292 SOME APPLICATIONS OF THE PRINCIPLES OF 
Of the well known types there is no doubt that the Wright propeller is 
the most efficient. It has an efficiency which is equal, if not superior to that 
reached by the most successful marine types. To engineers who are familiar 
with the inherent difficulties of the subject the Wrights’ success with the 
propeller gives an indication of the high ability of these pioneers in practical 
navigation in heavier-than-air machines. 
The Society’s Transactions for 1906, contains a paper on “The Limit of 
Propeller Efficiency,” by the writer of the present paper. The principles 
made use of at that time in dealing with the water propeller seem equally 
applicable tothe air propeller,and possibly are of sufficient interest to warrant 
a discussion along the same lines. 
For those who may not have at hand the 1906 paper, the following is 
given again, simply substituting “air” for ““water’’ in the notes: 
Let V; be the speed of advance, in feet per second; V2 the sternward 
velocity imparted to the air accelerated by the action of the propeller, and 
A the area of the circle swept by the tips of the propeller blades. 
Consideration makes it appear that the amount of air displaced per 
second is A(Vi+ V2). 
Its mass is A (V, +02). 
The constant force or thrust which must be applied to impart the 
velocity, V2 is 
W 
ren ae V2) Vo (1) 
W 
Useful work Wu= a A(Vit V2) VoVi (2) 
W W 
Gross work Wg= ot (Vit V2) V2Vi +304 (V+ V2) V2. (3) 
the last term being the expression for the kinetic energy imparted to the air. 
elie eels 
Efficiency Oe Vac Vs (4) 
"2 
Solving for V2 in (1) and substituting in (4): 
ae 
7) ae “aT a — @ 
