Sec. 59.13 



PROPULSION-DEVICE PERFORMANCE 



343 



The following references may be found useful 

 by the reader who wishes to pursue further the 

 study of inflow to a screw propeller: 



(1) Wood, R. MoK., "Multiplane Interference Applied to 



Airscrew Theory," ARC, R and M 639, 1919-1920, 

 Vol. 2, pp. 553-576 



(2) Betz, A., "Development of the Inflow Theory of the 



Propeller," NACA Tech. Note 24, Nov 1920 



(3) Betz, A., "The Theory of the Screw Propeller," 



NACA Tech. Note 83, Feb 1922 



(4) Munk, M. M., "Notes on Propeller Design-Ill. The 



Aerodynamical Equations of the Propeller Blade 

 Elements," NACA Tech. Note 95, May 1922 



(5) Lock, C. N. H., and Bateman, H., "The Measurement 



of Airflow Round an Airscrew," ARC, R and M 

 1955, Nov 1924, pp. 385-399 



(6) Weick, F. E., "Propeller Design: Practical Application 



of the Blade Element Theory-I," NACA Tech. 

 Note 235, May 1926 



(7) Weick, F. E., "Aircraft Propeller Design," McGraw- 



Hill, New York, 1930 



(8) Helmbold, H. B., "Goldstein's Solution of the Problem 



of the Aircraft Propeller with a Finite Number of 

 Blades," NACA Tech. Memo 652, Dec 1931 



(9) Glauert, H., "Airplane Propellers," AT, Vol. IV, 1936. 



59.13 Data on Induced Velocities and Differ- 

 ential Pressures. It is explained in Sec. 16.3 of 

 Volume I that the induced flow and the contrac- 

 tion of the jet passing through the imaginary 

 actuator disc representing a screw propeller are 

 functions of the thrust-load factor Ctl at which 

 the actuator is assumed to be working. The 

 relative magnitude of the — Ap ahead of the disc 

 and the +Ap abaft the disc for any given Ctl is 

 similarly a function of that thrust-load factor, 

 indicated by the graph of Fig. 16. B on page 249 

 of Volume I. Here, utilizing the Bernoulli Theo- 

 rem, the ratio 



3 + VCtl + 1 



1 +3VCrL + 1 



(59. ii) 



At zero speed of advance, where Ctl has a 

 nominal value of infinity, the ratio of — Ap to 

 4-Ap reaches its low limit of 0.333 [Troost, L., 

 IME, Mar 1946, Vol. 58, p. 14]. 



Numerical values of the ratio of half the induced 

 velocity far astern, 0.5 f// , to the undisturbed 



Longitudinal Scale in Terms of Hodius R 



\z 1 ob 1 



Fig. 59.G Theoretical Jet Outlines, Axial- Velocity Distribution, and Axial-Pressure Distribution 



FOR an Ideal Screw Propeller 



