Calculating the Probability of Hitting a Spinning Fan with a Dart

[Char. Limit]

Here's a question that I thought up while shooting darts through a five-bladed ceiling fan. I'm lazy, so I'll use symbols for the constants in the equation.

Say I have a five-bladed fan of radius R, with a blade width W, spinning at angular velocity V. I shoot a dart of length L through the fan at a speed S. What is the probability that I hit the fan?

Just do the equation, I'll fill in the measured constants later.

 

[tiny-tim]

Hi Char. Limit!

Calculate how long it takes the dart to pass through the fan, and how far round the fan goes in that time. Then subtract that distance from the distance between the blades.

 

[frustr8photon]

Awesome problem. But there's something missing here. It looks like the blades are rectangular. So...we either need to specify some definite radius at which you throw the dart, or define precisely the probability distribution determining where in the circle you are likely to throw the dart.

Let's see what you come up with, mr./mrs. char!

 

[Char. Limit]

The blades are about two feet long, and the radius of fire is about 1.5 feet.

And it's Mr. for future reference (learn something new every day.)

 

[Char. Limit]

Ok, thanks. Just two questions: what do the omega and the little v represent? I've measured the other three (W=5.25 in, R=24 in, and L=3 in). Now I just need those two.

 

[DaveC426913]

Man checks into hospital with dart buried up to hilt in forehead. Sez victim: "Who knew a ricochet could pack so much energy?" News at 11.