EXPERIMENTS ON THE FROUDE. 99 
are taken from the analysis in the original report. The new analysis 
shows appreciable but not large divergences from the earlier one. 
In order to estimate the shaft horse-power, it is now proposed to assign 
a mechanical efficiency of 0.90 at full speed, basing this estimate on the 
known efficiency of stationary engines and on the few investigations by aid 
of the torsion-meter on reciprocating marine engines now extant. As the 
engine of the Manning was in good condition and as the air-pumps were 
independent of the main engine this estimate is believed to be conservative. 
The initial reduced mean-effective pressure is taken to be 1.7 of a pound 
per square inch, as given in the first analysis; but the assignment of a 
mechanical efficiency at full-speed relegates this elusive function to a position 
of little importance except at low speeds where the unavoidable uncertainties 
are likely to cover its error. ‘The load-friction is assumed to increase with 
the power, as is known to be the case for stationary engines. Thus we 
readily obtain the first six lines in Table II. 
From the tests on the Froude the wake is estimated to be 0.07 with the 
propeller in the normal position; if this wake is assigned to the Manning in 
the analysis the real slip can be computed from the apparent slip, which 
latter is found in the usual way from the speed, pitch and revolutions. In 
general the wake of a ship will be somewhat less than that for its model; 
but the necessity of discussing this nice question for the case in hand can 
be avoided because a small variation in real slip will have only an inappreci- 
able effect on the analysis. The reason for finding the real slip is that we 
may assign an efficiency to the propeller, which can be done by aid of Fig. 5, 
Plate 39, provided that we may assume the propeller of the Manning to 
have the same efficiency as was found during the tests of the propeller of 
the Froude at the Model Basin. Within the limits of the trials of the 
Manning the efficiency of its propeller is taken to be 0.68. The power 
delivered by the propeller to drive the ship is found by multiplying the 
shaft horse-power by this efficiency. 
For steel ships with lean dead-wood and narrow stern-posts William 
Froude recommends that a hull-efficiency of unity shall be assigned. On 
the other hand the experiments on the Froude as analyzed on page 100, 
indicate a small value for the hull-efficiency when the propeller is in its 
normal position abaft the stern-post. In my opinion the hull-efficiency for 
the Manning should be appreciably larger than for the Froude as is likely 
to be true in any comparison of ship aid model, as both wake-gain and thrust- 
deduction vary inversely with the size, and the latter the more rapidly. After 
a careful study of this problem and after making certain plausible calculations 
that it will not be profitable to develop here, I have concluded to use a hull- 
