§ 30A. Relation between Static Thrust of Propeller and Total Weight of Model.—The thrust should be approx. = ¼ of the weight.
§ 31. How to find the Height of an Inaccessible Object by Means of Three Observations taken on the Ground (supposed flat) in the same Straight Line.—Let A, C, B be the angular elevations of the object D, as seen from these points, taken in the same straight line. Let the distances B C, C A and A B be a, b, c respectively. And let required height P D = h; then by trigonometry we have (see Fig. 56)
h2 = abc/(a cot2A - c cot2C + b cot2B).
§ 32. Formula for calculating the I.H.P. (indicated horse-power) of a single-cylinder double-acting steam-engine.
Indicated h.p. means the h.p. actually exerted by the steam in the cylinder without taking into account engine friction. Brake h.p. or effective h.p. is the actual h.p. delivered by the crank shaft of the engine.
I.H.P. = 2 × S × R × A × P/33,000.
Where S = stroke in feet.
R = revolutions per minute.
A = area of piston in inches.
P = mean pressure in lb. exerted per sq. in. on the piston.
The only difficulty is the mean effective pressure; this can be found approximately by the following rule and accompanying table.
Table VI.
| Cut-off | Constant | Cut-off | Constant | Cut-off | Constant |
| 1/6 | ·566 | 3/8 | ·771 | 2/3 | ·917 |
| 1/5 | ·603 | ·4 | ·789 | ·7 | ·926 |
| ¼ | ·659 | ½ | ·847 | ¾ | ·937 |
| ·3 | ·708 | ·6 | ·895 | ·8 | ·944 |
| 1/3 | ·743 | 5/8 | ·904 | 7/8 | ·951 |
Rule.—"Add 14·7 to gauge pressure of boiler, this giving 'absolute steam pressure,' multiply this sum by the number opposite the fraction representing the point of cut-off in the cylinder in accompanying table. Subtract 17 from the product and multiply the remainder by 0·9. The result will be very nearly the M.E.P." (R.M. de Vignier.)
APPENDIX A.
SOME MODELS WHICH HAVE WON
MEDALS AT OPEN COMPETITIONS.
Fig. 57.—The G.P.B. Smith Model.
The model shown in Fig. 57 has won more competition medals than any other. It is a thoroughly well designed[53] and well constructed model. Originally a very slow flyer, the design has been simplified, and although by no means a fast flyer, its speed has been much accelerated. Originally a one-propeller machine, it has latterly been fitted with twin propellers, with the idea of obtaining more directional control; but in the writer's opinion, speaking from personal observation, with but little, if any, success. The steering of the model is effected by canting the elevator. Originally the machine had ailerons for the purpose, but these were removed owing, I understand, to their retarding the speed of the machine.
In every competition in which this machine has been entered it has always gained very high marks for stability.
Fig. 58.—The Gordon-Jones Dihedral Biplane.
Up to the time of writing it has not been provided with anything in the nature of fins or rudder.
Fig. 58 is a biplane very much after the type of the model just alluded to, but the one straight and one curved aerofoil surfaces are here replaced by two parallel aerofoils set on a dihedral angle. The large size of the propeller should be noted; with this the writer is in complete agreement. He has not unfortunately seen this model in actual flight.
The scientifically designed and beautifully made models illustrated in Fig. 59 are so well known that any remarks on them appear superfluous. Their efficiency, so far as their supporting area goes, is of the highest, as much as 21 oz. per square foot having been carried.
Fig. 59.—Messrs. T.W.K. Clarke and Co.'s Model Flyers.
For illustrations, etc., of the Fleming-Williams model, see ch. v., § 23.
(Fig. 60.) This is another well-constructed and efficient model, the shape and character of the aerofoil surfaces much resembling those of the French toy monoplane AL-MA (see § 4, ch. vii.), but they are supported and held in position by quite a different method, a neat little device enabling the front plane to become partly detached on collision with any obstacle. The model is provided with a keel (below the centre of gravity), and rudder for steering; in fact, this machine especially claims certainty of directional control. The writer has seen a number of flights by this model, but it experiences, like other models, the greatest difficulty in keeping straight if the conditions be adverse.
The model which will do this is, in his opinion, yet to be evolved. The small size of the propellers is, of course, in total disagreement with the author's ideas. All the same, the model is in many respects an excellent one, and has flown over 300 yards at the time of writing.
Fig. 60.—The Ding Sayers Monoplane.
More than a year ago the author made a number of models with triangular-shaped aerofoils, using umbrella ribs for the leading edge and steel piano wire for the trailing, but has latterly used aerofoils of the elongated ellipse shape.
Fig. 61 is an illustration of one of the author's latest models which won a Bronze Medal at the Long Distance Open Competition, held at the Crystal Palace on July 27, 1910, the largest and most keenly contested competition held up to that date.
The best and straightest flight against the wind was made by this model.
On the morning of the competition a flight of about 320 yards (measured in a straight line) was made on Mitcham Common, the model being launched against the wind so as to gain altitude, and then flying away with the breeze behind the writer. Duration of flight 50 seconds. The following are the chief particulars of the model:—Weight, 7½ oz. Area of supporting surface, 1-1/3 sq. ft. Total length, 4 ft. Span of main aerofoil, 25 in. Aspect ratio, 4 : 1. Diameter of propeller, 14 in. Two strand geared rubber motor, carrying altogether 28 strands of1/16 square rubber cord 43 in. long. The propeller was originally a Venna, but with the weight reduced by one-third, and considerable alteration made in its central contours. The front skid of steel pianoforte wire, the rear of jointless cane wire tipped; the rear skid was a necessity in order to protect the delicate gearing mechanism, the weight of which was reduced to a minimum.
Fig. 61.—The Author's "Grasshopper" Model.
The very large diameter of the propeller should be noted, being 56 per cent. of the span. The fin, high above the centre of gravity, was so placed for transverse stability and direction. At the rear of the fin was a rudder. The small amount of rubber carried (for a long distance machine) should also be noted, especially when allowing for friction in gearing, etc.
The central rod was a penny bamboo cane, the large aerofoil of jointless cane and Hart's fabric, and the front aerofoil of steel wire surfaced with the same material.
LONDON: PRINTED BY WILLIAM CLOWES AND SONS, LIMITED,
GREAT WINDMILL STREET, W., AND DUKE STREET, STAMFORD STREET, S.E.
FOOTNOTES:
[1] The smallest working steam engine that the writer has ever heard of has a net weight of 4 grains. One hundred such engines would be required to weigh one ounce. The bore being 0·03 in., and stroke1/32 of an inch, r.p.m. 6000 per min., h.p. developed1/489000 ("Model Engineer," July 7, 1910). When working it hums like a bee.
[2] "Aero," May 3, 1910.
[3] Part of this retardation was, of course, "increased resistance."
[4] Personally I do not recommend aluminium.—V.E.J.
[5] "Aeronautical Journal," January 1897, p. 7.
[6] Vide "Invention," Feb. 15, 22, and 29, 1896.
[7] Really aerofoils, since we are considering only the supporting surface.
[8] I.e., to express it as a decimal fraction of the resistance, encountered by the same plane when moving "face" instead of "edge" on.
[9] If the width be not uniform the mean width should be taken.
[10] This refers, of course, to transverse stability.
[11] See ch. vi.
[12] Also there is no necessity for gearing.
[13] In his latest models the writer uses strands even three times and not twice as long, viz. fourteen strands 43 in. long.
[14] This refers to1/16 in. square sectioned rubber.
[15] Of uniform breadth and thickness.
[16] In practice I find not quite so high a proportion as this is always necessary.
[17] Steel pinion wire is very suitable.
[18] See Appendix.
[19] As high a pressure as 250 atmospheres has been used.
[20] There was a special pump keeping the water circulating rapidly through the boiler, the intense heat converting some of it into steam as it flowed. The making of this boiler alone consumed months of work; the entire machine taking a year to construct, with the best mechanical help available.
[21] Model Steam Turbines. "Model Engineer" Series, No. 13, price 6d.
[22] See Introduction, note to § 1.
[23] The voltage, etc., is not stated.
[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.
[37] Nevertheless some models with a very low aspect ratio make good flyers, owing to their extreme lightness.
[38] The chief advantage of cane—its want of stiffness, or facility in bending—is for some parts of the machine its chief disadvantage, where stiffness with resilience is most required.
[39] This is a good plan—not a rule. Good flying models can, of course, be made in which this does not hold.
[40] This is in theory only: in practice the monoplane holds both records.
[41] The best position for the propellers appears to be one in front and one behind, when extreme lightness is the chief thing desired.
[42] Because the number of strands of rubber in each bunch will be much less.
[43] Mr. Burge Webb claims a record of 500 yards for one of his.
[44] Flying, of course, with the wind.
Note.—In the "Model Engineer" of July 7, 1910, will be found an interesting account (with illustrations) of Mr. W.G. Aston's 1 oz. model, which has remained in the air for over a minute.
[45] These remarks apply to rubber driven motors. In the case of two-power driven propellers in which the power was automatically adjusted, say, by a gyroscope as in the case of a torpedo—and the speed of each propeller varied accordingly—the machine could, of course, be easily steered by such means; but the model to carry such power and appliances would certainly weigh from 40 lb. to 60 lb.
[46] Another and better way—supposing the model constructed with a central rod, or some suitable holdfast (this should be situated at the centre of gravity of the machine) by which it can be held in one hand—is to hold the machine with both hands above the head, the right hand grasping it ready to launch it, and the left holding the two propellers. Release the propellers and allow them a brief interval (about half a second) to start. Then launch boldly into the air. The writer has easily launched 1½ lb. models by this means, even in a high wind. Never launch a model by one hand only.
[47] Report on First Exhibition of Aeronautical Society of Great Britain, held at Crystal Palace, June 1868.
[48] The better way, undoubtedly, is to allow the competitor to choose his direction, the starting "circle" only to be fixed.
[49] Or 10 per cent. for duration of flight.
[50] In another competition, held under the rules and regulations of the Kite and Model Aeroplane Association for the best all-round model, open to the world, for machines not under 2 sq. ft. of surface, the tests (50 marks for each) were:—A. Longest flight in a straight line. B. Circular flight to the right. C. Circular flight to the left. D. Stability and landing after a flight. E. Excellence in building of the model.
[51] On the assumption that the model will fly straight.
[52] If permitted to enter; if not see Fig. 53.
[53] The design is patented.
October, 1910
A SHORT LIST OF
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AERONAUTICS.
| The Atmosphere: its characteristics and dynamics. By F.J.B. Cordeiro. With 35 illus. 129 pp. medium 8vo. (New York, 1910) | net | 10 6 |
| Theory and Practice of Model Aeroplaning. By V.E. Johnson. 61 illus. 150 pp. crown 8vo. (1910) | net | 3 6 |
| How to Build a 20-ft. Biplane Glider. By A.P. Morgan. 31 illus. 60 pp. crown 8vo, limp. (S. & C. Series, No. 14.) (New York, 1909) | net | 1 6 |
| Flight-Velocity. By A. Samuelson. 4 plates, 42 pp. 8vo, sewed. (1906) | net | 2 0 |
| Resistance of Air and the Question of Flying. By A. Samuelson. 23 illus. 36 pp. 8vo, sewed. (1905) | net | 2 0 |
AGRICULTURE.
| Hemp. A Practical Treatise on the Culture for Seed and Fibre. By S.S. Boyce. 13 illus. 112 pp. crown 8vo. (New York, 1900) | net | 2 0 |
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| Talks on Manures. By J. Harris. New edition, 366 pp. crown 8vo. (New York, 1893) | net | 6 6 |
| Coffee, its Culture and Commerce in all Countries. By C.G.W. Lock. 11 plates, 274 pp. crown 8vo. (1888) | 12 6 | |
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| Hops, their Cultivation, Commerce and Uses. By P.L. Simmonds. 143 pp. crown 8vo. (1877) | 4 6 | |
| The Future of Cocoa-Planting. By H. Hamel Smith. With illustrations, 95 pp. crown 8vo, sewed. (1908) | net | 1 0 |
| Estate Fences, their Choice, Construction and Cost. By A. Vernon. Re-issue, 150 illus. 420 pp. 8vo. (1909) | net | 8 6 |
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| Chimney Design and Theory. By W.W. Christie. Second edition, 54 illus. 200 pp. crown 8vo. (New York, 1902) | net | 12 6 |
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| Architectural Examples in Brick, Stone, Wood and Iron. By W. Fullerton. Third edition, 245 plates, 254 pp. demy 4to. (1908) | net | 15 0 |
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| Obstruction to Light. A Graphic Method of determining Problems of Ancient Lights. By H.B. Molesworth. 9 folding plates, 4to. (1902) | net | 6 0 |
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| New Formulæ for the Loads and Deflections of Solid Beams and Girders. By W. Donaldson. Second edition, 8vo. (1872) | 4 6 | |
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| The Barometrical Determination of Heights. By F.J.B. Cordeiro. Crown 8vo, limp leather. (New York, 1898) | net | 4 6 |
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| The Pocket Books of Sir G.L. Molesworth and J.T. Hurst, printed on India paper and bound in one vol. Royal 32mo, russia, gilt edges. | net | 10 6 |
| Metallic Structures: Corrosion and Fouling and their Prevention. By J. Newman. Illustrated, 385 pp. crown 8vo. (1896) | 9 0 | |
| Scamping Tricks and Odd Knowledge occasionally practised upon Public Works. By J. Newman. New impression, 129 pp. crown 8vo. (1908) | net | 2 0 |
| Earthwork Slips and Subsidences on Public Works. By J. Newman. 240 pp. crown 8vo. (1890) | 7 6 | |
| Co-ordinate Geometry as applied to Land Surveying. By W. Pilkington. 5 illus. 44 pp. 12mo. (1909) | net | 1 6 |
| Diagrams for the Graphic Calculation of Earthwork Quantities. By A.H. Roberts. Ten cards, fcap. in cloth case | net | 10 6 |
| Pioneering. By F. Shelford, illustrated. 88 pp. crown 8vo. (1909) | net | 3 0 |
| Topographical Surveying. By G.J. Specht. Second edition, 2 plates and 28 illus. 210 pp. 18mo, boards. (New York, 1898) | net | 2 0 |
| Spons' Dictionary of Engineering, Civil, Mechanical, Military and Naval. 10,000 illus. 4300 pp. super royal 8vo. (1874, Supplement issued in 1881). Complete with Supplement, in 11 divisions | net | 3 10 0 |
| Ditto ditto in 4 vols. | net | 3 3 0 |
| Surveying and Levelling Instruments. By W.F. Stanley. Third edition, 372 illus. 562 pp. crown 8vo. (1901) | 7 6 | |
| Surveyor's Handbook. By T.U. Taylor. 116 illus. 310 pp. crown 8vo, leather, gilt edges. (New York, 1908) | net | 8 6 |
| Logarithmic Land Measurement. By J. Wallace. 32 pp. royal 8vo. (1910) | net | 5 0 |
| Hints on Levelling Operations. By W.H. Wells. Second edition, 8vo, sewed. (1890) | 1 0 | |
| The Drainage of Fens and Low Lands by Gravitation and Steam Power. By W.H. Wheeler. 8 plates, 175 pp. 8vo. (1888) | 12 6 | |
| Stadia Surveying, the theory of Stadia Measurements. By A. Winslow. Fifth edition, 148 pp. 18mo, boards. (New York, 1902) | net | 2 0 |
| Handbook on Tacheometrical Surveying. By C. Xydis. 55 illus. 3 plates, 63 pp. 8vo. (1909) | net | 6 0 |
DICTIONARIES.
| Technological Dictionary in the English, Spanish, German and French Languages. By D. Carlos Huelin Y Arssu. Crown 8vo. | ||
| Vol. I. English-Spanish-German-French. 609 pp. (1906) | net | 10 6 |
| Vol. II. German-English-French-Spanish. 720 pp. (1908) | net | 10 6 |
| Vol. III. French-German-Spanish-English. In preparation. | ||
| Vol. IV. Spanish-French-English-German. 750 pp. (1910) | net | 10 6 |
| English-French and French-English Dictionary of the Motor-Car, Cycle and Boat. By F. Lucas. 171 pp. crown 8vo. (1905) | net | 5 0 |
| Spanish-English Dictionary of Mining Terms. By F. Lucas. 78 pp. 8vo. (1905) | net | 5 0 |
| English-Russian and Russian-English Engineering Dictionary. By L. Meycliar. 100 pp. 16mo. (1909) | net | 2 6 |
| Reed's Polyglot Guide to the Marine Engine, in English, French, German and Norsk. Second edition, oblong 8vo. (1900). | net | 6 0 |
DOMESTIC ECONOMY.
| Food Adulteration and its Detection. By J.P. Battershall. 12 plates, 328 pp. demy 8vo. (New York, 1887) | 15 0 | |
| How to Check Electricity Bills. By S.W. Borden. 41 illus. 54 pp. crown 8vo. (New York, 1907) | net | 2 0 |
| Practical Hints on Taking a House. By H.P. Boulnois. 71 pp. 18mo. (1885) | 1 6 | |
| The Cooking Range, its Failings and Remedies. By F. Dye. 52 pp. fcap. 8vo, sewed. (1888) | 0 6 | |
| The Kitchen Boiler and Water Pipes. By H. Grimshaw. 8vo, sewed. (1887) | net | 1 0 |
| Cookery and Domestic Management, including economic and middle class Practical Cookery. By K. Mellish. 56 coloured plates and 441 illus. 987 pp. super-royal 8vo. (1901) | net | 16 0 |
| Spons' Household Manual. 250 illus. 1043 pp. demy 8vo. (1902) | 7 6 | |
| Ditto ditto half-bound French morocco | 9 0 | |
| Handbook of Sanitary Information for Householders. By R.S. Tracy. 33 illus. 114 pp. 18mo. (New York, 1900) | 2 6 |
DRAWING.
| The Ornamental Penman's, Engraver's and Sign Writer's Pocket Book of Alphabets. By B. Alexander. Oblong 12mo, sewed | 0 6 | |
| The Draughtsman's Handbook of Plan and Map Drawing. By G.G. Andre. 87 illus. and 34 plain and coloured plates, 162 pp. crown 4to. (1891) | 9 0 | |
| Slide Valve Diagrams: a French Method for their Construction. By L. Bankson. 18mo, boards. (New York, 1892) | net | 2 0 |
| A System of Easy Lettering. By J.H. Cromwell. With Supplement by G. Martin. Sixth thousand, oblong 8vo. (New York, 1900) | net | 2 0 |
| Plane Geometrical Drawing. By R.C. Fawdry. Illustrated, 185 pp. crown 8vo. (1901) | net | 3 0 |
| Twelve Plates on Projection Drawing. By O. Gueth. Oblong 4to. (New York, 1903) | net | 3 0 |
| Hints on Architectural Draughtsmanship. By G.W.T. Hallatt. Fourth edition, 80 pp. 18mo. (1906) | net | 1 6 |
| A First Course of Mechanical Drawing (Tracing). By G. Halliday. Oblong 4to, sewed | 2 0 | |
| Drawings for Medium-sized Repetition Work. By R.D. Spinney. With 47 illus. 130 pp. 8vo. (1909) | net | 3 6 |
| Mathematical Drawing Instruments. By W.F. Stanley. Seventh edition, 265 illus. 370 pp. crown 8vo. (1900) | 5 0 |