利用空氣動力學估計白頭翁在不同飛行速度時的消耗功率

Abstract

記錄三隻白頭翁（No. 1, 2, 3）在不同距離時的飛行速度、揮翅頻率、揮翅幅度及身體傾斜角等動力學參數，根據其形態值如質量、翼展、翼面積等參數，並利用空氣動力學（aerodynamics）理論來估計其在飛行時所可能消耗的功率。 對第一隻白頭翁（No. 1）而言，其飛行距離固定為2.5m，飛行速度為2.27m／s （N＝57, SD＝0.12），No. 2的飛行距離固定為6.0m，飛行速度為6.11m／s (N＝101, SD＝0.32), No. 3的飛行距離則控制為1.5m, 3m, 4.5m, 6m, 7.5m，記錄得飛行速度介於2.55m／s至5.06m／s（N＝467）之間。結果發現揮翅頻率與揮翅幅度的大小，不隨飛行速度、個體的不同而有差異，僅有身體傾斜角隨著飛行速度的增加而減少，且其間呈線性關係。因此，白頭翁可能藉由改變身體的傾斜角來改變其飛行速度，然而其詳細的空氣動力學機制仍有待更進一步探討。 鳥類在飛行時的機械功率（mechanical power）依據其來源的不同，可分為誘導功率（induced power, Pind）、外形功率（profile power）、寄生功率（parasite power）與慣性功率（inertial power）。白頭翁在低速（2.27m／s）飛行時的機械功率中，誘導功率佔了80％的比例，而外形功率與寄生功率共佔機械功率的比例不到5％；在高速（6.11m／s）飛行時所消耗的機械功率中，誘導功率佔40％，而外形功率與寄生功率所佔的比例則升至33％。由於誘導功率與鳥類所受到的重力有關，而外形功率與寄生功率與所受到的空氣阻力有關，因此在低速飛行時大部分的消耗功率是用於克服本身所受到的重力，而在高速飛行時，大約有40％的消耗功率是用於克服自身所受到的重力外，另外33％則用來克服空氣阻力的影響。對慣性功率的消耗而言，在低速飛行時，慣性功率佔其機械功率的15％至17％，但在高速飛行時，慣性功率則佔其機械消耗的22.6％至27％，在機械功率中扮演了另一個重要的部分。因此我認為慣性功率的大小對鳥類在中、高速飛行時，可能也扮演了一個極重要的地位。 假設白頭翁的機械效率（η）的範圍在0.08至0.23之間，估計白頭翁在低速飛行時，代謝率的可能範圍為其基礎代謝率（BMR）的7.12倍至18.40倍之間，而在高速度飛行時，代謝率的可能範圍在基礎代謝率（BMR）的4.57倍至11.08倍之間。 就已知大小的鳥類而言，可以利用其質量或翼面積等資料計算其最小功率速度（minimum power speed, Vmp）與最大航程速度（maximum range speed, Vmr）。然而對同一個體（No. 3）而言，利用不同預測式所得到的結果卻有很大的差異。實際計算個體No. 3的Vmp為5.18m／s，若與預測的結果相比較，則現有的模式均無法準確的預測個體No. 3的Vmp；而其Vmr為7.89m／s，若與預測的結果相比較，則Tucker（1973）的預測式提供一個相當接近的預測值（error＝1.8％）。

The flight speeds and kinematic parameters of three Chinese bulbuls (Pycnonotus sinensis) (No. 1, 2, 3) were recorded. Using these data, and their morpholigical parameters, I estimated the power consumptions of these three birds at flight with the use of aerodynamic theory. The flight range of bird No. 1 was 2.5m and that of the bird No. 2 was 6.0m. The bird No. 3 was recorded flying at the range from 1.5m to 7.5m per 1.5m. The recorded data showed that the wingbeat frequency and amplitude did not change with flight speeds and among individuals. The body inclination angle decreased with the increasing flight speed and there existed a simple linear relationship. I suggest that the Chinese bulbuls may change their flight speeds simply by changing their body inclination angle. When flying at slow speed, the induced power of the bird was about 80% of its mechanical power requirements. The profile and parasite power were about 5% of mechanical power. At fast flight, the induced power was about 50% of its mechanical power requirements and the proportion of profile and parasite power in mechanical power were about 30%. As the induced power is concerned with the life generation and the profile and parasite power is concerned with the drag, I suggested that at slow flight most of the power expenditure is used to lift generation. But at high speed, 50% of its power expenditure is used to lift generation and another 28% to 30% is used to overcome the drag. Inertial power was sometimes ignored at early studies as some suggested the it may not be significant in the mechanical expenditure. However, in this study, the inertial power was 15% to 17% of its mechanical power at slow flight and 22.6% to 27% at fast flight. I suggest that the inertial power should not be ignored in the calculation of power consumption of flight. If the mechanical efficiency of flight muscle is assumed between 0.08 and 0.23, the possible range of flight metabolic rate could be 7.12 to 18.40 times of basal metabolic rate (BMR) at slow flight and 4.57 to 11.08 times of BMR at fast flight. The minimum power speed, Vmp, and the maximum range speed, Vmr of a known size bird can be found by their mass or other morphological parameters. However, in this study, it showed that the results from different regressions which predicts the Vmp or Vmr of the bird showed significant differences. The calculated value of Vmp and Vmr for bird No. 3 is 5.18 and 7.89 respectively. Compared with the results from prediction, no regression available could predicted Vmp precisely. In Vmr, only regression of Tucker (1973) could predicted well (error = 1.8%).