Coldplay Concert: Renewable Energy Sources

Problem Statement

Coldplay is organizing a sustainable concert for 50,000 people, intending to run the entire event using renewable energy sources. As part of their plan, they have various energy-generating installations. Your goal is to calculate the total energy generated and compare it with the concert's estimated energy consumption.

Energy Sources to Consider

1. Kinetic dance tiles: There are 60 kinetic dance tiles installed at the venue. Each tile can generate energy based on the time it is activated by people dancing on them.
2. Stationary bicycles: The concert will feature 20 stationary bicycles for attendees to pedal. The energy output depends on the number of people using the bicycles and how long they are pedaled.
3. Solar panels: Solar panels are installed at the concert venue. The energy generated will depend on the sun exposure during the day of the concert.
4. Portable wind turbines: 10 portable wind turbines are installed around the venue. The energy generated depends on the wind speed and the time they operate during the concert.
5. Piezoelectric stage floor: The stage floor is equipped with piezoelectric sensors to capture energy from the performers' movements. The energy generated will depend on the activity level on the stage.
6. Hydrogen fuel cell: A hydrogen fuel cell is installed to serve as a backup energy source.
7. Thermal energy from attendees: Participants generate thermal energy through body heat, which can be captured and converted into electricity.
8. Sound energy capture system: The loud music and crowd noise during the concert produce sound waves that can be converted into electricity.

Data for Calculations

The following data will be needed to calculate the energy from each source:

• Kinetic dance tiles: Each tile can generate 40 W of power when activated. It is estimated that 15% of attendees (7,500 people) will dance on the tiles for 1.5 hours.
• Stationary bicycles: Each bicycle can produce 120 W of power. They will be used for 2.5 hours during the concert, and the concert organizers estimate that there will be a continuous rotation of people using all bicycles.
• Solar panels: The solar panels have a total area of 200 m². The average solar irradiance on the day of the concert is expected to be 700 W/m², and the concert day will have 6 hours of sunlight.
• Portable wind turbines: Each wind turbine can produce power proportional to the cube of the wind speed. The wind speed is expected to be 6 m/s during the concert, and the turbines will operate for 3 hours. Each turbine has a blade radius of 2 meters.
• Piezoelectric stage floor: The piezoelectric sensors on the stage floor can generate 50 W per square meter during active use. The stage area is 100 m², and it is estimated that the performers will be moving on stage for 80% of the 3-hour concert duration.
• Hydrogen fuel cell: The fuel cell has an efficiency of 50% and can produce 30 kWh of energy using hydrogen as fuel during the concert.
• Thermal energy from attendees: Each person generates 0.1 kWh of thermal energy per hour. All 50,000 attendees will contribute this energy throughout the 3-hour concert.
• Sound energy capture: The sound system is designed to capture 0.005 kWh of energy from each attendee based on the crowd's noise and the music played during the concert.

Estimated Concert Energy Consumption

The estimated energy consumption for the entire concert is 800 kWh. This includes the power required for lighting, sound systems, video screens, and other necessary equipment to run the concert.

Task

Your task is to calculate:

1. The total energy generated from all renewable sources during the concert.
2. Compare the total energy generated with the estimated energy consumption (800 kWh).
3. Determine whether the concert can run entirely on renewable energy, and if there is an energy surplus or deficit.

Formulas and Hints

• Kinetic tiles energy: The energy generated is given by \( P = 40 \text{ W} \times t \), where \( t \) is the total time the tiles are activated.
• Bicycles energy: The energy generated is given by \( P = 120 \text{ W} \times t \), where \( t \) is the total usage time.
• Solar panels energy: The energy generated is \( P = \text{Area} \times \text{Irradiance} \times t \), where the irradiance is in watts per square meter, the area is in square meters, and \( t \) is the total sunlight hours.
• Wind turbines energy: Use the formula \( P = 0.5 \times \rho \times A \times v^3 \times t \), where \( \rho = 1.225 \, \text{kg/m}^3 \) is the air density, \( A = \pi \times r^2 \) is the swept area of the blades, \( v \) is the wind speed, and \( t \) is the operating time.
• Piezoelectric stage energy: The energy generated is \( P = 50 \text{ W/m}^2 \times \text{Area} \times \text{Active time} \), where the active time is a percentage of the concert duration.
• Hydrogen fuel cell energy: The total energy generated by the fuel cell is 30 kWh with a 50% efficiency.
• Thermal energy from attendees: The total energy is given by \( P = 0.1 \text{ kWh/person} \times \text{attendees} \times t \), where \( t \) is the total time in hours.
• Sound energy capture: The total energy is \( P = 0.005 \text{ kWh/person} \times \text{attendees} \).

Resolution Steps

Follow these steps to calculate the total energy generated and make a comparison:

1. Calculate the energy generated by each energy source using the data provided.
2. Sum up the energy from all sources to find the total energy generated.
3. Compare the total energy generated to the 800 kWh required for the concert.
4. Determine if the energy is sufficient, and if not, calculate the energy deficit.

Conclusion

Once you have completed the calculations, analyze whether the concert can be run fully on renewable energy and if any improvements or additional energy sources are needed to cover the total energy consumption.