A theme park is designing a new roller coaster and wants to maximize thrill while ensuring safety. The roller coaster will have a maximum height of 200 feet, a total track length of 4,000 feet, and an average speed of 60 miles per hour. Calculate the number of inversions, drops, and turns needed to achieve the desired thrill level while adhering to safety regulations. Also, estimate the construction cost based on materials, labor, and engineering expertise required.

To maximize thrill while ensuring safety, the roller coaster should have a good balance of inversions, drops, and turns. The number of each element will depend on factors such as track length, height, and speed.

1. Inversions: Roller coasters with more inversions tend to be more thrilling. However, too many inversions can cause excessive G-forces and discomfort for riders. A safe range for inversions is between 4-6 for a roller coaster of this size. Let's assume 5 inversions for our design.

2. Drops: Large drops create a feeling of weightlessness and are an essential part of any thrilling roller coaster. Given the maximum height of 200 feet, we can include one major drop (around 180 feet) and two smaller drops (approximately 60-80 feet each). This would result in a total of 3 drops.

3. Turns: High-speed turns add excitement and variety to the ride experience. Considering the average speed of 60 miles per hour and the total track length of 4,000 feet, we can estimate around 8-10 high-speed turns throughout the course of the ride. Let's assume 9 turns for our design.

Now let's estimate the construction cost based on materials, labor, and engineering expertise required:

1. Materials: Steel roller coasters typically cost around $100-$150 per linear foot. For a 4,000-foot track, this equates to approximately $400,000 - $600,000 in material costs.

2. Labor: Construction labor costs vary depending on location and complexity of the project. On average, labor costs for roller coaster construction can range from $500,000 to $1 million.

3. Engineering Expertise: Designing a safe and thrilling roller coaster requires specialized engineering knowledge. Engineering fees for roller coaster projects can range from $250,000 to $500,000 or more, depending on the complexity of the design.

Adding up these costs, we can estimate that the total construction cost for this roller coaster would be between $1.15 million and $2.1 million. Keep in mind that these are rough estimates and actual costs may vary based on factors such as location, specific materials used, and unforeseen challenges during construction.