this blade
derived from the formula (4):
4.
for a radius of 1* 50, a =
"
"
"
"
= 4º,12
== do
4° 12.
59° 45', Vp
-37° 42'
29° 45', Vp
"
=
"
„ 3, 00 α =
24° 37'
2 00, α =
for a radius of 2" 50, a =
33
"
"
=
do
In the various sections of this blade next to B H, the pitch is slightly increased.
This increase, which cannot be shewn in the figure, does not reach, at the extremity.
of the greatest section, one degree of increase of the initial angle of the section.
I have determined by means of precise formulae the increase of the pitch and the
theoretical eccentricity of the sections, and I have found that under practical.
conditions, that is to say for blades the angular aperture of which perpendicularly
upon the water does not exceed 45°, the eccentricity is of no account, and the
increase of the pitch does not exceed one degree. That is the reason why I do not
give these formulae which are very complicated; in practice it is sufficient to
determine the increase of pitch at a glance according to the above mentioned
indications.
°
The blade shewn in Figure 6 has 12% more power than that of the ordinary
comparable blade above mentioned. This power is calculated exactly in the same
manner as the propulsive power hereinbefore mentioned, it is the quotient of the
propulsive power divided by the sum of the propulsive and resistant power.
resisting power of a blade is obtained at one point by multiplying the pressure at
that point by the velocity of rotation at that point.
The
The blade shewn in Figure 7 has the same general superficial form as that shewn
in Figure 6, but it is extended under the same angles parallel to the extreme limit
that the blade should not exceed, moreover its curvature is diminished in proximity
to the initial section (B H, Figure 6).
It will be easily understood that the useful power of this blade increases
proportionately to its surface; its productive power does not vary.
2nd Equal propulsion, perpendicular to the surface of a blade at any point of the
initial edge
-When it is required, starting from a certain initial section (such
as B, H Figure 6) to obtain a constant propulsion not in the direction of the motion
as in the preceding case but perpendicular to the surface of the blade, the diagram
still conducts to the following formulae in which Vp, and a, are the quantities of
the initial section selected (such as 59° 45′ and 4", 12 in the above instance) and
T, Vp, a the quantities of the point which it is required to determine.
These formulae are
sin (a — a m)
-
=
V po cos a m
• cosa; V p =
COS
V po cos a
СОБ
All the preceding formulae have been obtained by referring to the diagram and
also by calculation. According to the same principles and with the same diagram
other conditions may be realised when starting from the same initial section, such
as, for instance, to have an equal pressure in the direction of the motion at any
point of the initial edge, (the pressure and the propulsion are simultaneously
constant only perpendicular to the blade); to have a constant productive power by
the whole of the blade (this case is that of screws with uniform pitch such as
heretofore constructed); or to have a minimum propulsion and a maximum
productive power and such like. This last form is particularly important for

page_text: economical purposes when it is not required to exceed a certain speed, its correct
formula is complicated but can be easily obtained by empirically reducing the
angles of the blade of constant propulsion in parts where the productive power is
least.
From the above elaborate study of the principles herein expounded the following
results are obtained that is to say: firstly by means of the peculiar constructions
which form the object of this invention, a screw propeller can be manufactured for
application to any desired vessel, with a propelling power four times greater than
that of screw propellers heretofore constructed; secondly, for economical purposes
and the same speed being obtained in the motion of the vessel, an amount of
productive power can be obtained which is 33% greater than that of screw
propellers heretofore constructed; that is to say, a total economy of at least
10% is effected.
Having now particularly described and ascertained the nature of my said
invention and in what manner the same is to be performed I declare that what
I claim is:
First. The above described characteristic forms of the surface and circumference
of the blade, determined by the solutions of the formulae stated above, and which
are based upon the particular conditions of the propulsion and of the special use to
which the propellers are adapted, two specimens of the latter being shown in the
accompanying drawing.
Second. In combination with the system of screw-propellers above described,
the application of a helicoidal portion without propulsive action, at the points
nearest to the centre of the active screw, for the purpose specified above.
Third. In combination with the same system of screw-propellers, the connection
of the blades by means of crowns arranged in the manner, and for the purposes,
described.
Dated this 24th day of December 1884.