time and average number present into a 

 standard against which performance can be 

 evaluated. 



The reader will recall (figure 1) that 

 we defined delay in terms of a minimum aver- 

 age time which we assumed would occur at low 

 numbers present. In practice, of course, 

 group behaviour effects might well lead to 

 a lower average time at moderate than at low 

 numbers present. Thus, it would be unreal- 

 istic to define capacity in terms of an 

 untested assumption. 



A simple way to avoid this and still to 

 provide a standard for evaluation is as fol- 

 lows : 



Let T = average time 



N = average number present 



T/N = average usage time 



Now il in fact T is not decreased by in- 

 creasing N, we have T = k, a constant. Then 

 if we let y = k/n and x = N, we have the 

 simple hyperbola 



transposing, 



xy = k 



y= k/x 



(equation 1) 

 (equation 2) 



The model given by equation 2 is shown in 

 figure 3, arbitrarily using T = k = 150 and 

 some arbitrary values of N. 



To use this model one would calculate 

 an average T from a series of T's observed 

 over a range of N, use his average T = k in 

 equation 2, and plot the hyperbola with his 

 values of N. Then where particular average 

 times increase with numbers present, his 

 observed values of average usage time will 

 be higher than those postulated by the model. 

 For the average number present at which this 

 begins to occur we propose the term capacity . 



The reader will note that observed 

 average usage times might also be less than 

 those given by the model. This would mean 

 that groups behaviour is decreasing the 

 average time for the average numbers present 

 at which this happens. 



AN ALTERNATIVE APPROACH 



It usually will be very hard to get, 

 under comparable conditions, enough points 

 on graphs like figure 3 to tell where capa- 

 city is reached. But one still may judge 



whether crowding hinders passage in a parti- 

 cular fishway section. Under the hypothesis 

 of delay due to crowding we would expect, 

 during an interval of non-declining entry 

 rate, that the relationship of exit rate to 

 numbers present would at some point fail to 

 increase. If we found this to be true over 

 a widely changing entry rate, we could not 

 interpret it simply on the basis of numbers 

 present. A changing entry rate might itself 

 stimulate movement out of a pool or section. 



So let us define this relationship only 

 for a period of relatively constant entry 

 rate. From tables 3 and 4 of Elling and 

 Raymond (1958) we give in table 1 the numbe 

 bers entering an6 leaving, and the numbers 

 present in the lowest fishway pool during 

 each of the first 30 minutes of a test. 



During minutes 6-22 the entry rate was 

 relatively constant; we accordingly plot, in 

 figure 4, exit rate on numbers present for 

 minutes 6 to 22. 



From the data of figure 4 we reject the 

 hypothesis that exit rate is independent of 

 numbers present (_t is about 15, with 15 de- 

 grees of freedom). Since this decreasing 

 exit rate occurred when entry rate was quite 

 stable, we conclude that movement was hin- 

 dered by crowding. 



For one section of a fishway the capa- 

 city, as defined in the previous section, 

 could be evaluated from a series of such 



2000 4000 6000 



Average Number Present (N) 



Figure 3. — Relationship between average 

 usage time and average number present 

 assuming average time Is independent 

 of number present. 



