CALCULATION OF BROKEN ICE RESISTANCE BASED ON MODEL TESTING
by 0. V. DuBrovin Translated by Michail AleksandrOV and Richard Moore
The Department of Naval Architecture and Marine Engineering The University of Michigan
College of Engineering April 1970
Experimental investigation of ice resistance was started in the 1940's and was related primarily to icebreakers.
Methods of model representation for ship motions in broken and solid ice were developed by Professor Nogrid, References
[1], [2], and [3]. Ship motions in broken ice are considered to be an ideal environment with main parameters (thickness of the ice, percentage of broken ice to open water in the broken channel, width of the channel, and the form of the ice blocks) constant. The second assumption is that the ship does not break the ice blocks. Considering the parts of ship resis-tance as independent, we can give the generairesisresis-tance as the sum of water resistance (R8) and resistance due only to ice (R,14 ). This second, part of resistance might be deter-mined from model testing using 'the formula:
RA RT
where RT is the total resistance.
To obtain the resistance of the actual ship from model
testing results, we use the Froude criterion with equal relative speeds and geometrical similarity of ice conditions, References
[1] , [21 , and [4]
Here we can use the following expressions: RAq,_
1Y2t
R,= kAVD,
t
(1)t,=t2t'
B,1.2t'
where the index (1) is related to the ship and the index (2) is related to the model. L is a scale factor, V, L, B and D are correspondingly ice resistance, ship speed,
length,, beam, and displacement. , Z, t, and BK are corres-pondingly ice cover, relative ice block length, ice thickness,
and ôhañnel width. Relative ice block length can be deter-mined as
where f is the area of the ice block (m2).
- coefficient of ice resistance;
K4=
(2)
(3)
A series of model tests were performed at LSI model
basin from l950-l955 including models of icebreakers "Sibiz,t' "mac]s," and models of cargo ships (see Table 1).
Tat. -t
Model tests were conducted in open water and in broken ice. The results of the broken ice test are given in Table 2.
Thbl.2.
2
Len'
I 50 4 2,L13 7 o'S 247 9,67 0,770
ErmacK
1:50
S2 I,G
o,43o,g L?.02$3 o,32
O715,,Sibir
I 40 1L02 2,G o,5S 0208 44o 216g
O6o
60Sbir1'
I 60 I,7i6( 072
oi 4 426
0,50
O60
model.
11Lena:59
ErmaK
t:50
j:L101Sibir"
1.o
1L1.8;8L.
4,;'2,
;3
2.Sea
8 5 6*
Mo0I6
0,016010i9
i 0,120O8
O,IZ 0,12 .e.All models were made from wax with scale factors for icebreaker "Sibiz" of 1:40 and 1:60, and for icebreaker
"Ezrnack" and the cargo ship of 1:50. The artificial ice was made of paraffin with specific density 0.85 gm/cm3 and ice blocks were hexagonal in plain view.
The main purpose Of the evaluation of the experimental results was to establish the relationships between ice resis-tance, width of channel, and parameters of the ice.
The mode data were collected as a function of:
R.
for the different Bk/B ratios shown in Figures 1 and 2.
Figures 3 and 4 show the relatiOn of: the broken ice resistance
coefficient as a function of
-j5
for different values of Bk/B for the model cargo ship and the icebreaker "Sibiz."
According to References [1], [2], and [41, these figures can be used to determine the ice resistance of iOebreakers and,
cargo ships using formula (3). If ice parameters t/D 1/3, 2/D 1/3 and percent ice cover in the channel differ fron para-meters given in figures, the data can be corrected using graphs
in Figure 5. Figure 6 gives a comparison of, ice resistance for the icebreakers "Sibiz" and "Captain Bllousov" calculated by this method to the ata obtained by.full scale (5) for 7-9 numeral of ice coverage and Bk/B ratios equal to 12.
__IJ
ui
au
___,a__
_ua
I sea I TI7odeZ cf carqo '.41p 46 11, 425-0-
e)cper,mnzL-X.-RM-fi.4,
I, I'D 45
6ea
055Ice. breaKer
,, - _-- 0 d'DeT.
1- - --- w 4CC. Q m.Figure 2
251
iuuiIPS
iiu
U
iasrn r
a.UIl
I
15 g seq 4D3177&'deZ 0/ CQrqo S,'ip
8
Figure 3
I0
Figure 4
1.4346
mode?of
ii1II
P
IJ!iiil1.
I.
dlllll
IilI!il
____,
______l____-
--__
aso 415 010 (*5oo.o 090V 0I çq; z ocob 8 9 oco'o Oeob I .0 cv S
:1:
UV
Pr
0J ci2
R4.i
20
to
Ice -brcaiCer 1<. Beeouov"
0 0 o 0 4uee -3 4 20 I0 2 cebreaer Si biz . 0 0 4 o o .fu L
*
.4 4
-C Figure 6For ice resistance we can recommend an empirical formula which was developed according to (3, 5, 6) and described by these tests.
2=p,A
tp211.
(4)
where parameters A and are given by:
7tB[f*tcZO(H+_tgc4)j
(5)where again:
= density of ice (kg/cm3)
= ice to steel friction coefficient = prismatic fore-body coefficient
25 20 20 fO
Q)Ccrqo ship
/uuri
Rrau1ir
3 Sea C2fldFigure 7
10 0 f0 8ir B sea'II
= waterline entrance angle P & P = numerical coefficient
1 2
f = Froude number
2
n = powering coefficjent
(n = 1.12 for icebreakers)
(n .1.5 for joe strengthened cargo ships)
Coefficients P & P are given by Figure 7 and Figures 1, 2 and 6 give results of calculation for these ships.
CONCLUSIONS
This method of predicting resistance of ships in broken ice provides adequate information-for most calculations. The method of calculation and model test results have been verified in full scale test. to produce results within accep-table error.
REFERENCE S
L. M. Noged, "Criterior of Similarity for Modeling of Ice Resistance Tests," Proceeding of Academy of Science of USSR, 1951
L. M. Noged, "Modeling of Ship Motisus in Solid and Broken Ice," Proceedings of Leningrad Shipbuilding In-stitute, Vol. 28, 1959
L. N. Noged, "Ship Resistance Calculations from Model Tests," proceedings of Leningrad Shipbuilding Institute, Vol. 29, 1959
. V. Bronnikov, "Investigation of Ship Resistance in
Broken Ice," Proceeding of Leningrad Shipbuilding In-stitute, Vol. 27, 1959
(5] A. J. Busuev, "Calculation of Ship Resistance in Small
Blocks of Broken Ice," Mcnt Fleet, No.
8, 1961A. J. Reblin, "Ship Resistance In Broken Ice, Method of Calculation," PHD Thesis, Leningrad Shipbuilding Institute, 1963
0. V. Dubrovin, "Model Basin Study of Ship Motions in Broken Ice," Proceedings of Arctic and Anarctic
Insti-tute,. 1950
