The "Calculate My Fuel" app leverages various APIs and technical components to provide accurate fuel cost estimates for your trips. Here’s an overview of how the app works:

1. Distance Calculation

The app uses the Google Maps API to calculate the distance between the starting point and the destination. Users input their start and end locations, and the app sends a request to the Google Maps Distance Matrix API, which returns the distance and estimated travel time.

                            
            fetch(`https://maps.googleapis.com/maps/api/distancematrix/json?origins=${startLocation}&destinations=${endLocation}&key=YOUR_API_KEY`)
                .then(response => response.json())
                .then(data => {
                    const distance = data.rows[0].elements[0].distance.value; // Distance in meters
                    const duration = data.rows[0].elements[0].duration.value; // Duration in seconds
                });
                            
                        

2. Fuel Consumption Calculation

The user provides their vehicle’s fuel consumption rate, either in liters per 100 kilometers (L/100km) or miles per gallon (mpg). The app then calculates the fuel needed based on the distance obtained from the Google Maps API.

                            
            // Example calculation for fuel needed in metric system
            const fuelNeeded = (distance / 1000) * (fuelConsumption / 100); // Distance converted to km
                            
                        

3. Adjusting for Driving Style

The app allows users to select their driving style, which affects fuel consumption. The driving style multiplier (S) is applied to the calculated fuel needed.

                            
            const drivingStyleMultiplier = getDrivingStyleMultiplier(userDrivingStyle);
            const adjustedFuelNeeded = fuelNeeded * drivingStyleMultiplier;
                            
                        

4. Adjusting for Elevation Gain

Elevation gain impacts fuel consumption. The app uses the Google Maps Elevation API to get elevation data for the route. The additional fuel needed due to elevation gain is calculated and added to the total fuel needed.

                            
            fetch(`https://maps.googleapis.com/maps/api/elevation/json?locations=${routeCoordinates}&key=YOUR_API_KEY`)
                .then(response => response.json())
                .then(data => {
                    const elevationGain = calculateElevationGain(data.results);
                    const additionalFuel = elevationGain * elevationFactor; // elevationFactor is a predefined constant
                    const totalFuelNeeded = adjustedFuelNeeded + additionalFuel;
                });
                            
                        

5. Total Fuel Cost Calculation

Finally, the app calculates the total fuel cost by multiplying the total fuel needed by the fuel price provided by the user.

                            
            const fuelCost = totalFuelNeeded * fuelPrice;
                            
                        

The app also provides an option to calculate the cost for a return trip by simply doubling the total fuel cost.

                            
            const returnTripCost = fuelCost * 2;
                            
                        

Summary

By integrating the Google Maps Distance Matrix API and Elevation API, the "Calculate My Fuel" app efficiently calculates the fuel cost for your trips. The app considers distance, fuel consumption rate, driving style, and elevation gain to provide accurate and reliable estimates, helping you plan your journeys better.

To explain how the "Calculate My Fuel" app works in calculus terms, we need to derive the formulas used to calculate the fuel cost, considering distance, fuel consumption, and elevation gain. Let's break it down step by step.

Distance Calculation

The distance between the starting point and destination is obtained using the Google Maps API. For simplicity, we assume the distance is given directly as \( D \) kilometers or miles.

Fuel Consumption Calculation

Let \( C \) be the fuel consumption in liters per 100 kilometers (L/100km) for the metric system, or in miles per gallon (mpg) for the imperial system.

1. Metric System (km, L):
\[ \text{Fuel Needed (liters)} = \frac{D \times C}{100} \]

2. Imperial System (miles, gallons):
\[ \text{Fuel Needed (gallons)} = \frac{D}{C} \]

Adjusting for Driving Style

The driving style affects the fuel consumption. Let \( S \) be the driving style multiplier:

- Passive: \( S = 0.8 \)
- Normal: \( S = 1.0 \)
- Aggressive: \( S = 1.2 \)

Thus, the adjusted fuel needed \( F \) is:

1. Metric System:
\[ F = \frac{D \times C}{100} \times S \]

2. Imperial System:
\[ F = \frac{D}{C} \times S \]

Adjusting for Elevation Gain

Elevation gain impacts fuel consumption due to the extra energy required to ascend. Let \( E \) be the total elevation gain in meters. The additional fuel needed due to elevation gain can be modeled as:

\[ \text{Additional Fuel (liters or gallons)} = E \times k \]

where \( k \) is a constant factor (e.g., \( k = 0.0001 \)).

Total Fuel Cost Calculation

Combining the fuel needed for distance and elevation gain, the total fuel needed \( F_t \) is:

1. Metric System:
\[ F_t = \left( \frac{D \times C}{100} \times S \right) + (E \times k) \]

2. Imperial System:
\[ F_t = \left( \frac{D}{C} \times S \right) + (E \times k) \]

The total fuel cost \( \text{Cost} \) is then:

1. Single Trip:
\[ \text{Cost} = F_t \times P \]

2. Return Trip (Distance doubled):
\[ \text{Cost} = 2 \times F_t \times P \]

where \( P \) is the price per liter or gallon.

Calculus Derivation

To derive these formulas using calculus, consider the following steps:

1. Distance Integral:
Suppose the path between the starting point and destination is a function \( D(x) \), where \( x \) is a parameter along the path. The total distance is:

\[ D = \int_{a}^{b} \sqrt{ \left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 } \, dt \]

2. Fuel Consumption Integral:
Let \( C(x) \) be the fuel consumption rate at point \( x \). The total fuel needed is:

\[ F = \int_{a}^{b} C(x) \, dx \]

3. Elevation Gain Integral:
Let \( E(x) \) be the elevation gain at point \( x \). The total additional fuel needed due to elevation gain is:

\[ \text{Additional Fuel} = k \int_{a}^{b} E(x) \, dx \]

Combining these, the total fuel cost \( \text{Cost} \) is:

1. Metric System:
\[ \text{Cost} = \left( \int_{a}^{b} \frac{C(x)}{100} \, dx \times S \right) + \left( k \int_{a}^{b} E(x) \, dx \right) \times P \]

2. Imperial System:
\[ \text{Cost} = \left( \int_{a}^{b} \frac{1}{C(x)} \, dx \times S \right) + \left( k \int_{a}^{b} E(x) \, dx \right) \times P \]

Example Calculations

Let’s go through a specific example in the metric system:

- Distance \( D = 200 \) km
- Fuel consumption \( C = 8 \) L/100km
- Driving style \( S = 1.0 \) (Normal)
- Elevation gain \( E = 500 \) meters
- Fuel price \( P = 1.5 \) USD/Liter

1. Fuel needed for distance:
\[ F = \frac{200 \times 8}{100} \times 1.0 = 16 \text{ liters} \]

2. Additional fuel for elevation gain:
\[ \text{Additional Fuel} = 500 \times 0.0001 = 0.05 \text{ liters} \]

3. Total fuel needed:
\[ F_t = 16 + 0.05 = 16.05 \text{ liters} \]

4. Total cost for a single trip:
\[ \text{Cost} = 16.05 \times 1.5 = 24.075 \text{ USD} \]

5. Total cost for a return trip:
\[ \text{Cost} = 2 \times 16.05 \times 1.5 = 48.15 \text{ USD} \]

This detailed explanation and calculus derivation provide a thorough understanding of the mathematical basis for the fuel cost calculations in the "Calculate My Fuel" app.