Thus, the time from when the order is given to go astern until full engine stop is achieved, as indicated in from sea trial records, was used as an approximation for the period t1. The results obtained from more than ten ships revealed an average value of 98.92 seconds and did not indicate any regressive relationship between D and t1.
Fig. 6 k over D curve.
Fig. 7 Vs over D curve.
t2 is calculated as the time needed to accelerate a propeller from an initial state of rest to resonant rotation speed, assuming that engine torque at maximum continuous rating is fully used to accelerate the propeller and letting ε represent the nominal angular acceleration of the propeller. The ratio of resonant rotation speed to maximum continuous rotational speed ranges from 0.3 to 0.7 with an average value of about 0.55 and shows no relation with propeller diameter. The relationship between the rotation speed of the propeller at maximum continuous rating, as well as the nominal angular acceleration of the propeller with the diameter of the propeller are shown in Figures 8 and 9, respectively.
Fig. 8 NMCR over D curve.
Fig. 9 ε over D curve.
Equation (6), which describes the relationship between λ and |JT|, may be rewritten as follows by substituting Equations (7) and (14).
where
t1 = period from the time the astern order is given to the time when propeller starts to rotate astern (approximately to propeller's state of rest); an average value of 98.92 seconds is used here.
t2 = time needed to accelerate propeller from rest to the resonant rotation speed; it is given in following Equation (16).
Furthermore, using the relations between propeller diameter D and the values k, Vs, NMCR and ε, respectively, as shown in Figures 6 through 9 above, the regressive proportion relationship between λ and D may be expressed as
A graphic representation of Equation (17) is given in Figure 10.
As can be seen from Figure 10, λ has a regressive relationship with D. This relationship may be approximated by the following Equation (18) with good agreement.
