EDWARD G. BOETTIGER III 



from equations 2 and j. In tlie best cases (fig. iC, dotted line) the experimental 

 loops resemble those of the model when the phase angle is 30°. The following 

 data may therefore by used to calculate the energy output: Po = 25 gm, 

 maximum recorded tension was 50 gm and Pu is one-half the tension change; 

 Xo = o.oi cm, one-half the jirobable movement;/ = lOo/sec. and the phase 

 angle, 30°. The calculation shows that in the work cycle of one muscle, 375 

 ergs are generated. In flight the insect uses two muscles in opposition. Assum- 

 ing they do equal work, the energy output per cycle for the insect is 750 ergs, 

 and the power output per second, 75,000 ergs. As the aerodynamic efficiency 

 of insect wings has been shown to be about 66 per cent (7) the power available 

 to move the insect is 50,000 ergs per second. This value is of the right order 

 of magnitude, though somewhat low considering the large size of the bumble 

 bee. An increase might be achieved if muscle tension and/or the phase angle 

 is greater in the insect than in the preparation. 



To gel the maximum size loop in the available area (the large loop of fig. 2) 

 the weight load, T', should be one-half the maximum tension. The click mecha- 

 nism acts in the same manner as a mass, and so contributes to the value of T'. 

 Wing inertia is also an important factor in determining the position of the 

 loop. 



From these calculations it is apparent that the flight muscle must operate 

 with remarkable efficiency and be able to use a very large portion of the ten- 

 sion-length area available to it. This available area is only a part of the total 

 area of figure 2 because of the restrictions to muscle shortening mechanically 

 imposed on the muscle in silu. The size of the work area depends upon the 

 position in the tension-length area of the shortening and lengthening curves. 



Shortening and Lengthening Phases. During flight the shortening and 

 lengthening strokes of the muscle are phases of a motion cycle. That the 

 motion is nearly sinusoidal has been shown by recording muscle length changes 

 during tethered flight. A tiny mirror was placed on the scutellum of a fly 

 and the time relations of its motion traced out on moving film by a reflected 

 light beam. Movements of the scutellum were shown to follow changes in 

 length of the muscles (2). If the movement is sinusoidal and the work cycle 

 uses most of the available tension-length area, the shortening and lengthening 

 phases during flight must be similar to those of the large loop in figure 2. 



Although the data obtained are only semi-quantitative, it appears that the 

 tensions during vibration are below the static tensions (curve OA of fig. 2) at 

 all lengths. In muscle, unless shortening is very slow, the tensions faU below 

 the isometric level by an amount that is a function of the shortening speed. 

 Non-fibrillar muscle driven through a cycle by an external force exhibits at 

 each length lower tensions on shortening than on lengthening. This is opposite 

 to the results reported here, and so in fibrillar muscle the shortening and 

 lengthening phases are reversed. Such a reversal was actually observed in 



