elliptical blades varies as %+%, where r is the radius from centre of

Mr R. E. Froudein 1908, it is probable that the effect of friction would be in the direction of giving higher efficiencies for large screws than for small. The results obtained with ships' propellers are in general accordance with those deduced from model propellers, although the difficulties inherent to carrying out experiments with full-sized Screws have hitherto prevented as exact a comparison being made as was done with resistance in the trials of the “ Greyhound ” and her model. Results of model experiments have been given by Mr R. E. Froude, Mr D. W. Taylor, Sir John Thomycroft and others; of these a very complete series was made by Mr R. E. Froude, an account of which appears in Trans. Inst. Nav. Archs., 1908. Propellers of three and four blades, of (pitch ratios varying from 0-8 to 1-5, and with blades of various wi ths and forms were successively tried, the slip ratio varying from zero to about 0-45. In each case the screw advanced through undisturbed water; the diameter was uniformly 0-8 ft., the immersion to centre of shaft 0-64 ft., and the speed of advance 300 ft. per minute. Curves are given in the paper which express the results in a form convenient for application. Assuming as in Froude's theory that the normal pressure on a blade element varies with the area, the angle of incidence, and the square of the speed, the thrust T would be given by a formula such as T=a R'-bR

where R is the number of revolutions per unit time. On rationalising the dimensions, and substituting for R in terms of the slip ratio s, the “conventional” pitch ratio p, the diameter D, and the speed of advance V, this relation becomes: 2 S

TW Di” '<1-TF

From the experiments the coefficient a was determined, and the final empirical formula below was obtained- 2-l-21 I'O2S(I-~OSS)

T D'V'>**<(V-V'); the effective or tow rope horse-power is
R XV, and the ratio of these two powers = (1 -t) (1 -1-w) is
termed the hull ejiciency.
**

**It is evident that the first factor (1 -I-w) represents the power
regained from the wake, which is itself due to the resistance of
the ship. As the wake velocity is usually a maximum close to
the stern, the increase of w obtained through placing the screw in.
a favourable position is generally accompanied by an increase
in t; for this reason the hull efficiency does not differ greatly from
unity with different positions of the screw. Model screw experiments
with and without a ship are frequently made to determine
the values of w, t, and the hull efficiency for new designs; a
number of results for different ships, together with an account
of some interesting experiments on the effect of varying the
speed, position of screw, pitch ratio, direction of rotation, &c.,
are given in a paper read at the Institution of Naval Architects in
1910 by Mr W. ]. Luke. 5
**

**The total propelling efficiency or propulsive coefficient (p) is the
ratio of the effective horse-power (RV) to the indicated horse-power,
or in turbine-driven ships to the shaft horse-power as determined
from the torque on the shaft. In addition to the factor “ hull
efficiency, " it includes the losses due to en ine friction, shaft friction,
and the propeller. Its value is generally aiout 0-5, the efficiencies of
the propeller and of the engine and shafting bein about 65 and 80 %
respectively. The engine losses are eliminated in the propulsive
coefficient as measured in a ship with steam turbines; but the
higher rate of revolutions there adopted causes a reduction in the
propeller efficiency usually sufficient to keep the value of the propulsive
coefficient about the same as in ships with reciprocating
engines.
**

**The table on the following page gives approximate values of w, t,
and p in some ships of various types.
The action of a screw propeller is believed to involve the acceleration
of the water in the race before reaching the screw, which is
necessarily accompanied by a diminution of pressure; “Yuma
and it is quite conceivable that the pressure may be °
reduced below the amount which would preserve the natural flow of
water to the screw. This would occur at small depths of immersion
where the original pressure is low, and with relatively small blade areas
in relation to the thrust, when the acceleration is rapid; and
it is in conjunction with these circumstances that so-called “ cavitation”
is generally experienced. It is accompanied by excessive
slip, and a reduction in thrust; experiments on the torpedo-boat
destroyer “ Daring, ” made by Mr S. W. Barnaby in 1894, ' showed
that cavitation occurred when the thrust per square inch of projected
blade area exceeded a certain amount (11% lb). Further
trials have shown that the conditions under which cavitation
is produced depend upon the depth of immersion and other
factors, the critical pressure causing cavitation varying to some
extent with the type of ship and with the details of the
propeller; the phenomenon, however, provides a lower limit to
the area of the screw below which irregularity in thrust may be
low values of the
**

**disk ratio. A skewback
**

**of the blades to an angle of 15° was found to make no material
diHerence to the results., V
**

**expected, and the data for other screws (whether model or
full-size) become inapplicable.
**

**
1 Trans. I .N.A. 1897 (vol. xxxix.).**

**
**