Man as Locomotive Engine
Kazuho KAWAI, Masashi HARADA
Abstract
The mechanical output from rowing and cycling were measured to get available data for design of a human powered ornithopter. The results indicate that the powerduration characteristic curve for rowing and cycling is given by same equation for longer duration time than 40 seconds. The power ratio of rowing and cycling is 0.889 for the long duration time, and 0.589 for duration time of 10 seconds. The effective power for flight is independent of the body mass of the engine pilot.
Introduction
Remarkable success has been achieved concerning the research of characteristics of the cycling power of the man as a rotary engine. Nonweiler^{1)} and Wilkie^{2)} investigated mechanical output of cycling as function of exercise duration. On the other hand, Henderson et.al.^{3)} and di Prampero et.al.^{4)} investigated the characteristic of rowing power for application to a rowing race, but not to human powered aircraft. No data is available for the characteristics of the power of locomotive action which is efficient to get propulsion by wing flapping.
The purpose of this study is to present the measured result of the characteristic of the power of rowing action and to make clear the fact that the rowing action can be used for the human powered ornithopter.
Experiments concerning the mechanical output from rowing and cycling have been done. The measured results are;
a) The relation of mechanical output and duration time of the rowing exercise.
b) The comparison of the mechanical output of rowing and cycling for a nonathlete.
c) The relation of body weight and the mechanical output of rowing.
Characteristics of Power about Rowing and Cycling
We measured the duration time of exercise and the mechanical output of rowing and cycling using one subject. The subject (KK) was a healthy male (30 years) and a nonathlete. A rowing ergometer and a bicycle ergometer were used. During the experiment, the subject exercised and maintained constant power for as long a duration as possible. The pedaling frequency of cycling was 90 r.p.m., but the rowing frequency was not controlled. The results of the relation of duration time (t) and mechanical output (P) are shown in Fig. 1. The solid line in Fig.1 is plotted by the equation proposed by Wilkie^{5)} for t>40 s. The equation is:
P_{c}=Et^{1}+A[1(t_{0}/t){1exp(t_{0}/t)}] (1)
t_{0}=10 s

Fig. 1 Power of rowing (œ) and cycling (›) in relation to duration of exercise for subject KK. The solid line has been fitted from Eq. (1), the dotted one from Eq. (2)
The constant values in Eq. 1 for this subject were E=13900 Ws, A=175 W. The solid line in Fig.1 fit well with the results of cycling for t>40 s. The broken line is plotted by the equation:
P_{r}=0.80P_{c}=0.80(Et^{1}+A[1(t_{0}/t){1exp(t/t_{0})}]) (2)
The broken line agreed with the results of rowing for t>40 s. The reasons why the characteristic curves of power for rowing and cycling are the same are follows;
Di Prampero^{6)} proposed the equation about maximal speed of locomotion (v^{max}) and duration time (t):
v^{max}=C^{1}(EAt^{1}+MPA[1(t_{0}/t){1exp(t/t_{0})}] (3)
In this equation EA is the total energy from anaerobic sources (joules), MPA is maximal power from aerobic sources (watts), and C is the energy cost for 1 m distance (joules/meter). This equation yields, on rearrangement for maximal power (P^{max}):
P^{max}=h(EAt^{1}+MPA[1(t_{0}/t){1exp(t/t_{0})}] (4)
h is the mechanical efficiency of exercise and a function of P.
Seabury et.al.^{7)} found that the efficiency of the bicycle exercise is almost independent of the mechanical output P and its value at 90 r.p.m. is about 0.24. di Prampero et.al^{4)} reported that the efficiency of the rowing exercise is independent of rowing frequency, therefore independent of P, and its value is about 0.23. The independence of mechanical efficiency on mechanical output causes the similarity of equations (1),(2) and (4).
So the characteristic of power of rowing and cycling are expressed by eq. (4) and constant values hr and hc. The power ratio of rowing and cycling i.e. ratio h_{r}/h_{c} for the subject (KK)in this experiment is 0.80.
Efficiency of Rowing
To get the standard value h_{r}/h_{c} another experiment was performed with a rowing ergometer and bicycle ergometer. Subjects were male (1930 years), and nonathletes. We measured the average power (P^{(10)}) and maximal power (P^{max}) during rowing and cycling exercise with maximum effort for 10 s. The torque of the bicycle ergometer was 6KP based on the method of Ikuta et.al.^{8)}. The maximal power is defined for one stroke of rowing (including the time to bring the handle back to its original position) or one rotation of pedaling. And we measured the duration time (t^{(200)}) for exercise at a constant power of 200 W for rowing and cycling. The pedaling frequency for cycling was 90 r.p.m.. The measured results are given in Table 1.
Table 1 Power characteristics of test subjects.
The value of t^{(200)}_{r}/t^{(200)}_{c} is not equal to h_{r}/h_{c}. To get the value h_{r}/h_{c} for each subject we need the values E and A in eq. (1) for each subject. The measured power for 10 s (P^{(10)}_{exp}) is not available for the calculation of E and A, because eq. (1) is defined for a longer duration time than 40 s. At this point, we assumed that the relation of the measured power (P^{(10)}_{exp}) and the calculated power (P^{(10)}_{cal}) from eq. (1) are linear. The ratio of P^{(10)}_{cal}/P^{(10)}_{exp} of the subject (KK) was 2.5. The calculated results of E, A, and h_{r}/h_{c} with this ratio P^{(10)}_{cal}/P^{(10)}_{exp} =2.5 are given in Table 1. The average ratio h_{r}/h_{c} is 0.889}0.086. This result leads to the conclusion that a man can row with the power of 90% that which he pedals with, and this value is hopeful for flight using rowing power. Further, it is said that rowing skill seriously affects the rowing power, and the subjects used for the experiments were nonrowers, so we assume that the ratio h_{r}/h_{c} should improve for persons trained in rowing.
On the contrary, the power ratio of rowing and cycling for 10 s maximal effort was P^{(10)}_{r}/P^{(10)}_{c}=0.589}0.042. Rowing for a short time is not so powerful, and this is a weak point about using the rowing movement for first flight of the ornithopter. But note that the instant maximum power of the rowing may be three times of P^{max}_{r}, because the period of the rowing force exerted is 1/3 of the stroke period.
Correlation of Power and Body Weight
We estimated the maximal power of rowing and cycling for 600 s exercise (P^{(600)}), for each subject with the value A, E and h_{r}/h_{c} in Table 1. The results of P^{(600)} and measured P^{(10)} and P^{max} are shown in Fig. 2 as a function of body mass of the subjects (W_{M}).

Fig. 2 Relation between body weight and mechanical power of rowing (closed marks), and cycling (open marks) . The power for 10 s (›œ), and for 600 s ( ¡), and the maximal power (¢£). The lines are described from the regression Eqs. (5),(6),(7), and (8).
The regression equations are:
P^{(600)}_{r}=2.302W_{M} +14.61 (r=0.631, p<0.05) (5)
P^{(600)}_{c}=1.060W_{M} +112.9 (r=0.337, n.s.) (6)
P^{(10)}_{r}= 6.77W_{M} 65.1 (r=0.791, p<0.01) (7)
P^{(10)}_{c}=10.24W_{M} 52.3 (r=0.704, p<0.01) (8)
The mechanical output correlates well with the body mass, and the heavier the subject is, the more powerful the estimated output is.
At this point, we consider whether a heavy person has a disadvantage due to his weight , or has the advantage of his power for the flight of the ornithopter. If the empty weight of an ornithopter (W_{AC}) is 40 kg and the weight of a pilot is W_{M}, the minimum power for flight is proportional to (W_{M}+W_{AC})^{1.5}. The relation of the body weight of the subject (W_{M}) and the effective power for flight (P/(W_{M}+W_{AC})^{1.5}) is shown in Fig. 3.

Fig. 3 Relation between body weight and effective power for flight. The symbols are the same as Fig. 2. The lines are calculated from the regression Eqs. (9),(10),(11), and (12).
And the regression equations are:
P^{(10)}_{r}/(W_{M}+W_{AC})^{1.5}=0.00177W_{M}+0.232 (r=0.30 ) (9)
P^{(10)}_{c/}(W_{M}+W_{AC})^{1.5}=0.00183W_{M}+0.449 (r=0.19 ) (10)
P^{(600)}_{r}/(W_{M}+W_{AC})^{1.5}=0.00106W_{M}+0.146 (r=0.038 ) (11)
P^{(600)}_{c}/(W_{M}+W_{AC})^{1.5}=0.001417W_{M}+0.262 (r=0.44 ) (12)
We cannot find any disadvantage nor advantage for a heavy pilot for flight from Fig. 3 and equations (9),(10), (11), and (12) as long as reinforcement of the aircraft is not necessary.
Possibility of Rowing
We measured the rowing power of athletes. The subjects used were players (male) of the Kyoto University rowing team. We measured the average power (P^{(10)}) and maximal power (P^{max}) during rowing exercise with maximal effort for 10 s. And also we measured their mechanical output with the rowing ergometer and duration time of exercise. These measurements are performed for imaginary distances (500 m, 1500 m, 2000 m, 2500 m and 3000 m) calculated by the ergometer and for a period of 720 s.

Fig. 4 The power maintained by athletes in relation to duration of exercise. The symbols ›; top rowing player, Ref. 2, œ; top rowing player, Ref. 10, other symbols; rowing players of the Kyoto University rowing team. The solid line has been fitted to the results for the rowing players of the Kyoto University rowing team using Eq. (4). The dotted line indicates the power of cycling for top cyclists from Ref. 11
The result is shown in Fig. 4. The solid line is the fitted curve using eq. (4). The value of h_{r}EA is 22,000 J and h_{r}MPA is 280 W. These values may be almost the same as the values h_{c}EA and h_{c}MPA of athletes for cycling. For example, Wilkie^{5)} reported the values, h_{c}EA=16,000 J and h_{c}MPA=273 W for a competitive cyclist. However, the values of P^{(10)}_{r} and P^{max}_{r} for the most powerful subject are 656 W and 743 W, and these values may be about 60% of P^{max}_{c}. Satoh^{9)} reported the value P^{max}_{c} of rowing players from 746 W to 1285 W . The data for top athletes from references^{2)10)11)} are added in Fig. 4. The mechanical output of rowing by the top athletes is almost equal to that of cycling.
Therefore, for long periods t>300 s, the rowing movement is as powerful as the cycling movement. But for short time rowing exercises the power is only 60% of the power of cycling. We must design a human powered ornithopter for first flight more efficiently concerning aeronautics than the human powered aircraft with a propeller.

Fig. 5 Relation between body weight of the rowing players and mechanical power for 10 s (›), and 90 s(ž) and maximum values (¢). The lines are the regression line.

Fig. 6 Relation between body weight of the rowing players and effective power for flight for 10 s (›), and 90 s(ž) and maximum values (¢). The lines are the regression line.
Fig. 5 shows the relation of body weight of the rowing player subjects and power (P^{(90)}_{r}, P^{(10)}_{r} and P^{max}_{r}), and Fig. 6 shows the relation of body weight of the rowing players and the effective power as Fig. 2 and Fig. 3. The regression equations are:
P^{(90)}_{r}= 3.903W_{M}+ 83.96 (r=0.674) (13)
P^{(10)}_{r}= 6.202W_{M}+ 117.09 (r=0.375) (14)
P^{max}_{r}= 5.480W_{M}+ 218.07 (r=0.305) (15)
P^{(90)}_{r}/(W_{M}+W_{AC})^{1.5}=  0.00084W_{M}+ 0.368 (r=0.223) (16)
P^{(10)}_{r}/(W_{M}+W_{AC})^{1.5}=  0.00103W_{M}+ 0.549 (r=0.081 ) (17)
Similar to nonathletes, the mechanical output increases with the weight of the athlete subject, and the effective power for flight is independent of the weight of the subject.
Limitations in the Applicability of the Results of Rowing for the Ornithopter
In the rowing ergometer, the tension of the handle is caused by the resistance of the windwheel rotation. Therefore, the changing of tension in one stroke in the rowing ergometer is different from that in the ornithopter. The difference may cause a change of the characteristic of power. Actually, di Prampero^{4)} reported that the relation of the stroke rate and the mechanical output in simulated rowing in a basin and in actual rowing is different. So the results of rowing may not necessarily be applicable to the ornithopter.
For actual rowing and simulated rowing using the ergometer, the oarsman pulls the oars and pushes the oars forward with his own power. And the period of pushing the oars is about 2/3 of the stroke period. But for locomotive motion in an ornithopter, the handle goes forward automatically. The locomotive movement for the ornithopter is different from actual rowing and we need more information about the locomotive movement for the ornithopter.
Conclusions
We obtained the experimental results for rowing and cycling as follows:
(1) The powerduration curve for rowing and cycling is given by
P^{max}=h(EAt^{1}+MPA[1(t_{0}/t){1exp(t/t_{0})}] (t>40 s)
h is constant .
(2) The power ratio of rowing and cycling are
(3) The heavier the subject is, the more powerful the output of rowing or cycling is. However no correlation is found between the body mass and the effective power for flight (P/(W_{M}+W_{AC})^{1.5}).
Recently, the human powered aircraft with a propeller can fly at the power of 200 W. The maximal power of rowing is much more than 200 W. We suppose that by using the locomotive movement of a man, the flight with flapping wing is possible as long as the wing is designed appropriately. We should never give up on human flight similar to that of a bird.
Reference
1) Nonweiler T.R.F., "The ManPowered Aircraft," Journal of Royal Aeronautical Society, vol.62, 1958, pp.723734
2) Wilkie D.R., "Man as an Aero Engine," Journal of Royal Aeronautical Society, vol.64, 1960, pp.477481
3). Henderson Y and Haggard H.W., "The Maximum of Human Power and Its Fuel," American Journal of Physiology, vol.72, 1925, pp.264282
4) di Prampero P.E., Cortili G., Celentano F., and Cerretelli P., "Physiological Aspects of Rowing," Journal of Applied Physiology, vol.31, 1971, pp.853856
5) Wilkie D.R., "Equations Describing Power Input by Humans as a Function of Duration of Exercise." in "Exercise Bioenergetics and Gas Exchange". Ed. P. Cerretelli, B.J. Whipp. Elsevier/North Holland, 1980, pp.7580
6) di Prampero P.E., "La Locomozione Umana Su Terra, in Acqua, in Aria", Ed. Ermes S.R.L., Milano, 1985
7) Seabury J.J., Adams W.C., and Ramey M.R., "Influence of Pedaling Rate and Power Output on Energy Expenditure during Bicycle Ergometry," Ergonomics, vol.20, 1977, pp.491498
8) Ikuta K. and Ikai M., "Study on the Development of Maximum Anaerobic Power in Man with Bicycle Ergometer," Research of Physical Education, vol.17, no.3, 1972, pp.151157
9) Satoh N., Proc. 45th Symposium of Physical Fitness and Sports Medicine, 1990
10) Celentano F., Cortili G., di Prampero P.E., and Cerretelli P., "Mechanical Aspects of Rowing," Journal of Applied Physiology, vol.36, no.6, 1974, pp.642647
11) U.S. National Aeronautics and Space Administration, Bioastronautics Data Book, document SP3006, 1964
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