SEAGOING men in general and naval personnel in particular should certainly have such clear ideas of how propellers work that necessary explanations can be made to inquisitive children or to prying landlubbers.
How does a propeller propel? Referring only to final effect, as the name suggests, the propeller pushes the ship horizontally against the resistance of the water. The airplane wing, while moving horizontally, develops “lift” to hold the airplane up against the downward pull of gravity. The “thrust” of the propeller and the “lift” of the airplane wing are therefore similar, the former acting to overcome the resistance of the water, the latter acting to overcome the pull of gravity. The action of the airplane wing being easier to understand, a partial explanation will first be given of the development of lift by the airplane wing.
In Fig. 1 an airplane wing is shown in section, side elevation. The plain arrow indicates the direction of motion; the feathered arrow shows the direction of the relative wind with which the chord of the wing section makes the angle a, the angle of incidence. It has been shown by experience and experiment that under these conditions an increase in pressure develops under the wing and a decrease in pressure develops above the wing with the result that there are produced a “lift” (L) “perpendicular to the direction of motion” which supports the weight of the plane, and a “drag” (D), opposite to the direction of motion which resists the forward motion. With so called airfoil sections the lift is ten or more times the drag. Airplane operations are now so common that the foregoing physical facts have become part of the experience of most people who have thought about this matter at all.
Kutta and Joukowski early in this century developed a mathematical theory, agreeing very well with experimental work, to explain how under such circumstances a “circulation” is set up around the airplane wing which, acting with the relative wind, gives rise to the lift acting perpendicular to the direction of velocity. Readers interested in going into this theory are referred to National Advisory Committee for Aeronautics Report No. 116. For present purposes the fact that lift is developed may be accepted as an experimental fact.
Now consider the action of the ship propeller; Fig. 2 shows, in perspective, successive views of a propeller blade, supposed to be turning at a uniform rate and developing thrust, the Roman numerals I, II, and III indicating three positions of a section of the blade taken perpendicular to the radius and at distance r feet from the center line of the shaft which is turning at R revolutions per minute, while the shaft, propeller, and ship advance at v feet per minute through the water. At each marked position the instantaneous forward velocity z; (ft/min), rotational velocity 2p r R (ft/min) and resultant velocity vr = √(v^2+?(2? r R)?^2 ) ft/min),of the section under consideration, equal in each case, have been drawn. The feathered arrow shows that the relative water flow is equal and opposite to vr.
To make it easier to visualize the similarity of the action of the propeller to the action of the airplane wing, velocity diagrams for the sections as seen from above at position I of Fig. 2 have been redrawn in Fig. 3; at 3(a) it is assumed that the section is at 2 feet radius; at 3 (b) is shown a section of 4 feet radius and at 3 (c) one at 6 feet radius, drawn roughly to scale, representing the propeller of the U.S.S. Tennessee. It should, however, be noted that the blade section is not to scale.
To simplify this next step in explanation it is assumed that the water is undisturbed in front of the propeller. Seeking now the similarity of action to that of the airplane wing it is believed to be clear from the diagrams that the direction of the relative flow of water in each case is indicated by the
feathered arrow; that the relative flow is opposite in direction and equal in amount to the resultant of the forward and rotational velocities of the sections of the propeller being considered; that a is the angle made by the chord (driving face) of the section with the relative flow and corresponds to the angle of attack a of the airplane, Fig. 1; and, as in the case of the airplane wing there will be a pressure exerted on the face of the propeller, a suction on the back, and a resultant force L perpendicular to the direction of motion; finally, now looking at the force diagram, Fig. 3(f), this force may be resolved into a forward thrust to drive the ship and a twisting force which must be overcome by the turning force (torque) of the engine. The motion of the blade through the water will also give rise to a reaction D, corresponding to the drag of the airplane wing, which, resolved into components, parallel and perpendicular to the shaft, reduces the effective thrust and adds to the component which must be overcome by the torque of the engine. Finally the total effect of the propeller at any instant will of course be a summation of the simultaneous actions of all sections of all blades.
The angle in the diagram of Fig. 3 is the pitch angle, that is, the angle at which the section being considered stands relative to the athwartship line of the ship. When the nominal pitch, measured in feet, is uniform over the driving face, as in the case of the Tennessee propeller, as well as in practically all propellers used in the U. S. Navy q varies at each section as is clearly seen by comparison of the sections shown in Fig. 3 (a), (b), (c), (d), and (e).
The ratio (PR –v)/PR in each diagram is called the apparent slip ratio; the angle a, which, as seen in Fig. 3, measures (PR-v), is the apparent slip angle and corresponds to the angle of attack of the airplane wing.
In summarizing the foregoing explanation the following facts may be stated:
- The propeller develops thrust and requires torque to turn it due to its many blade sections, each being at an angle a (slightly different for each section) with respect to the relative water flow incident to the movement of the ship and the turning of the propeller.
- At a certain value of the angle a, negative with common sections, no thrust will be developed, although, due to the blade friction, torque will be required to turn the propeller.
- At still greater negative values the thrust will be reversed (from which follows the principles of reversible propellers).
- Slip is necessary (like the angle of attack of an airplane wing) for propeller (thrust producing) action, and not a “preventable loss,” an idea doubtless suggested by the supposed similarity of the propeller action in water to the machine screw action in solid materials.
- The slip angle is normally small.
As an example to test his understanding of the method of analysis given above it is suggested that the reader work the following problem: In what direction will a propeller turn if it is drawn through the water after being disconnected and allowed to turn freely, as in the case of a 4-shaft electric drive ship dragging two propellers while being propelled by the other two ? Then prove the result by using two electric fans in tandem.
The above explanation has been made, and Figs. 2 and 3 have been drawn, assuming that the propeller was working in undisturbed water and moving through the water parallel to the axis of the shaft.
The wake of the ship. When a propeller works behind a ship, however, these assumptions clearly do not hold. For a ship in its forward motion affects the water so as to give rise to the wake, usually considered as a current in the direction of ship motion, which affects the relative flow of water to the propeller.
Using the data of Fig. 3(d), Fig. 4 has been drawn to a larger scale to show the effect of wake. Wake is usually expressed as a fraction of the speed of the ship and in this case has been assumed to be 0.1.v. In Fig. 4 this value has been laid off as an instantaneous velocity and compounded with the previously obtained value of relative water flow, vr, to obtain the new value, ve, of the relative flow of water to the propeller. Under these conditions the thrust and torque reactions correspond with the reduced relative velocity Ve. But it should be noted that the thrust actually works through v feet per minute, the distance the ship moves.
The suction of the propeller. Another factor which must be accounted for in the problem is the suction caused by the propeller. This reacts on the ship so as to interfere with the flow of water past the hull, and to increase the speed of flow and consequently the resistance, with the result that for a given speed the thrust of the propeller must be greater than the towrope pull which would be found necessary by towing the ship at the given speed through undisturbed water.
Conclusion. It will doubtless be realized
that the foregoing explanation is made up largely of mathematical concepts representing average and resultant conditions and has made the problem appear simpler than it really is. The interaction of wake and propeller suction is very complicated, making the relative and actual flow of the water to the propeller turbulent, that is, in different directions at different points of the propeller disc; with the result that the slip angle, and relative flow velocity, ve, vary considerably from this cause. It was seen above that the slip angle a varies due to the construction of the propeller, considering only the driving face of the sections of the blade. Further, the actual slip at which a propeller will work is dependent also on the shape of the back of each section, with the result that the effective (true) slip angle at any section is practically indeterminate. To emphasize how the slip angle varies in amount, the theoretical values of true slip angle are calculated above for the conditions of Fig. 4. The calculations incident to the construction of Figs. 3 and 4 are also given.
Although the foregoing may not be a simple explanation, it is hoped that enough thought on the subject may have been stimulated in a reader to enable him to satisfy himself and possibly to give a simple explanation to the inquiring child or landlubber.
TABLE I
U.S.S. Tennessee Propellers
Diameter 13’-6” Pitch 14’-3”
Projected area 52.1 sq. ft. Pa/Da=0.364
Angles of Fig. 4 | |||
r (feet) | 2 | 4 | 6 |
tan ?=[PR/(2?rR? | 1.134 | .567 | 0.378 |
q | 48°-36’ | 29°-33’ | 20°-12’ |
tan (?-?)=[(v-Wv)/(2?rR? | 0.925 | 0.4625 | 0.3083 |
?-? | 42°-46’ | 24-49’ | 17°-08’ |
(true slip angle) a | 5°-50 | 4°-44’ | 4°04’ |
Calculations for Figs. 3 and 4
v (Knots) | v (ft/min) | Corresponding R (r.p.m.) | P.R. | 2prR | ||
r=2 | r=4 | r=6 | ||||
10 | 1013 | 78 | 1111 | 980 | 1960 | 2940 |
15 | 1521 | 117.8 | 1667 | 1480 | 2960 | 4440 |
19 | 1926 | 152.3 | 2170 | 1914 | 3828 | 5742 |
With wake applied to Fig. 4 | ||||||
|
|
| ve |
|
|
|
| vr | ve | -- |
|
|
|
|
|
| vr |
|
|
|
r=2 | 2122 | 2015 | 0.95 |
|
|
|
r=4 | 3328 | 3260 | 0.98 |
|
|
|
r=6 | 4694 | 4648 | 0.99 |
|
|
|