Interpretation of the Data
Speeding up:
Each time a voyage starts, fuel usage relative to miles travelled per hour is extraordinary high the first hour of the voyage. This is because it requires much power to speed up the ship.
Currents:
In a scenario where the ship sails “with” the current it requires less power for the ship to move with a certain Speed Over Ground (SOG). In contrast it will require more than average power for a ship to move
Regression and Formulation
In order to find out the optimal sailing speed, the columns actual speed (“ACT.SPEED SOG[KN]”) and the fuel consumption(“ACT.FOC PER NM BASED ON SOG [KG/NM]”) are used. The graph is plotted, and the interpolation tool is used to obtain the fitted equation for speed vs. fuel usage graph. The resulting equation was the following:
y = 0.7052x^2 -15.79x + 118.82
In the equation, x represents the speed so dividing the distance by x and multiplying it with the fitted equation, we have obtained our objective function which we wanted to minimize. Then, taking the derivative and setting it equal to zero, the optimal speed to minimize the fuel usage (so that the emissions) throughout the journey is obtained.
Then, using the optimal speed we have derived and the data that is provided, we have calculated the potential emission savings. To do this, we have simulated the all journey with the optimal speed we have found. While simulating the journey, there were constraints that needed to be carefully analyzed. For example, ship should not be late to its destination. Therefore, minimum sailing speed is calculated by dividing distance of the journey to duration between start of the journey and Estimated Arrival Time (ETA). Consequently, the maximum of minimum sailing speed and optimal sailing speed was taken in order to prevent the delay of the ships. Considering these constraints, potential emissions are calculated for different journeys that is provided in the data set.