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 LEC Sustainable Shipping Technologies Forum 2021
Fuel Tool
Fuel Consumption Tool
The purpose of the Fuel Consumption Tool is to make it possible for ship operators to estimate the fuel consumption of a given ship with a selected hull surface condition. The fuel consumption is always expressed relatively, i.e. the difference in fuel consumption between two conditions.
The tool will be executed from the Skin Friction Database webpage after that the user has entered data for a specific ship. Therefore, the tool has to be rather simple, quick, and require only input data that is easily available to the ship operator.
The following input is required:
· Length of ship (m)
· Operational speed (knots)
· Operational power (kw)
· Number of propellers
· Two deltaCf
· Specific fuel oil consumption (g/kWh)  optional
The output is given as:
· Change in power in kW
· Change in power in %
· Change in fuel oil consumption in t/day
Method
Power difference
The target is to extract a DP=P_{1}P_{2} corresponding to two different hull surface roughness.
The power difference should be valid roughly around a given operational power, which we call P_{0}.
We use the ITTC method for sea trial evaluation (ITTC 7.5040101.1) to derive the change in power due to a change in resistance:
where
V_{ }ship’s speed through water
η_{D} propulsion efficiency coefficient in ideal condition
x_{P}: overload factor derived from load variation model test
ΔR: resistance increase.
In a sea trial evaluation, P_{1} is the ideal power and P_{2} is the power affected by an added resistance. In the roughness evaluation tool we assume instead that P_{1} and P_{2 }are the powers corresponding to two different hull roughness.
The first equation can be rewritten as:
with
The added resistance DR is the difference in resistance between the two hull surfaces:
Hence, B is
with
A can be extracted from:
which gives
where P_{0} is the actual power that the user wants to analyse the difference around. C_{F0} is the ITTC57 plate friction. C_{R} , k and x are taken from statistics.
Theoretically, P_{0}, V_{0}, h_{D}, C_{R} and C_{FO} should be valid for the same condition, and P_{0} should be equal to P_{1}. However, sensitivity analysis have shown that deviating from this is not at all important for derived value of DP.
Difference in fuel oil consumption
The change in fuel consumption can be computed from the power difference DP, in the following way:
DFOC=DP*SFOC*24/1E6,
where
DFOC is the difference in fuel oil consumption in t/day
DP is the difference in fuel oil consumption in kw
SFOC is the specific fuel oil consumption in g/kWh.
It is common that the ship operator knows the SFOC from performance logging or engine control panel onboard. If the user does not enter SFOC, a standard value of 170 g/kWh will be used.
Verification
The method described here is a simplified procedure instead of evaluating the power for the two conditions with the full ITTC78 methods, which would require more ship specific input.
To verify that this simplified approach is close enough, a comparison has been done for one case. The power is extracted using the full ITTC78 method for various k_{s}. This is then compared with the simplified approach. DC_{F} is computed with Bowdens formula in both cases. Figure 20 shows that the resulting power difference is very close with both methods.
Verification of simplified tool method against ITTC78
Extracting statistical data
Three hydrodynamic factors are required: the load variation factor x_{P} is, the residuary resistance coefficient C_{R} and the form factor k. These can only be derived from model test. In practice, it is very unlikely that the intended user of the tool has any information on these factors. A majority of the vessels are chartered, and the ship operator has no access to the ships model test reports. Even for owned vessels, it is not likely that the superintendent can find the ships model test report. Even if they would find a model test report, the factors can well be extracted with using a different definition that SSPA standard. Every towing tank use their own version of ITTC78 method. Therefore, a better option is to use empirical values instead of ship specific.
Statistical relations
Statistics of x_{P} , C_{R} and k is extracted from the most recent, normal hulls in design condition tested at SSPA, in total 298 single skeg and 125 twin skeg. The median values are used in the tool in the webpage.
The vessels are within the following limits:
· Fn<0.35
· Cb>0.4
· 11<L<380 m
Sensitivity analysis
What is the effect of using empirical values instead of using the actual values for each ship? Table and figures below show the error for the 424 vessels from the database, expressed in %units.
It is clear that assuming C_{R} is the largest error source. Instead of using a fixed empirical value, an option could be to use regression formulas to get C_{R}. This was tried here but gave no improvement. C_{R} is simply too ship specific. However, the resulting error when assuming a standard value for C_{R} is totally acceptable considering the context where the method will be used.
With these assumptions, for 95% of the ships the expected error is smaller than ~1 percentunit. This means that if the power increase DP is predicted to be 10% with the computation tool, it means DP is between 9%11%.
Errors from assuming empirical values

For 95% of the ships the error is smaller than: 
From assuming k, x_{P} and C_{R} 
1.2 %units 
From assuming k 
0.1 %units 
From assuming x_{P} 
0.2 %units 
From assuming C_{R} 
1.3 %units 
Sensitivity analysis
Error from assuming k, x_{P} and C_{R} from statistics