The interactive calculation form enables the analysis of energy demand and costs when driving a car. By entering fuel properties, vehicle parameters, and driving conditions, the influence of air resistance on fuel consumption can be calculated.
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Source
Based on a template by Volker Torgau: https://technik-unterricht.de
Description of the application
The calculation form is divided into four sections, which together enable a complete analysis of fuel consumption due to air resistance.
The air resistance force is calculated as follows:
[ F_{text{air}} = frac{1}{2} cdot c_w cdot rho cdot A cdot v^2 ]
The power required to overcome air resistance is given by:
[ P_{text{air}} = F_{text{air}} cdot v ]
- Fuel energy: Here, fuel characteristics such as calorific value and density are entered. The application calculates the usable energy per liter from these values, taking into account a typical engine efficiency of η = 0.25.
- At the gas station: Entry of fuel price and refueling amount to calculate refueling costs and the total energy filled.
- The vehicle: Selection of various vehicle types (sports car, mid-size car, SUV) with predefined values for drag coefficient cw, frontal area A, and mass.
- Calculation example: Entry of speed and driving distance to calculate air resistance force, required power, energy demand, and resulting costs.
Interactive control
The application offers various input options:
- Fuel characteristics: Calorific value (kWh/kg) and density (kg/m³) can be adjusted. The dependent values are calculated automatically.
- Vehicle selection: A dropdown menu allows quick selection of typical vehicle categories with realistic parameters.
- Vehicle parameters: The cw value and frontal area can also be adjusted manually to simulate custom vehicles.
- Driving conditions: Fuel price, refueling amount, speed, and driving distance are controlled via numeric input fields.
Physical background
At higher speeds, air resistance is the dominant factor for fuel consumption. Since the air resistance force increases quadratically with speed and the required power even increases cubically, doubling the speed leads to an eightfold increase in the power required to overcome air resistance.
The application considers a typical efficiency of η = 0.25 for internal combustion engines, which means that only about one quarter of the chemical energy contained in the fuel is actually converted into mechanical driving power.