The auther investigated theoretically the relation between the size of the stabilizer and the amplitude of rolling in several cases;
1. When the ship is forced to roll by the stabilizer, Δθ_n=2Θ-a (θ_n+Θ) -b (θ_n+Θ) ²denoting the couple produced by the stabilizer by WmΘ and the maximum attainable amplitude is given by 2Θ-a (θ_n+Θ) -b (θ_n+Θ) ²=0
2. When the rolling is quenched by the stabilizer in the still water, -Δθ_n=2Θ+a (θ_n-Θ) +b (θ_n-Θ) ²
3. Rolling amongst regular waves. In the case of synchronism, the maximum amplitude is reduced by the stabilizer to θ given by the equation 2Θ+a (θ_n-Θ) +b (θ_n-Θ) ²-φπ/2=0 provided Θ≤φπ/4. If the size of the stabilizer is so chosen as Θ=φπ/4, the maximum amplitude is only φπ/4. The larger the size, the less the amplitude, but a vibratory rolling occurs in some cases owing to the too large power of the stabilizer.
The theory is compared with the model experiment made by Dr. Motora, showing a fair coincidence.

抄録全体を表示

Ocean waves are not regular, as are assumed in the ordinary theory of rolling, and accordingy the max angle of roll deduced therefrom is not directly applicable in practical case. In this paper, the waves are not assumed to be regular, but only one wave, which passes the ship in one swing, is considered as sine form, and the limiting angle of swing possible in that ease is found. The angle of swing is generally given by
θ=K-∞Σn=1θn cos nkt.
But a large swing can safely be represented by
θ=K-θ₀cos κt…(1)
This fact, valid both for apparent and absolute rollings, can be mathematically proved in both cases(Appendix)and also is observed from the record of actual rolling on sea as Fig.1
Assuming the form(1), only the swing, whose final amplitude is not less than the initial one, need to be taken into consideration for the present problem, then this condition gives the relation that σ must be less than unity. The final amplitude of swing θ_f is given by
θ_f = [2eσ⁸+a_e(1-σ²)] sinσπ/2/e√4σ²(e²σ²-1)²+a_e²e²(1-σ²)²tan²σπ/2…(2)
The maximum value of θ_f for various σ is the desired limiting angle, which occurs, practically σ= 1/e. Consequently θ_fmax occurs at σ=1 for e>1, and at σ= 1/e for e>1, the results being as follows,
θ_fmax=1/√(e²-1)² +(2a_ee/π)² for e<1 or T_w<T_s
T=T_w.
θ_fmax=2+a_e(e²-1)/a_ee²(e²-1)cosπ/2e for e>1 or T_w>T_s
T=T_s
θ_fmax=π/2a_e for e=1 or T_w=T_s
T=T_w=T_s.…(3)
The effective extinction coef. a_e in these expression is to be determined by the following equations
a_e=a+√2b_γΘw/e [(1-e²)²+(2a_ee/π)²] for e<1.
a_e=a+2b_γΘw/a_ee²(e²-1)cosπ/2e for e>1.
a_e=a+b_γΘw/2a_eπ for e=1.…(4)
For the absolute rolling, the limiting angles are given by multiplying e² to the results (3), and the a_e, by taking e²γΘw instead of γΘHw in (4).
These results are calculated and given, in Fig. 2.
The same method can also be applied for the swing on waves affectedby wind, in which the, new. variable θ=θ-φ is to be used instead of θ and the_fmax is given by(3), then the limitting angle is equal to θ_fmax plus φ.
These treatment is based on the assumption of isochronous stability curve, but the above results can also be applied to the non-isochronous case. The approximate θ'_fmax for non-isochronous ship can be got by taking the same area below the stability curve in both cases.

抄録全体を表示

Thirty-three new species of the genus Diostracus are described from eastern Nepal based on the collections brought by the Kyushu University Scientific Expedition to the Nepal Himalaya in 1972 and by Mr. J. Emoto in 1981. Three described species included in the collections are also noted. A key to all the named Nepalese species (37 species) is given.

抄録全体を表示