1. 1 School of Mech., Civil Engg. &Architect. Application of image processing method in water impact force measurement Northwest Polytech Univ, Xi’an Shaanxi, P.R.China, 710072 Reporter: Menghua Zhao Email:zhaomenghua@mail.nwpu.edu.cn

2. 2 School of Mech., Civil Engg. &Architect. Outlines Research Background And Goals Studies On Water entry Measurement of impact force Experimental Apparatus Techniques For Impact Force Measurement Problems analysis Sub-pixel edge detection Filter and verification of the method Filter designed for impact force measurement Results References

3. 3 School of Mech., Civil Engg. &Architect. Research Background And Goals Studies on Water entry In 1897, Worthington [1] started the investigation of water impact phenomenon. According to what done by von Karman [2], Wagner [3], Miloh [4], Moghisi [5], Duez [6], Jeffrey [7], etc, studies of the impact have been mainly of two kinds: 1.Formation of cavity and splash 2.Force of impact on the object Water entry of aluminum sphere Fig 1 (a) D=50mm,V I =3m/s (b) D=50mm,V I =5.2m/s ab

4. 4 School of Mech., Civil Engg. &Architect. Research Background And Goals Measurement of impact force Features of impact force: 1.Transience Impact force occurs in the very early stage of water entry where penetration depth is about 0~0.2 radius. 2. Dramatic change Sphere would experience an acceleration ranging from about 0~50g. In 2007,Duez’s finding [6] shows that surface properties play an important role in the formation of cavity and splash, which motivates us to test impact force under the influence of wettability. Contacting measurement method Non-contacting measurement method

5. 5 School of Mech., Civil Engg. &Architect. Experimental Apparatus Water High Speed Camera Sphere Release Device Diffuser Lights Releasing height : 46cm-184cm Water impact velocity: 3m/s~6m/s Recording speed: 2000fps Fig 2

6. 6 School of Mech., Civil Engg. &Architect. Techniques For Impact Force Measurement Problem analysis Impact force Acceleration from video Displacement from video Displacement Acceleration Difficult! Image sequences displacement velocity Acceleration (a) Acceleration filtered (a f ) Sub-pixel detection Low-pass filter Error amplified by A(A=1/Δt 2 )

7. 7 School of Mech., Civil Engg. &Architect. Techniques For Impact Force Measurement Sub-pixel edge detection Sub-pixel edge detection is achieved by a two-step procedure: 1.Localization by Canny’s method 2.Gaussian fit i, j X Y Fig 3 Profile along the movement Fig 4 Comparison of Gaussian fit and difference directly

8. 8 School of Mech., Civil Engg. &Architect. Techniques For Impact Force Measurement Filter and verification of the method Filter is chosen as digital Butterworth filter. 1.Eliminate noise as much as possible 2.Preserve real information to the best The aforementioned procedure is applied to standard sinusoidal motion: 1.A spherical nose is fixed on a Fatigue Testing Machine 2.Amplitude is 16mm and frequency is 2Hz. Parameters: 1.Low pass-band cutoff frequency:18Hz 2.Stop-band cutoff frequency:25Hz 3.Maximum attenuation in pass-band:0.5dB 4.Mininum attenuation in stop-band: 20dB Maximum error:0.13m/s 2 ; Maximum relative error: 10% Fig 5(a) Fig 5(b) Fig 6(a) Fig 6(b)

9. 9 School of Mech., Civil Engg. &Architect. Techniques For Impact Force Measurement Filter designed for impact force measurement Too few points are available from high speed camera in view of the transience of impact stage. Extra points added before impact: NP Spectrum of theoretical prediction [4] Spectrum of impact acceleration under NP Table 1 Effect of NP on η for V I =5m/s η NP 0369121518 η0.96060.96010.95540.95530.95040.95020.9499 Fig 7

10. 10 School of Mech., Civil Engg. &Architect. Techniques For Impact Force Measurement Filter designed for impact force measurement Spectrum of impact force differenced directly the parameters of zero phase low-pass Butterworth filter is set as: Low pass-band cutoff frequency is 400Hz, Stop-band cutoff frequency is 600Hz maximum attenuation is 0.5dB in pass-band minimum attenuation is 10dB in stop-band.

11. 11 School of Mech., Civil Engg. &Architect. Results Experimental results are the average values of series of spherical nose impacts with entry speed ranging from 3-6m/s, showing that: 1. The dimensionless depth where peak of C d occurs coincides with theoretical and numerical results 2.The peak of C d is smaller possibly because of filtering 3.Surface properties make little difference on the impact force before impact peak occurs

12. 12 School of Mech., Civil Engg. &Architect. References [1] Worthington, A. M. & Cole, R. S. 1897 Impact with a liquid surface, studied by the aid of instantaneous photography. Phil. Trans. R. Soc. Lond. A 189, 137–148. [2] Von Karman, T. 1929 The impact on seaplane floats during landing. Tech Rep. 321. NACA. [3] H. Wagner, Phenomena associated with impacts and sliding on liquid surfaces, Z.A.M.M. 12 (1932) 193-235. [4] T. Miloh, On the initial-stage slamming of a rigid sphere in a vertical water entry, Appl. Ocean Res. 13 (1991) 43-48. [5] M. Moghisi, P. Squire, An experimental investigation of the initial force of impact on a sphere striking a liquid surface, J. Fluid Mech. 108 (1981)133- 146. [6] C. Duez, C. Ybert, C. Clanet, Making a splash with water repellency, Nature Phys. 3 (2007) 180-183. [7]M.A.Jeffrey, W.M.Bush. Water entry of small hydrophobic spheres, J.Fluid Mech.(2009) vol. 619, pp. 45–78

13. 13 School of Mech., Civil Engg. &Architect. Thank you~