# Environmental and Economic Aspects of a Containership Engine Performance in Off-Design Conditions
## 1 Introduction
Namely, the savings in fuel oil consumption per route are significantly higher compared to the ones obtained when yearly transport work is constant [19]. In addition, certain cargoes are sensitive to transportation time [20]. It was already shown that the relationship between speed and power is not cubic for speeds below the designed one, which diminishes the benefits of slow steaming [21]. It may cause misleading economic implications or even misguided policies [22]. [PERSON] et al. [23] developed a model that combines the shipping time, bunker costs, and delivery reliability, and highlighted the importance of slow steaming with the flexibility to increase the speed to counteract the randomness of port times. The authors concluded that despite the need for additional ships when slow steaming is applied, the operating cost of additional ships is lower than the savings in fuel consumption. [PERSON] [24] conducted an economic analysis based on real voyage data of a general cargo ship and concluded that when slow steaming is applied, operating costs increase and fuel costs decrease, i.e., the total costs per voyage decrease by approximately 23%. During slow steaming, the ships sail in off-design conditions and their resistance and propulsion characteristics are notably different compared to those at the designed speed [25]. Additionally, at lower sailing speeds, the main engine load is significantly reduced, which may lead to lower cylinder pressure and lower temperature, causing poor combustion efficiency and soot formation. [PERSON] et al. [26] showed that the highest value of CO is emitted from a diesel engine fueled by heavy fuel oil at half-load. In other words, considering slow steaming as an operational measure to increase the energy efficiency of ships without evaluating the main engine performance is insufficient. [PERSON] et al. [27] analyzed the operation of the main engine for a large containership in slow steaming conditions. Operation of the two-stroke marine diesel engine was simulated based on a cycle mean value approach as the best compromise between simplicity and accuracy. The authors concluded that for engines operating at reduced loads, a significant increase in the exhaust gas temperature and resultant thermal loading occur. Considering that the shipping industry is faced with increasingly stringent regulations for the control of sulfur dioxide and nitrogen oxide emissions [28], [PERSON] et al. [29] combined data for wind, waves, and current with the Automatic Identification System (AIS) data to establish a model for the NOx emissions' prediction of the main engine for bulk carriers. To select the sailing speed in slow steaming conditions which could result in an optimal correlation between reduced fuel costs, CO2 emissions, and NOx emissions and increased operating costs, the propeller-delivered power, engine performance and emissions must be estimated with a high level of accuracy. In this paper, the propeller-delivered power was derived from the experimental measurements for the ship at a model scale. The engine performance and emissions were calculated with a thermodynamic 1D/0D engine model. The goal of the research conducted was to investigate the influence of engine variant on the selection of slow steaming speed and its environmental and economic impact. This research was conducted on a case study of a containership with three different two-stroke marine diesel engine variants (six-cylinder, seven-cylinder and eight-cylinder engine). The delivered power is extrapolated based on the measurements in towing tank for the range of speeds from 16 knots to 22 knots. The thermodynamic 1D/0D engine simulation model incorporates an in-cylinder combustion model, turbocharger model and emission submodels which can calculate NOx and soot emissions. The novelty introduced in this article is the use of a comprehensive thermodynamic model of the two-stroke marine diesel engine to calculate the fuel consumption and emissions of NOx and soot in slow steaming conditions.