INTRODUCTION 



69 



o.-S 



• - a 



— 



£ rt 



£.5 



50 

 Efficiency, % 



Fig. 31. A representation of the power produced as a function of the effi- 

 ciency of using the force being applied. The efficiency of power production is 

 equal to 50% when the power delivered is at its maximum value. (From Odum 

 and Pinkerton, American Scientist, 43, 331, 1955; courtesy the authors and 

 American Scientist, Princeton, N. J.) 



resistance. You will see that his hand is rapidly displaced, but that you 

 are exerting very little force. Second, have him offer his maximal re- 

 sistance. You will see that his hand is displaced at a minimal rate, but 

 that you are now exerting your own maximum force. 



One interesting point seems worth an appreciable digression here. This 

 concerns the design of biological structure from the point of view of 

 energy expenditure. Are biological systems designed to give maximum 

 efficiency (least energy loss) or maximum power deliverable? Clearly, 

 we could conceive that some systems producing energy could be designed 

 for one purpose and some for the other, and perhaps some for other 

 purposes, too. What differences are involved in making this decision? 



In an interesting paper on this topic, Odum and Pinkerton point 

 out that the work done depends on the forces and rates. When the 

 rates of displacement are very small, there is maximum force exerted. 

 The power delivered is the product of these two factors so that, since v 

 is very small, the power delivered is small. On the other hand, when the 

 force is very small, the value of v is large, but the product is again small. 

 It is then plausible, and they actually prove, that at intermediate forces 

 and displacement rates, the power delivered is greater than at the two 

 extreme values we have mentioned. This is sketched in Fig. 31. In the 

 cases they discuss, Odum and Pinkerton were able to deduce the exact 

 form of the curve. There is an optimal force to be expected for maximum 

 power delivered. At this value of the force, the efficiency proved to be 

 only 50% for ideal, loss-free systems; for real systems it is less than 

 50%. That is, by exerting either a very large force at a slow rate or a 

 very small force at a great rate, the physical efficiency is greatest, ap- 



