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An ergonomic study on the optimal gear ratio for a multi-speed bicycle
International Journal of Industrial Ergonomics 23 (1999) 95—100
An ergonomic study on the optimal gear ratio for a multi-speed bicycle Chang K. Cho!, Myung Hwan Yun",*, Chang S. Yoon#, Myun W. Lee! ! Department of Industrial Engineering, Seoul National University, Seoul 151-742, South Korea " Dept of Industrial Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea # Arthur D. Little International, Inc. 13th Floor. Kyobo Building, 1-1 Chongro, Chongro-ku, Seoul 110-714, South Korea Received 15 September 1996; received in revised form 22 January 1997; accepted 25 June 1997
Abstract With respect to human performance and power efficiency, the gear system in typical multi-speed bicycles is often biased and redundant. A preliminary user survey in this study reveals that the average utilization of each shift for a multi-speed gear system is less than 40%. This study attempts to measure the optimal pedaling rates for given power output levels as well as design the optimal number of gears and the corresponding gear ratios. Heart rate, ratings of perceived exertion and electromyogram of quadriceps femoris for five male subjects are measured at three different power output levels (40, 80 and 120 W) and four different pedaling rate levels (40, 60, 80 and 100 rpm). Various riding conditions including slope gradient and cruising velocity are also converted to the equivalent power output level. The optimal pedaling rates for the given power output are 40 rpm for 40 W power output level, 40 — 60 rpm for 80 and 120 W power output levels. By using a heuristic rule which finds the least number of gears and the most efficient gear ratio under the given physiological condition, a four speed gear system with the ratio of 0.26—0.38, 0.38—0.53, 0.53—0.7 and 0.7—1.0 is recommended as the most efficient gear system. Based on the optimal gear ratio suggested in this study, an ergonomic gear system using a novel/unique type of planet gear sets (US patent No. 5 378 201) is developed. Relevance to industry A bicycle’s gear system is frequently designed without ergonomic expertise in terms of performance and efficiency. This study provides guidelines, design specifications, and performance measures to design an efficient bicycle gear system. This study also contributes valuable finding regarding the optimal performance during bicycle riding, thereby facilitating the efficiency and effectiveness of human exercise using a bicycle. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Gear ratio; Bicycle riding; Ergonomic design; Human performance; Multi-speed bicycle
* Corresponding author. Tel.: #82 562 279 2207; fax: #82 562 279 2870; e-mail: [email protected]. 0169-8141/99/$19.00 Copyright ( 1999 Elsevier Science B.V. All rights reserved PII S 0 1 6 9 - 8 1 4 1 ( 9 7 ) 0 0 1 0 4 - 2
96
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
1. Introduction In accordance with the growth of bicycle market, multi-speed gear systems have become increasingly popular. In Korea, more than 60% of the bicycles sold in 1995 had a multi-speed gear system (Korea Bicycle Industry Institute, 1995). A preliminary user survey revealed that the average utilization of multi-speed gear system is less than 40%. Fig. 1 displays the nominal gear values in commercialized multi-speed gear system and their actual gear ratios. Gear ratios in Fig. 1 are biased and even redundant. Thus, with respect to human performance and power efficiency, current design of gear system is inefficient and hard to use because of the many number of unnecessary shifts. This study not only measures the optimal pedaling rates for given power output levels, but also designs the optimal number of gears and corresponding gear ratios.
Fig. 1. Gear ratio distribution of the commercialized multispeed gear system.
2. Background During the bicycle riding, the power generated from human muscles is used to overcome the rolling, air, acceleration and gradient resistance. Whitt and Wilson (1982) calculated the required power output relevant to the given bicycle velocity and slope gradient [(Eq. (1)].
G C
D A H
B
C s a m ¼" V +mg C # # 1# 8 R g 100 g +m #0.5C Ao(C #C )2 , D V W
(1)
where ¼ is the power required on pedal, C the V bicycle velocity, g the transmission efficiency, &m the weight of bike and man, g the gravity acceleration, C the rolling resistance, s the slope gradiR ent, a the bicycle acceleration, m the moment of W inertia, C the air resistance, A the frontal area, D o the air density and C the head wind. 8 In the above equation, air and acceleration resistance tend to be ignorable for the non-competitive cyclist. Thus, bicycle velocity and slope gradient can be considered as major factors in
Fig. 2. Force—velocity relationship on the bicycle.
determining the power requirement during the normal, non-professional level, bicycle riding. Power output during bicycle riding can be expressed as the product of pedaling force and pedaling rate. This finding suggests that a trade-off exists between pedaling force and pedaling rate for a given power output. The physiological characteristics of human muscle and power output, called ‘force—velocity relationship’ can explain the tradeoff (Sj+gaard, 1978; Faria and Cavanagh, 1978). As Fig. 2 indicates, under the same power level, a human can either pedal fast with a small amount of force (high-speed gear), or pedal slowly with a large amount of force (low-speed gear). Thus, the main function of multi-speed gear system can be considered to provide the shifting mechanism that a human can select his/her own combination of pedaling force and rate under certain degree of power output (Kyle, 1988; Whitt and Wilson, 1982).
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
Therefore, the optimal gear ratio of a bicycle can be defined as the most physiologically efficient combination of pedaling force and pedaling rate. Previous studies revealed that the optimal pedaling rate exists for non-competition cyclist between 40—80 rpm [(Grosse-Lordmann and Mu¨ller, 1936; Brown, 1944; Japanese Bicycle Product and Technical Institute, 1968; Seabury et al., 1977; Carnevale and Gaesser, 1991)]. Above studies used various physiological measures such as oxygen consumption, heart rate, and EMG as well as riding performance.
Table 1 Analysis results of variance (ANOVA)
3. Methods Five male undergraduate students participated in this study. (age: 23—24, height: 165—180 cm, weight: 59—73 kg). To obtain the optimal gear ratio, three different power output levels (40, 80, and 120 W) and four different pedaling rates (40, 60, 80, and 100 rpm) were used as independent variables. (Russel and Dale, 1986). Heart rate, ratings of perceived exertion, and electromyogram of quadriceps femoris were measured at three different power output levels. The experimental design was 3 by 4 factorial design without repetition. Ergometer and Pulsemeter (Tunturi F250) were used to provide a constant power level and measure the heart rate. Metronome (TAKEI MP50) was also used to provide the signal relevant to the given rpm. EMG was measured by surface electrodes (S&W) and a telemetry system (SANEI, medical telemeter 270) and digitalized to IBM PC through an AD converter (UEI 200). 4. Results Table 1 summarizes the analysis results of variance (ANOVA) for the effect of power output and pedaling rate on the heart rate, RPE, and EMG, respectively. According to those results, power output and pedaling rate significantly influence heart rate and RPE, but not EMG. Although EMG does not significantly change, the root mean square values of EMG increased with power output.
97
Heart rate Source
DF
SS
F-value
P-value
Power Output (A) Pedaling Rate (B) A*B
2 3 6
2237.9 5056.8 245.9
10.64 16.02 0.39
0.0001 0.0001 0.8821
RPE Source Power Output (A) Pedaling Rate (B) A*B
DF 2 3 6
SS 0.6705 1.7775 0.2029
F-value 5.99 10.58 0.6
P-value 0.0048 0.0001 0.7255
EMC Source Power Output (A) Pedaling Rate (B) A*B0
DF 2 3 6
SS 0.0081 0.0271 0.0286
F-value 0.63 1.41 0.74
P-value 0.5383 0.2519 0.6191
Fig. 3. Optimal range of pedaling rate for the given power output.
Results obtained from Duncan’s grouping for heart rate and RPE indicate that the physiologically optimal pedaling rates are 40 rpm for 40 W and 40—60 rpm for 80 and 120 W, respectively. Fig. 3 depicts the area of optimal pedaling rate for the given power output. By using the above statistical analysis result, the optimal pedaling rates for the given power output level can be derived. To obtain the optimal gear ratio based on the results of optimal pedaling rate, additional factors should be considered (De Groot
98
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
Fig. 4. Procedure to determine optimal gear ratio. Fig. 6. Optimal gear ratio for given riding condition in terms of slope gradient and cruising velocity.
et al., 1994; Patterson and Moreno, 1990; Raine and Amor, 1991). Fig. 4 presents the related factors and procedure for determining the optimal gear ratio. By using Eq. (1), various riding conditions including slope gradient (0°—15°) and cruising velocity (0—5.5 m/s) were converted to the equivalent power output levels (see Fig. 5). Above riding conditions are realistic because the average capacity of human engine on the bicycle is about 0.1 hp if we confine attention to the non-competition cyclist (Whitt and Wilson, 1982; Burke, 1986). By applying the calculated power requirement to the result of this study, the optimal pedaling rate for each riding condition can be calculated. And with
wheel revolution relevant to the cruising velocity, it can be converted again into the optimal gear ratio for each riding condition, (see Fig. 6). The optimal gear ratio in Fig. 6 has both an upper and lower boundary, implying that any gear ratio between this range is physiologically optimal for the given riding condition in terms of slope gradient and cruising velocity. Therefore, by using the heuristic rule in Fig. 7, the least number of gears and most efficient gear ratio can be derived. For example, when we confine the gear ratio equivalent to the customized 18-speed gear system (0.26—1.0), only four gear ratios of 0.26—0.38,
Fig. 5. Power output relevant to the riding condition in terms of slope gradient and cruising velocity.
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
99
0.38—0.53, 0.53—0.7, 0.7—1.0 satisfy the condition of the physiological optimum (see Fig. 8).
5. Conclusions and discussion
Fig. 7. Heuristic procedure to find the least number of gears and the most efficient gear ratio.
This study has presented the optimal pedaling rates for the given power output. Heart rate and RPE are used as a physiological criteria. Although the change of power level and pedaling rate does not influence EMG, root mean square values of EMG increase with power output. While direct measurements of energy consumption, such as VO , were not used in this study, it is 2 argued that heart rate and RPE can be a sensitive measure of energy consumption under the controlled conditions (Astrand and Rodahl, 1970). Results in this study imply that a fewer number of gears which are optimal can provide a performance equivalent to the multi-speed gear system. As expected, reducing the number of gears without a loss of physiological efficiency would result in easier gear shifting. By using the results in this study, an ergonomic gear system by Lee (1995), (U.S. Patent 5.378.201) has been developed. Until now, initial consumer response to the prototype has been favorable.
References
Fig. 8. Recommended optimal gear ratio for four-speed gear system.
Astrond, P., Rodahl, K., 1970. Textbook of Work Physiology. Mcgraw-Hill KogaKusha, Tokyo. Brown, W., 1944. Cycle gearing in theory and practice. Cycling, July 5, 12—13. Burke, E.R., 1986. Science of Cycling. Human Kinetics, Champaign. Carnevale, T.J., Gaesser, G.A., 1991. Effect of pedaling speed on the power—duration relationship for high-intensity exercise. Medicine and Science in Sports and Exercise 23 (2), 242—246. Faria, I.E., Cavanagh, P.R., 1978. The Physiology and Biomechanics of Cycling. Wiley, New York. De Groot, G., Clijsen, W.L., Clarijs, J., Cabri, J., Antonis, J., 1994. Power, muscular work, and external factors in cycling. Ergonomics 37 (1), 31—42. Grosse-Lordemann, H., Mu¨ller, E.A., 1936. Der Einfluss der Leistung und der Arbeitsgeschwindigkeit auf Arbeitsmaximum und den Wirkungsgrad beim Radfahren. Kaiser Wilhelm Institut fu¨r Abeitsphysiologie. Dortmund-Mu¨nster. Korea Bicycle Industry Institute, 1995. Bicycle News No. 6. Seoul, Korea. [Korean]
100
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
Kyle, C.R., 1988. The mechanics and aerodynamics of cycling. In: Burke, E.R., Newsom, M.M. (Eds.), Medical and Scientific Aspects of Cycling. Human Kinetics, IL, pp. 235—251. Japanese Bicycle Production and Technology Institute, 1968. Report of the Bicycle Production and Technical Institute. Lee, M.W., Lee, W.I., Kim, M.S., 1995. Multi-geared bicycle transmission assembly comprising internal gear sets. United States Patent. d5 378 201. Patterson, R.P., Moreno, M.I., 1990. Bicycle pedalling force as a function of pedalling rate and power output. Medicine and Science in Sports and Exercise 22 (4), 512—516. Raine, J.K., Amor, M.R., 1991. Design and energy consumption of a human-powered vehicle. International Journal of Vehicle Design 12 (5), 630—643.
Russel, J.C., Dale, J.D., 1986. Dynamic torquemeter calibration of bicycle ergometers. Journal of Applied Physiology 61 (3), 1217—1220. Seabury, J.J., Adams, W.C., Ramey, M.R., 1977. Influence of pedaling rate and power output on energy expenditure during bicycle ergometry. Ergonomics 20, 491—498. Sj+gaard, G., 1978. Force—Velocity Curve for Bicycle Work. Biomechanics. Vol VI-A. University Park Press, Baltimore, pp. 86—92. Whitt, F.R., Wilson, D.G., 1982. Bicycling Science. MIT Press, Cambridge, MA.
An ergonomic study on the optimal gear ratio for a multi-speed bicycle Chang K. Cho!, Myung Hwan Yun",*, Chang S. Yoon#, Myun W. Lee! ! Department of Industrial Engineering, Seoul National University, Seoul 151-742, South Korea " Dept of Industrial Engineering, Pohang University of Science and Technology, Pohang 790-784, South Korea # Arthur D. Little International, Inc. 13th Floor. Kyobo Building, 1-1 Chongro, Chongro-ku, Seoul 110-714, South Korea Received 15 September 1996; received in revised form 22 January 1997; accepted 25 June 1997
Abstract With respect to human performance and power efficiency, the gear system in typical multi-speed bicycles is often biased and redundant. A preliminary user survey in this study reveals that the average utilization of each shift for a multi-speed gear system is less than 40%. This study attempts to measure the optimal pedaling rates for given power output levels as well as design the optimal number of gears and the corresponding gear ratios. Heart rate, ratings of perceived exertion and electromyogram of quadriceps femoris for five male subjects are measured at three different power output levels (40, 80 and 120 W) and four different pedaling rate levels (40, 60, 80 and 100 rpm). Various riding conditions including slope gradient and cruising velocity are also converted to the equivalent power output level. The optimal pedaling rates for the given power output are 40 rpm for 40 W power output level, 40 — 60 rpm for 80 and 120 W power output levels. By using a heuristic rule which finds the least number of gears and the most efficient gear ratio under the given physiological condition, a four speed gear system with the ratio of 0.26—0.38, 0.38—0.53, 0.53—0.7 and 0.7—1.0 is recommended as the most efficient gear system. Based on the optimal gear ratio suggested in this study, an ergonomic gear system using a novel/unique type of planet gear sets (US patent No. 5 378 201) is developed. Relevance to industry A bicycle’s gear system is frequently designed without ergonomic expertise in terms of performance and efficiency. This study provides guidelines, design specifications, and performance measures to design an efficient bicycle gear system. This study also contributes valuable finding regarding the optimal performance during bicycle riding, thereby facilitating the efficiency and effectiveness of human exercise using a bicycle. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Gear ratio; Bicycle riding; Ergonomic design; Human performance; Multi-speed bicycle
* Corresponding author. Tel.: #82 562 279 2207; fax: #82 562 279 2870; e-mail: [email protected]. 0169-8141/99/$19.00 Copyright ( 1999 Elsevier Science B.V. All rights reserved PII S 0 1 6 9 - 8 1 4 1 ( 9 7 ) 0 0 1 0 4 - 2
96
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
1. Introduction In accordance with the growth of bicycle market, multi-speed gear systems have become increasingly popular. In Korea, more than 60% of the bicycles sold in 1995 had a multi-speed gear system (Korea Bicycle Industry Institute, 1995). A preliminary user survey revealed that the average utilization of multi-speed gear system is less than 40%. Fig. 1 displays the nominal gear values in commercialized multi-speed gear system and their actual gear ratios. Gear ratios in Fig. 1 are biased and even redundant. Thus, with respect to human performance and power efficiency, current design of gear system is inefficient and hard to use because of the many number of unnecessary shifts. This study not only measures the optimal pedaling rates for given power output levels, but also designs the optimal number of gears and corresponding gear ratios.
Fig. 1. Gear ratio distribution of the commercialized multispeed gear system.
2. Background During the bicycle riding, the power generated from human muscles is used to overcome the rolling, air, acceleration and gradient resistance. Whitt and Wilson (1982) calculated the required power output relevant to the given bicycle velocity and slope gradient [(Eq. (1)].
G C
D A H
B
C s a m ¼" V +mg C # # 1# 8 R g 100 g +m #0.5C Ao(C #C )2 , D V W
(1)
where ¼ is the power required on pedal, C the V bicycle velocity, g the transmission efficiency, &m the weight of bike and man, g the gravity acceleration, C the rolling resistance, s the slope gradiR ent, a the bicycle acceleration, m the moment of W inertia, C the air resistance, A the frontal area, D o the air density and C the head wind. 8 In the above equation, air and acceleration resistance tend to be ignorable for the non-competitive cyclist. Thus, bicycle velocity and slope gradient can be considered as major factors in
Fig. 2. Force—velocity relationship on the bicycle.
determining the power requirement during the normal, non-professional level, bicycle riding. Power output during bicycle riding can be expressed as the product of pedaling force and pedaling rate. This finding suggests that a trade-off exists between pedaling force and pedaling rate for a given power output. The physiological characteristics of human muscle and power output, called ‘force—velocity relationship’ can explain the tradeoff (Sj+gaard, 1978; Faria and Cavanagh, 1978). As Fig. 2 indicates, under the same power level, a human can either pedal fast with a small amount of force (high-speed gear), or pedal slowly with a large amount of force (low-speed gear). Thus, the main function of multi-speed gear system can be considered to provide the shifting mechanism that a human can select his/her own combination of pedaling force and rate under certain degree of power output (Kyle, 1988; Whitt and Wilson, 1982).
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
Therefore, the optimal gear ratio of a bicycle can be defined as the most physiologically efficient combination of pedaling force and pedaling rate. Previous studies revealed that the optimal pedaling rate exists for non-competition cyclist between 40—80 rpm [(Grosse-Lordmann and Mu¨ller, 1936; Brown, 1944; Japanese Bicycle Product and Technical Institute, 1968; Seabury et al., 1977; Carnevale and Gaesser, 1991)]. Above studies used various physiological measures such as oxygen consumption, heart rate, and EMG as well as riding performance.
Table 1 Analysis results of variance (ANOVA)
3. Methods Five male undergraduate students participated in this study. (age: 23—24, height: 165—180 cm, weight: 59—73 kg). To obtain the optimal gear ratio, three different power output levels (40, 80, and 120 W) and four different pedaling rates (40, 60, 80, and 100 rpm) were used as independent variables. (Russel and Dale, 1986). Heart rate, ratings of perceived exertion, and electromyogram of quadriceps femoris were measured at three different power output levels. The experimental design was 3 by 4 factorial design without repetition. Ergometer and Pulsemeter (Tunturi F250) were used to provide a constant power level and measure the heart rate. Metronome (TAKEI MP50) was also used to provide the signal relevant to the given rpm. EMG was measured by surface electrodes (S&W) and a telemetry system (SANEI, medical telemeter 270) and digitalized to IBM PC through an AD converter (UEI 200). 4. Results Table 1 summarizes the analysis results of variance (ANOVA) for the effect of power output and pedaling rate on the heart rate, RPE, and EMG, respectively. According to those results, power output and pedaling rate significantly influence heart rate and RPE, but not EMG. Although EMG does not significantly change, the root mean square values of EMG increased with power output.
97
Heart rate Source
DF
SS
F-value
P-value
Power Output (A) Pedaling Rate (B) A*B
2 3 6
2237.9 5056.8 245.9
10.64 16.02 0.39
0.0001 0.0001 0.8821
RPE Source Power Output (A) Pedaling Rate (B) A*B
DF 2 3 6
SS 0.6705 1.7775 0.2029
F-value 5.99 10.58 0.6
P-value 0.0048 0.0001 0.7255
EMC Source Power Output (A) Pedaling Rate (B) A*B0
DF 2 3 6
SS 0.0081 0.0271 0.0286
F-value 0.63 1.41 0.74
P-value 0.5383 0.2519 0.6191
Fig. 3. Optimal range of pedaling rate for the given power output.
Results obtained from Duncan’s grouping for heart rate and RPE indicate that the physiologically optimal pedaling rates are 40 rpm for 40 W and 40—60 rpm for 80 and 120 W, respectively. Fig. 3 depicts the area of optimal pedaling rate for the given power output. By using the above statistical analysis result, the optimal pedaling rates for the given power output level can be derived. To obtain the optimal gear ratio based on the results of optimal pedaling rate, additional factors should be considered (De Groot
98
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
Fig. 4. Procedure to determine optimal gear ratio. Fig. 6. Optimal gear ratio for given riding condition in terms of slope gradient and cruising velocity.
et al., 1994; Patterson and Moreno, 1990; Raine and Amor, 1991). Fig. 4 presents the related factors and procedure for determining the optimal gear ratio. By using Eq. (1), various riding conditions including slope gradient (0°—15°) and cruising velocity (0—5.5 m/s) were converted to the equivalent power output levels (see Fig. 5). Above riding conditions are realistic because the average capacity of human engine on the bicycle is about 0.1 hp if we confine attention to the non-competition cyclist (Whitt and Wilson, 1982; Burke, 1986). By applying the calculated power requirement to the result of this study, the optimal pedaling rate for each riding condition can be calculated. And with
wheel revolution relevant to the cruising velocity, it can be converted again into the optimal gear ratio for each riding condition, (see Fig. 6). The optimal gear ratio in Fig. 6 has both an upper and lower boundary, implying that any gear ratio between this range is physiologically optimal for the given riding condition in terms of slope gradient and cruising velocity. Therefore, by using the heuristic rule in Fig. 7, the least number of gears and most efficient gear ratio can be derived. For example, when we confine the gear ratio equivalent to the customized 18-speed gear system (0.26—1.0), only four gear ratios of 0.26—0.38,
Fig. 5. Power output relevant to the riding condition in terms of slope gradient and cruising velocity.
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
99
0.38—0.53, 0.53—0.7, 0.7—1.0 satisfy the condition of the physiological optimum (see Fig. 8).
5. Conclusions and discussion
Fig. 7. Heuristic procedure to find the least number of gears and the most efficient gear ratio.
This study has presented the optimal pedaling rates for the given power output. Heart rate and RPE are used as a physiological criteria. Although the change of power level and pedaling rate does not influence EMG, root mean square values of EMG increase with power output. While direct measurements of energy consumption, such as VO , were not used in this study, it is 2 argued that heart rate and RPE can be a sensitive measure of energy consumption under the controlled conditions (Astrand and Rodahl, 1970). Results in this study imply that a fewer number of gears which are optimal can provide a performance equivalent to the multi-speed gear system. As expected, reducing the number of gears without a loss of physiological efficiency would result in easier gear shifting. By using the results in this study, an ergonomic gear system by Lee (1995), (U.S. Patent 5.378.201) has been developed. Until now, initial consumer response to the prototype has been favorable.
References
Fig. 8. Recommended optimal gear ratio for four-speed gear system.
Astrond, P., Rodahl, K., 1970. Textbook of Work Physiology. Mcgraw-Hill KogaKusha, Tokyo. Brown, W., 1944. Cycle gearing in theory and practice. Cycling, July 5, 12—13. Burke, E.R., 1986. Science of Cycling. Human Kinetics, Champaign. Carnevale, T.J., Gaesser, G.A., 1991. Effect of pedaling speed on the power—duration relationship for high-intensity exercise. Medicine and Science in Sports and Exercise 23 (2), 242—246. Faria, I.E., Cavanagh, P.R., 1978. The Physiology and Biomechanics of Cycling. Wiley, New York. De Groot, G., Clijsen, W.L., Clarijs, J., Cabri, J., Antonis, J., 1994. Power, muscular work, and external factors in cycling. Ergonomics 37 (1), 31—42. Grosse-Lordemann, H., Mu¨ller, E.A., 1936. Der Einfluss der Leistung und der Arbeitsgeschwindigkeit auf Arbeitsmaximum und den Wirkungsgrad beim Radfahren. Kaiser Wilhelm Institut fu¨r Abeitsphysiologie. Dortmund-Mu¨nster. Korea Bicycle Industry Institute, 1995. Bicycle News No. 6. Seoul, Korea. [Korean]
100
C.K. Cho et al. / International Journal of Industrial Ergonomics 23 (1999) 95—100
Kyle, C.R., 1988. The mechanics and aerodynamics of cycling. In: Burke, E.R., Newsom, M.M. (Eds.), Medical and Scientific Aspects of Cycling. Human Kinetics, IL, pp. 235—251. Japanese Bicycle Production and Technology Institute, 1968. Report of the Bicycle Production and Technical Institute. Lee, M.W., Lee, W.I., Kim, M.S., 1995. Multi-geared bicycle transmission assembly comprising internal gear sets. United States Patent. d5 378 201. Patterson, R.P., Moreno, M.I., 1990. Bicycle pedalling force as a function of pedalling rate and power output. Medicine and Science in Sports and Exercise 22 (4), 512—516. Raine, J.K., Amor, M.R., 1991. Design and energy consumption of a human-powered vehicle. International Journal of Vehicle Design 12 (5), 630—643.
Russel, J.C., Dale, J.D., 1986. Dynamic torquemeter calibration of bicycle ergometers. Journal of Applied Physiology 61 (3), 1217—1220. Seabury, J.J., Adams, W.C., Ramey, M.R., 1977. Influence of pedaling rate and power output on energy expenditure during bicycle ergometry. Ergonomics 20, 491—498. Sj+gaard, G., 1978. Force—Velocity Curve for Bicycle Work. Biomechanics. Vol VI-A. University Park Press, Baltimore, pp. 86—92. Whitt, F.R., Wilson, D.G., 1982. Bicycling Science. MIT Press, Cambridge, MA.