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Table 1.

Collection of all valid data from horizontal and vertical cross sections of frog-produced vortex rings, showing the parameters used to calculate thrust forces, and the final results

SeriesFramesR (m)R* (m)α (deg.)vfoot (m s-1)Circ. (m2 s-1)T (s)T* (s)I (kg m s-1)Ffoot (N)Ftot (N)
Horizontal            
    k1s8c 44-45 0.0146 0.011023 14 0.54 0.00757 0.06 0.045 0.00289 0.0642 0.1284 
 45-46 0.0162 0.012231 14 0.54 0.00805 0.06 0.045 0.00378 0.084 0.168 
    k3s7 75-76 0.0108 0.008154 12 0.35 0.00713 0.088 0.066 0.00149 0.0226 0.0452 
 76-77 0.0131 0.009891 12 0.35 0.00672 0.088 0.066 0.00207 0.0314 0.0628 
 77-78 0.0145 0.010948 12 0.35 0.00866 0.088 0.066 0.00326 0.0494 0.0988 
    k3s8b 53-54 0.0131 0.009891 34 0.51 0.00562 0.068 0.051 0.00173 0.0339 0.0678 
 54-55 0.0145 0.010948 34 0.51 0.00876 0.068 0.051 0.0033 0.0647 0.1294 
 55-56 0.014 0.01057 34 0.51 0.00775 0.068 0.051 0.00272 0.0533 0.1066 
Vertical            
    k1s4c 119-120 0.00465          
 120-121 0.00555          
    k3s4b 99-100 0.00948          
 100-101 0.0094          
SeriesFramesR (m)R* (m)α (deg.)vfoot (m s-1)Circ. (m2 s-1)T (s)T* (s)I (kg m s-1)Ffoot (N)Ftot (N)
Horizontal            
    k1s8c 44-45 0.0146 0.011023 14 0.54 0.00757 0.06 0.045 0.00289 0.0642 0.1284 
 45-46 0.0162 0.012231 14 0.54 0.00805 0.06 0.045 0.00378 0.084 0.168 
    k3s7 75-76 0.0108 0.008154 12 0.35 0.00713 0.088 0.066 0.00149 0.0226 0.0452 
 76-77 0.0131 0.009891 12 0.35 0.00672 0.088 0.066 0.00207 0.0314 0.0628 
 77-78 0.0145 0.010948 12 0.35 0.00866 0.088 0.066 0.00326 0.0494 0.0988 
    k3s8b 53-54 0.0131 0.009891 34 0.51 0.00562 0.068 0.051 0.00173 0.0339 0.0678 
 54-55 0.0145 0.010948 34 0.51 0.00876 0.068 0.051 0.0033 0.0647 0.1294 
 55-56 0.014 0.01057 34 0.51 0.00775 0.068 0.051 0.00272 0.0533 0.1066 
Vertical            
    k1s4c 119-120 0.00465          
 120-121 0.00555          
    k3s4b 99-100 0.00948          
 100-101 0.0094          

Ftot,av=0.101±0.041 (mean ± S.D.).

The horizontally sectioned rings were used for force derivation after radius correction using the vertically sectioned rings: Rhor=0.0128±0.0026); Rvert=0.0073±0.0025;→ R*=0.0096±0.0026=0.755Rhor.

hor, horizontal; vert, vertical.

k1s8c, etc, series code containing frog number (k#), series number (s#) and shot indicator (a,b,c).

R, ring radius; R*, corrected radius; α, angle of ring normal axis with mean swimming path; vfoot, max. foot velocity during kick; Circ., circulation from intergral; T, extension time; T*, propulsion time; I, ring momentum; Ffoot=average propulsive force per foot; Ftot, total average propulsive force.

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