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SS A Study of the Design of Side and Stern Wheels—Feath- ering Paddles Gain Efficiency at Expense of Thrust N THE year 1913 tests were made in the model basin of the Uni- versity of Michigan upon: certain models of radial and feathering paddle- wheels. These tests were made for a board of army engineers appointed to investigate the. question of towboats and barges for the Mississippi river. The complete report upon the subject can be found in House Document. No. 857, entitled “Experimental Towboats”. Since the publication of this report I have taken the results for feathering wheels and plotted them in a more compact form and have compared the results obtained from the model wheels with those for full-sized wheels. It may not be out of place to call attention to some of the differences which exist be- tween radial and feathering wheels. Radial paddles give more thrust than the feathering for the same slip, but work at a lower efficiency. The radial wheel has its maximum efficiency at about 10 per cent slip, while the maxi- mum efficiency of the feathering wheel occurs at about 15 per cent slip. The efficiency for both types decreases with increase of dip, but the decrease is less for feathering blades than for radial blades. ' Eccentricity Ratio The eccentricity ratio is usually be- tween 0.55 and 0.70. Larger values of eccentricity ratio are accompanied by a reduction of thrust and an increase in efficiency, dependent upon the slip. For each position of the eccentric and each dip of the blade there is a certain slip at which the blade will enter the water without disturbance. If the slip is less than this amount, there is pressure upon the back of the blade when it first enters, and if the slip is greater there is pressure on the driving face when the blade enters the water. The author’s investigations would seem to indicate the desirability of using a true slip of about 15 per cent and an eccentricity ratio of about 0.55. While a larger ec- centricity ratio would give a slight in- crease in efficiency, the thrust would be considerably smaller and a larger, heavier wheel would be needed. Wheels are often made with the eccentric placed from 0 inch to 4 inches above the Abstract of a paper presented at the twenty- fourth general meeting of the Society of Naval Architects and Marine Engineers, New York, Nov. 16-17, 1916. The author, E. M. Bragg, is assistant professor of Naval Architecture, University of Michigan, Ann Arbor, Mich. center of the wheel. It does not seem probable that this has any appreciable effect upon the thrust or efficiency. The dip ratio is the ratio of the greatest immersion of the blade to the width of the’ blade. The thrust in- creases with increased dip, but the eff- ciency falls off. The true dip used will depend upon what is of most importance in the design in hand, effi- ciency or power. For Stern Wheel Boats The object of the model tests was to determine the best proportions for stern wheels on boats of moderate speed. The dip ratios used were between 1 and 1.5. In applying these results to side wheels on boats of rather high speed it was necessary to extend the curves to dip ratios of 2.5. This was done on the assumption that the maxi- mum.thrust would occur when the wheel was immersed to the center and that the thrust would be approximately zero when the wheel was fully immersed. The pitch ratio is the ratio of the distance between the trunnions, measured on the arc of the circle, to the width of the blade. As a rule, it would be better to sacrifice a little thrust. in order to gain in efficiency. If a blade-width ratio of 0.16 is used, a pitch ratio of 1.85 would call for nine blades in the model ‘wheel, while a pitch ratio of 1.5 would call for 11 blades. At 15 per cent slip the unit pressure at pitch ratio 1.85 is 16 pounds and the efficiency is 0.668, while at pitch ratio 1.5 the thrust is 1.66 pounds and the efficiency is 0.64. Each of the nine blades would have to be 4 per cent larger than each of the 11 blades, but the efficiency would be a little over 4 per cent greater, and the total blade area would be about 86 per cent of the 1l-blade wheel. Some designers use a large number of blades to reduce vibration. An attempt has been made to cor- relate the results obtained from model feathering wheels with the trial trip results of full-sized wheels. It is obvi- ous that the location of the wheel relative to the bow wave is going to influence the working of the wheel to a large degree. In the determination of the wheel location relative to the crest of the bow wave it was assumed that the length of the wave created by the passage of the boat would be 0.5573 V?, and that the first crest would be 12 per cent of the wave length aft of the bow. 31 _axis of the wheel, but rake aft. ‘wake and waves. By E. M. Bragg Vis the velocity of the boat in knots. per hour. It will be noticed that the maximum quantities do ‘not occur at the wave crest, but a little aft of it. This seems plausible when it is consid- ered that the blades enter the water some distance forward of the center of the wheel and it is the first part of the stroke which is most effective. Also the wheels have considerable length, and the wave crests are not parallel to the An- other possibility is that the wave crest is more than 12 per cent. aft of the bow. : The model wheels, when tested in the tank, were not adjacent to the hull of a boat, and by reason of this. condition the dip observed when at rest would be very close to the dip when in motion. The apparent slip and true slip of the model wheel would be practically the same. The only condition tending to affect these would be the velocity of approach of the water to the wheel, which would be very small. Side ‘Wheel Conditions Different The paddle wheel of a side wheel boat is working under quite different conditions as regards dip and slip. The velocity of approach would be somewhat larger, due to the proximity of the hull. Due to the passage of the boat through the water there will be stream-line flow, The dip of the blades when the boat is in motion may differ considerably from the dip when at rest, depending upon the part of the wave in which the wheel is working. The true slip of the wheel will differ from the apparent slip because of the velocity of approach, wake; stream-line flow, and orbital \motion of the water in wave formation. If the wheel is working in the hollow of the wave all of these except the wake make the true slip less than the apparent slip. If the wheel is working in the crest of the wave the wake and orbital motion are opposed to the stream line flow and velocity of approach, and the true slip is probably greater than the apparent slip. It would appear, however, that the change in slip is much less in degree than the change in dip. In addition to this uncertainty re- garding the true slip and true dip of the full-sized wheels, there is further uncertainty regarding the variation of thrust with speed of advance. The usual © assumption is that the thrust varies as PP Oe