Hurricane Evacuation, how l long will it take to evacuate100 000 people?

chrisman10

1. The problem statement, all variables and given/known data
There is a single two ane road connecting the Keys with the mainland. The south-
bound lane must remain open for emergency vehicles, so only one lane is available for
evacuation. In summer, 100,000 residents live on the Keys. Past data taken on the
bridge that connects the Keys to the mainland suggest that cars, during emergencies,
typically hold three people, move no faster than 8 km/hour, and maintain a spacing of
about 10 metres (one car length of 9.2 metres plus 0.8 metres).
(b) How long will it take to evacuate completely these people from the Keys?

(c) In your answer to (b), does it make any difference if all cars leaving the Keys enter
the one open lane of the two-lane road at one single location or if the cars leaving
the Keys enter the one open lane of the two-lane road at multiple locations along
the road? Explain. [Hint: think of the same situation on Highway 401 during
Toronto's rush hour.]

(d) You have to issue the evacuation order in time for a complete and safe evacuation.
If the hurricane, approaching Key West from the southwest, follows a straight path,
where would it be located geographically at the time you issue the evacuation order


2. Relevant equations

No equation were given.


3. The attempt at a solution

Since there are 100 000 thousands people, and 3 people per car, it comes out to 33333 cars because 100000/3= 33333

0.8 meters distances between cars, makes 0.8 x 33333 = 80 000
80 000 / 1000

I'm having trouble figuring out how long the distance is the cars have to travel.
1. The problem statement, all variables and given/known data

voko

Take some location on the bridge. How many cars go through it per second?

Pkruse

I get a little less than two days. But we need to understand that this is an academic exercise only with little relationship to reality. I've done many hurricane evacuations. The only way to make sure you get out safely is to leave about two days before the official order. That is when the real evacuation starts.

chrisman10

Pkruse can you please help me understand how you came up with two days?

chrisman10

How will I do that?

HallsofIvy

How far can one car go in one hour? If that was the last car to pass you in one hour, how far was it from from you when that hour started? How many cars were between you and it when that hour started? So how many cars passed you in that hour? How many cars passed you in one minute? How many in one second?

voko

For one car to go through a location on the bridge, its entire "cell" (10 m) must pass through it.

Pkruse

Chrisman: I base what I say on five decades of living with hurricanes in Florida. I stay put for most of them, even when ordered to evacuate. My house has survived all of them in the last 40 years, always with little or no wind damage. So I look more at the storm surge forecast. If it is high enough to maybe flood me, then I leave. Leaving when told once resulted in me being dead stopped in traffic as the hurricane blew over the top of me. It is very dangerous to depend on the government for my safety. Leaving before the official order works much better.

The numbers in this problem are too optimistic to trust in a real evacuation. Something will happen to completely stop the traffic as the hurricane gets closer. You need to be gone by then.

Pkruse

As for how I worked your problem, that was quick and easy because the numbers selected eliminated the need for a calculator. Speed works out to 8000 m per hr. If each car needs 10 m of space, then that is 800 cars per hr. Can you take it from there?

chrisman10

I get 41.66 hours to evacuate. 33333/800 = 41.66H

chrisman10

Pkruse, do you think it would make a difference on the time for each car if we had a two way lane.

[U][In your answer to (b), does it make any difference if all cars leaving the Keys enter
the one open lane of the two-lane road at one single location or if the cars leaving
the Keys enter the one open lane of the two-lane road at multiple locations along
the road? Explain

chrisman10

Pkruse, do you think it would make a difference on the time for each car if we had a two way lane.

[U][In your answer to (b), does it make any difference if all cars leaving the Keys enter
the one open lane of the two-lane road at one single location or if the cars leaving
the Keys enter the one open lane of the two-lane road at multiple locations along
the road? Explain

chrisman10

Sorry for the double post :( accident

Pkruse

That would have two advantages that are commonly observed in places where they do that. Under nominal conditions, it doubles the flow rate. But even more important traffic continues to flow when one lane is blocked by an accident or breakdown, or more likely you can expect people to start running out of gas because the gas stations are often either shut down or the increased demand has emptied their storage tanks. Part of my evacuation supplies includes 30 gallons of gas so both cars can start with a full tank.

chrisman10

Thanks a lot for your help and knowledge. One last thing, could confirm my answer? 41.67 hours.

Pkruse

That's what I got.

D H

A simple way to see this: with cars moving at 8 km/hr and separated (front bumper to front bumper) by 10 meters, that's 800 cars leaving every hour, or 2400 people per hour given that cars have three passengers. Diving those 100,000 people to be evacuated by that 2400 people/hour yields 41.67 hours to complete the evacuation.