An Introduction to the Aerofoil Theory of Screw Propulsion.
BY M. A. S. Riach
NEW YORK, D. APPLETON AND COMPANY, MCMXVI
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With the coming of the Aeroplane the quantitative study of screws working in air has assumed a great importance.
Formerly in the design of propellers for marine work experiments with models were carried out and the performance of the full size screw calculated from them, and it was not until 1882 that Drzewiecki first drew attention to a possible more powerful method of design obtained by considering each element along the blade as independent and behaving in the same manner as if moving through the fluid in a straight line.
This method has since assumed great importance in the practical design of airscrew blades, and the results obtained seemed to justify the utilization of this theory as at least approximately correct provided certain limits are not exceeded.
In the present work the theory has been assumed to be absolutely correct, and the results obtained have been carried to their logical conclusions. This has been done for various reasons.
It does not make for completeness in any argument if the results of the initial hypothesis are not carried to their ultimate logical conclusions, and although in the present instance the results so obtained may not be completely borne out in practice, yet, in giving an insight into the applications of the theory, and in establishing at any rate an approximate method for dealing with the many cases arising out of the performances of aircraft, the conclusions arrived at will, it is hoped, not be without interest.
I have endeavoured to present the subject of airscrew design in as simple a manner as possible, so that the ordinary non-mathematical reader may be able to follow the train of reasoning, at any rate as far as its qualitative nature is concerned.
It may be that the first chapter is unnecessarily drawn out, but it appears to me that in any investigation of this kind the first essential is to be able to clearly visualize what is being done, the mere application of analytical processes being but a secondary matter.
I have introduced graphical methods wherever it seemed to be necessary, or where it was impossible to obtain solutions without them. At the same time the results for the design of an airscrew to fulfill any specified outside conditions have been put into such a form that it is hoped that the design will be able to be correctly carried out by the rules given, even if the analytical processes have not been able to be followed by the reader.
With regard to the possible errors involved in the application of the results given in the text, these should not be found to materially affect any but the last chapters of the book. The chapters on "static" thrust, efficiency of airscrews from (V) equal to zero up to the velocity of flight, and on direct lifting systems, are admittedly of a speculative character.
It did not seem that a work of this kind could be regarded as complete without some reference to the stresses occurring in an air-screw blade, and accordingly a chapter on centrifugal and bending stresses has been included.
It is hoped that the book will be found to be not without interest to engineers desiring an introduction to the theory of airscrews, while at the same time it may perhaps conduce to a more scientific study of the subject, in place of what has been aptly described as the "make it 4 by 2" methods so dear to the heart of the " practical " man.
The Controller of His Majesty's Stationery Office has permitted me to quote from certain of the Technical Reports of the Advisory Committee for Aeronautics.
- PRESSURE ON AEROFOILS
- THE PITCH OF AN AIRSCREW
- THE FORCES ACTING ON AN AIR-SCREW BLADE
- BLADE SHAPE AND EFFICIENCY
- BLADE SECTIONS, AND WORKING FORMULAE
- "LAYING OUT" THE AIRSCREW
- STRESSES IN AIRSCREW BLADES
- STATIC THRUST
- EFFICIENCY OF AN AIRSCREW AT DIFFERENT SPEEDS OF TRANSLATION
- DIRECT LIFTING SYSTEMS
- NOTE ON THE INFLUENCE OF "ASPECT RATIO"
- NOTE ON THE EFFECT OF THE INDRAUGHT IN FRONT OF AN AIRSCREW
THE PITCH OF AN AIRSCREW
It is fairly obvious that when an air-screw is moving through the air with some definite translational velocity the distance it traverses in each revolution will be constant, providing the line of flight be horizontal.
Now if we consider any portion of the blade at a distance of (x) feet say from the centre of the boss of the airscrew, we shall find that as the air-screw as a whole moves forward, the portion of the blade under consideration moves up some particular helicoidal path due to the air-screw rotating about its axis at the boss centre.
The steepness of the helix traversed by the portion of the blade at radius (x) will depend upon the value of the distance traversed translationally by the air-screw in each revolution.
It will also depend upon the value of (x), that is upon the distance of the portion of the blade considered from the centre of the boss of the air-screw.
This may perhaps be more clearly visualized if we imagine a cylinder having a radius of (x) and a depth of (P), as in Fig.(1.
Or it may be demonstrated by taking a rectangular piece of paper and drawing a diagonal line as in Fig. (2).
Then if the paper be rolled so as to form a cylinder having both ends open, the diagonal line will represent the path or helix traversed by the point under consideration; the diameter of the cylinder so formed will represent twice the distance of the point considered from the centre of the cylinder (i.e. the centre of the boss of the airscrew).
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