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Study of Airscrews for High Speed Aeroplanes
Published online by Cambridge University Press: 28 July 2016
Résumé
It is demonstrated how, with increase in speed, the diameter of optimum efficiency and the maximum possible value of efficiency of an airscrew diminish. The efficiency of a system of two counter-revolving airscrews with different angular velocities is then determined, and the variation of efficiency with variation in the relation between the angular velocities of the two airscrews.
With increase in the height and speed of flight, airscrew performance inevitably falls off, frequently in a marked degree; this being mainly due to the decrease in aerodynamic efficiency of the blade sections at high Mach numbers.
The object of the present article is to analyse the influence exerted upon the performance of an airscrew by the various parameters that determine it, wit-h special reference to those connected with the speed and height of flight.
A similar study has also been made of systems constituted of two counter-rotating airscrews, with a view to comparing them with isolated airscrews designed to absorb the same power under identical conditions.
By the methods here described, an approximate numerical evaluation of the performance can be made, utilising the experimental results which are already to hand.
- Type
- Research Article
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- Copyright
- Copyright © Royal Aeronautical Society 1940
References
1 A. Betz, in a brief article (“Luftschrauben für grosse Fluggeschwindigkeit,” Jahibuch 1937 der deutschen Luftfahrtforschung) has made a synthesis of the problems of highspeed propulsion, mentioning some of the points that are treated in the present article.
2 (c.f. Pistolesi: “Aerodinamica,” Chapter VI.)
3 c.f. Wenzig: “Luftschrauben für schnelle Flugzeuge” (Jahrbuch 1937 der Deutschen Luftfahrtforschung), who gives the following figures:—
| Height | m. | … | … | 0 | 2000 | 4000 | 6000 | 8000 | 10,000 |
| Speed of sound | m./sec. | … | … | 342 | 335 | 328 | 319 | 310 | 301 |
4 Formulae (2), (3), (4), (6), (7), (8) can be deduced from Chapter VI of E. Pistolesi's “Aerodinamica.”
5 If it is desired to take into account the terms αi 2 and є αi, omitted above, formula (5) becomes:—
6 c.f. I. Stack and A. E. von Doenhofl; Tests of 16 Related Airfoils at high speeds. N.A.C.A. Report No. 492, 1934 ; A. Ferri: Studi e ricerche eseguite alia Galleria Ultrasonora di Guidonia. Hauptversammlung 1938 der Lilienthal Gesellschaft. (Translated, R.Ae.S. Journal, October, 1939.)
7 c.f. A. Buseman: Sostentazione aerodinamica a velocitá superiore a quella del suono. Aerotecnica, August-September, 1936.
8 c.f. M. Castoldi: “Gli Apparecchi Italiani di alta Velocità”; Conference of Physical, Mathematical and Natural Sciences, 1935. R. Accademia d'Italia.
9 One could, on the other hand, take the value of C given by (22), leaving the factor (Ω1 – Ω2), which appears in the denominator, as an unknown. For (31') must be substituted:—
which, integrated with regard to x and equated to zero, gives rise to a fourth degree algebraic equation, whose solution still does not give the exact value of x opt because A 1, A 2, B 1, B 2 are approximate.
10 Note that the values are the same for ξ and 1 – ξ.
11 The values 0.727, 0.725 are obtained by exterpolating the experimental results for the blade-tips, which in the case of an isolated airscrew have less influence on the efficiency than in the other two cases, owing to the different distribution of along the blade.
12 c.f., for example, R. Doherty and E. G. Keller, Mathematics of Modern Engineering, Chapter V.