*This is a Guest Blog by our U. Mich summer intern Sam Edwards.*

I was handed off progress on Project 114 by a previous intern in the office. He had added in a feature to plot the sections of files that were input to the “Hydro2A” calc engine as well as started the design of a “Marine High School Research Vessel”, or MHSRV. My goal was to continue tinkering with Project 114 as well as to continue design on the MHSRV.

The original design of the MHSRV, was a 67 foot long catamaran with a deck beam of 25 ft, a draft of 2.5 ft and a displacement of 19 tons. After converting the offsets to a GHS file, I was able to put the hull into Project 114’s “Hydro2A” application to receive estimates of different hydrostatic properties. With the initial hull form, I found the displacement to be around 30 tons. After estimating the weight of the aluminum and outfitting, I figured that 30 tons was too much. I then changed the MHSRV dimensions to 67 ft long, 20 ft deck beam, 5 ft hull beam and 2 ft of draft. After converting this hull into GHS, I found the displacement to be 19 tons, which appeared to be appropriate.

After some further thought, I realized that the hull beam to draft ratio was perhaps not optimal. Hull speed is 1.34*SQRT(LWL) for normal vessels, which in the case of the MHSRV, is about 10 kts. At and above hull speed, wave making resistance becomes the driving factor. However, given that the MHSRV is slender-hulled, the hull speed becomes (LWL/3b)*SQRT(LWL). For a hull beam of 5 ft and L_{WL} of about 56 ft, the hull speed is about 28 kts. Since the MHSRV will be running below that speed, friction drag becomes the driving factor. To reduce the friction drag, the hull surface area should be minimized. Since a sphere has the lowest surface area for a given volume, I reasoned that the optimal hull form would be of semi-circular nature, with a hull beam two times the draft to ensure the lowest surface area to volume ratio and with a hard chine, to help lower the construction costs.

I wrote a hull generation macro that would churn out .ghs files of the 67 ft by 25 ft hull at 38,000 lbs of displacement. The different hulls varied in deadrise, from 0-32.5°, and hull beams from 3.8 to 4.7 ft and draft at half the hull beam. From there, I added a hull loop feature to the “Hydro2A” calc engine that would output the wetted surface area. Next, I plotted wetted surface area vs. deadrise to show the following relationship:

This plot indicates that the wetted surface area was minimized at a deadrise angle of 25°.

In discussing this in the office, the elders suggested that I should look for optimal dead rise angles closer to 20°. This led me to an investigation to determine what the deadrise for minimum drag would be when using the Project 114 Savitsky and Holtrop calc engines.

I created another macro that generated hulls from 4.5-7 ft that varied in deadrise, displacement and draft (which remained half of the hull beam). After running the hulls through the “Hydro2A” calc engine, I tied in the “Savitsky2A” calc engine to the “Hydro2A” calc engine so that the hydrostatic results would be input into the “Savitsky2A” spreadsheet and output results such as resistance and effective horsepower. Then, to find the hull beam required to produce a displacement of 19 tons, I fit a curve to the data from the “Hydro2A” calc engine and found that the hull beam required would be 4.58 ft with a dead rise of about 22°. Then, I fit a curve to the horsepower data from the “Savitsky2A” calc engine to find the necessary effective horsepower for the vessel would be around 115 ehp to make 20 kts. (This is single hull ehp unadjusted for catamaran hull interactions.) To determine if I was at an optimal hull shape and deadrise, I generated a curve of total resistance/displ vs. midshiparea coefficient/draft*b where R_{T }is total resistance of one hull. Each hull varied in dead rise and as a result also varied in area coefficient. I found the following relationship:

This relationship provided me with the optimal area coefficient and thus the optimal deadrise. I found that the design is towards the left hand side of the curve, which indicates there is room for improvement. The optimal midship area coefficient is 0.81 (which results in an optimal midship deadrise of 20.81°). In inputting this in the resistance calc engines the corresponding hull beam is 4.35 ft. With that beam, it would take between 105 (Savitsky) and 113 (Holtrop) ehp to achieve 20 kts. I already had picked a pretty optimal deadrise in the 4.58 ft hull beam iteration but an improvement is an improvement.

In order to find the interaction between the two hulls in terms of resistance, I referred to research done by T. Jeff Sherman on Planing Catamaran Hull and Tunnel Interactions. In his research, Sherman sought to find the interactions between the two hulls in terms of resistance. Instead of simply doubling the resistance, there were different mechanics at work. Based on his tests with symmetrical catamarans, the relationship of resistance to displacement ratio between a single 6” wide sponson and two 6” sponsons spaced 12” apart for speeds up to 20 kts is a factor of 1.12 (12% drag increase) This means that the value for EHP calculated above needs to be multiplied by 2.24 to achieve EHP for the catamaran vessel.Since the catamaran hulls are 4.35’ wide and the tunnel is 16.3’ wide, the vessel does not compare geometrically to any of the hulls Sherman used. However, based on increased distance between the hulls and the trends in the data, I used the results from the 6” sponson with the 12” spacing as an upper bound to the effective horsepower required.

In order to compare the hulls with the deadrise angles of 20.81° and 25°, I ran both hulls through the “Savitsky2A” and “Holtrop1A” calc engines from speeds of 0 kts to 20 kts. The results were as follows:

In the Holtrop calculation, the results are nearly indistinguishable. However, the hull with the deadrise angle 20.81° has a slightly higher powering requirement at the hump speed (which would actually be higher for slender hulls). In the Savitsky calculation, the hull with the deadrise angle of 20.81° is marginally better; it reduces required horsepower by 5%.

Given the results, I decided to continue with the hull with a deadrise angle of 21° (an easier angle to construct than 20.81°). Though it does not minimize the surface area, it seems to perform similarly if not better than the 25° deadrise in the Savitsky and Holtrop calculations. Below is a plot showing the two methods of power predicition shown side by side for the hull with a deadrise angle of 20.81°.

The required effective horsepower in Savitsky to achieve 20 kts is 235 ehp and 270 ehp in Holtrop.

At the bottom of this blog are some CAD model pictures of the proposed design for the MHSRV. The final particulars are 67’ LOA, 55.925’ LWL, a hull beam of 4.35’, a deck beam of 25’, a depth of 10’, a draft of 2.175’, a displacement of 19 tons and two 250 hp outboard engines.

Project 114 proved to be a very powerful tool in this design exercise. With some minor looping additions, I was able to study the optimal deadrise and hull beam for this research vessel within just two linked spreadsheets. As a student, I can say that Project 114 would be extremely helpful to use as a reference and design tool given the flexibility, customization ability and affordability of this system.

*RVH note: I asked Sam to drive Savitsky and Holtrop into the extreme edges of applicability. It looks like it provided meaningful output, but it needs to be stressed that this exercise was meant to evaluate the Project 114 philosophy, rather than establish an accepted powering calculation approach. As the senior engineer, it was particularly enjoyable to be able to ask the intern to use this system to perform parametric analyses on any variables that came to my mind and to get remarkably fast results.*