Sports-Lesson
Calculating the expended physical energy in various sports.
Here, you and your class can input statistics about your athletic performance in football, biking and other types of sport. We calculate the expended physical energy for you and compare that to the energy output of a small PV-plant (1kWp). We test your performance against the PV-plant's by comparing how long different daily electrical utilities can be powered with the energy.
Choose here from a pool of sports. You can jump to the input form for a sport by clicking on the corresponding row in the summary table. On selection of a sport, all other options will be hidden. If you remove a sport from these selection tags, all information associated with your input (if any) will be lost.
Type of sport | Produced energy [Wh] | Energy through PV [Wh] |
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Error Text
How long can different daily utilities be powered?
And other comparisons
A 6W LED lamp:
0 min
0 min
A 650W vacuum cleaner:
0 min
0 min
A 2000W hairdryer:
0 min
0 min
A streaming provider like netflix:
0 min
0 min
A warm shower:
0 min
0 min
Your own device à
Watt:
0 minutes
0 min
Boil this many liters of water:
0 l
0 l
Advanced
Here, you can see how the mechanically expended energy varies corresponding to the input parameters (sliders).
This is a way to inspect the energy functions we have implemented. The x-axis always shows the parameter that was fixed lastly.
Calculating for: {Type of sport}
Change in energy
Distance travelled
Average Weight
Number of participants
Time needed
Number of games played
Documentation
We consistently neglect the actual muscle energy needed to move the body. Most of the energies displayed here are calculated as the sum of a kinetic energy part and work that needs to be done against earth's gravitational field (e.g. when lifting up one's foot). To calculate the latter, we make such assumptions that the number of traveled steps N over a distance is fixed. Together with the height to which one foot is raised, h, the total energy is calculated in most cases as E = 1/2 mv^2 + Nmgh, where g=9.81m/s^2 denotes the gravitational acceleration.
If not specified otherwise, the velocity is taken to be the mean velocity over the time interval.
We now list our assumptions for the various sports activities:
Download xlsx
Short distance race
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Stepping frequency of 4/s
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Foot is raised by 50cm each step
Middle distance race
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Stepping frequency of 3/s
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Foot is raised by 20cm each step
Long distance run
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Fixed step-size of 0,8m
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Foot is raised by 5cm each step
Football:
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One player runs 10.000m per game
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This player accelerates ten times every five minutes. Each of those sprints has a duration of four seconds and the distance traveled during that time is 10m on average
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When jogging: Step-size 1m, foot is raised by 15cm each step
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When sprinting: Step-size 1,5m, foot is raised by 40cm each step
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50 "Start-Stops" during the whole game per player (If a player sprints a distance of 5m twice with a short brake inbetween, we calculate their energy as two times 1/2mv^2 for each 5m section, not just one time 1/2mv^2 over the whole 10m)
Basketball:
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One player runs 4.000m per game
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This player accelerates ten times per minute. Each of those sprints has a duration of three seconds and the distance traveled during that time is 5m on average
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When jogging: Step-size 1m, foot is raised by 15cm each step
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When sprinting: Step-size 1,5m, foot is raised by 40cm each step
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80 "Start-Stops" during the whole game per player (see explanation football)
Biking:
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We calculate the mean power needed as a function of the velocity of the biker by reading off the values of the corresponding diagram at the webpage https://www.leifiphysik.de/mechanik/arbeit-energie-und-leistung/ausblick/energie-und-leistung-beim-fahrradfahren and fitting a power-law function to the velocity-power-diagram data
Rope-Jumping:
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Jumping frequency of 2/s
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Height of each jump: 5cm
For calculating the energy consumption of a streaming provider, we use the value P_stream = 6500W (Source: https://energiemarie.de/energietipps/stromverbrauch/streaming, accessed on the 12.11.2023).
For the shower calculation, we assume that a 7-minute shower à 91l of water consumes 3,5kWh (Source: https://www.enex.me/blog/wie-viel-energie-braucht-duschen), this is equivalent to a power of P_showering = 30kW.
For the boiling water calculation, we note that the energy needed for a temperature increase ΔT of the water, can be written as E=m*c_m*ΔT. Here, c_m is the specific heat capacity of water and M the water mass. We take the necessary temperature increase to be 80 deg. cels., meaning that the water is at room temperature before the boiling stars, T_0 = 20 deg. cels. This means, that the increase in temperature must be around ΔT=350K. With this, we can solve for the energy consumption per mass and since for water 1kg~1l, we can estimate the energy consumption per liter as: 1.463.350 J/l .
Update to the documentation, 09.Sept.2024:
In the sports "short" and "middle distance race" we now also include the work done against air resistance. We calculate this as force times distance, where the force is calculated from the drag equation (cf. https://en.wikipedia.org/wiki/Drag_equation). For the latter we take 1.3 to be the Drag-Coefficient for the human body for its surface area we use 180cm x 30cm.
Furthermore, from now an we calculate the step frequency as a function of velocity for all running disciplines (exponential fit): The bigger the velocity, the smaller the step frequency, the larger the step size over the same distance.
Exercise problems
For inspiration, we have collected ideas for exercise problems that employ this calculator in our Lessons Table in a small PDF; we strive to extend these examples as soon as possible.