Вестник МГТУ. 2018, №4.

Вестник МГТУ. 2018. Т. 21, № 4. С. 566-576. DOI: 10.21443/1560-9278-2018-21-4-566-576 Materials and methods How to obtain Lammeren's curves of the screw action was presented in detail in the proceedings of the Annual Meeting of the Society of Naval Architects and Engineers in New York in 1969 [2]. The authors point out that the researches in this area which they are familiar with [3-5] concern special cases of constructing the curves of screw action. They also offer a universal approach to this problem. Further, in their work, the action curves are represented in the form of the Fourier series with 20 terms of 4-blade B-series screws for a number of values of pitch ratio P/D. We have chosen a pitch ratio equal to 1 for certainty, although all further decisions and principal conclusions are valid for any value of P/D in the range 0.6-1.4. Fig. 1 shows Lammeren's curves of the screw action as a function of the angle P , the angle itself is determined by its tangent: v 0.7 n nD (1) Although such a universal curve is of great interest, there are some doubts concerning its correctness. First of all, attention must be paid to the fact that nothing is said about it in our classic reference books [1; 6] widely used by both shipbuilders and specialists engaged in the operation of ships. Also, a simple visual analysis of the curves in Fig. 1 suggests that they do not quite correspond to reality. Indeed, if we take the positive values of the speed of the ship and the rotation speed of the screw, we get the value of the angle P according to the formula (1) in the first quadrant (which is indicated by the author himself). But in the first quadrant, the screw thrust and torque coefficients take negative values. This is fundamentally counterintuitive - in this case, they should both be positive. Similar contradictions arise in the other quadrants o f the angle p . Of course, when taking arctangent, some amendments on quadrant can be introduced, but the materials [2] say nothing about it. For more valid conclusions we should consider Table 1 where we give the values of the coefficients of the propeller thrust CT and torque CQ for all the quadrants of the angle p . This is done for the initial curve in Fig. 1 (Lammeren), for the modified curve (Fig. 2) using the shift of the original curve (Lammeren Shifted), for shifted and smooth curve (Lammeren Smooth) in Fig. 3 for eliminating dips in the coefficients in the areas o f transition the angle P = 90 ° and P = 270 ° . 0 CQLam{x) 10 1571 7 1 1 / 1717 Й И Fig. 1. The initial Lammeren's curves of screw action Рис. 1. Исходные кривые действия винта Ламмерена In order to eliminate dips, the pair of characteristics - the velocity v and the screw revolution speed n - the values that translate the angle P in the desired plane were given. After that, with the help of MathCad "Tracing" tool, where the graphs were built, the values of the coefficients CT and CQ were defined. All these data are listed in Table in the relevant sections. A simple view of the results shows the inconsistency o f the values in the first paired row. These contradictions are eliminated by shifting (the second pair line), and smoothing eliminates dips. It is the last representation of the Lammeren's curve that we will use in the future solution. In order to enter the curves the angle has to be calculated in a certain way using the built-in MathCad function angle(), which is as follows: Pe(v, n): = be angle [ v, (0.7л- n ■ D) ] return be (2) 567