Early-stage system-level opti­miza­tion of a fast planing monohull

The advan­tages of early-stage Design Space Explo­ration (DSE) are well rec­og­nized within the fast-ship design com­mu­nity. By eval­u­at­ing design vari­a­tions in the process, DSE can sig­nif­i­cantly influ­ence both fun­da­men­tal design and business deci­sions, and enhance the effec­tive­ness of later sim­u­la­tions that rely on resource-inten­sive, higher-order methods.

This study is a col­lab­o­ra­tive effort between Hydro­Comp Inc. and FRIEND­SHIP SYSTEMS AG. It was pre­sented at the SNAME FAST 2025 Con­fer­ence, and serves as an exten­sion of the AutoPlan R&D project, which included viscous CFD analyses, towing tank exper­i­ments, and full-scale sea trials.

In AutoPlan, the opti­miza­tion of an 11-meter planing craft oper­at­ing at 27.5 knots was per­formed using high-fidelity tools such as RANS-based CFD (Sim­cen­ter STAR-CCM+). While these methods provide highly detailed and accurate results, they are com­pu­ta­tion­ally expen­sive and time-con­sum­ing, making them less suitable during con­cep­tual design stages.

This raises the central question:

Can faster, reduced-order sim­u­la­tion tools be used to effec­tively explore the design space with enough con­fi­dence to support informed design decisions?

To answer this, the study follows the same design process used in the AutoPlan project, allowing side-by-side com­par­isons of outcomes and resource require­ments, and replaces the high-fidelity CFD sim­u­la­tions with a resource-effi­cient, reduced-order workflow using CAESES® for para­met­ric hull design and NavCad® for early-stage per­for­mance prediction.

Method­ol­ogy

The table below sum­ma­rizes the method­ol­ogy followed in this study for com­par­ing the outcomes and resource require­ments of the AutoPlan project:

FC-DSE

FS-DSE uses a sim­pli­fied force model that excludes appendages and does not account for pro­peller-induced forces.

Com­pu­ta­tion is per­formed at model scale to reduce com­pu­ta­tional cost, and full-scale values are obtained using a non­stan­dard expan­sion method, in which power is treated as an expo­nen­tial function of the scale ratio.

SERO-DSE

SERO-DSE uses a more complete force model that includes lift from appendages and pro­pellers, as well as spray drag. Com­pu­ta­tion is per­formed at model scale using dimen­sional analysis of model test data, and expan­sion to full scale is carried out through a combined Froude and Reynolds scaling approach.

Obvi­ously, both approaches rep­re­sent sim­pli­fied models of reality. Neither is fully correct, and each is an approx­i­ma­tion that is useful in dif­fer­ent ways. The dis­tinc­tion lies between the data model, which defines how the hull and forces are rep­re­sented and applied, and the ana­lyt­i­cal model, which defines how the cal­cu­la­tions them­selves are performed.

Val­i­da­tion

Of course, speed is useless without accuracy, so the first step was val­i­da­tion. The NavCad pre­dic­tions for the baseline hull were compared with the original model test data and CFD results. As shown in the drag curve, the pre­dic­tions are in very close agree­ment, espe­cially at the design speed, pro­vid­ing strong con­fi­dence in the workflow.

Data Flow

As shown below, the con­nec­tion setup between CAESES and NavCad illus­trates how data flow is managed and exchanged between the two software packages using batch script­ing. Para­met­ric modeling is carried out in CAESES, which triggers the sim­u­la­tion process, while NavCad performs the cor­re­spond­ing cal­cu­la­tions and returns the result­ing per­for­mance outcomes.

Para­met­ric Model in CAESES

A para­met­ric model, using the same param­e­triza­tion employed in the AutoPlan project, was devel­oped in CAESES. The ani­ma­tions below illus­trate the design space and the range of design vari­ables explored.

The NavCad Simulation

Regard­ing the NavCad sim­u­la­tion, it is useful to look briefly under the hood at how the system operates.

Resis­tance Prediction

Resis­tance is computed using an equi­lib­rium method based on the well-known Savitsky (1964) planing theory, which has been enhanced with modern exten­sions that account for hull tunnels, spray drag, and bow-wave for­ma­tion. A key com­po­nent is the propul­sor lift model, which captures the vertical forces gen­er­ated by the shaft line described earlier.

Propul­sion Simulation

Propul­sion is handled through a more advanced process than a single, fixed cal­cu­la­tion. For each hull variant, the sim­u­la­tion performs its own sub-opti­miza­tion to deter­mine the ideal pro­peller con­fig­u­ra­tion for that specific design. This approach ensures a fair, like-for-like com­par­i­son of the best achiev­able per­for­mance for every hull. Per­for­mance is then eval­u­ated using a steady-state equi­lib­rium con­di­tion in which thrust and resis­tance are balanced.

The Opti­miza­tion Process

Since the modeling phase, sim­u­la­tion phase, and con­nec­tion setup are covered, an auto­mated loop can be applied, enabling design space explo­ration and opti­miza­tion driven by CAESES.

Design of Exper­i­ments (DoE)

A Sobol sequence was used to effi­ciently explore the design space and identify key rela­tion­ships between hull para­me­ters and performance.

Local Opti­miza­tion

A T‑search method was then used to refine the most promis­ing variants iden­ti­fied in the DoE.

Com­pa­ra­ble Per­for­mance Gains

A direct com­par­i­son is dif­fi­cult because the CFD analysis was con­ducted at model scale, used a sim­pli­fied appended-drag model and applied a scaling pro­ce­dure that differed from the standard ITTC approach. For this reason, the com­par­i­son is based on relative improve­ments rather than absolute values. Both paths, however, resulted in sig­nif­i­cant and similar reduc­tions in drag and power.

Com­par­ing relative improvement

• FC-DSE (CFD): 10.9% reduc­tion in shaft-line thrust, which cor­re­lates directly with total drag and an 11.6% reduc­tion in shaft power
• SERO-DSE (NavCad): 11.9% reduc­tion in drag and a 14.9% reduc­tion in shaft power

The dif­fer­ence in shaft-power improve­ment relative to drag is attrib­uted to pro­peller sizing effects and oblique-angle correction.

Com­par­ing Baseline with SERO-DSE Optimized

Geo­met­ric Similarity

Even more com­pelling is that both methods produced remark­ably similar final designs. The CFD-opti­mized hull is shown (see image below) in purple and the semi-empir­i­cal hull in green, while the ghosted blue line rep­re­sents the baseline hull used for both studies. Both approaches con­verged on similar strate­gies for improv­ing effi­ciency, such as nar­row­ing the chine beam and mod­i­fy­ing the deadrise. This demon­strates that the reduced-order tool is not only pro­duc­ing accurate per­for­mance esti­mates, but also iden­ti­fy­ing the same geo­met­ric trends.

• Chines shifted inward and downward
• Rising keel result­ing in a flatter deadrise
• FC-DSE exhibits a higher static draft, driven by a narrower chine beam and increased bottom warp; the deadrise is higher forward and flatter aft

Gains in Workflow Efficiency

Putting every­thing together, the semi-empir­i­cal approach deliv­ered per­for­mance gains com­pa­ra­ble to those from CFD and produced an opti­mized geometry that is nearly iden­ti­cal. A full design-space explo­ration using the semi-empir­i­cal tool can be com­pleted on a laptop in less time than it takes to run a single CFD variant on a com­put­ing cluster. This does not imply that CFD lacks value or should be ignored; rather, it suggests that CFD should be posi­tioned later in the design process. By invest­ing less time and fewer resources early on, fun­da­men­tal design deci­sions can be made before com­mit­ting to costly CFD analyses, ensuring that the result­ing data is more relevant, more accurate, and more useful to the design team.

Con­clu­sion and Future Work

In con­clu­sion, this study demon­strates that semi-empir­i­cal, reduced-order sim­u­la­tion provides a powerful frame­work for early-stage marine design. It is not a replace­ment for CFD, but serves as a highly effec­tive front-end filter that iden­ti­fies the most promis­ing can­di­dates for detailed analysis. The next steps involve expand­ing the method­ol­ogy to include off-design per­for­mance and sea­keep­ing criteria.

Duty profile optimization

This effort will extend the focused design-point opti­miza­tion to include per­for­mance at off-design speeds. By defining a time- or distance-based duty profile, the objec­tive function can be for­mu­lated as total mission fuel con­sump­tion, account­ing for partial-load effi­cien­cies of internal-com­bus­tion engines and electric motors.

Obser­va­tion of addi­tional per­for­mance parameters

Although effi­ciency at speed is typ­i­cally a key opti­miza­tion metric, the optimum design may or may not satisfy other critical criteria. It is there­fore impor­tant to incor­po­rate addi­tional per­for­mance para­me­ters into the opti­miza­tion process. These include lon­gi­tu­di­nal and trans­verse dynamic sta­bil­ity (such as por­pois­ing) and sea­keep­ing char­ac­ter­is­tics (such as impact accel­er­a­tions in irreg­u­lar seas).

Refine­ment of shape parameters

A new pre­dic­tion model for stern lift asso­ci­ated with pro­peller-tunnel aft-exit cur­va­ture is cur­rently under development.

The full paper that was pre­sented at the FAST 2025 con­fer­ence is avail­able from SNAME here.