Extrapolate towing-tank model test results to full scale using ITTC-1957 friction scaling, correlation allowance, and optional Prohaska form factor estimation.
Scale ratio λ: —
Ship speed Vs: — m/s
Total resistance RT,s: — kN
Delivered power PD,s: — kW
Estimated k: —
Ship speed Vs: — m/s
Total resistance RT,s: — kN
Delivered power PD,s: — kW
Model–ship correlation is the standard engineering workflow used to extrapolate towing-tank model test results to full-scale ships. Because a scale model cannot simultaneously satisfy both Reynolds similarity (viscous effects) and Froude similarity (wave-making effects), practical scaling methods separate resistance into components and apply established ITTC procedures to “transfer” the model measurements to ship scale.
In most conventional extrapolation approaches, the model test provides a measured total resistance at one or more speeds. The analyst then removes the model’s frictional component (computed from ITTC-1957) to obtain a residuary term, assumes that residuary term transfers at equal Froude number, and finally reconstructs the ship-scale total resistance by adding ship-scale friction, a correlation allowance, and (optionally) a form factor contribution.
Wave-making resistance is primarily governed by the Froude number: Fn = V / √(gL). Towing-tank practice typically matches the model and ship at the same Froude number so that the dominant free-surface wave pattern scales correctly. Under this assumption, the “residuary” component (commonly treated as wave-making + remaining non-friction terms) is carried from model to ship at the same Fn.
Viscous effects depend on Reynolds number: Re = VL/ν. For typical scale ratios, the ship Reynolds number is orders of magnitude larger than the model Reynolds number. This creates a scale effect in friction and viscous pressure drag. The ITTC-1957 friction line provides a widely used empirical friction coefficient relation to compute the frictional component at both model and ship scale.
A practical “classic” workflow used in many preliminary studies can be summarized as:
This calculator implements a simplified but transparent form of that workflow so you can see how each piece influences the final ship prediction.
The form factor k is used to represent viscous pressure resistance that is not captured by a flat-plate friction line. In many practical methods, the viscous component is modeled as: (1 + k) · CF. If k is known from prior tests, similar hulls, or a dedicated Prohaska analysis, direct scaling becomes straightforward and consistent.
The Prohaska method is a widely used technique to estimate (1 + k) using low-speed model test points, where wave-making is small and the relationship between coefficients can be linearized. A common representation uses a plot of CT/CF versus Fn4, where the intercept at Fn → 0 approximates (1 + k).
In this calculator’s Prohaska tab, two low-speed points are used as a helper estimate for k. For serious work, more points improve robustness and reduce sensitivity to measurement noise.
A correlation allowance is commonly added at ship scale to account for real-world effects not captured by idealized model testing and friction lines—such as surface roughness, appendages, small geometry differences, and general uncertainty. Many preliminary studies start with a typical value around CA ≈ 0.0004, but appropriate values depend on vessel type, condition, and test practice.
Model–ship correlation is typically used alongside resistance prediction and propulsion sizing tools during preliminary design and test analysis:
Tip: For best engineering confidence, compare scaled results against a baseline resistance method (e.g., Holtrop–Mennen) at similar speeds. Large discrepancies often indicate input inconsistency (S, k, or CA) or operation outside the method’s assumptions.