# New AP System possible?

#### Zetta_x

##### The Insane Statistician
OP
Member
If you want to get to the point, skip down to the conclusion. Otherwise here was my thought process.

-------------
AP System = Accident Prevention System

While sitting in my class bored, sipping on my energy drink to keep concentration in class, I was thinking of a new AP system for cars.

Last year, I took a whole physics sequence (the hard one for Physics majors vs other majors), if there is on thing I got out of the classical motion class was:

Using the property that the difference of positions in respect to time is velocity and the difference of velocities with respect to time is acceleration, we get this relation (where x represents distance, t represents time):

a = constant acceleration

dx/dt(dx/dt(x)) = a
or
dx/dt(x) = at + c
or
x(t) = a/2t^2 + v_0t + r_0

Obviously I skipped initial conditions to save space, but we get that under the assumption of a constant acceleration, the distance can be mapped out given an initial velocity and initial position.

How does this have anything to do with AP with cars?

Let car 1 position be mapped with x_1(t) and car 2 position be mapped with x_2(t). If we take everything to a unique reference point, a_i, v_0i, r_0i are all defined => x_i(t) can be defined. Let two cars be in an accident, which implies that x_1(t) = x_2(t) + E, for E is a constant defined to be relatively small. Since E is relatively small, we can take a specific case where E is equal to 0.

=> x_1(t) = x_2(t)
=> x_1(t) - x_2(t) = x_2(t) - x_1(t) = 0

What does this mean? It means, if you take the difference of any two positions and subtract them to get into a neighborhood around 0 with this neighborhood having a increasingly small epsilon, this implies that the cars have got into an accident.

However, when we drive, who drives with constant acceleration? A computer program can calculate these formulas hundreds of times per second. What does this mean, as we calculate the formula hundreds of times per second, we will be using the acceleration given about a millisecond and this acceleration between intervals will be pretty much constant not violating the assumption.

Driving isn't a one dimensional motion, why am I using a one dimensional model? Simple, when you are driving, you are usually traveling in a one dimensional direction not counting the road moving up and down as you are driving. The altitude can easily be calculated without the use of a formula and cars that have significantly greater altitude (such as an overpass) won't be detected as a warning.

---

Conclusion

Using GPS services,

With today's GPS Technology, it is easy to draw information such as a cars acceleration, position with a unique reference point and initial velocities. Using a position function, we can make inferences whether or not a car is about to get into an accident. If the difference of two objects positions is approaching 0 at a defined rate, chances are these two objects are heading for a collision. The car could warn the user seconds before an impact with some type of notification settings.

Neglecting security concerns that your car is being mapped by a GPS to prevent accidents, this could be developed to be a new AP system for cars.

#### murkurie

##### Well-Known Member
Member
A lot of expensive cars already have something like this, generally they can only detect you hitting something, and they can brake for you to prevent a rear end collision, and a few cars also will warn you if you are about to go over the line, the only brand that I know has all of this is Mercedes, And a few Acura's. The only problem for gps is its always a few Feet off for cilivan use.

#### Zetta_x

##### The Insane Statistician
OP
Member
Hmm interesting. I remember watching a video demonstrating the auto breaking system and the car didn't stop at all lol. Considering a few feet is highly significant in detecting a collision, we would need a new wave of better satellites or some type of local system with more precision (radio towers or something)

#### murkurie

##### Well-Known Member
Member
I've seen that video and I believe it was preventing accidents with people walking in the street, not with other cars. Military gps is pretty much exact, but cilivan gps is not. My question is how well dothese systems work in stop and go traffic,

#### Zetta_x

##### The Insane Statistician
OP
Member
Ahhh I see.

That's a good question. Where I live, the freeways (such as 215, 91, 60) were not built for so many people to use them at once, we face an average of 15 mph in most parts. I can imagine something flukeing =P

#### Veho

##### The man who cried "Ni".
Former Staff
The answer is giving cars the ability to "see" obstacles. Echo-location, infra-red laser radar, laser distance measuring, proximity sensors, cameras and object recognition software, watching in all directions. Imagine a hyperadvanced Kinect watching in all directions and keeping track of everything that's around the car (and not just two people, like the current version
). Even with increased accuracy, GPS and similar systems can't give you pinpoint precision.

#### Zetta_x

##### The Insane Statistician
OP
Member
Veho said:
The answer is giving cars the ability to "see" obstacles. Echo-location, infra-red laser radar, laser distance measuring, proximity sensors, cameras and object recognition software, watching in all directions. Imagine a hyperadvanced Kinect watching in all directions and keeping track of everything that's around the car (and not just two people, like the current version
). Even with increased accuracy, GPS and similar systems can't give you pinpoint precision.

I agree,

but I sort of like accidents. Gives me something to look forward to when I hit bumper to bumper traffic everyday; the random two cars that are all balled up and causing traffic. Gives me something I can vent my anger out. I'm such a hypocrite but it's ok, because I am human.

#### Veho

##### The man who cried "Ni".
Former Staff
Well in that case strap giant inflatable rubber bumpers to all cars and drive them around like those amusement park bumper cars. Park them by crashing into a lamp post

#### Zetta_x

##### The Insane Statistician
OP
Member
Veho said:
Well in that case strap giant inflatable rubber bumpers to all cars and drive them around like those amusement park bumper cars. Park them by crashing into a lamp post

That would be insane, driving to school/work would never be the same. Oh how dare you cut in front of me! *Slams on gas*
There would be random people who just slam on their break and cause accidents just to have fun bumping into each other.

#### Veho

##### The man who cried "Ni".
Former Staff
And the insurance claims for whiplash injuries would clog the courts for decades to come.

#### Zetta_x

##### The Insane Statistician
OP
Member
More courts, more jobs, more spending on cars, I declare guilty!

#### murkurie

##### Well-Known Member
Member
Zetta_x said:
Ahhh I see.

That's a good question. Where I live, the freeways (such as 215, 91, 60) were not built for so many people to use them at once, we face an average of 15 mph in most parts. I can imagine something flukeing =P
I live off the 10, and drive the 15, 91, 215 all the time, not really the 60 I avoid that like the plague, ever been stuck on the toll road too the 91?

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