Need help calculating the odds on a falling object.

[freerangequark]

I am working on a product development project for an aircraft application.

I need a rough calculation of the odds of a particular part falling off a particular aircraft during a particular emergency of hitting a person(s) on the ground. This is to cover the contiguous United States.

Variables I have:

1. Population density of the contiguous United States, 79.6 people per square mile (79.6 people per 27,878,400 sq. ft.)

2. Land area of the contiguous United States, 3,043,615 sq miles (84,851,116,416,000 sq. ft.)

3. Average area per person, 3.7 sq. ft.

4. Max. size of the falling part. 3' X 9' (27 sq. ft.)

5. Frequency of the emergency. 1 instance per 96,429 flight hours


How can I determine the chances per occurance (or per flight hour) of this falling part hitting a person(s)?

I realize there are many other variables to consider such as the population density of a given geographic area, but all I need is an average.

Any help is greatly appreciated.

Thanks,
Glenn

 

[Jhero]

The chance of a particular part falling off a particular aircraft and hitting a person(s) on the ground depends on several factors, including the population density of the area where the aircraft is flying, the size of the part that could potentially fall off, and the frequency of the emergency situation. To calculate the odds of this happening, you can use the following formula: Odds per Occurrence = (Population Density x Average Area per Person) / (Land Area x Size of Part) For example, if the Population Density of the contiguous United States is 79.6 people per square mile, the Average Area per Person is 3.7 sq. ft., the Land Area is 3,043,615 sq miles, and the Max. Size of the Part is 27 sq. ft., then your odds per occurrence would be:Odds per Occurrence = (79.6 people/sq mile x 3.7 sq. ft./person) / (3,043,615 sq miles x 27 sq. ft.) Odds per Occurrence = 0.000002To calculate the odds per flight hour, you need to adjust the formula to account for the frequency of the emergency situation. In this case, the frequency is 1 instance per 96,429 flight hours, so the odds per flight hour would be: Odds per Flight Hour = (Population Density x Average Area per Person) / (Land Area x Size of Part x Frequency of Emergency) Odds per Flight Hour = (79.6 people/sq mile x 3.7 sq. ft./person) / (3,043,615 sq miles x 27 sq. ft. x 96,429 flight hours) Odds per Flight Hour = 0.000000002The odds of a particular part falling off a particular aircraft and hitting a person(s) on the ground during a particular emergency situation are extremely small. However, it is important to remember that these numbers are averages, and the actual odds can vary significantly depending on the population density of a given geographic area.