PROPELLERS OR SCREWS.
§ 1. The design and construction of propellers, more especially the
former, is without doubt one of the most difficult parts of model
aeroplaning.
With elastic or spring driven models the problem is more complicated
than for models driven by petrol or some vaporized form of liquid
fuel; and less reliable information is to hand. The problem of
_weight_, unfortunately, is of primary importance.
We will deal with these points in due course; to begin with let us
take:--
THE POSITION OF THE PROPELLER.
In model aeroplanes the propeller is usually situated either in front
or in the rear of the model; in the former case it is called a TRACTOR
SCREW, i.e., it pulls instead of pushes.
As to the merits of the two systems with respect to the tractor, there
is, we know, in the case of models moving through water a distinct
advantage in placing the propeller behind, and using a pushing or
propulsive action, on account of the frictional "wake" created behind
the boat, and which causes the water to flow after the vessel, but at
a lesser velocity.
In placing the propeller behind, we place it in such a position as to
act upon and make use of this phenomenon, the effect of the propeller
being to bring this following wake to rest. Theoretically a boat,
model or otherwise, can be propelled with less horse-power than it can
be towed. But with respect to aeroplanes, apart altogether from the
difference of medium, there is _at present_ a very considerable
difference of _form_, an aeroplane, model or otherwise, bearing at
present but little resemblance to the hull of a boat.
Undoubtedly there is a frictional wake in the case of aeroplanes,
possibly quite as much in proportion as in the case of a boat,
allowing for difference of medium. Admitting, then, that this wake
does exist, it follows that a propulsive screw is better than a
tractor. In a matter of this kind constructional considerations, or
"ease of launching," and "ability to land without damage," must be
given due weight.
In the case of model aeroplanes constructional details incline the
balance neither one way nor the other; but "ease in launching" and
"ability to land without damage" weigh the balance down most decidedly
in favour of a driving or propulsive screw.
In the case of full-sized monoplanes constructional details had most
to do with the use of tractors; but monoplanes are now being built
with propulsive screws.[24]
In the case of models, not models of full-sized machines, but actual
model flyers, the writer considers propulsive screws much the
best.[25]
In no case should the propeller be placed in the centre of the model,
or in such a position as to _shorten the strands of the elastic
motor_, if good flights are desired.
In the case of petrol or similar driven models the position of the
propeller can be safely copied from actual well-recognised and
successful full-sized machines.
§ 2. =The Number of Blades.=--Theoretically the number of blades does
not enter into consideration. The mass of air dealt with by the
propeller is represented by a cylinder of indefinite length, whose
diameter is the same as that of the screw, and the rate at which this
cylinder is projected to the rear depends theoretically upon the pitch
and revolutions (per minute, say) of the propeller and not the number
of blades. Theoretically one blade (helix incomplete) would be
sufficient, but such a screw would not "balance," and balance is of
primary importance; the minimum number of blades which can be used is
therefore _two_.
In marine models three blades are considered best, as giving a better
balance.
In the case of their aerial prototypes the question of _weight_ has
again to be considered, and two blades is practically the invariable
custom.[26] Here, again, constructional considerations again come to
the fore, and in the case of wooden propellers one of two blades is of
far more easy construction than one of three.
By increasing the number of blades the "thrust" is, of course, more
evenly distributed over a larger area, but the weight is considerably
increased, and in models a greater advantage is gained by keeping down
the weight than might follow from the use of more blades.
§ 3. =Fan versus Propeller.=--It must always be most carefully borne
in mind that a fan (ventilating) and a propeller are not the same
thing. Because many blades are found in practice to be efficient in
the case of the former, it is quite wrong to assume that the same
conclusion holds in the case of the latter.
By increasing the number of blades the skin friction due to the
resistance that has to be overcome in rotating the propeller through
the air is added to.
Moreover a fan is stationary, whilst a propeller is constantly
_advancing_ as well as _rotating_ through the air.
The action of a fan blower is to move a small quantity of air at a
high velocity; whereas the action of a propeller is, or should be, to
move _a large quantity of air at a small velocity_, for the function
of a screw is to create thrust. Operating on a yielding fluid medium
this thrust will evidently be in proportion to the mass of fluid
moved, and also to the velocity at which it is put in motion.
But the power consumed in putting this mass of fluid in motion is
proportional to the mass and to the _square_ of the velocity at which
it moves. From this it follows, as stated above, that in order to
obtain a given thrust with the least loss of power, the mass of fluid
acted on should be as large as possible, and the velocity imparted to
it as little as possible.
A fan requires to be so designed as to create a thrust when stationary
(static thrust), and a propeller whilst moving through the air
(dynamic thrust).
§ 4. =The Function of a Propeller= is to produce dynamic thrust; and
the great advantage of the use of a propeller as a thrusting or
propulsive agent is that its surface is always active. It has no
_dead_ points, and its motion is continuous and not reciprocating, and
it requires no special machinery or moving parts in its construction
and operation.
§ 5. =The Pitch= of a propeller or screw is the linear distance a
screw moves, backwards or forwards, in one complete revolution. This
distance is purely a theoretical one. When, for instance, a screw is
said to have a pitch of 1 ft., or 12 in., it means that the model
would advance 1 ft. through the air for each revolution of the screw,
provided that the propeller blade were mounted in _solid_ guides, like
a nut on a bolt with one thread per foot. In a yielding fluid such as
water or air it does not practically advance this distance, and hence
occurs what is known as--
§ 6. =Slip=, which may be defined as the distance which ought to be
traversed, but which is lost through imperfections in the propelling
mechanism; or it may be considered as power which should have been
used in driving the model forward. In the case of a locomotive running
on dry rails nothing is lost in slip, there being none. In the case of
a steamer moored and her engines set going, or of an aeroplane held
back prior to starting, all the power is used in slip, i.e. in putting
the fluid in motion, and none is used in propulsion.
Supposing the propeller on our model has a pitch of 1 ft., and we give
the elastic motor 100 turns, theoretically the model should travel 100
ft. in calm air before the propeller is run down; no propeller yet
designed will do this. Supposing the actual length 77 ft., 23 per
cent. has been lost in "slip." For this to be actually correct the
propeller must stop at the precise instant when the machine comes to
ground.
Taking "slip" into account, then--
_The speed of the model in feet per minute = pitch (in feet) ×
revolutions per minute -- slip (feet per minute)._
This slip wants to be made small--just how small is not yet known.
If made too small then the propeller will not be so efficient, or, at
any rate, such is the conclusion come to in marine propulsion, where
it is found for the most economical results to be obtained that the
slip should be from 10 to 20 per cent.
In the case of aerial propellers a slip of 25 per cent. is quite good,
40 per cent. bad; and there are certain reasons for assuming that
possibly about 15 per cent. may be the best.
§ 7. It is true that slip represents energy lost; but some slip is
essential, because without slip there could be no "thrust," this same
thrust being derived from the reaction of the volume of air driven
backwards.
The thrust is equal to--
_Weight of mass of air acted on per second × slip velocity in feet per
second._
In the case of an aeroplane advancing through the air it might be
thought that the thrust would be less. Sir Hiram Maxim found, however,
as the result of his experiments that the thrust with a propeller
travelling through the air at a velocity of 40 miles an hour was the
same as when stationary, the r.p.m. remaining constant throughout. The
explanation is that when travelling the propeller is continually
advancing on to "undisturbed" air, the "slip" velocity is reduced, but
the undisturbed air is equivalent to acting upon a greater mass of
air.
§ 8. =Pitch Coefficient or Pitch Ratio.=--If we divide the pitch of a
screw by its diameter we obtain what is known as pitch coefficient or
ratio.
The mean value of eighteen pitch coefficients of well-known full-sized
machines works out at 0·62, which, as it so happens, is exactly the
same as the case of the Farman machine propeller considered alone,
this ratio varying from 0·4 to 1·2; in the case of the Wright's
machine it is (probably) 1. The efficiency of their propeller is
admitted on all hands. Their propeller is, of course, a slow-speed
propeller, 450 r.p.m. The one on the Blériot monoplane (Blériot XI.)
pitch ratio 0·4, r.p.m. 1350.
In marine propulsion the pitch ratio is generally 1·3 for a slow-speed
propeller, decreasing to 0·9 for a high-speed one. In the case of
rubber-driven model aeroplanes the pitch ratio is often carried much
higher, even to over 3.
Mr. T.W.K. Clarke recommends a pitch angle of 45°, or less, at the
tips, and a pitch ratio of 3-1/7 (with an angle of 45°). Within limits
the higher the pitch ratio the better the efficiency. The higher the
pitch ratio the slower may be the rate of revolution. Now in a rubber
motor we do not want the rubber to untwist (run out) too quickly; with
too fine a pitch the propeller "races," or does something remarkably
like it. It certainly revolves with an abnormally high percentage of
slip. And for efficiency it is certainly desirable to push this ratio
to its limit; but there is also the question of the
§ 9. =Diameter.=--"The diameter (says Mr. T.W.K. Clarke) should be
equal to one-quarter the span of the machine."
If we increase the diameter we shall decrease the pitch ratio. From
experiments which the writer has made he prefers a lower pitch ratio
and increased diameter, viz. a pitch ratio of 1·5, and a diameter of
one-third to even one-half the span, or even more.[27] Certainly not
less than one-third. Some model makers indulge in a large pitch ratio,
angle, diameter, and blade area as well, but such a course is not to
be recommended.
§ 10. =Theoretical Pitch.=--Theoretically the pitch (from boss to
tip) should at all points be the same; the boss or centre of the blade
at right angles to the plane of rotation, and the angle decreasing as
one approaches the tips. This is obvious when one considers that the
whole blade has to move forward the same amount. In the diagrams Figs.
23 and 24 the tip A of the propeller travels a distance = 2 {pi} R every
revolution. At a point D on the blade, distant _r_ from the centre,
the distance is 2 {pi} _r_. In both instances the two points must advance
a distance equal to the pitch, i.e. the distance represented by P O.
[Illustration: FIG. 23.]
[Illustration: FIG. 24.
A O = 2 {pi} R; D O = 2 {pi} _r_.]
A will move along A P, B along B P, and so on. The angles at the
points A, B, C ... (Fig. 24), showing the angles at which the
corresponding parts of the blade at A, B, C ... in Fig. 23 must be set
in order that a uniform pitch may be obtained.
§ 11. If the pitch be not uniform then there will be some portions of
the blade which will drag through the air instead of affording useful
thrust, and others which will be doing more than they ought, putting
air in motion which had better be left quiet. This uniform total pitch
for all parts of the propeller is (as already stated) a decreasing
rate of pitch from the centre to the edge. With a total pitch of 5
ft., and a radius of 4 ft., and an angle at the circumference of 6°,
then the angle of pitch at a point midway between centre and
circumference should be 12°, in order that the total pitch may be the
same at all parts.
§ 12. =To Ascertain the Pitch of a Propeller.=--Take any point on one
of the blades, and carefully measure the inclination of the blade at
that point to the plane of rotation.
If the angle so formed be about 19° (19·45),[28] i.e., 1 in 3, and the
point 5 in. from the centre, then every revolution this point will
travel a distance
2 {pi} _r_ = 2 × 22/7 × 5 = 31·34.
Now since the inclination is 1 in 3,[29] the propeller will travel
forward theoretically one-third of this distance, or
31·43/3 = 10·48 = 10½ in. approx.
Similarly any other case may be dealt with. If the propeller have a
uniform _constant angle_ instead of a uniform pitch, then the pitch
may be calculated at a point about one-third the length of the blade
from the tip.
§ 13. =Hollow-Faced Blades.=[30]--It must always be carefully borne
in mind that a propeller is nothing more nor less than a particular
form of aeroplane specially designed to travel a helical path. It
should, therefore, be hollow faced and partake of the "stream line"
form, a condition not fulfilled if the face of the blade be flat--such
a surface cutting into the air with considerable shock, and by no
means creating as little undesirable motion in the surrounding medium
as possible.
It must not be forgotten that a curved face blade has of necessity an
increasing pitch from the cutting to the trailing edge (considering,
of course, any particular section). In such a case the pitch is the
_mean effective pitch_.
§ 14. =Blade Area.=--We have already referred to the fact that the
function of a propeller is to produce dynamic thrust--to drive the
aeroplane forward by driving the air backwards. At the same time it is
most desirable for efficiency that the air should be set in motion as
little as possible, this being so much power wasted; to obtain the
greatest reaction or thrust the greatest possible volume of air should
be accelerated to the smallest velocity.
In marine engineering in slow-speed propellers (where cavitation[31]
does not come in) narrow blades are usually used. In high-speed marine
propellers (where cavitation is liable to occur) the projected area of
the blades is sometimes as much as 0·6 of the total disk area. In the
case of aerial propellers, where cavitation does not occur, or not
unless the velocity be a very high one (1500 or more a minute), narrow
blades are the best. Experiments in marine propulsion also show that
the thrust depends more on the disk area than on the width of the
blades. All the facts tend to show that for efficiency the blades of
the propeller should be narrow, in order that the air may not be acted
on for too long a time, and so put too much in motion, and the blades
be so separated that one blade does not disturb the molecules of air
upon which the next following one must act. Both in the case of marine
and aerial propellers multiplicity of blades (i.e. increased blade
area) tends to inefficiency of action, apart altogether from the
question of weight and constructional difficulties. The question of
increasing pitch in the case of hollow-faced blades, considered in the
last paragraph, has a very important bearing on the point we are
considering. To make a wide blade under such circumstances would be to
soon obtain an excessive angle.
In the case of a flat blade the same result holds, because the air has
by the contact of its molecules with the "initial minimum width" been
already accelerated up to its final velocity, and further area is not
only wasted, but inimical to good flights, being our old bugbear
"weight in excess."
Requisite strength and stiffness, of course, set a limit on the final
narrowness of the blades, apart from other considerations.
§ 15. The velocity with which the propeller is rotated has also an
important bearing on this point; but a higher speed than 900 r.p.m.
does not appear desirable, and even 700 or less is generally
preferable.[32] In case of twin-screw propellers, with an angle at the
tips of 40° to 45°, as low a velocity of 500 or even less would be
still better.[33]
§ 16. =Shrouding.=--No improvement whatever is obtained by the use of
any kind of shrouding or ring round the propeller tips, or by
corrugating the surface of the propeller, or by using cylindrical or
cone-shaped propeller chamber or any kind of air guide either before
or after the propeller; allow it to revolve in as free an air-feed as
possible, the air does not fly off under centrifugal force, but is
powerfully sucked inwards in a well-designed propeller.
[Illustration: FIG. 25.
A TUBE OF AIR.]
[Illustration: FIG. 26.
A CYLINDER OF AIR.]
§ 17. =General Design.=--The propeller should be so constructed as to
act upon a tube and not a "cylinder" of air. Many flying toys
(especially the French ones) are constructed with propellers of the
cylinder type. Ease of manufacture and the contention that those
portions of the blades adjacent to the boss do little work, and a
slight saving in weight, are arguments that can be urged in their
favour. But all the central cut away part offers resistance in the
line of travel, instead of exerting its proportionate propulsive
power, and their efficiency is affected by such a practice.
§ 18. A good =Shape= for the blades[34] is rectangular with rounded
corners; the radius of the circle for rounding off the corners may be
taken as about one-quarter of the width of the blade. The shape is not
_truly rectangular, for the width of this rectangular at (near) the
boss should be one-half the width at the tip_.
The thickness should diminish uniformly from the boss to the tip. (In
models the thickness should be as little as is consistent with
strength to keep down the weight). _The pitch uniform and large._
[Illustration: FIG. 27.--O T = 1/3 O P.]
§ 19. =The Blades, two in number=, and hollow faced--the maximum
concavity being one-third the distance from the entering to the
trailing edge; the ratio of A T to O P (the width) being 0·048 or 1 :
21, these latter considerations being founded on the analogy between a
propeller and the aerofoil surface. (If the thickness be varied from
the entering to the trailing edge the greatest thickness should be
towards the former.) The convex surface of the propeller must be taken
into account, in fact, it is no less important than the concave, and
the entire surface must be given a true "stream line" form.
[Illustration: FIG. 28.]
[Illustration: FIG. 29.]
If the entering and trailing edge be not both straight, but one be
curved as in Fig. 28, then the straight edge must be made the
_trailing_ edge. And if both be curved as in Fig. 29, then the
_concave_ edge must be the trailing edge.
§ 19. =Propeller Design.=--To design a propeller, proceed as follows.
Suppose the diameter 14 in. and the pitch three times the diameter,
i.e. 52 in. (See Fig. 30.)
Take one-quarter scale, say. Draw a centre line A B of convenient
length, set of half the pitch 52 in. -- ¼ scale = 5¼ in. = C - D.
Draw lines through C and D at right angles to C D.
With a radius equal to half the diameter (i.e. in this case 1¾ in.)
of the propeller, describe a semicircle E B F and complete the
parallelogram F H G E. Divide the semicircle into a number of equal
parts; twelve is a convenient number to take, then each division
subtends an angle of 15° at the centre D.
Divide one of the sides E G into the same number of equal parts
(twelve) as shown. Through these points draw lines parallel to F E or
H G.
And through the twelve points of division on the semicircle draw lines
parallel to F H or E G as shown. The line drawn through the successive
intersections of these lines is the path of the tip of the blade
through half a revolution, viz. the line H S O T E.
S O T X gives the angle at the tip of the blades = 44°.
Let the shape of the blade be rectangular with rounded corners, and
let the breadth at the tip be twice that at the boss.
Then the area (neglecting the rounded off corners) is 10½ sq. in.
[Illustration: FIG. 30.--PROPELLER DESIGN.
One quarter scale. Diameter 14 in. Pitch 52 in. Angle at tip 44°.]
The area being that of a rectangle 7 in. × 1 in. = 7 sq. in. plus area
of two triangles, base ½ in., height 7 in. Now area of triangle =
half base × height. Therefore area of both triangles = ½ in. × 7
in. = 3½ sq. in. Now the area of the disc swept out by the
propeller is
{pi}/4 × (diam.)² ({pi} = 22/7)
[Illustration: FIG. 31.--PROPELLER DESIGN.
Scale one-eighth for A B and B C; but sections of blade are
full-sized.]
And if _d_ A _r_ = the "disc area ratio" we have
(_d_ A _r_) × {pi}/4 × (14)² = area of blade = 10½,
whence _d_ A _r_ = 0·07 about.
[Illustration: FIG. 32.]
[Illustration: FIG. 33.]
In Fig. 31 set off A B equal to the pitch of the propeller (42 in.),
one-eighth scale. Set off B C at right angles to A B and equal to
{pi} × diameter = 22/7 × 14 = 44 in. to scale 5½ in.
Divide B C into a convenient number of equal parts in the figure; five
only are taken, D, E, F, G, H; join A D, A E, A F, A G, A H and
produce them; mark off distances P O, S R, Y T ... equal to the width
of the blade at these points (H P = H O; G S = G R ...) and sketch in
the sections of blade as desired. In the figure the greatest concavity
of the blade is supposed to be one-third the distances P O, S R ...
from PS.... The concavity is somewhat exaggerated. The angles A H B, A
G B, A F B ... represent the pitch angle at the points H, G, F ... of
the blade.
Similarly any other design may be dealt with; in a propeller of 14 in.
diameter the diameter of the "boss" should not be more than 10/16 in.
§ 20. =Experiments with Propellers.=--The propeller design shown in
Figs. 32 and 33, due to Mr. G. de Havilland,[35] is one very suitable
for experimental purposes. A single tube passing through a T-shaped
boss forms the arms. On the back of the metal blade are riveted four
metallic clips; these clips being tightened round the arm by
countersunk screws in the face of the blade.
The tube and clips, etc., are all contained with the back covering of
the blade, as shown in Fig. 35, if desired, the blade then practically
resembling a wooden propeller. The construction, it will be noticed,
allows of the blade being set at any angle, constant or otherwise;
also the pitch can be constant or variable as desired, and any "shape"
of propeller can be fitted.
The advantage of being able to _twist_ the blade (within limits) on
the axis is one not to be underestimated in experimental work.
[Illustration: FIG. 34.--THE AUTHOR'S PROPELLER TESTING APPARATUS.]
With a view to ascertain some practical and reliable data with respect
to the _dynamic_, or actual thrust given when moving through free air
at the velocity of actual travel, the author experimented with the
apparatus illustrated in Figs. 34 and 35, which is so simple and
obvious as to require scarcely any explanation.
The wires were of steel, length not quite 150 ft., fitted with wire
strainers for equalising tension, and absolutely free from "kinks."
As shown most plainly in Fig. 35, there were two parallel wires
sufficiently far apart for the action of one propeller not to affect
the other. Calling these two wires A and B, and two propellers _x_ and
_y_, then _x_ is first tried on A and _y_ on B. Results carefully
noted.
[Illustration: FIG. 35.--PROPELLER TESTING.
Showing distance separating the two wires.]
Then _x_ is tried on B and _y_ on A, and the results again carefully
noted. If the results confirm one another, the power used in both
cases being the same, well and good; if not, adjustments, etc., are
made in the apparatus until satisfactory results are obtained. This
was done when the propellers "raced" one against the other. At other
times one wire only was made use of, and the time and distance
traversed was noted in each case. Propellers were driven through
smoke, and with silk threads tied to a light framework slightly larger
than their disc area circumference. Results of great interest were
arrived at. These results have been assumed in much that has been said
in the foregoing paragraphs.
[Illustration: FIG. 36.--ONE GROUP OF PROPELLERS TESTED BY THE AUTHOR.]
Briefly put, these results showed:--
1. The inefficiency of a propeller of the fan blower or of the static
thrust type.
2. The advantage of using propellers having hollow-faced blades and
large diameter.
3. That diameter was more useful than blade area, i.e. given a certain
quantity (weight) of wood, make a long thin blade and not a shorter
one of more blade area--blade area, i.e., as proportionate to its
corresponding disc area.
4. That the propeller surface should be of true stream-line form.
5. That it should act on a cylinder and not tubes of air.
6. That a correctly designed and proportioned propeller was just as
efficacious in a small size of 9 in. to 28 in. as a full-sized
propeller on a full-sized machine.
[Illustration: FIG. 37.--AN EFFICIENT PROPELLER, BUT RATHER HEAVY.
Ball bearings, old and new. Note difference in sizes and weights.
Propeller, 14 in. diam.; weight 36 grammes.]
A propeller of the static-thrust type was, of course, "first off,"
sometimes 10 ft. or 12 ft. ahead, or even more; but the correctly
designed propeller gradually gathered up speed and acceleration, just
as the other fell off and lost it, and finally the "dynamic" finished
along its corresponding wire far ahead of the "static," sometimes
twice as far, sometimes six times. "Freak" propellers were simply not
in it.
[Illustration: FIG. 38.--"VENNA" PROPELLER.
A 20 per cent. more efficient propeller than that shown in Fig. 41; 14
per cent. lighter; 6 per cent. better in dynamic thrust--14 in. diam.;
weight 31 grammes.]
Metal propellers of constant angle, as well as wooden ones of uniform
(constant) pitch, were tested; the former gave good results, but not
so good as the latter.
The best angle of pitch (at the tip) was found to be from 20° to 30°.
In all cases when the slip was as low as 25 per cent., or even
somewhat less, nearly 20 per cent., a distinct "back current" of air
was given out by the screw. This "slip stream," as it is caused, is
absolutely necessary for efficiency.
§ 21. =Fabric-covered= screws did not give very efficient results; the
only point in their use on model aeroplanes is their extreme
lightness. Two such propellers of 6 in. diameter can be made to weigh
less than 1/5 oz. the pair; but wooden propellers (built-up principle)
have been made 5 in. diameter and 1/12 oz. in weight.
§ 22. Further experiments were made with twin screws mounted on model
aeroplanes. In one case two propellers, both turning in the _same_
direction, were mounted (without any compensatory adjustment for
torque) on a model, total weight 1½ lb. Diameter of each propeller
14 in.; angle of blade at tip 25°. The result was several good
flights--the model (_see_ Fig. 49c) was slightly unsteady across the
wind, that was all.
In another experiment two propellers of same diameter, pitch, etc.,
but of shape similar to those shown in Figs. 28 and 29, were tried as
twin propellers on the same machine. The rubber motors were of equal
weight and strength.
The model described circled to the right or left according to the
position of the curved-shaped propeller, whether on the left or right
hand, thereby showing its superiority in dynamic thrust. Various
alterations were made, but always with the same result. These
experiments have since been confirmed, and there seems no doubt that
the double-curved shaped blade _is_ superior. (See Fig. 39.)
§ 23. =The Fleming-Williams Propeller.=--A chapter on propellers would
scarcely be complete without a reference to the propeller used on a
machine claiming a record of over a quarter of a mile. This form of
propeller, shown in the group in Fig. 36 (top right hand), was found
by the writer to be extremely deficient in dynamic thrust, giving the
worst result of any shown there.
[Illustration: FIG. 39.--CURVED DOUBLE PROPELLER.
The most efficient type yet tested by the writer, when the blade is
made hollow-faced. When given to the writer to test it was flat-faced
on one side.]
[Illustration: FIG. 40.--THE FLEMING-WILLIAMS MODEL.]
It possesses large blade area, large pitch angle--more than 45° at the
tip--and large diameter. These do not combine to propeller efficiency
or to efficient dynamic thrust; but they do, of course, combine to
give the propeller a very slow rotational velocity. Provided they give
_sufficient_ thrust to cause the model to move through the air at a
velocity capable of sustaining it, a long flight may result, not
really owing to true efficiency on the part of the propellers,[36] but
owing to the check placed on their revolutions per minute by their
abnormal pitch angle, etc. The amount of rubber used is very great for
a 10 oz. model, namely, 34 strands of 1/16 in. square rubber to each
propeller, i.e. 68 strands in all.
[Illustration: FIG. 41.--THE SAME IN FLIGHT.
(_Reproduced by permission from "The Aero."_)]
On the score of efficiency, when it is desired to make a limited
number of turns give the longest flight (which is the problem one
always has to face when using a rubber motor) it is better to make use
of an abnormal diameter, say, more than half the span, and using a tip
pitch angle of 25°, than to make use of an abnormal tip pitch 45° and
more, and large blade area. In a large pitch angle so much energy is
wasted, not in dynamic thrust, but in transverse upsetting torque. On
no propeller out of dozens and dozens that I have tested have I ever
found a tip-pitch of more than 35° give a good dynamic thrust; and for
length of flight velocity due to dynamic thrust must be given due
weight, as well as the duration of running down of the rubber motor.
§ 24. Of built up or carved out and twisted wooden propellers, the
former give the better result; the latter have an advantage, however,
in sometimes weighing less.
FOOTNOTES:
[24] _Note._--Since the above was written some really remarkable
flights have been obtained with a 1 oz. model having two screws, one
in front and the other behind. Equally good flights have also been
obtained with the two propellers behind, one revolving in the
immediate rear of the other. Flying, of course, with the wind,
_weight_ is of paramount importance in these little models, and in
both these cases the "single stick" can be made use of. _See also_ ch.
iv., § 28.
[25] _See also_ ch. viii., § 5.
[26] Save in case of some models with fabric-covered propellers. Some
dirigibles are now being fitted with four-bladed wooden screws.
[27] Vide Appendix.
[28] Vide Equivalent Inclinations--Table of.
[29] One in 3 or 0·333 is the _sine_ of the angle; similarly if the
angle were 30° the sine would be 0·5 or ½, and the theoretical
distance travelled one-half.
[30] _Flat-Faced Blades._--If the blade be not hollow-faced--and we
consider the screw as an inclined plane and apply the Duchemin formula
to it--the velocity remaining the same, the angle of maximum thrust is
35¼°. Experiments made with such screws confirm this.
[31] Cavitation is when the high speed of the screw causes it to carry
round a certain amount of the medium with it, so that the blades
strike no undisturbed, or "solid," air at all, with a proportionate
decrease in thrust.
[32] In the Wright machine r.p.m. = 450; in Blériot XI. r.p.m. = 1350.
[33] Such propellers, however, require a considerable amount of
rubber.
[34] But _see also_ § 22.
[35] "Flight," March 10, 1910. (Illustration reproduced by
permission.)
[36] According to the author's views on the subject.