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 p R every revolution. At a point D on the blade, distant r from the centre, the distance is 2 p r. In both instances the two points must advance a distance equal to the pitch, i.e. the distance represented by P O.

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 p 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.

§ 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.

§ 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.

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.

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

p/4 × (diam.)² (p = 22/7)

And if d A r = the "disc area ratio" we have

(d A r) × p/4 × (14)² = area of blade = 10½,

whence d A r = 0·07 about.

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

p × 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.

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.

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.

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.

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.

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.

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.

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.

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