# Thread: What is the average turning angle I should take to stay within a defined circle?

1. ## What is the average turning angle I should take to stay within a defined circle?

I know that a boat has enough gas to travel 120 km. I also know that the maximum distance it can reach from a central point is 60 km (because the lake it's in is a circle with radius 60 km).

How frequently should the boat turn on average if it is constrained to turn at 45 degrees to keep it within this circle?

2. I'm sorry, but I don't understand what you're asking. When you say the boat is "constrained to turn at 45 degrees," do you mean it can turn at any angle up to 45 degrees, or that it can only turn at exactly 45 degrees? Further, what do you mean by "How frequently should the boat turn on average?" There is literally an infinite number of paths the boat can take to stay within the circle, so we can't consider all of them to compute an average.

3. Originally Posted by ksdhart
I'm sorry, but I don't understand what you're asking. When you say the boat is "constrained to turn at 45 degrees," do you mean it can turn at any angle up to 45 degrees, or that it can only turn at exactly 45 degrees? Further, what do you mean by "How frequently should the boat turn on average?" There is literally an infinite number of paths the boat can take to stay within the circle, so we can't consider all of them to compute an average.

I mean the boat can turn at exactly 45 degrees only. In the case of it heading in a straight line the boat would hit a point 120 km away from the start but if it turned 180 degrees every time step it would only reach the 60 km point. Obviously that's unrealistic so I thought there'd be some way to find out how often it should turn if it could only turn 45 degrees. Hope that makes a bit more sense.

4. Originally Posted by killbot2000
I know that a boat has enough gas to travel 120 km. I also know that the maximum distance it can reach from a central point is 60 km (because the lake it's in is a circle with radius 60 km).

How frequently should the boat turn on average if it is constrained to turn at 45 degrees to keep it within this circle?
What are your thoughts? What have you done so far? Please show us your work even if you feel that it is wrong so we may try to help you. You might also read
http://www.freemathhelp.com/forum/th...Before-Posting

The angle of turn is not the only thing that determines where the boat/aircraft/car/... goes. You also need the velocity. So together you need a turn angle and velocity as a function of time [both could be constant but, as ksdhart said, the question, as posed, leaves that ambiguous]

5. My original post was too vague. I want to assume a constant velocity, say 30km/hr, and a constant turning angle for the boat.
If it's going in a straight line from the centre it'll reach the edge of the lake in 2 hours, but still have gas to go for another 2.
Like I said before, if the boat turns 180 degrees every time step it would proceed along a straight line and never go beyond the edge.
Something like a 45 degree turning angle seems more realistic.

I'm trying to build a game for this where the movement parameters for the boat prevent it from going beyond the lake.