Test 14

Free heave response of axisymmetric bodies with a round base.

By Peter K. Stansby (University of Manchester, UK), Efrain Carpintero Moreno (Ghent University, Belgium)

(Download full test case data files here: SPHERIC_TestCase14.zip)


Radiation damping is an important component determining the response of floating bodies. Drag also causes damping and cannot be separated. Radiation damping force may be estimated from a linear radiation coefficient from a standard panel method, e.g. WAMIT, and the remainder may be assumed to be due to drag, enabling an estimate of drag coefficient which may be compared with reference below (Gu et al. 2018). In the experiment without any external constraint the motion provides a clean data set for validation of numerical models.

Flow phenomena

Radiation damping, drag, free response, axisymmetric bodies, hemispherical/rounded base.


Axisymmetric floats, dimensions in metres.

Boundary conditions

The body surface is smooth aluminium. 

Initial conditions

The water is stationary initially and body is released from rest, above or below water. The zero vertical level is when a stationary body is floating in still water. 


The sample rate is 200 Hz. The displacement was obtained from a Qualisys motion capture system.

Results specification

The results simply show vertical displacement (mm) variation with time (s). They are shown in Figs.1, 2, 3 in section Benchmark Results. The error bars show range of values across tests and the line shows the mean values.

Results format

Three txt files with column 1 = time (s), column 2 = mean vertical displacement (mm) with sample rate of 200 Hz are:
Float 1 offset -0.074 m : “Fl1-0p074.txt”
Float 1 offset +0.076 m : “Fl2+0p076.txt”        
Float 2 offset-0.088 m : "Fl2-0p088.txt"

Benchmark results

Benchmark results showing mean and error bars

Fig. 1 Displacement (mm) time history of Float 1, initial offset -74 mm (mean of 2 tests).

Fig. 2 Displacement (mm) time history of Float 1, initial offset +76 mm (one test).

Fig. 3 Displacement (mm) time history of Float 2, initial offset -88 mm (mean of 3 tests).

SPH Publications using this Case

    If you have published results for this case, please email the webmaster to have your papers added.


    • Gu,H., Stansby,P., Stallard,T., Carpintero Moreno,E. 2018 Drag, added mass and radiation damping of oscillating vertical cylindrical bodies in heave and surge in still water, J. Fluids Struct, 82, 343-356. doi.org/10.1016/j.jfluidstructs.2018.06.012.