{"title"=>"How Many People are Needed for Crowd GPS Coverage?", "description"=>"Showing how math can be used to calculate the number of people needed for crowd gps coverage in your city"}
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We get this question all the time. Crowd GPS is a innovative alternative to traditional GPS and offers customers a subscription free way to locate and recover lost or stolen items such as bikes, pets, and more. However, we need to build a network of people to participate in the Crowd GPS network in order to have the most effective solution possible. While we have shown our Crowd GPS coverage, people often ask "Exactly how many people are required in my city for Crowd GPS to be effective?" In honor of Pi day, we'll answer that for you.

We derived the formula with basic geometry (Note: If you don't care about math, just skip to the bottom and we'll give numbers for specific cities and the end formula). Let's say we have a city that is a perfect square. The city area would be simply be the distance of each side multiplied (L^{2}). If we then had a circle approximate the area of the city where the radius of the circle is L/2. The approximated area of the city would be π(L/2)^{2}.

Now imagine that we had everyone participating in the Crowd GPS network start from the center of the circle and begin to walk outward until the edge of the circle. If they did this each day, everyone in the city would get at least one Crowd GPS update on the item every day (as long as no one called in sick). The piece of area an individual covers would be the (distance traveled per day) * (width of their cell phone bluetooth covereage)^{1}. With this we can say an approximate number of people required to have daily Crowd GPS coverage in the city would be (Approximated Area of City)/(Individual Crowd GPS Coverage Area).

Now to let math do its work...

number of people required for Crowd GPS coverage = A_{approximate}/A_{person}=π*r^{2}/(d_{person}*w_{bluetooth}) = π*(L/2)^{2}/(d_{person}*w_{bluetooth}) = π*A_{city}/(4*d_{person}*w_{bluetooth})

Now we'll add a factor to account for people overlapping themselves (imagine that a certain percent of the people walking from the center of your town all end up at the same spot...probably the bar...)

**number of people required for Crowd GPS coverage = (1+O _{v})*π*A_{city}/(4*d_{person}*w_{bluetooth}), where O_{v} is the percentage of overlap**. Done!

Let's calculate the number of people required in each city. For these calculations I'm assuming a 20% overlap. I'm using the distance per person per day is 1 mile . The Bluetooth diameter is 200ft.

- San Francisco - 1,248 people
- Manhattan - 569 people
- Los Angeles County - 12,541 people

I think these numbers show the possibility of Crowd GPS and we are excited to build a world wide network for finding lost items.

1 - I understand that maybe a better means would be to use area of triangles rather than squares. If you have suggestions on some better math, please email me chris (at) thetrackr.com and I'll improve the accuracy of the formula.

Note - The square assumption works for any city, even if your city is not a square because any city can be approximated as a collection of smaller squares and we can perform an summation adding up all the smaller squares.