I must adjust the arithmetic since a reviewer, “msnemo”, found and explained the error in my bullet/raindrop calculation. She did a great job without making me feel overly ashamed. We believe that the following is correct, and welcome comment and correction.
A bullet will hit a raindrop when the bullet and a raindrop are in the same space at the same time.
A bullet travels a path from muzzle to target at an average speed, over the distance traveled. The bullet is in a volume of space equal to the cross-sectional area of the bullet times the distance traveled; and is in that space for a time-the Time of Flight.
Raindrops are of varied size from about .5 to 5 mm diameter; and rainfall rates vary from .5 to 8mm per hour and above.
The volume of rain, water, in the bullet volume of space, for any rainfall rate per hour and Time of Flight, is easily calculated.
We then know that the bullet and a quantity of rain is in the same space for the same time, Time of Flight, and if that quantity of rain is greater than zero, the bullet will hit one or more raindrops.
Another calculation tells us the raindrop size/quantity in the space.
The EXCEL worksheet with the calculations and simple calculator is available on request.
Note: Read fractional numbers of raindrops as probabilities, for simplicity.
