Abstract
We present a technique for simulating dynamic field (freerange) exercise, using a novel computercontrolled cycle ergometer. This modified cycle ergometer takes into account the effect of friction and aerodynamic drag forces on a 70kg cyclist in a racing position. It also affords the ability to select different gear ratios. We have used this technique to simulate a known competition cycle route in Cape Town, South Africa. In an attempt to analyze the input stimulus, in this case the generated power output of each cyclist, eight subjects cycled for 40 min at a selfselected, comfortable pace on the first part of the simulated route. Our results indicate that this exercise input excites the musculocardiorespiratory system over a wide range of power outputs, both in terms of amplitude and frequency. This stimulus profile thereby complies with the fundamental requirement for nonlinear (physiological) systems analysis and identification. Through a computer simulation, we have devised a laboratory exercise protocol that not only is physiologically real but also overcomes the artificiality of most traditional laboratory exercise protocols.
 laboratory exercise test
 field exercise
 stimulus profile
for many years laboratory exercise testing has been an important tool whereby athletes could be evaluated and their progress monitored during training. Laboratory testing also forms a vital part of basic research into the physiological responses to exercise, and the control mechanisms involved in those responses.
The traditional approach to physiological systems analysis has concentrated primarily on the linear systems approach, using deterministic exercise inputs (i.e., its values as a function of future time can be predicted with accuracy). However, it is clear from the literature that the physiological (cardiorespiratory) responses to exercise do not always conform to all the assumptions and prerequisites associated with linear systems (2, 6). The ideal profile of input stimuli for physiological systems analysis and, ultimately, the ideal exercise protocol for laboratory testing purposes, will be one that overcomes both the theoretical and practical constraints of deterministic input stimuli. It should thus not assume systems linearity, and it should test the systems over their complete natural dynamic range, in terms of both amplitude and frequency.
As a first step toward defining such a stimulus profile, we set out to discover how normal trained and untrained persons choose to exercise under “natural” or “freerange” conditions. To this end we constructed an adjustable bicycle ergometer that resembled the subjects’ own bicycles as closely as possible. This individualized bicycle could be “cycled” along a highresolution simulation of an actual mountainous cycle route. The cyclist’s selfimposed work rates, with resulting heart rate, minute ventilation, and O_{2} uptake (V˙o _{2}) and CO_{2} production (V˙co _{2}) responses, were compared with the results of each subject’s own standard ramp test results.
METHODS
Part 1: Computer Simulation of a Competition Cycling Route
As cyclists often find conventional cycle ergometers uncomfortable, forcing them into unusual riding positions, we developed a computercontrolled cycle ergometer that suited not only our experimental needs but also those of the cyclists.
The horizontal length of the ergometer, as well as the handlebar and seat height, could be adjusted to reproduce the cyclist’s posture on his own bicycle. Conventional racing equipment (chainset, saddle, pedals, and so on) was used to make the cycle as comfortable as possible. An electronic gearing system, consisting of standard shift levers and secured to rotary switches, was mounted to the handlebar stem, so that the cyclist had a selection of 10 gear ratios. The pedal cadence (rpm) was shown on a liquid crystal display fitted to the handlebars. The ergometer could produce work rates of up to 580 W; this has been shown to cover the work rates typically encountered during prolonged exercise testing (3).
Calibration of the cycle ergometer.
The calibration unit consists of a 750W series motor, which drove the pedal crankshaft of the ergometer via a reduction gearbox, a torque transducer, and an optical sensor to measure the cadence (rpm). Torque in the coupling shaft was measured by four strain gauges and amplified by an instrumentation amplifier that was mounted on, and rotated with, the shaft. Power to the amplifier, as well as the amplifieroutput signal, was assessed via four carbon brushes and brass sliprings on the shaft. Torque readings were then taken at 60, 80, and 100 rpm throughout the poweroutput range, and the calibration curve was then constructed from the results. It is important to note that the ergometer has no flywheel, which allows for rapid changes in work rate. The ergometer was therefore linear over the specific frequency range (0–1 Hz).
Simulation of freerange cycling.
When cycling is performed on the road, three major factors influence the power that must be produced by the cyclist:1) the speed at which the cyclist is traveling; 2) the slope of the road; and 3) aerodynamic, rolling, and frictional resistance (7, 8). A bidirectional serial (RS232) communication interface between the ergometer and a personal computer was designed to monitor and simulate these three factors at a rate of 0.5 Hz.
CALCULATION OF THE CYCLING SPEED (FIG. 1).
The computer received the angular velocity of the rear wheel (ω_{1}; rad/s) from the ergometer. By using ω_{1} and the gear ratio (n
_{1}/n
_{2}), the speed (v; m/s) of the cyclist can be calculated with the following equation
SIMULATION OF THE GEAR RATIO.
The bicycle ergometer had no mechanical gears resembling those of a normal recreational and/or racing bicycle. However, the effect of gears on velocity and pedal load could be simulated through changing then _{1}/n _{2}ratio (Eq. 1 ) whenever the computer program detected a change in the rotary switch setting.
EFFECT OF THE ROAD GRADIENT.
When cycling is performed along a sloped surface, an additional force contributes to the power that must be produced by the cyclist. Figure2 shows that when cycling is performed uphill [the slope of the road (θ; °) > 0°], the force component (F_{θ}; N) exists against the direction of travel, whereas on a downhill slope (θ < 0°), F_{θ} exists in the direction of travel. When θ = 0°, i.e., when cycling is performed on a level road, this component has no influence. Therefore
To determine the slope of the road, a crosssectional map of a wellknown competition cycling route in Cape Town, South Africa, was constructed by using orthophoto maps (1:10,000). After the route (≃101 km) was marked on the map, a thin wire was used to trace the route. The wire was marked whenever an altitude contour line was crossed. The wire was then straightened, and the altitude was plotted against the distance along the route. A set of 2,000 altitudedistance values was thus obtained. These were smoothed by interpolation to provide a resolution of one point every 5 m. By using the derivatives of the crosssectional map, the slope could be determined at any point along the route. A lookup table was constructed, consisting of the distance covered and the corresponding slope. This table was saved in the computer memory for use in the simulation.
AERODYNAMIC, ROLLING, AND FRICTIONAL RESISTANCE.
The aerodynamic drag forces experienced by a cyclist on the road depends on numerous factors, the most important of which are speed, frontal area and shape (i.e., cycling position), and air density. Rolling resistance is mainly dependent on tire characteristics, i.e., type, total weight, deformation, as well as the nature of the road surface. Frictional resistance is mainly incurred in the transmission system, i.e., gear train and bearings. Because these factors are difficult to measure, and would differ from subject to subject, we decided to use existing data from Kyle (7) on the rolling and aerodynamic drag forces to determine the drag forcespeed relationship.
By fitting a secondorder polynomial through Kyle’s data (7), we obtained an equation that is representative of the aerodynamic (A) and rolling (R) forces that act on a 70kg cyclist in the racing position. Thus
CALCULATION OF TOTAL POWER (P_{TOT}).
If power (W) = force (N) ⋅ speed (m/s), theP
_{tot} required to cycle at a certain speed and slope is
THE SIMULATION.
By using Eq. 5 , it was thus possible to simulate freerange cycling in the exercise laboratory. (It should be remembered that the constants in Eq.5 are dependent on riding position and bicycle characteristics and would therefore differ from cyclist to cyclist.) The simulation software was written in Turbo Pascal. In short, the computer receives the angular velocity from the ergometer and, knowing the selected gear ratio, calculates the cycling speed and the distance covered. Then, by using a lookup table to find the corresponding slope, the P _{tot} is calculated and is sent back to the ergometer controller.
A visual display of a cross section of the entire route was displayed on a personal computer screen positioned in front of the cycle ergometer. The cyclist could also see his present position on the route, a graphical illustration of the gear ratio, the slope of the road, his present speed (km/h), as well as the distance (km) completed. The power output (work rate), velocity, slope, and cadence were stored continuously to the hard disk at a sampling frequency of 0.5 Hz.
Part 2: Power Distribution
To examine the nature of the input signal, in this case the generated work rate of each individual cyclist, eight subjects [age: 22 ± 2.19 (SD) yr] of various levels of athletic ability completed two exercise tests during one testing session: a standard (or traditional) continuous, progressive loadincremented exercise test and a 40min freerange exercise test on the simulated route. At least 1 h of recovery was allowed for each subject between tests.
During the loadincremented test, subjects were instructed to maintain a constant pedal frequency of 80 rpm. After a 3min period of unloaded cycling (the warmup period), the first exercise stage was performed against “zero” resistance, after which the work rate was increased by 20 W every 60 s until the subject could no longer maintain a pedaling frequency above 70 rpm despite verbal encouragement. The ventilatory threshold (VT) was derived by the Vslope method by using plots of V˙o _{2} andV˙co _{2} (1), where VT was defined as the nonlinear breakpoint inV˙co _{2} relative to the rise inV˙o _{2}.
During the freerange exercise test, subjects were instructed to
select an intensity that you prefer, and cycle at a comfortable speed. This should be an intensity that you would choose for a 40 minute workout on the road and it should be an intensity that feels appropriate for you. You are permitted to change both the pedal cadence and gear ratio at will.
All experiments were performed indoors, under controlled, uniform environmental conditions: temperature, 21 ± 1°C; relative humidity, 54 ± 2%; and barometric pressure, 101–102 kPa. A fan provided airflow (and thus body cooling) from the front.
RESULTS
Dynamic Input Stimulus
Figure 4 displays the work rate in relation to the profile of the simulated route for one randomly chosen competitive (experienced) cyclist (A) and a similarly randomly chosen “recreational” cyclist (B). In neither case did the work rate reflect the course profile. This was typical of all the individual results. The only partial exception occurred at a distance of ≃9.5 km, where there was a long, steep uphill slope for ≃2 km. On this slope, most of the subjects’ pedaling frequencies fell below their respective mean values for the route, whereas their work rates were persistently above their mean work rates over 40 min.
As the work rate did not reflect the course profile in any obvious way, we determined whether the variations in the generated work rate of each subject were randomly distributed around the mean value. To this end we performed two statistical tests for randomness:1) an even randomness test (4), in which the number of runs (sequential sets of data points) was calculated so that the work rate remained completely above or completely below the mean work rate value (calculated over a period of 40 min) for an individual subject; and2) a Gaussian distribution test. AP < 0.05 indicated that the null hypothesis for a random distribution could not be accepted.
The P values of both the even randomness tests for the variation in work rate and those for the random Gaussian distribution tests were (for all the subjects) highly significant (P < 0.001), indicating that the distribution of work rates around the mean work rate for each cyclist was not random, or Gaussian.
To test whether the stimulus profile resembled white noise, or a possible chaotic (socalled “1/f”) signal, wheref is frequency, the power spectral density of the generated work rate was calculated. The spectral exponent β was calculated for each subject as the slope of the graph on a loglog plot of the power spectral density of the generated work rate (Fig. 5). The independent variable in this plot was the frequency content of the work rate signal. The dependent variable was the work rate generated by the cyclist. This indicated whether the variability of the generated work rate corresponded to bandlimited Gaussian white noise (i.e., equal power at all frequencies) or whether the data had a typical 1/f distribution, indicative of chaos.
The spectral exponents of the generated work rate ranged between −0.496 and −0.824 (Table 1), indicating that the generated work rate did not conform to Gaussian white noise (in which case β = 0) but tended toward 1/f − noise (β = 1). In all cases, the spectral exponents were significantly different from zero and one (P < 0.05).
Our results therefore indicate that the nature of the exercise input (the generated work rate) was neither random, nor periodic, nor steady, nor Gaussian white noise. Rather, the stimulus profile may be best described as stochastic in nature.
Frequency Distribution of the Generated Work Rate
The input signal of a system should, in addition, ideally span a wide frequency range to identify both the high and lowfrequency behavior of the system. In general, the power spectral density of an input signal is an indication of the power distribution at the different frequencies. Ideally, from a mathematical analysis point of view, all frequencies should have equal power weighting as this greatly simplifies the systems analysis.
Figure 5 shows the power spectral density of the generated work rate for the two representative subjects. Although all frequencies do not have equal power weighting, as in the case of bandlimited Gaussian white noise, the stimulus profile that resulted from this study (in which each subject generated his own work rate) excited the physiological system over a wide range of frequencies (0–1 Hz). It is possible that the stimulus profile excited the system over a range wider than 0–1 Hz, but, because of the sampling frequency, input and response frequencies >1 Hz could not be analyzed in this study.
Amplitude Distribution of the Generated Work Rate
Figure 6 depicts the power distribution of the two subjects during the freerange exercise test and relates it to the uniform power distribution during progressive loadincremented exercise. All the subjects had a large component present at the lowest work rate (60 W), which represents the time they spent on the downhills. The rest of the work rate distribution covers a wide range, extending up to 580 W for seven of the eight subjects. The maximum work rate for the remaining subject was 500 W. On average, the subjects exercised almost onehalf the exercise time (49.5 ± 11.3%) at an intensity (work rate) that was above the estimated ventilatory threshold. There was no significant difference between the percentage of time that the experienced and recreational cyclists exercised above VT [46.8 ± 6.10 vs. 52.3 ± 5.62 (SE) %;P = 0.47].
During spontaneous freerange exercise, therefore, the physiological systems were challenged over a substantially wider range of work rates than during the forced incremental (ramp) exercise.
DISCUSSION
We have shown that “free” dynamic exercise can be readily simulated in the laboratory environment. If the equation relating the power, velocity, and surface gradient is known, a closedloop configuration can be implemented to accommodate the simulation. Although we simulated a known cycling route (renowned for its mountainous profile), an entirely artificial route could also be generated and implemented.
Because an electromagnetically braked cycle ergometer was used, it was impossible to simulate downhill cycling below the terminal velocity (Fig. 3). Therefore, whenever the cycling velocity was below the terminal velocity, the work rate was set to zero. Although this might appear to be a shortcoming of the simulation, cyclists (by nature of their bicycles) are never exposed to “negative work” while cycling in a reallife situation. They can either freewheel downhill or try to exceed the terminal velocity (i.e., do positive work on the downhill stretches of the route). The only artificiality of the simulation in this respect was that the subjects were forced to do at least 60 W of positive work on the downhill stretches of the route.
When cyclists engage in noncompetitive freerange exercise, they spend a substantial proportion of time at levels that are above their VT. This finding is in accordance with those of Loftin and Warren et al. (10), who grouped cyclists by ventilatory threshold and found that, during a 16.1km simulated time trial, both the highVT [77 ± 4.0 (SD) % of maximal V˙o _{2}(V˙o _{2 max})] and the lowVT (68 ± 2.8% ofV˙o _{2 max}) groups exercised at a percentage ofV˙o _{2 max} that was 12 and 14% above their respective ventilatory thresholds.
In contrast to the progressive, incremental (ramp) exercise test, which was limited to a narrower power range (60–440 W), the freerange exercise test was found to excite the physiological systems over a broader range of work rates (60–580 W), irrespective of the individual’s athletic ability (competitive or recreational). The freerange exercise input thus covered both the high and low work rates in every subject. It should be noted that what is regarded as the “input signal” in this discussion is the individual’s work rate, which, in the freerange exercise test, was determined by the individual himself (i.e., it was not externally imposed on the subject).
Although the subjects were instructed to cycle at “their own comfortable rate,” the input signal in all cases spanned a wide frequency range (0–1 Hz) and thus would be suitable for the identification of both high and lowfrequency behavior of the physiological control systems during exercise. The input signal (the generated work rate) did not, however, comply with the strict mathematical requirements of a Gaussian whitenoise signal. Thus, although the input signal covered the complete working range and frequency distribution of the physiological system during freerange exercise, the power spectral density analysis (Fig. 5) showed that all the frequencies did not have equal power weighting. Furthermore, although the work rate changed continuously and fluctuated in an apparently unpredictable manner around the mean value, statistical analysis showed that the stimulus profile was not randomly distributed. This imperfection in the mathematical characteristics of the input signal precludes the use of known nonparametric system identification techniques, such as the whitenoise approach (11, 13) and the crosscorrelation technique of kernel estimation (9). Future studies might be able to refine the input signal and develop an appropriate whitenoise input. Alternatively, the analysis techniques could be adapted to cope with the physiological realities of exercise.
An interesting observation was the fact that the generated work rate showed power law behavior, which is generally associated with complex dynamical systems. This can be seen from the 1/f ^{β}like power spectrum, where spectral exponent β ranged from 0.496 to 0.824 (Table1). Thus the generated work rate lies somewhere between white noise (β = 0) and 1/f noise (β = 1). In general, systems that exhibit 1/flike power spectra are described as having a fractal or chaotic nature, which implies that, although the data look noisy and totally lack repetition, there is a definite deterministic pattern embedded within it. The cyclists’ work rates under noncompetitive circumstances were thus found to have a 1/flike power spectrum, which thus must be considered the physiological response to freestyle exercise. This finding is not surprising, because it has recently been shown that normal gait is also associated with a 1/flike spectrum, with β in the range 0.83 ± (SD) 0.23 (5).
Although it is not possible to measure work rate very easily in the field, there are published results of heart rate variations during the actual cycle race. Palmer et al. (12) have shown that these heart rate variations also appeared to be chaotic and were exactly similar to the heart rate changes when our subjects cycled the simulated route. We therefore presume that, during the simulation, the other variables (V˙o _{2},V˙co _{2}, minute ventilation, and so on), including work rate, closely mimic those that would be obtained in the field. Hence, we conclude that the simulation is a more complex stimulus than the “artificial” profiles typically used.
Although the input signal of the freerange exercise test (the generated work rate of the individual subject) has mathematical imperfections, it allows for a comprehensive analysis of many physiological responses to exercise in a relatively shortduration test. There is also no requirement to induce or coerce the subjects to exercise to exhaustion. They spontaneously exercise to produce work rates in excess of those encountered in traditional tests, without becoming “exhausted” or being unable to complete the test. We believe that this technological innovation has opened the way to a new, scientifically valid, and technically feasible method for investigating the physiological responses to exercise and their control mechanisms.
Footnotes

Address for reprint requests and other correspondence: E. Terblanche, Dept. of Medical Physiology and Biochemistry, PO Box 19063, Tygerberg, Cape Town, South Africa 7505 (Email:et2{at}gerga.sun.ac.za).

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 Copyright © 1999 the American Physiological Society