Thin or bulky: Optimal aspect ratios for ship hulls

Boucher, Jean‐Philippe; Labbé, Romain; Clanet, Christophe; Benzaquen, Michael

doi:10.1103/physrevfluids.3.074802

Cited by 12 publications

(18 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many existing studies use the inviscid theories of Michell (1898) and Havelock (1919, 1932) to investigate the optimum design of ship hulls (Zakerdoost, Ghassemi & Ghiasi 2013; Zhao, Zong & Zou 2015; Dambrine, Pierre & Rousseaux 2016; Boucher et al. 2018). However, asymmetric hull shapes are not addressed, since there is no well-accepted predictive theory for the effect of asymmetry on wave resistance.…”

Section: Introductionmentioning

confidence: 99%

Wave drag on asymmetric bodies

et al. 2019

View full text Add to dashboard Cite

An asymmetric body with a sharp leading edge and a rounded trailing edge produces a smaller wave disturbance moving forwards than backwards, and this is reflected in the wave drag coefficient. This experimental fact is not captured by Michell's theory for wave drag (Michell 1898). In this study, we use a tow-tank experiment to investigate the effects of asymmetry on wave drag, and show that these effects can be replicated by modifying Michell's theory to include the growth of a symmetry-breaking boundary layer. We show that asymmetry can have either a positive or a negative effect on drag, depending on the depth of motion and the Froude number.

show abstract

Section: Introductionmentioning

confidence: 99%

Wave drag on asymmetric bodies

et al. 2019

View full text Add to dashboard Cite

show abstract

“…The viscous resistance R viscous accounts for the effects of viscosity which are not present in Michell's model. In (6), C F is the viscous drag (or friction) dimensionless coefficient and A (in m 2 ) is the surface area of the ship's wetted hull. The coefficient C F is a positive constant.…”

Section: 1mentioning

confidence: 99%

“…The situation is even more complicated in reality, but statistical observations can be gathered concerning the main characteristics of ship hulls. In [6] 1. Comparison of the area Froude number F r, the length L of the optimal domain and the length Froude number F r L (a = 1) 7.1.2.…”

Section: 1mentioning

confidence: 99%

See 1 more Smart Citation

Continuity with respect to the speed for optimal ship forms based on Michell's formula

Dambrine¹,

Pierre²

2023

MCRF

View full text Add to dashboard Cite

<p style='text-indent:20px;'>We consider a ship hull design problem based on Michell's wave resistance. The half hull is represented by a nonnegative function and we seek the function whose domain of definition has a given area and which minimizes the total resistance for a given speed and a given volume. We show that the optimal hull depends only on two parameters without dimension, the viscous drag coefficient and the Froude number of the area of the support. We prove that, up to uniqueness, the optimal hull depends continuously on these two parameters. Moreover, the contribution of Michell's wave resistance vanishes as either the Froude number or the drag coefficient goes to infinity. Numerical simulations confirm the theoretical results for large Froude numbers. For Froude numbers typically smaller than <inline-formula><tex-math id="M1">\begin{document}$ 1 $\end{document}</tex-math></inline-formula>, the famous bulbous bow is numerically recovered. For intermediate Froude numbers, a "sinking" phenomenon occurs. It can be related to the nonexistence of a minimizer.</p>

show abstract

“…The effect of bathymetry, or water depth, on the drag of an object moving through a body of water has numerous important applications, ranging from naval and coastal engineering to boat sports and swimming [1,2]. It is well known that there is significant difference between the waves generated by a body moving in deep water and shallow water, and this is reflected in the drag properties.…”

Section: Introductionmentioning

confidence: 99%

Hysteretic wave drag in shallow water

Benham,

Bendimerad,

Benzaquen

et al. 2020

Preprint

View full text Add to dashboard Cite

During motion from deep to shallow water, multiple equilibria may emerge, each with identical drag -a phenomenon that can be explained by a localised amplification of the wave drag near the shallow wave speed. The implication of this is the emergence of several previously unstudied bifurcation patterns and hysteresis routes. Here, we address these nonlinear dynamics by considering the quasi-steady motion of a body between deep and shallow water, where the depth is slowly varying. We survey several theoretical models for the drag, compare these against our tow-tank experimental measurements, and then use the validated theory to explore the bifurcation patterns using two parameters: the depth of motion and the forcing. In particular, using a case study of a lake with a sinusoidal depth profile, we illustrate that hysteresis effects can play a significant role on the speed of motion and journey time, presenting interesting implications for naval and racing applications.

show abstract

Thin or bulky: Optimal aspect ratios for ship hulls

Cited by 12 publications

References 19 publications

Wave drag on asymmetric bodies

Wave drag on asymmetric bodies

Continuity with respect to the speed for optimal ship forms based on Michell's formula

Hysteretic wave drag in shallow water

Contact Info

Product

Resources

About