EP1813313A1 - Method and arrangement in connection with exercise device - Google Patents

Abstract

The invention relates to a method and an arrangement in connection with an exercise device, which comprises a flywheel, wherein resistance of an exercise being performed is adjusted by decelerating the rotation of the flywheel. The method and arrangement also comprise adjusting the magnitude of the exercise resistance by means of a virtual flywheel simulation.

Description

• The invention relates to a method in connection with an exercise device, which comprises a flywheel, wherein resistance of an exercise being performed is adjusted by decelerating the rotation of the flywheel. The invention also relates to an arrangement in connection with an exercise device, which comprises a flywheel, wherein resistance of an exercise being performed is arranged to be adjusted by decelerating the rotation of the flywheel.
• In connection with exercise equipment, as natural a performance as possible has been an important goal for a long time. For example, various exercise bikes attempt to imitate pedalling similar to riding a bicycle in a natural setting, and rowing equipment attempt to imitate rowing by a boat as closely as possible, etc.
• In connection with exercise bikes, for example, the attempt at a natural event involves generation of a "free wheel" and consideration of the cyclist's kinetic energy when the cyclist rides downhill or does not pedal, for instance. In a conventional exercise bike, where resistance is generated by decelerating the flywheel, the motion of the flywheel stops relatively fast if the user stops pedalling. Thus the event does not completely correspond to riding a bicycle.
• To eliminate the above-mentioned drawback, solutions have been devised in the art where the element functioning as a flywheel has been provided with a motor brake, which facilitates the rotation of the flywheel in a downhill situation, i.e. rotates the flywheel when the cyclist pedals downhill. A drawback associated with this solution is its complexity, which results in an expensive apparatus. A further disadvantage is the relatively frequent need for service due to the complex structure, which in turn increases the costs.
• The object of the invention is to provide a method and an arrangement which eliminate the drawbacks associated with prior art. This is achieved by a method and arrangement according to the invention. The method according to the invention is characterized in that the magnitude of the exercise resistance is further adjusted by a virtual flywheel simulation. The arrangement according to the invention is characterized in that the arrangement comprises a means which is further arranged to adjust the resistance by means of a virtual flywheel simulation.
• The major advantage of the invention is that an exercise event, such as a pedalling event, can be rendered as natural as possible in an advantageous manner. An advantage is that resistance can be adjusted automatically according to the route and conditions without complicated motors or other solutions which increase the need for maintenance, etc. A further advantage of the invention is its flexibility since the invention may be applied to different situations, such as various riding routes, in a very advantageous manner.
• In the following, the invention will be described in greater detail by means of an example illustrated in the accompanying drawings, in which
• Figure 1 schematically illustrates an exercise bike,
• Figure 2 illustrates implementation of a simulation situation of a bicycle, and
• Figures 3 to 15 illustrate functions of the solution according to the invention in different situations.
• Figure 1 schematically illustrates an exercise bike. The exercise bike comprises a frame structure 1, and a seat structure 2 and a handle structure 3 attached thereto. The exercise bike further comprises a flywheel, which in the example of Figure 1 is encased in a case structure 4. A pedal structure 5 for rotating the flywheel by pedalling is connected to the flywheel by an appropriate power transmission arrangement. The flywheel is further provided with means for decelerating the rotation of the flywheel so as to achieve a desired pedalling resistance. The exercise bike illustrated in Figure 1 further comprises a user interface 6 for controlling the course of the exercise, for example by adjusting the resistance, etc. The user interface also comprises a display 7 where exercise-related information may be shown.
• The issues described above are fully conventional art to a person skilled in the art, for which reasons these issues will not be described in greater detail in this context.
• An essential feature of the invention is that, in addition to the real flywheel, a virtual, i.e. a computational, flywheel is used. In other words, the invention employs a virtual flywheel simulation.
• Clear formulae exist for calculating momentary pedalling efficiency from the angle, speed, mass and cross-sectional area of the user and bike, and rolling resistance. Simulation of a free wheel and kinetic energy of the cyclist by software has caused problems because the simulation uses no motor which could facilitate the motion of the flywheel in a simulated downhill situation, for example, or in the simulation of a situation with no pedalling.
• The starting point of the invention is simulation of a bicycle. The following dependencies may be noted by examining the bicycle illustrated schematically in Figure 2.
• Torque Nc is transmitted to the crank shaft through the pedals. This is transformed into torque Nc/s of the drive wheel, where s is the transmission ratio of the gear system of the bicycle to be simulated. Force Fw which tries to move the bicycle forward is directed to the interface between the bicycle and the ground. In Figure 2, resisting force Fr is also illustrated at the interface between the bicycle and the ground. The diameter of the drive wheel is d.
• On the basis of the above-mentioned starting information, it may be stated that the ground speed v of the bicycle is $$v=s\pi d\left(R/60\right)$$

  

  
  where R is the pedalling speed in rpm (rounds/minute).
  Let
  Y = air resistance coefficient
  ρ = air density (kg/m³)
  A = cross-sectional area of the cyclist and bicycle (m²)
  µ = rolling friction coefficient
  m = total mass (kg) of the cyclist and bicycle
  g = acceleration of gravity (m/s²)
  θ = angular coefficient of the terrain
  In that case, the resisting force is $$F_R=\frac{1}{2}\cdot \mathrm{\gamma }\mathrm{\cdot }\mathrm{\rho }\cdot A\cdot {\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">v</figure-callout>}}^2+\mathrm{\mu }\cdot m\cdot g+\mathrm{\theta }\cdot m\cdot g$$

  
• The first term is air resistance, the second one rolling friction and the third term is caused by the steepness of the terrain.
• The force moving the bicycle forward can be expressed as follows: $$F_W=\frac{2\cdot N_C}{s\cdot d}$$

  
• The bicycle's equation of motion can now be written in the following form: $$m\cdot \frac{dv}{dt}=F_W-F_R$$

  
• In addition to the forces, the equation of motion includes acceleration.
• In an ergometer, the total mass of the bicycle and cyclist is represented by the flywheel's moment of inertia. It is assumed that the kinetic energies of the simulated flywheel and the real flywheel are the same at the point under consideration. The moment of inertia required of the flywheel is then calculated from this. Kinetic energies can be written as follows: $$\frac{1}{2}\cdot m\cdot {\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">v</figure-callout>}}^2=\frac{1}{2}\cdot I\cdot {\mathrm{<figure-callout\; id="2"\; label="\omega "\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\omega </figure-callout>}}^{\mathrm{2}}$$

  
• In the above equation, I is the flywheel's moment of inertia and w is the flywheel's angular speed. The flywheel's angular speed ω can be calculated from the crank speed R when the transmission ratio k from the crank shaft to the flywheel is known. The transmission ratio k is different from the transmission ratio s of the gearing of the simulated bicycle. $$\mathrm{\omega }\mathrm{=}\mathrm{2}\mathrm{\cdot }\mathrm{\pi }\cdot k\cdot \frac{R}{60}$$

  
• The formula derived at the beginning is used for the ground speed, which results in the following equation $$\frac{1}{2}\cdot m\cdot {\left(s\cdot \mathrm{\pi }\cdot d\cdot \frac{R}{60}\right)}^2=\frac{1}{2}\cdot I\cdot {\left(2\cdot \mathrm{\pi }\cdot k\cdot \frac{R}{60}\right)}^2$$

  

  
  from which the moment of inertia can be solved. $$I=\frac{m\cdot s^2\cdot {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}^2}{4\cdot {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}$$

  
• It can be seen that the suitable moment of inertia is a function of the transmission ratio, i.e. the simulated gear used, and that the dependency is quadratic.
• The model is used to correct the following deficiencies:
• A light flywheel does not help at the beginning of a hill or when a transition occurs from downhill to an even surface.
• The bicycle does not roll downhill.
• Acceleration is too light at the start of riding on an even surface.
• When gears are shifted, the bicycle speed changes immediately.
• When gears are used, it should also be noted that the ground speed cannot be totally separated from the crank speed since the ground speed must at least somehow correspond to the crank speed and the gear used when the cyclist pedals actively. This requirement increases the complexity of the model. Since the bicycle to be simulated includes a free wheel, this requirement does not apply to free rolling.
• One feasible approach is to decrease the resisting force of the break in a slowing motion and thus to simulate the fact how the lost part of kinetic energy is utilized in overcoming the resistance. In an accelerating motion, the breaking force would be correspondingly increased.
• In the following, motion in the standard gear will be examined. Equations of motion are written for a simulated bicycle and the flywheel of a real ergometer. $$\begin{array}{cc}m\cdot \frac{dv}{dt}=F_W-F_R& F_W=\frac{2\cdot N_C}{s\cdot d}\end{array}$$

  

  $$\begin{array}{cc}I\cdot \frac{d\omega }{dt}=N_W-N_R& N_W=\frac{N_C}{k}\end{array}$$

  
• A change in the speed and a change in the angular speed can be presented by means of a change dR/dt in the crank speed in both equations. This variable must be the same for both equations. $$\frac{1}{60}\cdot \frac{dR}{dt}=\frac{2\cdot N_C}{\mathrm{\pi }\cdot m\cdot s^2\cdot d^2}-\frac{F_R}{\mathrm{\pi }\cdot m\cdot s\cdot d}$$

  

  $$\frac{1}{60}\cdot \frac{dR}{dt}=\frac{{\mathrm{<figure-callout\; id="2"\; label="N\; C"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">N</figure-callout>}}_C}{2\cdot \mathrm{\pi }\cdot {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\cdot I}-\frac{{\mathrm{<figure-callout\; id="2"\; label="N\; R"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">N</figure-callout>}}_R}{2\cdot \mathrm{\pi }\cdot k\cdot I}$$

  
• The resisting moment or the target moment of the crank shaft can be solved from the equation pair $$N_R=\left(1-\frac{4<figure-callout\; id="2"\; label="\cdot \; k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\cdot </figure-callout>k^{}{}^2\cdot I}{s^2\cdot {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\cdot m}\right)\cdot \frac{N_C}{k}+\frac{2\cdot k\cdot I}{s\cdot d\cdot m}\cdot F_R$$

  

  $${\left(N_C\right)}^{\langle t\arg \mathit{et}\rangle }=\left(1-\frac{4<figure-callout\; id="2"\; label="\cdot \; k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\cdot </figure-callout>k^{}{}^2\cdot I}{s^2\cdot {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\cdot m}\right)\cdot {\left(N_C\right)}^{\langle \mathit{now}\rangle }+\frac{2\cdot {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\cdot I}{s\cdot d\cdot m}\cdot F_R$$

  
• This way, changes in the speed of the simulated bicycle and in the speed of the flywheel follow each other at least approximately when the cyclist rides in the standard gear.
• At a constant speed $$N_C=s\cdot F_R\cdot \frac{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}{2}$$

  

  
  and thus $${\left(N_C\right)}^{\langle t\arg \mathit{et}\rangle }={\left(N_C\right)}^{\langle \mathit{now}\rangle }$$

  
• When gears are shifted to a lower one, resistance disappears. The crank speed must be increased until the free wheel is clutched. The same situation occurs when the cyclist starts to pedal after rolling downhill. In practice, the resistance of the ergometer does not totally disappear since the flywheel must be accelerated.
• When the gear is shifted to a higher one, the resisting moment grows stepwise. Here the breaking capacity sets a practical limit to the change.
• These situations require introduction of an additional term, which disappears when the speed of the flywheel corresponds to the simulated speed. This term relates to the operation of the bicycle gearing and engagement of gears. A physical model may be derived for this additional term.
• Considering the computational model, the algorithm may be presented as follows.
1. 1) Measuring breaking current and crank speed R
2. 2) Calculating Nc and Fw $$F_W=\frac{2\cdot N_C}{s\cdot d}$$
   
3. 3) Calculating Δv and v $$\mathrm{\Delta }v=\frac{1}{m}\cdot \left(F_W-F_R\right)\cdot \mathrm{\Delta }t$$
   
   $$v=v+\mathrm{\Delta }v$$
   
   
   where Δt is the adjustment range of the break
4. 4) Calculating a new FR $$F_R=\frac{1}{2}\cdot \mathrm{\gamma }\mathrm{\cdot }\mathrm{\rho }\cdot A\cdot {\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">v</figure-callout>}}^2+\mathrm{\mu }\cdot m\cdot g+\mathrm{\theta }\cdot m\cdot g$$
   
5. 5) Setting a new target moment $$v\left(\mathit{rpm}\right)=\mathrm{\pi }\cdot s\cdot d\cdot \frac{R}{60}$$
   
   • 5a) if v(rpm) ≥ v-δ $${\left(N_C\right)}^{\langle t\arg \mathit{et}\rangle }=\left(1-\frac{4<figure-callout\; id="2"\; label="\cdot \; k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">\cdot </figure-callout>k^{}{}^2\cdot I}{s^2\cdot {\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">d</figure-callout>}}^2\cdot m}\right)\cdot {\left(N_C\right)}^{\langle \mathit{now}\rangle }+\frac{2\cdot {\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="imgf0001.png,imgf0002.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\cdot I}{s\cdot d\cdot m}\cdot F_R+K\cdot \left(v\left(\mathit{rpm}\right)-v\right)$$
     
   • 5b) if v(rpm)< v-δ $${\left(N_C\right)}^{\langle t\arg \mathit{et}\rangle }=0$$
     
• As already stated above, the essential feature of the invention is the use of a virtual flywheel simulation. In the virtual flywheel simulation, the desired exercise route is stored as a course and elevation file. The storing may be performed by means of a GPS device and an elevation sensor device, for instance. The above-mentioned information may be obtained as a result of storing performed by the user. It is also feasible to use stored route information that is for sale or otherwise available. The route is repeated virtually by the software in the user interface of the exercise device so that the resistance and the inertia derived from computational kinetic energy and potential energy are adjusted automatically as functions of the route's angle of ascent and descent and of air and rolling resistance dependent on the speed. The adjustment may be implemented according to the calculation principles described above.
• Storing of the route may also involve its videoing. A videoed route is repeated according to the user's travel speed.
• The route is preferably repeated on the display 7 of the user interface of the exercise device as the exercising person proceeds. The route may be repeated as an elevation profile, etc. The route is repeated virtually so that the resistance is adjusted automatically according to the route as stated above. The exercising person may influence the resistance by shifting the gears of the virtual bicycle. A lower gear results in a lower speed, smaller air resistance and smaller amount of work to be performed uphill. A higher gear correspondingly results is a higher speed, greater air resistance and larger amount of work to be performed uphill.
• The following embodiments may be presented as examples of the application of the invention.
• The total mass of the bicycle and cyclist is 80 kg. The cyclist rides on a flat terrain at a crank speed of 91 rpm and in a gear having a transmission ratio of 3. In that case, the ground speed is 10 m/s. The resisting force is 16.1 N. To maintain a constant speed, the cyclist needs a constant torque of 16.9 Nm.
• The cyclist encounters an uphill having an angular coefficient of 0.01 (inclination 0.6 degrees). Now the resisting force shoots up to a value of 24 N. Since the cyclist was riding at a constant torque, his speed starts to slow down at an acceleration rate of -0.1 m/s2. This is illustrated in Figure 3. Correspondingly, the target moment of the break behaves as shown in Figure 4. The maximum value of the resisting moment is 20.7 Nm, which corresponds to a force of 19.7 N. Taking the slowing down into account thus drops the virtual resisting force from 24 N to 19.7 N, i.e. the hill is faced more smoothly.
• In the case of a light flywheel, the resisting moment is increased in an even more controlled manner as shown in Figure 5.
• Figures 6 and 7 illustrate a situation where the gears are shifted downwards from gear 3 to gear 1.5. In this situation, the moment of inertia of the flywheel should be small. In the situation of Figures 6 and 7, it takes a few seconds until pedalling starts to accelerate the speed of the bicycle.
• Figures 8 and 9 illustrate shifting downwards when a light flywheel is used. It can be seen from Figures 8 and 9 that shifting occurs faster when a light flywheel is used. On the basis of Figures 6 to 9, it may be assumed that different time constants are needed for a light and a heavy flywheel.
• Figures 10 and 11 illustrate a situation where the gears are shifted upwards from gear 3 to gear 3.5. For a moment, the cyclist experiences a high resistance at the pedals if he tries to maintain the same crank speed as before shifting.
• Figures 12 and 13 illustrate a situation where the cyclist accelerates on a flat surface using gear 3. The resistance is considerable even before the air resistance becomes predominant.
• Figures 14 and 15 illustrate a situation where the cyclist rides from a flat surface downhill without pedalling. In the figures, the slope of the downhill is assumed to be more than 2 degrees (0= -0.04). The motion of the flywheel does not reach the simulated speed until pedalling starts.
• The issues and examples illustrated above are by no means intended to limit the invention, but the invention may be modified freely within the scope of the appended claims. The invention was illustrated above by means of an exercise bike/ergometer. The invention is not, however, in any way limited to such a device but the invention is applicable to any exercise device provided with a flywheel, such as spinning bikes, elliptical exercise devices, rowing devices, etc.

Claims (10)

1. A method in connection with an exercise device, which comprises a flywheel, wherein resistance of an exercise being performed is adjusted by decelerating the rotation of the flywheel, characterized in that the magnitude of the exercise resistance is further adjusted by a virtual flywheel simulation.
2. A method according to claim 1, characterized in that the virtual flywheel simulation comprises storing a desired exercise route as a course and elevation file and repeating the route virtually by software in a user interface of the exercise device so that the resistance and the inertia obtained from computational kinetic and potential energy are adjusted automatically as a function of the route's angle of ascent/descent and of air and rolling resistance dependent on the speed.
3. A method according to claim 1 or 2, characterized in that the user of the exercise device changes the resistance by using the gears of the exercise device virtually.
4. A method according to claim 2, characterized in that the desired exercise route is videoed in connection with storing and the stored exercise route is repeated as the exercising person proceeds.
5. A method according to claim 2 or 4, characterized in that the stored exercise route is repeated on a display (7) of the user interface (6) of the exercise device.
6. An arrangement in connection with an exercise device, which comprises a flywheel, wherein resistance of an exercise being performed is arranged to be adjusted by decelerating the rotation of the flywheel, characterized in that the arrangement comprises a means arranged to further adjust the resistance by means of a virtual flywheel simulation.
7. An arrangement according to claim 6, characterized in that in the virtual flywheel simulation, a desired exercise route is arranged to be stored as a course and elevation file and the stored information is arranged to be repeated virtually by software in a user interface of the exercise device so that the resistance and the inertia obtained from computational kinetic and potential energy are adjusted automatically as a function of the route's angle of ascent/descent and of air and rolling resistance dependent on the speed.
8. An arrangement according to claim 7, characterized in that the arrangement is provided with means allowing the user of the exercise device to use the gears of the exercise device virtually and thus to change the resistance.
9. An arrangement according to claim 7, characterized in that the exercise route is arranged to be videoed in connection with storing and that the arrangement comprises means for repeating the stored exercise route as the exercising person proceeds.
10. An arrangement according to claim 9, characterized in that the exercise route is arranged to be repeated on a display (7) of the user interface (6) of the exercise device.

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