The Theory and Practice of Model Aeroplaning Part 7

But the power consumed in putting this ma.s.s of fluid in motion is proportional to the ma.s.s 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 ma.s.s 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 a.s.suming 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 ma.s.s 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 ma.s.s 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 062, which, as it so happens, is exactly the same as the case of the Farman machine propeller considered alone, this ratio varying from 04 to 12; 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 Bleriot monoplane (Bleriot XI.) pitch ratio 04, r.p.m. 1350.

In marine propulsion the pitch ratio is generally 13 for a slow-speed propeller, decreasing to 09 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 15, 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.

[Ill.u.s.tration: FIG. 23.]

[Ill.u.s.tration: 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 circ.u.mference of 6, then the angle of pitch at a point midway between centre and circ.u.mference 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 (1945),[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 = 3134.

Now since the inclination is 1 in 3,[29] the propeller will travel forward theoretically one-third of this distance, or

3143/3 = 1048 = 10 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 06 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 circ.u.mstances 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.

[Ill.u.s.tration: FIG. 25.

A TUBE OF AIR.]

[Ill.u.s.tration: 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._