目的：為了澄清相對最大攝氧量與耐力跑能力之間的關係，假設相對最大攝氧量與耐力跑能力之公式：VO2max ∙M^-b= f ∙v + c(由VO2max = a ∙M^b推導)成立，我們可以根據耐力跑能力(V)調整指數b ,以修正過去的相對最大攝氧量的計算公式，如此將能藉由修正指數b 後的相對最大攝氧量來推論耐力跑能力(FFM的指數b也做同樣的調整)。
方法：受試者為30名大專男子運動員(年齡21.5±2.83歲、身高173.9±3.35 公分、體重63.2±4.61 公斤)，其中十五人為為中長跑運動員，其他十五人非中長跑運動員。在本研究中，我們利用Lamb protocol來評估最大攝氧量，並且以Inbody2.0來測量身體組成，並且在室外的400公尺跑道接受1600公尺以及12分鐘跑走的測試。最後將實驗數據(最大攝氧量、體重與耐力跑速度)帶入VO2max ∙ M^-b = f ∙ v + c公式。經由成冪迴歸分析可得到最適合此方程式的指數b。
結果：實驗結果顯示：1)對於耐力較佳的運動員其最適的體重與去脂體重次方b各為0.9(R2 = .56)與0.76(R2 = .58)；2)對於優秀中長跑運動員其最適的體重與去脂體重次方b各為0.8(R2 = .61)與0.68(R2 = .62)。
結論：利用這些修正後的方法，運動員將更了解他們的耐力跑能力，為了評估耐力較佳的運動員的耐力跑能力，我建議利用M^0.9 與 FFM^0.76 來計算相對最大攝氧量；評估中長跑運動員的耐力跑能力，我建議利用M^0.8 與 FFM^0.68 來計算相對最大攝氧量。

Purpose: To clarity the relationship between relative maximal oxygen uptake and the endurance running capacity, the model VO2max ∙ M^-b = f ∙ v + c(modify from VO2max=a ∙ M^b) is assumed. We adjust b according to the endurance running capacity, and then we may modify conventional calculation of relative VO2max. In this way, we infer endurance running capacity from relative VO2max by considering the power b of the body mass (we have a same analysis with FFM).
Methods: Subjects are 30 college male athletics (21.5±2.83 yrs, 173.9±3.35 cm, 63.2±4.61 kg). Fifteen of the subjects are middle-long distance athletics and the others are not. In this study, we estimate relative VO2max by Lamb protocol and the body composition by Inbody2.0. They performed 1600m and 12min running test on an outdoor 400m track. The obtained data (VO2max, the body mass and the velocity of running test) are applied to VO2max ∙ M^-b = f ∙ v + c. By power regression we found the power b which matches the equation best.
Results: The present data indicate that: 1) the most suitable power b of body mass and FFM for highly endurable athletics are 0.9 (R2 = .56) and 0.76 (R2 = .58), respectively; 2) for elites middle-long distance athletics are 0.8 (R2 = .61) and 0.68(R2 = .62).
Conclusions: In these modified way, athletics will understanding more about their endurance running capacities. In order to evaluate endurance running capacity for highly endurable athletics, we suggest M^0.9 and FFM^0.76 for calculating relative VO2max; for elite middle-long distance runners, we suggest M^0.8 and FFM^0.68.

一、中文部分

林正常。(1996)。運動生理學實驗指引。台北市：師大書苑有限公司。
彭郁芬。(1998)。不同目標取向與自覺能力對耐力跑能力評估方式的相關研究。未出版的碩士論文，國立台灣師範大學體育研究所，台北市，台灣。
林正常。(2002)。運動科學與訓練。台北縣：銀禾文化。
林正常譯。(2002)。運動生理學。台北縣：藝軒圖書出版社。

二、日文部分

山地司，池田岳子，山泰行，松井秀治。(1990)。最大酸素取量陸上中長距離走，競技記占可能。研究，1，7-14。
山地司。(1997)。性影響要因。日本運動生理誌，4，81-98。

三、英文部分

Astrand, P. O., ＆ Rodahl, K. (1986). Textbook of Work Physiology. New York: McGraw-Hill Companies.
Allen, D., Freund B. J., ＆ Wilmore, J. (1986). Interaction of test protocol and horizontal run training on maximal oxygen uptake. Medicine and Science in Sport and Exercise, 18, 581-587.
Balke, B. (1963). A simple field test for assessment of physical fitness. Civil Aeromedical Research Institute Report, 63-66.
Bergh, U., Thorstensson, A., Sjodin, B., Hulten, B., Piehl, K., ＆Karlsson, J. (1978). Maximal oxygen uptake and muscle fiber types in trained and untrained humans. Medicine and Science in Sports, 10, 151-154.
Bergh, U., Sjdin, B., Forsberg, A., ＆ Svedenhag, J. (1991).The relationship between body mass and oxygen uptake during running in humans. Medicine and Science in Sports and Exercise, 23(2), 205-211.
Bergh, U., ＆ Forsberg, A. (1992). Infulence of body mass on cross country ski racing performance. Medicine and Science in Sport and Exercise, 24, 1033-1039.
Bassett, D. R.Jr., ＆ Howley E. T. (1997). Maximal oxygen uptake: Classical versus contemporary viewpoints. Medicine and Science in Sport and Exercise, 29, 591-603.
Copper, K. H. (1968). A means of assessing maximal oxygen uptake. Journal of American Medical Association, 203, 135-138.
Costill, D. L., Sparks, L., Gregor, R., ＆ Turner, M. C. (1971). Muscle glycogen utilization during exhaustive running. Journal of Applied Physiology, 31, 353-353.
Costill, D. L., Jansson, E., Gollnick, P. D., ＆ Saltin, B. (1974). Glycogen utilization in leg muscles of men during level and uphill running. Acta Physiologica Scandinavica, 91, 475-481.
Camus, G. (1992) Relationship between record time and maximal oxygen consumption in middle-distance running. European Journal of Applied Physiology, 64, 534-537.
Dobeln, W. V. (1956). Maximal oxygen uptake, body size and total hemoglobin in normal man. Acta Physiology of Scandinavia, 38, 193-199.
Froelicher JrV. F., Brammel, H., Davis, G., Noguera, I., Stewart, A., ＆Lancaster, M. C. (1974). A Comparison of three maximal treadmill exercise protocols. Journal of Applied Physiology, 36, 720-725.
Gibson, T. M., Harrison, M. H., ＆ Wellicome, R. M. (1979). An evaluation of a treadmill work test. British Journal of Sports Medicine, 13, 6-11.
Heusner, A. A. (1984). Biological similitude: statistical and functional relationships in comparative physiology. America Journal of Physiology, 246, R839-R845.
Howley, E. T. (1988). Exercise testing laboratory. In Resource Manual for Guidelines for Exercise Testing and Prescription, chap. 47. Philadelphia: Lea and Febiger.
Ingjer, F. (1991). Maximal oxygen uptake as a predictor of performance ability in women and men elite cross-country skiers. Scandinavian Journal of Medicine & Science in Sports, 1, 25-30.
Howley, E. T. ＆ Franks, B. D. (1997). Health/Fitness Instructor’s Handbook (3rd Ed.). IL: Human Kinetics.
Hawkins S. A., ＆ Wiswell R. A., (2003). Rate and mechanism of maximal oxygen consumption decline with aging. International Journal of Sports Medicine, 33(12), 877-888.
Joyner, M. J. (1991). Modeling: optimal marathon performance on the basis of physiological factor. Journal of Applied Physiology, 70, 683-687.
Krahenbuhl, G. S., Pangrazi, R. P., Petersen, G. W., Burkett, L. N., ＆Schneider, M. J. (1978). Field testing of cardiorespiratory fitness in primary school children. Medicine and Science in Sports and Exercise, 10, 208-213.
Katch, F. I., Pechar, F. I., McArdle, W. D., ＆ Weltman, A. L. (1973). Relation between individual differences in steady state endurance running performance and maximum oxygen intake. Research Quarterly for Exercise and Sport, 44, 206-215.
Kenney, W. L., ＆ Hodgson, J. L. (1985) Variable predictive of performance in elite middle-distance runners. British Journal of Sport Medicine, 19, 207-209.
McArdle, W. D., ＆ Magel, J. R. (1970) Physical work capacity and maximum oxygen uptake in treadmill and bicycle exercise. Medicine and Science in Sports, 2, 118-123.
Mayhew, J. L., ＆ Gross, P. M. (1975). Comparison of grade-incremented versus speeds-incremented maximal exercise tests in trained men. British Journal of Sport Medicine, 9, 191-195.
MacDougall, J., ＆ Wenger, H. (1991). The purpose of physiological testing. In Physiological Testing of the High Performance Athlete. IL: Human Kinetics.
Mccann, D. J., ＆ Adams, W. C. (2002). A theory for normalizing resting VO2 for differences in body size. Medicine and Science in Sports and Exercise, 34(8), 1382-1390.
Pollock, M. L., Bohannon, R. L., Cooper, K. H., Ayres, J. J., Ward, A., White, S. R., ＆ Linnerud, A. C. (1976). A comparative analysis of four protocols for maximal treadmill stress testing. American Heart Journal, 92, 39-46.
Seals, D. R., ＆ Mullin, J. P. (1982). VO2max in variable type exercises among well-trained upper body athletes. Research Quarterly for Exercise and Sport, 53, 58-63.
Siconolfi, S. F., Cullinane, E. M., Carleton, R. A., ＆ Thompson, P. D. (1982). Assessing VO2max in epidemiologic studies: Modification of the Astrand-Ryhming test. Medicine and Science in Sports and Exercise, 14, 335-338.
Takeshima, N., ＆ Tanaka, K. (1995). Prediction of endurance running performance for middle-aged and older runners. British Journal of Sports Medicine, 29, 20-23.
Vaccaro, P., Gray, P. R., Clarke, D. H., ＆ Morris, A. F. (1984) Physiological characteristics of world class white-water slalom paddlers. Research Quarterly for Exercise and Sport, 55, 206-210.
Withers, R. T., Sherman, W. M., Miller, J. M., ＆ Costill, D. L. (1981). Specificity of the anaerobic threshold in endurance trained cyclists and runners. European Journal of Applied Physiology, 47, 93-104.
Weltman, A. (1982) Practicality of inclined treadmill VO2max testing for level running exercise prescription. Journal of Sports Medicine, 22, 191-198.