PERFORMANCE OF MARINE VEHICLES – I
ASSIGNMENT – PART II
Fresh water Sea water
Density 1000 kg per m3 1025 kg per m3
Acceleration of gravity 9.81 m per sec2
1. The resistance of a model of length 6 m at different speeds is found to be as follows :
V m/s : 0.977 1.132 1.286 1.440 1.595
RT N : 16.286 23.352 32.469 44.564 61.082
Determine the effective power of the ship of length 150 m and wetted surface 5120 m 2
for different speeds using the ITTC Line with a form factor of 1.100 and roughness
allowance of 0.0004.
[ Answer : 3806 kW at 14 k.]
2. The pitch P, the expanded blade width (chord) c and the blade thickness t at different
radii r of a four bladed propeller of diameter 5 m are as follows :
r m: 0.500 0.750 1.000 1.250 1.500 1.750 2.000 2.250 2.500
Pm: 3.576 3.898 4.113 4.239 4.260 4.193 4.025 3.790 3.504
cm: 1.372 1.587 1.773 1.926 2.021 2.013 1.904 1.591 0
t m: 0.244 0.216 0.188 0.160 0.132 0.104 0.076 0.048 0.020.
Determine the mean pitch ratio, the expanded blade area ratio and the blade thickness
fraction of the propeller. The boss diameter ratio is 0.200.
[ 0.8, ]
3. A ship with a propeller of 5 m diameter and 0.9 (face) pitch ratio has a speed of 16 k
when the propeller runs at 120 rpm, the speed of advance of the propeller being 12 k.
Determine the apparent slip and the real slip of the propeller. If the propeller produces
zero thrust when the speed of advance is 19 k, determine the effective pitch of the
propeller.
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4. A propeller of diameter 4 m has a speed of advance of 6 m/s when producing a thrust of
150 kN. Using the axial momentum theory, determine the relative velocities of the
propeller with respect to the water in the slipstream at the propeller and far behind it.
Calculate the thrust loading coefficient of the propeller, its ideal efficiency and the
delivered power.
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5. A four bladed propeller of diameter D = 5 m has blades that have an expanded blade
width c at different radii as follows:
r/R : 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
c/D : 0.119 0.138 0.154 0.167 0.176 0.175 0.166 0.138 0
All the blade sections from the root section at 0.2R to the tip have a lift coefficient of 0.5
and a drag coefficient of 0.008. The propeller has a speed of advance of 7.5 m/s at 180
rpm. Determine the thrust, torque and efficiency of the propeller neglecting induced
velocities.
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6. The open water characteristics of a five bladed propeller of 4.5 m diameter and 0.9 pitch
ratio are as follows:
J : 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8534
KT : 0.3415 0.3114 0.2831 0.2489 0.2115 0.1707 0.1266 0.0792 0.0284 0
10KQ : 0.4021 0.3767 0.3471 0.3133 0.2753 0.2331 0.1867 0.1361 0.0813 0.0503
The propeller has an rpm of 180. Determine the thrust and torque of the propeller at zero
speed of advance, the speed of advance and torque at zero thrust and the thrust, torque
and efficiency at a speed of advance of 8.1 m per sec. If the propeller has an rpm of 210
with a torque of 540.088 kN m, determine the thrust, speed of advance and the open
water efficiency. [
7. A single screw ship has an effective power of 6000 kW at a speed of 16 knots. The wake
fraction is 0.200, the thrust deduction fraction is 0.160 and the relative rotative efficiency
is 1.060 based on thrust identity. The propeller has an rpm of 150 with the engine having
a brake power of 9000 kW. The shafting efficiency is 0.980. Determine the thrust and
torque of the propeller, the thrust power and the delivered power. Also determine the hull
efficiency, the propeller open water efficiency, the propulsive efficiency and the overall
propulsive efficiency.
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8. A propeller of diameter 4.0 m, pitch ratio 0.8 and expanded blade area ratio 0.50 has its
centre line 2.2 m below the surface of water. The propeller runs at 150 rpm,
corresponding to J = 0.600, KT = 0.110. Determine the cavitation number based on speed
of advance and the thrust per unit projected blade area. Atmospheric pressure = 101.325
kN/m2, vapour pressure = 1.704 kN/m2 and the ratio of projected area to expanded area =
1.067 – 0.229 P/D, where P/D is the pitch ratio.
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9. A propeller of 4 m diameter and 0.8 pitch ratio runs at 180 rpm. Each blade of the
propeller has a mass of 1000 kg, the centre of mass being at a radius of 1.33 m. The root
section at 0.2R has an area of 0.1 m2 and a section modulus of 0.003 m3 about the
principal axis parallel to the chord. The distance between the centroid of the blade and
2
the centroid of the root section measured parallel to the propeller axis is 0.25 m.
Determine the centrifugal force and the stress due to it in the root section.
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10. A twin screw ship of length 150 m and wetted surface 6400 m 2 has a speed of 16 k, the
effective power being 6000 kW. The propellers are each of diameter 4.8 m. A self-
propulsion test is carried out with a model of length 4 m, and at the model speed
corresponding to the ship speed of 16 k, it is found that the model propellers run at 900
rpm, each propeller having a thrust of 8.03 N and a torque of 0.155 N m, the tow force
applied to the model being 2.513 N. The open water characteristics of the model show
that each propeller at 900 rpm produces a thrust of 8.03 N and a torque of 0.150 N m at a
speed of advance of 1.150 m/s and a thrust of 8.15 N and a torque of 0.155 N m at a
speed of advance of 1.160 m/s. Determine the wake fraction, thrust deduction fraction,
hull efficiency, relative rotative efficiency and propulsive coefficient by thrust identity
and by torque identity. What is the resistance of the model? Determine also the
propeller rpm and the delivered power of the ship at 16 knots.
[ ,
11. A ship has an engine of 25000 kW brake power at 90 rpm directly connected to the
propeller of diameter 8.284 m and pitch ratio 1.0. The open water characteristics of the
propeller are as follows:
J :0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
KT : 0.4250 0.3984 0.3689 0.3365 0.3013 0.2631 0.2221 0.1782 0.1314 0.0818
10KQ : 0.5994 0.5698 0.5357 0.4971 0.4540 0.4064 0.3543 0.2976 0.2365 0.1708
The shafting efficiency is 0.980, the wake fraction is 0.225, the thrust deduction fraction
is 0.200 and the relative rotative efficiency is 1.030. Determine the speed and effective
power of the ship.
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12. A tug has a propeller of 3.1 m diameter and 0.6 pitch ratio. The open water
characteristics of the propeller are as follows :
J : 0 0.1 0.2 0.3 0.4 0.5 0.6
KT : 0.2517 0.2254 0.1949 0.1603 0.1215 0.0786 0.0315
10KQ : 0.2455 0.2247 0.2001 0.1718 0.1369 0.1036 0.0639
The shafting efficiency is 0.950 and the relative rotative efficiency is 1.000. The thrust
deduction fraction in the bollard pull condition is 0.050. Determine the brake power and
the propeller rpm for a bollard pull of 200 kN.
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3
13. A ducted propeller of 4 m diameter and 0.9 pitch ratio has open water characteristics as
follows:
J : 0 0.2 0.4 0.6 0.8 1.0
KT : 0.525 0.375 0.287 0.195 0.087 -0.027
10KQ : 0.402 0.389 0.354 0.292 0.189 0.033
KTD : 0.247 0.159 0.088 0.022 -0.072 -0.223
KT and KQ are the thrust and torque coefficients of the propeller as a whole, while KTD is
the thrust coefficient of the duct alone. The propeller runs at a constant 115.74 rpm.
Determine the thrust and torque of the propeller and the thrust of the duct at speeds of
advance of 0, 3, 6, 9 and 12 knots. At what speed will the duct thrust be zero?
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14. A hovercraft of 3125 kN weight has a speed of 60 k. The air cushion is rectangular and
has a length-breadth ratio of 2.5. The air cushion has a pressure of 2 kN per m 2. Air
leaks from the air cushion at the rate of 2 kg per sec for every metre of the cushion
boundary. Determine the dimensions of the air cushion and the momentum drag of the
hovercraft.
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15. A hydrofoil craft of length 20 m has a surface piercing main foil 2.5 m forward of
amidships and a fully submerged foil 8.5 m aft of amidships. The lift coefficients of the
forward and aft foils are 0.9 and 1.0 respectively. The aft foil has an area of 4 m 2. If the
craft becomes foil-borne at 25 m per sec, when the area of the forward foil (projected on
a horizontal plane) is 16 m2, determine the weight of the craft and the distance of its
centre of gravity from amidships.
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