Analysis & results
Compute uses your ship inputs and the manoeuvre settings below. Reset clears all completed tests and keeps your inputs. Open saved results restores a results JSON for viewing; a setup JSON restores inputs.
IMO manoeuvring assessment
Run a standard manoeuvre to compare individual criteria.
| Criterion | Result | Maximum | Status / reason |
|---|
Assessment basis and input sources
Run the simulation, then press Play to reveal the motion. The summary metrics describe the complete computed run.
Trajectory
Equal scales · midship trackShip symbol not to scale.
Balanced auto limits lateral magnification to 4×. Lateral detail fills the available width. Both project the ship’s heading through the displayed scales. Choose Equal scales for geometric proportions.
Heading & rudder
Heading: left · Rudder and command: rightPress Play to trace the motion, or move the time slider. Show full run displays the complete result. Summary values always refer to the complete run. Heading is unwrapped and relative to the initial course. Positive angles turn to starboard.
Model diagnostics
Directional stability near straight motion
The two rudder-inflow branches are assessed separately. Positive eigenvalue real parts indicate growing perturbations in that frozen branch; a full spiral or pull-out test is still needed.
Hull, propeller and rudder force budget
| State | Component | X (N) | Y (N) | N (N·m) |
|---|
Downloads and run record
The PDF combines completed tests for the same vessel, with inputs, results and references. Its attachments retain every included results JSON and the software notices. Results JSON saves the currently displayed test, including its configuration and trajectory, for reopening.
Run record
No completed run.
Ahead operation, single propeller and rudder, constant prime resistance. No roll coupling, shallow water, wind, current, waves or stopping. Changing inputs does not alter an existing result until you run again.
For learning, teaching and early design exploration. Documented numerical checks and experimental comparisons guide ongoing validation; engineering use requires further qualification.
Inputs
1 Hull geometry
The example supplies a complete illustrative MMG input set for exploring the controls. Vessel-specific predictions require documented coefficients and their validation evidence.
Current setup: example ship.
Choose the hull file and confirm its units, axes and loading waterline. Read and check the hull, then review the preview and extracted values below.
Choose a mesh, state its units and loading waterline, then read the hull.
Enter Lpp and the location of amidships below. Waterline length is not necessarily Lpp. Applying a new hull starts a new ship setup and clears the example coefficients.
Choose a JSON file saved by this tool. A setup restores editable inputs; a simulation opens its saved results.
: inputs you can edit and upload before calculating.
: the same example with recorded results, ready to open and view.
These files use an authored example, not an experimental benchmark.
Estimate missing coefficients
Use preliminary estimates from the ship particulars. Every estimate shows its method and remains editable. Enter measured or calculated values wherever available.
For a conventional displacement monohull with one propeller and one rudder, in calm deep water at even keel. The hull regression covers 2.6 < Lpp/B < 7.1, 0.25 < T/B < 0.46 and 0.51 < Cb < 0.65. Other hulls can use imported geometry and supplied coefficients.
Complete the ship particulars, then review the estimates.
User-entered values are protected by default. Select a row to replace one deliberately. Changes to the ship particulars mark dependent estimates for review.
Ship and force model
SI units; angles labelled in degrees. Prime coefficients use instantaneous speed and Lpp.
- Synthetic example
- Illustrative inputs for learning and trying the controls; not a validated vessel.
- Model scale
- Inputs for a physical test model, using its dimensions and test conditions.
- Full scale
- Inputs for the actual ship, using its dimensions and operating conditions.
Changing this selection does not rescale any values or load another ship. Supply dimensions, mass, speed and coefficients for the same scale. Use Reset example to restore the example inputs.
Input sources and methods
Use the stated coordinate frame and normalization. Record the coefficient source and scale treatment with the configuration. Geometry-based estimates are a starting point. Review each method and replace estimates with vessel-specific coefficients when available.
Save setup
Save the current editable .json setup. An incomplete hull-based setup is saved as a draft so you can complete it later. Measured-control replay inputs retain their own format.
Benchmarks & validation
Numerical checks pass for the documented cases, including equation, integration and solver comparisons. In the comparisons with measurements, 2 of 8 KVLCC2 trials predicted by the tool’s MMG model, and 0 of 8 Esso Osaka segments predicted by a separate research model, meet all three targets; none of these trials or segments was used in fitting. The targets are this project’s screening targets, not an industry or ITTC criterion: a time-weighted root mean square error (RMSE) of at most 2° in heading, 10% of Lpp in position and 5% of the initial surge speed in surge. The tool has no validated vessel preset.
Numerical checks and solver comparisonEquations, integration and the documented comparison with ShipMMG
Numerical verification
The checks below assess the equations, integration and software behaviour. Comparisons with measurements are in the sections that follow.
| Check | Result | Coverage |
|---|
Comparison with ShipMMG
Four 100-second calculations with constant rudder angles of ±10° and ±25° were compared with the unmodified ShipMMG solver. Identical constructed coefficients, zero wake and a centre of gravity at midship make the tested force equations coincide. The largest heading difference is 7.36 × 10⁻¹¹°. No tolerance set before the comparison is recorded, so it is reported as a numerical comparison, not as a release-acceptance test.
This verifies agreement for the common formulation and stated inputs. The two programs’ default wake models and heading-reversal algorithms differ. This comparison does not assess KVLCC2 prediction accuracy or agreement with commercial software.
KVLCC2 experimental comparisonsThe tool’s MMG model on held-back trials, and two research force models
The tool’s MMG model on eight test trials
KVLCC2 assessment with the tool’s MMG model
This comparison runs the tool’s MMG model with a KVLCC2 parameter set. Five hull coefficients were fitted to five HSVA zig-zag trials, the fitting trials, and then fixed. Eight further HSVA zig-zag trials were set aside before fitting and are used only to test the predictions; these are the held-back test trials. Each calculation starts from the measured initial state and follows the recorded rudder angle and propeller rate for 100 model seconds, without resetting the predicted motion.
Two of the eight test trials meet all three targets, which were set before the trials were scored. Six exceed at least one target.
| Zig-zag | Baseline heading error (°) | Fitted heading error (°) | Baseline position error (% Lpp) | Fitted position error (% Lpp) | Fitted surge error (% initial) | Targets |
|---|
The first angle denotes rudder amplitude; the second is the heading at reversal. All eight trials start to starboard at the same nominal approach speed and loading. None was used to fit or select the fitted coefficients. The two research force models below were fitted and selected using these records, so the records are not unseen test data for those models.
These comparisons assess the full time history. Standard turning and zig-zag quantities assess particular events; agreement in those quantities does not remove an error in the complete trajectory.
Alternative force model
Alternative force model compared with the MMG model
The plots compare two models: the tool’s MMG model with the fitted KVLCC2 coefficients (labelled Fitted MMG), and an alternative force model of twenty terms, chosen using four selection records (labelled Alternative model). The alternative model is a separate research model, not part of the tool; it does not affect the tool’s results. It reduces some errors and increases others, and it is not offered as a vessel preset. Lower values indicate smaller errors. All records used here were inspected during model development, so none is unseen test data. On narrow screens, scroll plots and tables sideways.
Heading and position errors
Error growth in the six trials outside the targets
Heading error during each manoeuvre
Rudder-response and propeller-thrust comparisons
A common effective rudder delay and response time, estimated from five trials, reduce mean rudder-signal RMSE on the other eight from 1.729° to 0.059°. Mean absolute error in their first two overshoots decreases from 1.208° to 0.444°. The same hydrodynamic coefficients are used in both calculations. This control response is a research model, not part of the tool.
First and second zig-zag overshoots
Fitting the propeller inflow relation separately, as the alternative model does, reduces mean relative thrust RMS error on the four selection records from 7.52% to 2.46%. Thrust is evaluated at measured ship states and controls, so this comparison does not include errors caused by predicting the ship motion.
Propeller thrust
Measurements are from the cited HSVA and MARIN records. The archive does not provide uncertainty bands applicable to these individual time histories. The test conditions, other alternative models and unsuccessful comparisons are kept in the author’s investigation records, which are not distributed.
Complete effective-force model: not adopted
Complete effective-force model: not adopted
This study tested a separate research model, not part of the tool, as a possible improvement to it; it does not affect the tool’s results. The model fits the overall surge, sway and yaw response to the 13 HSVA zig-zag trials. It was not adopted because fitting the available trials did not produce reliable predictions of trials excluded from the fit.
The research model meets all three targets in 8 of the 13 trials used to fit it. When each trial is excluded and the model is fitted to the other 12, 0 of 13 predictions meet the targets; 2 leave the propeller model's valid range. The tool’s MMG model gives 2 passes and 6 failures in its separate eight-trial assessment.
The two pass counts come from different models and assessment procedures. They do not mean that the tool’s accuracy has fallen from 2 of 8 to 0 of 13.
Complete effective-force model: fitting and prediction errors
Force models and fitting procedure
The alternative force model above keeps some coefficients calibrated in other studies. This model instead estimates its complete effective force response and propeller inflow relation separately for each split. Three lateral force bases were examined, including all third-order rudder, sway and yaw interactions. These fits use eight fitting trials, four selection trials and four omitted pairs; the study then extends the coverage to all 13 HSVA trials.
| Force model | Fitting trials meeting the targets | Omitted pairs meeting the targets | Selection trials meeting the targets | Omitted predictions outside the valid range |
|---|---|---|---|---|
| 8 terms; independent observation errors | 1 / 8 | 0 / 8 | 0 / 4 | 0 |
| 8 terms; correlated observation errors | 1 / 8 | 0 / 8 | 0 / 4 | 0 |
| 12 terms; independent observation errors | 8 / 8 | 0 / 8 | 1 / 4 | 0 |
| 12 terms; correlated observation errors | 8 / 8 | 0 / 8 | 1 / 4 | 0 |
| 17 terms; independent observation errors | 6 / 8 | 2 / 8 | 2 / 4 | 1 |
Training and prediction accuracy
What the study shows and its limits
Continuing the fits with a corrected optimizer gradient reduces the eight-record fitting objective by 23.1%. This percentage describes the fitting objective, not an improvement in predictive accuracy, and the correction does not resolve the errors in the excluded low-angle trials. Of the 19 continued fits, 9 reach the stated stationarity criterion. The results distinguish numerical implementation from identification of the vessel response. Independent equation, integration and state-estimator checks pass. Prediction accuracy is sensitive to which manoeuvres are included in the fit, and the estimated measurement errors remain correlated. The available records therefore do not establish stable coefficients or a qualified uncertainty range. Several fits also stop before the stated stationarity criterion; these results cannot isolate a physical-model limitation from incomplete optimization.
Optimizer convergence has not been qualified. Separating the hull and rudder contributions would need a matched set of captive forces that varies drift, yaw rate and rudder angle independently, together with the test uncertainty and propulsion condition. Such measurements constrain forces that can compensate for each other when only free-running motion is fitted. The supplied captive subset contains no nonzero yaw-rate cases. A model fixed after such fitting would need a separate free-running campaign to test it.
All 13 records were inspected during model development. Excluding a record from its own fit is useful for diagnosing prediction error, but it does not make this an independent validation campaign.
Esso Osaka experimental comparisonsTwo research hull models tested on held-back trials
Nonlinear hull model on eight test segments
Esso Osaka: nonlinear hull model
This comparison uses a separate research model, not the tool’s MMG model; it does not affect the tool’s results. The research model includes wind forces, which the tool’s MMG model omits. Its nonlinear polynomial hull and rudder-interaction coefficients were fitted to 17 fitting trials: 13 standard turning and zig-zag trials and 4 random-manoeuvre segments. It was then tested on 8 held-back test segments, continuous parts of four random-manoeuvre records that were set aside before fitting. Against the source configuration, mean heading error decreased from 12.39° to 8.92° (28.0%). Mean position error changed from 31.71% to 31.34% of Lpp (1.2%). None of the eight segments meets all three targets. This model is not offered as a validated vessel preset.
The records contain the required ship motion, rudder, propeller and wind measurements. Each prediction starts once and runs continuously for its preselected duration, between 55.3 and 100 seconds. The coefficients were fixed before these predictions. The segments come from two test dates; segments from the same record are related observations.
Source configuration and nonlinear hull model
| Segment | Source interval (s) | Heading (°) | Heading change | Position (% Lpp) | Position change | Nonlinear-model surge (% initial) | All targets |
|---|---|---|---|---|---|---|---|
| R1 random_03-Aug-2020_11_04_37.csv | 702.5–771.4 | 12.42 → 6.82 | -45.1% | 27.90 → 31.65 | +13.4% | 9.71% | Not met |
| R2 random_31-Jul-2020_12_29_58.csv | 59.4–159.4 | 35.61 → 5.35 | -85.0% | 99.91 → 79.79 | -20.1% | 21.57% | Not met |
| R3 random_31-Jul-2020_12_29_58.csv | 439.0–499.7 | 8.63 → 3.92 | -54.6% | 20.47 → 9.41 | -54.1% | 10.45% | Not met |
| R4 random_31-Jul-2020_12_48_39.csv | 81.1–181.1 | 7.89 → 2.70 | -65.8% | 12.70 → 26.84 | +111.4% | 21.75% | Not met |
| R5 random_31-Jul-2020_12_48_39.csv | 429.7–507.1 | 18.20 → 14.86 | -18.4% | 35.31 → 21.71 | -38.5% | 18.82% | Not met |
| R6 random_31-Jul-2020_12_48_39.csv | 777.5–872.4 | 2.91 → 19.90 | +583.0% | 13.96 → 36.48 | +161.4% | 36.75% | Not met |
| R7 random_31-Jul-2020_12_48_39.csv | 886.5–967.9 | 7.64 → 8.76 | +14.6% | 21.24 → 24.65 | +16.0% | 16.97% | Not met |
| R8 random_31-Jul-2020_14_52_18.csv | 40.4–95.7 | 5.81 → 9.03 | +55.5% | 22.20 → 20.22 | -8.9% | 5.06% | Not met |
How the error develops
How the model was chosen
The fit of the crossflow hull model below uses an initial-speed weighting that overemphasizes a trial starting near rest. A common speed scale corrects that imbalance, but refitting the crossflow model with it does not improve its predictions of the seven standard test trials overall. Replacing the crossflow hull with a nonlinear polynomial and fitting its rudder interaction gives a better comparison on those seven trials, so that model was chosen for the test on the eight held-back segments.
The chosen fit has a projected gradient of 9.14 × 10⁻⁹, computed with direct sensitivities; these resolve the discrepancy in the finite-difference convergence check. Alternative starting-state estimates have only a small effect. A fit with greater emphasis on the targets did not meet the numerical convergence requirement and was not chosen.
Two coefficients lie at their bounds: linear yaw damping and the effective rudder location. The fitted response is sensitive to combinations of coefficients, and its improvement does not carry consistently across the held-back segments. These are model-identification and predictive-accuracy limitations.
Independent checks and published comparisons
The source-form equations were compared with the authors’ unmodified executable at 600 states and in two complete trajectories. The polynomial implementation agrees with a separate equation calculation at 331 observed states. All 64 predictions have step-refinement and independent error checks; two complete trajectories of the nonlinear model also agree with an independent adaptive integration.
Hatayama et al. (2026) report 30- and 100-second Esso forecasts. Their Table 8 reports a 100-second random-manoeuvre surge RMSE of 0.0299 m/s for MMG and 0.0126 m/s for the hybrid model in the D2/u column; D2 includes random manoeuvres in the training data. The nonlinear model’s mean over the held-back segments is 0.0164 m/s, over different 55–100-second intervals. The protocols differ, so these values do not establish a ranking or reproduce the paper’s result. A published validation study does not imply zero error in every manoeuvre.
Data: FRT-DS-ESSO, fixed source version. Reference equations: the authors’ MMG simulator. The protocols, the coefficients fitted to these records and the numerical checks are kept in the author’s investigation records; the records and the fitted coefficients are not distributed.
Crossflow hull model on seven test trials
Esso Osaka: crossflow hull model
This comparison uses a separate research model, not the tool’s MMG model; it does not affect the tool’s results. The research model is a published crossflow hull model with wind forces. Twenty standard trials have the motion and control records needed: 13 are the fitting trials, and 7 were set aside before fitting as held-back test trials. The fitted model reduces position error in six of the seven test trials. None meets all three targets, so this model is not offered as a validated vessel preset.
Each calculation follows the recorded rudder, propeller rotation and wind for 100 seconds from the measured initial state. The prediction runs continuously, without resetting it to the measured ship position or heading.
Predictions on the seven held-back test trials
| Trial | Heading (°) | Heading change | Position (% Lpp) | Position change | Fitted surge (% initial) | All targets |
|---|---|---|---|---|---|---|
| T1 14-Oct-2020 14:17:39 | 12.96 → 11.09 | -14.4% | 49.33 → 17.86 | -63.8% | 4.38% | Not met |
| T2 14-Oct-2020 14:39:54 | 8.63 → 14.23 | +65.0% | 87.70 → 101.43 | +15.7% | 5.84% | Not met |
| T3 14-Oct-2020 15:06:53 | 40.15 → 11.77 | -70.7% | 195.14 → 104.96 | -46.2% | 7.55% | Not met |
| T4 14-Sep-2020 13:51:45 | 7.03 → 9.37 | +33.4% | 58.02 → 29.31 | -49.5% | 5.59% | Not met |
| Z1 31-Jul-2020 13:29:19 | 12.70 → 3.69 | -71.0% | 79.39 → 21.86 | -72.5% | 40.39% | Not met |
| Z2 31-Jul-2020 13:50:28 | 17.26 → 10.09 | -41.5% | 121.53 → 30.60 | -74.8% | 8.01% | Not met |
| Z3 31-Jul-2020 14:10:05 | 23.72 → 21.78 | -8.2% | 159.54 → 113.78 | -28.7% | 22.19% | Not met |
Z1 begins near rest, so its percentage surge error is much larger than its absolute error. The targets were not adjusted after the results were seen.
Data selection and fitting
All 24 downloaded turning and zig-zag files were checked against the pinned source version. One cut duplicates part of an included experiment, and three other preselected windows enter stopping or reverse operation, which this ahead-motion study does not cover. These four are excluded; the remaining twenty trials are all used, whatever their prediction error.
The source rudder formulation switches between two coefficients at a different velocity condition from the one used in the force calculation. Unequal coefficients produce a force discontinuity. Both fits with the source formulation stopped without satisfying the convergence check. The fitted model therefore uses one shared rudder coefficient, which removes that discontinuity. Two optimizer starts converge to the same fitting objective, and the chosen coefficients were fixed before the seven test predictions.
Convergence does not make the fitted coefficients physically acceptable. The fitted straight-ahead resistance and linear yaw damping reach their zero bounds, and the shared rudder coefficient reaches its upper bound. These results require force-level investigation before adoption. Some source coefficient versions differ, and individual experimental uncertainty bands are not supplied.
This fit gives strong velocity weighting to a fitting trial that starts near rest. The nonlinear hull model above uses a common speed scale instead and is tested on eight held-back segments. The seven test trials of this section were used to choose that model, so they are no longer unseen test data.
Numerical checks compare the force equations with an independent mass-matrix calculation, compare complete trajectories with an adaptive integrator and halve the integration step. They pass within the stated tolerances. They establish numerical consistency, not experimental accuracy.
Sources: Osaka University trial records; reference model configuration; Miyauchi et al. (2022); Hatayama et al. (2026). Only aggregate errors calculated by this project are published here.
Published-model comparisonsResearch reconstructions and the limits of their source records
Published-model comparison
A reconstruction of the model by Alexandersson, Mao and Ringsberg (2022) (Ocean Engineering, open access under CC BY 4.0) agrees with its published tactical diameters within 0.10% and advances within 1.86%, without fitting to those results. It uses a whole-ship force model: a separate research model, not the tool’s MMG model, which does not affect the tool’s results.
The table separates agreement with the published simulation from agreement with experiments. All distances are divided by the model length, Lpp = 7 m. A positive difference means the reconstruction is larger than the stated reference.
| Turn | Quantity | Published experiment (Lpp) | Published simulation (Lpp) | Reconstruction (Lpp) | Difference from experiment (%) | Difference from simulation (%) |
|---|---|---|---|---|---|---|
| Port | Advance | 3.084 | 3.030 | 3.086 | +0.06 | +1.85 |
| Port | Tactical diameter | 3.103 | 3.296 | 3.292 | +6.11 | -0.10 |
| Starboard | Advance | 3.220 | 3.157 | 3.171 | -1.51 | +0.45 |
| Starboard | Tactical diameter | 3.364 | 3.470 | 3.473 | +3.24 | +0.09 |
Turning comparison plot and interpretation
The turning dimensions agree more closely than the complete motion histories. Over 200 model seconds, this reconstruction has heading RMSE of 32.20° for the port turn and 46.03° for the starboard turn. Its port calculation also enters nonpositive propeller inflow, outside this tool's ahead-flow assumption.
The reconstruction follows the archived added-mass formulas and MARIN data processing. Rounded published coefficients and an unresolved fixed thrust multiplier remain; the final fitted model and filtered states are absent from the archive. These limits prevent an exact reproduction claim.
The 2015 MMG paper specifies the L7 propeller, but the published inputs do not fully define the resistance extrapolation needed to reproduce its 7 m simulation.
Model identification and force checksRecovery tests, measurement sensitivity and force corrections
Model identification and force checks
These checks apply to the nonlinear hull model of the Esso Osaka comparisons, a separate research model, not the tool’s MMG model; they do not affect the tool’s results. The coefficient-estimation procedure recovers all 24 known-model trajectories in the clean synthetic recovery test. Against the measurements, the model and its variants remain outside the targets. A shared rudder-neutral correction improves the mean errors, but meets all targets in only 1 of the 17 fitting trials and in none of the held-back test trials or segments. It is not adopted.
These checks use only the Esso Osaka records described above, all of which were inspected before this study, so they include no independent test data. The model does not reproduce its fitting trials adequately, so no independent assessment has been made.
Effect of the model variants on experimental errors
| Model | Data used | Heading (°) | Position (% Lpp) | Surge (m/s) | All targets |
|---|---|---|---|---|---|
| Nonlinear model | Fitting trials (17) | 6.98 | 22.96 | 0.0157 | 1 / 17 |
| Nonlinear model | Standard test trials (7) | 9.67 | 52.40 | 0.0220 | 0 / 7 |
| Nonlinear model | Random test segments (8) | 8.92 | 31.34 | 0.0164 | 0 / 8 |
| Position/heading fit | Fitting trials (17) | 6.09 | 26.93 | 0.0183 | 0 / 17 |
| Position/heading fit | Standard test trials (7) | 8.82 | 50.32 | 0.0210 | 0 / 7 |
| Position/heading fit | Random test segments (8) | 8.64 | 32.01 | 0.0185 | 0 / 8 |
| Rudder-neutral correction | Fitting trials (17) | 5.47 | 21.43 | 0.0154 | 1 / 17 |
| Rudder-neutral correction | Standard test trials (7) | 7.58 | 50.92 | 0.0234 | 0 / 7 |
| Rudder-neutral correction | Random test segments (8) | 8.71 | 27.02 | 0.0153 | 0 / 8 |
| Four force corrections | Fitting trials (17) | 5.14 | 19.59 | 0.0161 | 0 / 17 |
| Four force corrections | Standard test trials (7) | 10.14 | 60.75 | 0.0235 | 0 / 7 |
| Four force corrections | Random test segments (8) | 8.69 | 31.23 | 0.0182 | 0 / 8 |
What the recovery test shows
Seventeen synthetic trajectories were used to estimate the coefficients, followed by seven additional synthetic trajectories with different recorded control histories. Their true responses were generated with known coefficients. Without the coefficient penalty, all 24 satisfy the stricter numerical recovery limits of 0.02° heading, 0.1% Lpp position and 0.1% initial surge speed. This checks the identification implementation; it is not experimental validation.
The coefficient penalty used in the fits shifts some poorly determined coefficients substantially, although the resulting trajectory differences are small. Deliberately filtering the synthetic velocity channels also biases the fitted coefficients. Fitting synthetic position and heading directly largely removes that effect. The noise and filters in this sensitivity test are assumed; they are not measured experimental uncertainties.
Measurement and initial-state checks
A common time-shift correction reduces the ten-second position/velocity inconsistency by only 0.37%, and the heading/yaw-rate inconsistency by 0.04%. It does not explain the main trajectory errors. Fitting experimental position and heading directly, the position/heading fit above, also fails the targets. Both starting guesses reach the same objective, but neither satisfies the numerical convergence threshold; their results are included in the figure and table above.
Estimating the initial velocities from the preceding ten seconds does not improve the results for the fitting trials overall. A separate diagnostic allows the initial velocities to use the entire future comparison window; even that reaches all targets in only 2 of the 17 fitting trials. The latter is a calibration diagnostic and is not counted as a prediction or validation result.
Force balance and model corrections
The inferred mean yaw-moment discrepancy has the same negative sign in 16 of the 17 fitting trials. Its negative mean persists when velocities and yaw rate are estimated from position and heading instead. This indicates a systematic discrepancy, but does not uniquely assign it to the hull, propeller or rudder.
The fitted effective rudder-neutral correction is −1.93°. This is a model parameter, not a demonstrated sensor calibration error. It reduces mean heading error on the fitting trials from 6.98° to 5.47° and position error from 22.96% to 21.43% Lpp. A separate extension adds four smooth sway-force and yaw-moment terms proportional to speed squared and propeller rate squared. That extension improves the fit to the fitting trials but worsens the predictions of the seven standard test trials, so it is rejected.
A capacity check fits five coefficients separately to each fitting trial. Only 4 of 17 meet all targets. Those individual fits are diagnostic and cannot be combined into a validated vessel preset. The experiments therefore remain inadequately represented by the tested parameterizations; another broad coefficient fit or a constant correction is insufficient.
Numerical checks and assessment status
The added force terms agree with a separate mass-matrix calculation. Independent scalar calculations reproduce all 96 synthetic error records and 64 corrected-model experimental error records. All 64 corrected-model predictions pass time-step refinement; four complete trajectories agree with an independent adaptive integration.
The state-dependent force discrepancies are not resolved. The model does not meet the targets on its fitting trials, it has not been assessed on an independent dataset, and the tool has no validated vessel preset. The ITTC validation procedure requires both adequate force representation and manoeuvre comparisons. Hatayama et al. (2026) provides a published hybrid-model candidate for the same Esso collection; its reported improvements do not establish that the targets can be met.
The protocols, the implementation, the fitted research parameters and the diagnostic results are kept in the author’s investigation records and are not distributed; nor are the experimental records, the coefficients fitted to them or the third-party reference configurations.
Hull input and coefficient estimatesGeometry checks, estimation methods and their limits
Hull input and coefficient estimates
STL and OBJ files provide geometry at the waterline you specify. Length between perpendiculars, loading distribution, propeller design and rudder arrangement need your input. The importer checks closed surfaces and orientation, but cannot detect every mesh defect.
The estimate assistant is restricted to conventional single-screw merchant ships at even keel within the displayed hull ratios. Each field states whether it was calculated from geometry, estimated from a published relation, assumed or entered by the user. These estimates have not been experimentally validated for your hull.
Hull derivatives use a local conversion of the Yoshimura–Masumoto 2012 equations to this solver’s velocity polynomial. It is an approximation, with a fourth-order mixed surge term and higher orders omitted. Larger drift requires particular care. The benchmark results on this page describe the documented test configurations, not hulls you import.
Methods and references
- Hull geometry reader of the OpenNAOE hydrostatics and stability engine; analytic box and Wigley comparisons check the geometric calculations.
- Yoshimura & Masumoto (MARSIM 2012) (opens in a new tab), Eqs. 3, 7, 11 and 13–18: hull and rudder estimates. The English 2012 equations are used; this is not the 2011 regression variant.
- Peeters et al. (2020) (opens in a new tab): added-mass relations attributed to Zhou et al. The yaw relation is treated as an amidships estimate.
- Chalmers DEToSC (2016), Eq. 2.21 (opens in a new tab): Taylor single-screw wake estimate. No model-to-full-scale correction is applied.
- Yaw radius, surge added-mass fraction and thrust-deduction/wake ratio are declared design assumptions. R0′ is converted from total resistance supplied at a stated speed; the tool holds it constant.
Evidence scope and sourcesDetailed status, model scope, references and measured-trial input
Detailed benchmark status
Benchmark status
This tool uses the MMG standard method to calculate surge, sway and yaw from separate hull, propeller and rudder forces. It covers ahead motion in calm, deep water for a ship with one propeller and one rudder.
The numerical checks pass within the tested scope. The KVLCC2 and Esso Osaka comparisons on this page show the prediction errors that would need to be reduced before a validated vessel preset could be offered.
| Evidence | Result | What it means |
|---|---|---|
| MMG numerical implementation | Checks passed | Equations, integration and saved results are checked for the documented cases. This does not establish vessel accuracy. |
| KVLCC2, the tool’s MMG model | 2 of 8 held-back test trials meet all targets | Six trials exceed at least one target. |
| Esso Osaka, a separate research model | 0 of 8 held-back test segments meet all targets | The nonlinear hull model reduces mean heading error by 28.0% relative to the source configuration. Mean position error changes little. A crossflow hull model tested on seven standard trials is also shown. |
The Esso Osaka comparisons use twenty standard manoeuvre windows and twelve eligible random-manoeuvre segments, all with the required motion and control measurements. Equation checks, direct fitting sensitivities and independent integration pass. No force model tested on these records predicts the held-back motion within the targets. The 2015 KVLCC2 simulation of Yasukawa and Yoshimura is not reproduced, because its published inputs do not fully define the resistance extrapolation.
The example coefficients are illustrative. Use documented vessel data for a ship-specific study. Comparable predictive accuracy with commercial software has not been established.
Model scope
The model omits roll coupling, shallow-water effects, wind, current, waves and stopping. Its resistance coefficient is constant in prime form. Accuracy outside the tested speed and loading condition has not been established. A coupled model is needed where roll materially affects the horizontal motion.
Turning distances and zig-zag overshoots are calculated. Individual criteria from IMO Resolution MSC.137(76) are assessed for declared standard-trial conditions. Stopping and overall compliance are not assessed.
References and measured-trial input
Sources
- Yasukawa and Yoshimura (2015), Introduction of MMG standard method for ship maneuvering predictions. Force model and published KVLCC2 comparisons.
- Quadvlieg and Brouwer (2011), KVLCC2 benchmark data. MARIN test conditions and uncertainty of reported manoeuvre quantities.
- Manoeuvring Models research archive. HSVA and MARIN trial records used in the time-history comparisons.
- ITTC 7.5-02-06-03, Rev. 05 (2024). Validation of manoeuvring simulation models. ITTC 7.5-02-06-05, Rev. 03 (2024). Uncertainty analysis for free-running model tests.
- IMO Resolution MSC.137(76). Standards for ship manoeuvrability.
- ShipMMG, pinned source version. Independent software used for the restricted equation comparison.
Import a measured trial
Use schema opennaoe.mmg.measured-replay/1 with a complete configuration, source information, maximum time step, and the following columns: time_s, u_m_s, v_midship_m_s, r_rad_s, x_midship_m, y_midship_m, heading_rad, delta_actual_rad, n_rps. Use SI units, increasing timestamps, unwrapped heading and axes directed forward, starboard and down, with the origin at midship.
The tool runs offline. Source links require an internet connection.
About
For learning, teaching and early design exploration. Documented numerical checks and experimental comparisons guide ongoing validation; engineering use requires further qualification.
Methods and limits
The tool uses the MMG standard method (Yasukawa and Yoshimura, 2015) to calculate surge, sway and yaw, three degrees of freedom, from hull, propeller and rudder forces. MMG is the Maneuvering Modeling Group of the Japan Towing Tank Conference, which proposed the model. It covers ahead motion in calm, deep water for one propeller and one rudder.
The model omits roll coupling, shallow-water effects, wind, current, waves and stopping. Its resistance coefficient is constant in prime form. Accuracy outside the tested speed and loading condition has not been established. A coupled model is needed where roll materially affects the horizontal motion.
Turning distances and zig-zag overshoots are calculated. Individual criteria from IMO Resolution MSC.137(76) are assessed for declared standard-trial conditions. Stopping and overall compliance are not assessed.
Each input identifies whether it is supplied, calculated, estimated, assumed or part of the example. Review the methods and supporting vessel data before using a prediction.
Version & licence
Manoeuvring · Version 1.0.0 · .
Free to use under the OpenNAOE Tool Licence. Original text and the synthetic example retain CC BY 4.0.
OpenNAOE Tool Licence, version 1.0
OpenNAOE Tool Licence, version 1.0 Copyright (c) 2026 Mohammed Abdul Hannan. All rights reserved. 1. Use. You may use this tool free of charge, for any purpose, and make copies of it for your own use. A school, university or other organization may also install it on the computers it manages, for the people who use them. It is intended for learning, teaching and early design exploration, not for commercial engineering work: if you use it for other work, including consultancy, or rely on its results, you do so entirely at your own risk. 2. Your inputs and results. This licence claims no rights in the inputs you give the tool or in the results it produces for you, and places no conditions on how you use, publish or share them. 3. Restrictions. You may not modify the tool, use any part of its code in other software, or distribute the tool or any part of its code, modified or not. Preparing your own inputs, including by editing copies of the example and configuration files the tool provides, is use, not modification. Others can obtain the tool from opennaoe.org. 4. Other licences. Third-party components are under their own licences, and any part of the tool that a third-party licence requires to be licensed under it is under that licence; the tool's notices list them. Those licences, not this one, govern those parts, and nothing in this licence restricts what they permit. 5. No warranty; no liability. The tool is provided "as is", without warranty of any kind, express or implied, including any warranty of accuracy or of fitness for a particular purpose. Its scope and limits are stated in the tool. The author is not liable for any claim, damage or other liability arising from the tool, its use, its results or any decision made with them. These exclusions apply to the extent permitted by applicable law. 6. Name and logo. This licence gives no right to use the OpenNAOE name or logo.
Third-party and data licences
Bundled shared hydrostatics/stability engine and geometry support
Copyright (c) 2026 Mohammed Abdul Hannan
The author's own code, distributed as part of this tool under the OpenNAOE Tool Licence, version 1.0, whose full terms are on the About page.
Authored explanatory text, synthetic examples and benchmark data retain CC BY 4.0.
External cited studies retain their own rights; source datasets are not licensed by this tool.
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PDF report layout
-----------------
The report layout code is by Mohammed Abdul Hannan, adapted from the OpenNAOE Hydrostatics & stability tool. The Adobe core-14 font metrics it uses are under APAFML; their complete notices follow below and are also kept with the metrics in the tool's code. The PDF standard fonts are not embedded; reports are tagged but are not claimed to conform to PDF/UA.
Adobe font-metric notices (APAFML)
--------------------------------
Copyright (c) 1985, 1987, 1989, 1990, 1997 Adobe Systems Incorporated. All Rights Reserved.Helvetica is a trademark of Linotype-Hell AG and/or its subsidiaries.
Copyright (c) 1985, 1987, 1989, 1990, 1997 Adobe Systems Incorporated. All rights reserved.
Copyright (c) 1985, 1987, 1988, 1989, 1997 Adobe Systems Incorporated. All Rights Reserved.ITC Zapf Dingbats is a registered trademark of International Typeface Corporation.
Modified by OpenNAOE (2026): only the advance widths (WX) are kept, rearranged by scripts/pdf-fonts.mjs for the
WinAnsi encoding (Helvetica) and for the Unicode characters listed (Symbol, ZapfDingbats); the header values
Ascender, Descender, CapHeight and XHeight of Helvetica are kept. Nothing else is taken from the AFM files.
This file and the 14 PostScript(R) AFM files it accompanies may be used, copied, and distributed for any purpose and
without charge, with or without modification, provided that all copyright notices are retained; that the AFM files are
not distributed without this file; that all modifications to this file or any of the AFM files are prominently noted
in the modified file(s); and that this paragraph is not modified. Adobe Systems has no responsibility or obligation to
support the use of the AFM files.
PDF engineering glyph outlines: Inter Regular 4.000.
Copyright 2016-2023 The Inter Project Authors (https://github.com/rsms/inter).
Modified by OpenNAOE (2026): subset glyph outlines and widths, scaled to thousandths of an em; nabla from Delta and four mapped signs.
This Font Software is licensed under the SIL Open Font License, Version 1.1.
This license is copied below, and is also available with a FAQ at:
http://scripts.sil.org/OFL
-----------------------------------------------------------
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
-----------------------------------------------------------
PREAMBLE
The goals of the Open Font License (OFL) are to stimulate worldwide
development of collaborative font projects, to support the font
creation efforts of academic and linguistic communities, and to
provide a free and open framework in which fonts may be shared and
improved in partnership with others.
The OFL allows the licensed fonts to be used, studied, modified and
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does not apply to any document created using the fonts or their
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DEFINITIONS
Font Software refers to the set of files released by the
Copyright Holder(s) under this license and clearly marked as such.
This may include source files, build scripts and documentation.
Reserved Font Name refers to any names specified as such after
the copyright statement(s).
Original Version refers to the collection of Font Software
components as distributed by the Copyright Holder(s).
Modified Version refers to any derivative made by adding to,
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of the Original Version, by changing formats or by porting the Font
Software to a new environment.
Author refers to any designer, engineer, programmer, technical
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PERMISSION & CONDITIONS
Permission is hereby granted, free of charge, to any person
obtaining a copy of the Font Software, to use, study, copy, merge,
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in Original or Modified Versions, may be sold by itself.
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redistributed and/or sold with any software, provided that each
copy contains the above copyright notice and this license. These
can be included either as stand-alone text files, human-readable
headers or in the appropriate machine-readable metadata fields
within text or binary files as long as those fields can be easily
viewed by the user.
3) No Modified Version of the Font Software may use the Reserved Font
Name(s) unless explicit written permission is granted by the
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TERMINATION
This license becomes null and void if any of the above conditions
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THE FONT SOFTWARE IS PROVIDED AS IS, WITHOUT WARRANTY OF ANY KIND,
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The numerical and experimental checks are documented on Benchmarks & validation.
Verify the download
SHA-256 is a fingerprint of a file’s contents. Each release of this file is published with its SHA-256 checksum, on the tool’s page at opennaoe.org and in its Zenodo record. Compute the checksum of your copy and compare the two. A matching checksum confirms that the bytes match that version; it does not establish prediction accuracy.
Windows PowerShell: Get-FileHash <file> -Algorithm SHA256
macOS: shasum -a 256 <file>
Linux: sha256sum <file>
If you find an error, use Feedback in the header. Include the build number, inputs and steps needed to reproduce it.