# Numerical Analysis of the Take-Off Performance of a Seaplane in Calm Water
## 5 Results and Discussion
### Resistance  
Resistance characteristics, including water resistance and air resistance, are the main concern of a seaplane design. Especially, the magnitude and corresponding speed of the resistance hump are critical in determining take-off performance and the requirement for propulsion. It can be seen from Figure 16 that there are two humps of total resistance: the first hump occurred at the speed of 4 m/s when the seaplane was transiting from the displacement to the planing stage, and the second hump occurred at the speed of 14 m/s around the corner of the takeoff. At the first hump, the hydrodynamic resistance contributed 97% of the total resistance and the residual thrust was about 15%. For the second hull, the hydrodynamic resistance contributed 65% of the total resistance while the residual thrust was only 7%. Since the propeller thrust decreased with speed, it is surprising to find that the second hump was a more critical point in a takeoff compared with the first hump, which was not concerned in previous studies [14; 15]. As shown in Figure 16, it is no doubt that hydrodynamic resistance played the dominant role in total resistance. Next, the hydrodynamic resistance characteristics will be further analyzed. Based on the planing theory, the hydrodynamic resistance can be divided into the pressure component and friction component that fundamentally satisfy the relationship \(R_{w}=\triangle\tan\tau+0.5\rho v^{2}S_{w}C_{f}\). The pressure resistance, including the wave drag and viscous drag due to the separation of boundary layer, is proportional to the water load and trim angle. And the friction resistance could be evaluated with the dynamic pressure, wetted surface area, and skin friction coefficient. Figure 16: Variations of resistance components against speed. Figure 15: Trim curve against speed. With CFD-post technique, the pressure component and friction component acting on forebody and afterbody could be calculated directly as shown in Figure 17. At low-speed regime, the main source of forebody pressure resistance was the generation of water waves at bow. Also, the water flow separating at step caused turbulence behind the step, which added to the pressure resistance. In theory, the pressure resistance is supposed to increase as the trim rises with speed. Surprisingly, we noticed that the pressure resistance started to decrease at a velocity of 5 m/s when the trim angle was still rising. This phenomenon is related to the convex surface of the fuselage. At low speeds, the water surface encountered with the convex bow making the local trim angle of the stagnation line higher than the trim angle measured from the keel, which produced a larger backward component of pressure force that increased the resistance. As the seaplane heaved, the stagnation line moved backward to the straight section, and the local trim angle has been reduced, resulting in the decrease of the pressure resistance. It can be seen from the Figure 18a that the wetted surface area of forebody gradually decreased that limited the increase of friction resistance. Additionally, we found the reversed flow in the spray area provided a forward shear force that could slightly decrease the overall friction resistance. For the afterbody, due to the upward stern, the pressure acting on the afterbody always provided a forward component that reduced the total hydrodynamic resistance. Since the fuselage is narrower toward the stern, the afterbody sinked farther into the water as the trim increased, significantly increasing the wetted surface area and afterbody friction resistance. Taken together, the increase of pressure resistance at forebody and friction resistance at afterbody determined that the total hydrodynamic resistance reached the first hump at the velocity of 4 m/s. At rest, the step was entirely submerged under the water surface. As shown in Figure 12, with the water flowing over the step, the low-pressure region formed behind the step essentially forced the water surface to sag and allowed air to be sucked in.