March 14, 2008

 
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Calculations

Moderately Technical Discussion

Guardian & Semi-Guardian

The Technology of Guardian

Guardian Weakness

Guardian Safety

Guardian Carpools & Convenience

Guardian Car Technology Is Now

Transportation Challenge

Order of Magnitude - Great Investment

Traffic Capacity Calculations

 

Guardian & Semi-Guardian

 

A fully developed Guardian transportation system will have no traffic accidents. No police, no bicyclists, and no pedestrians die because some fool drifts onto the road shoulder. No back injuries from inattentive rear-enders. No T-bone deaths at intersections. No inexperienced kids dying with one quick bad decision.

 

Initially, used or classic cars, pedestrians, and bicycles will be at least semi-Guardian.  A car or a person can be semi-Guardian with only a cell-phone (soon smaller) semi-Guardian device.  The device would have location and motion sensors to telegraph intentions, but without the automatic control of brakes, wheel, and accelerator.  A small semi-Guardian device would provide the semi-Guardian car drivers with visual or aural warnings of a pedestrian, while also warning the pedestrian of the car.  Fully-Guardian cars would avoid equipped pedestrians or bicyclists automatically.

 

The Technology of Guardian

The best cars are likely to rely on a combination of global positioning system (GPS) and inertial navigation, perhaps with one or two sensors on either car or road to detect a "passive" car or obstruction.  The device requires only inertial sensors, a global positioning system, radio, and a computer all on one silicone chip.  See comments by Steve Underwood, a research scientist at the Center for Automotive Research atAnn Arbor,Mich. http://www.vindy.com/content/local_regional/290576013614689.php

A Guardian vehicle could drive itself on a maintained road with a GPS base station or earth "satellite" every few miles.  Full-Guardian vehicles would include a drive-by-wire control system.  A simple proximity sensor might be necessary to calibrate the 2-foot follow distance.  Guardian technology is, therefore, much less expensive than individual intelligence.  It is a few thousand dollars more efficient for vehicles to converse (communicate simultaneously) and tell each other where they are and where they are going, rather then for each vehicle to independently track all vehicles, in order to avoid a collision.  Guardian vehicles might best be thought of as very polite vehicles, always telling each other what they are doing and coordinating so that everyone can proceed smoothly.

A GPS receiver calculates its location by measuring how long it takes for the radio signal from several satellites to travel to it.  Earth based “satellites” may be in tunnels, on the sides of buildings, or in parking garages where space satellites are obscured from view.

Wikipedia, http://en.wikipedia.org/wiki/Global_Positioning_System has a very detailed discussion of GPS accuracy.  The short answer is that the relative position of two GPS receivers can be precise within a few centimeters (inch).  The accuracy of GPS continues to improve and costs reduce.  Also more satellites, such as the European’s Galileo system, are launching.  The higher accuracy and precision is obtained several ways.

First, the vehicles don’t require accuracy, they require precision.  Precision vs. Accuracy – Suppose you shot ten holes in a pistol target.  If you could cover ten shots with a quarter but the quarter was 6” from the bulls-eye, you have great precision but poor accuracy.  Some accuracy errors are caused by differing atmospheric conditions causing slight changes in the time it takes for the radio waves to travel.  Some errors are cause by clock error.  Some errors persist for a few minutes after the satellite fires a booster rocket to adjust orbit.  In all of those situations, two close receivers will calculate their distance from each other with precision of a few inches using the space satellite signals available in 2000.

For survey accuracy of less than an inch, surveyors install a base station.  A base station calculates its position within fractions of an inch by averaging out the accuracy errors over time.  The base station broadcasts a radio signal which allows every GPS receiver within about 10 miles to quickly calculate its position to within fractions of an inch. The Trimble MS750 is a base station with a range of about 20 km (13 miles). A single base station can be used by any number of grade control or GPS site positioning systems at one time.  Find out more about similar units with a Google of ‘GPS base station’

There are at least two ways for moving vehicles to update their location in tunnels or concrete canyons.  One way is use a local "satellite" stuck on the tunnel ceiling or on the wall of a building.  Or use future versions of this http://www.u-blox.de/products/tim_lr.html.  Another is to use inertial navigation to cover the times when satellite signals are not available.  (A more robutst system would use both.)  See the April 2007 Popular Science How It Works for a description of how the Wii controller uses small and inexpensive inertial sensors.  The vehicle needs inertial sensors in any case.  Inertial sensors track linear and rotational accelerations.  Acceleration for a known time generates velocity.  Velocity for a known time equates to distance and direction.  Inertial navigation works by calculating velocity, distance, and direction from a series of accelerations.

Inertial sensors also serve to warn other vehicles.  For example, a sudden flat tire would have an instantly recognizable “acceleration signature.”  A vehicle with a flat tire would inform all the nearby vehicles of the flat tire quicker than the vehicle driver could react.  Also, the inertial sensors would inform nearby cars of their performance.  Suppose a Hummer is closely following a Porsche on a dry road when the Porsche hits the brakes hard.  The Hummer would inform the Porsche not to stop at faster than the 0.7g, that the Hummer can stop at.  On a snow covered road, the situation may be reversed with the following Porsche telling the Hummer not to stop faster than the 0.2g it can manage.  (A ‘g’ is one unit of earth gravity.  Accelerating at 1g would be accelerating the same as if you were dropped off a cliff, before air resistance slowed your acceleration.)

It would be extremely difficult for independently intelligent vehicles, such as the DARPA Challenge vehicles, to even identify all the “threats” around them.  It’s tough for sensors to distinguish a pedestrian from a tree, let alone notice a pedestrian between parked cars or a bicycle approaching from the left along a row of parked cars.  “Robot” researchers have known for a long time it is very difficult to make a robot that will find the milk in the refrigerator, but it is trivial for the robot to find milk tagged with radio frequency identification.  Instead of the milk hiding behind the eggnog, the milk is saying, “I’m in the refrigerator.  Open the door.  Move the eggnog, then reach to coordinates X, Y, Z.”

It requires a tremendous computing power, after identifying the “threats” recognize what the threat is doing.  Is it going straight or turning right.  Imagine teaching a computer to recognize a turn signal, especially when a lot of people forget to use their turn signals.  It requires very little computing power or time, if the “threats” are all super-polite.  Every car communicates their location and acceleration, “I’m on your left front turning right at 0.1g.”

The Federal Highway Administration has identified a radio frequency http://www.its.dot.gov/vii for vehicle-road and vehicle-vehicle communications.  Their project uses the relatively obtuse nomencalture of Vehicle Infrastructure Integration (VII).  Notice the American site lags behind the European site in graphical presentation http://www.car-to-car.org/index.php?id=130  The Europeans also have a better name, Car2Car Communication Consortium, for their project.  Also check on the Center for Automotive Research atAnn Arbor, Mich http://www.cargroup.org/.  

 

Guardian Weakness

 

While the cost efficiency of Guardian technology and the ability to protect pedestrians is its strength, its coordinated approach is also its weakness.  As demand increases, individually intelligent vehicles will evolve on their own.  Evolving Guardian vehicles, however, requires a deliberate and coordinated effort by both government and private sectors.  Imitating the DARPA Grand Challenge with a Civilian Transportation Challenge, would provide that coordinated effort.

 

Guardian Safety

 

Every fully-Guardian or semi-Guardian car, motorcycle, bicycle, or pedestrian is protected by an invisible shield controlling the brakes of approaching Guardian cars (and providing an early warning to semi-Guardian cars and people).  This technology fixes every dangerous intersection and road.  For an understanding of the tragedy of unsafe intersections visit http://www.sandyjohnsonfoundation.org/.

 

Guardian Carpools & Convenience

 

If we couple the accident avoidance capabilities of Guardian Cars with fuel efficiency incentives, we can set (and enforce) higher (and more uniform) speed limits.  Consider a 4 lane highway numbered from the left.  (Cars may converse about their current passenger miles per gallon (pmpg).)  Lane 1 could be a minimum of 40 pmpg, maximum of 80 mph.  Lane 2 could be 30 pmpg, maximum of 70 mph.  Lane 3 could be 25 pmpg, maximum of 65 mph.  Lane 4 could be 20 pmpg, maximum of 60 mph.  Except for acceleration time during lane changes, inclement weather, or sparse traffic, all the cars in a given lane would be traveling exactly the maximum speed.

 

Commercial and industrial traffic will benefit from the congestion-free and highly predictable transit times.  Liability insurance needs would be reduced along with the reduced accidents.

 

Guardian Cars would make impromptu carpools easy to arrange while vehicles are enroute.  Drivers and riders would be pre-qualified as “safe and reliable.”  A driver would phone in (using a PIN) with intended destination.  The system already knows her origin and possible routes.  A rider would do the same, and also tell the system his origin and any special needs.  The rider would pay the driver with automatic funds transfers.  This system can provide better service for elderly, disabled, emergency bicycle commuters, and even business car pool users.  The carpool could be run by charities, business, or government.

 

Guardian Car Technology Is Now

 

DARPA is running an Urban Challenge for robotic vehicles racing in city streets.  The first Urban Challenge race is November, 2007, http://www.darpa.mil/grandchallenge/index.asp.

 

You are already safer with a computer controlling your brakes.  40% of 2007 model year vehicles (and all vehicles by 2010) have electronic stability control, which adjusts brake force at each wheel individually to prevent roll-over.  The Federal Highway Administration has concluded that robotic cooperation between the vehicle and the roadway is necessary to achieve major safety improvements.  The Federal Communication Commission has already picked a radio frequency, 5.9 GHz. http://www.its.dot.gov/vii. In September 2006, the site and the name "Vehicle Infrastructure Integration" is still too boring. The Europeans have a better name, "Car2Car," and a better web site http://www.network-on-wheels.de/vision.html (which you need to copy and paste).


You can buy the Honda Accord Advanced Driver Assist System in the United Kingdom now.  It steers itself by sensing lane lines and adjusts speed to traffic conditions with radar to sense the car ahead.  (The May 2006 Popular Science.)  Other cars with partial robotic features listed on page 20: 2007 Mercedes-Benz S-Class, 2007 Lexus LS 460, 2006 BMW 5-Series, 2006 Land Rover LR3.  Toyota has the gas pedal that warns of collision.  Cell phones are already available with navigation systems accurate within a traffic lane.  General Motors showed off its V2V system at the November 2005 Intelligent Transportation Systems World Congress.  General Motors believes its system could be on 2007 model cars adding as little as $200 to the cost of the car.

 

Cell phones and car navigation systems are already accurate to within a few feet.  The Garmin Forerunner, www.garmin.com $377 in March 2006, is a watch that uses GPS navigation to calculate calories burned, distance, pace, elevation, and heart rate.  Nieman Marcus offers a dog collar that phones the owner, if the dog wanders out of a preset area.  Celestron, www.celestron.com, is selling the SkyScout handheld telescope.  The SkyScout uses GPS, accelerometers, magnetic sensors, and memory to guide your gaze to the celestrial object of desire.  You can buy a pen and reciever from EPOS that will "track" your writing 240 times per second accuarte to half the width of a human hair.

 

 

Transportation planners and engineers appear to be just starting to grasp the opportunities for this technology.  Although currently, little attention is paid to having the vehicles communicate and coordinate with each other.  Also, “Guardian” is a new (2005) term for this higher level communicating intelligence.  Most of the web sites listed below are about a year behind the current state of available technology:

http://www.itsa.org

http://www.popsci.com/popsci/futurecar

http://www.its.dot.gov

http://www.ivsource.net/

http://www.cargroup.org/

http://www.cybercars.org

http://www.darpa.mil/grandchallenge

Or order books from the American Society of Civil Engineer www.pubs.asce.org   Intelligent Vehicle Technology and Trends by Richard Bishop or Perspectives on Intelligent Transportation Systems by Joseph M. Sussman.  As of February 2006, the above web sites reflect limited visions for future applications of computer technology or demonstrate the kindergarten class in a candy factory approach to investigating opportunities.

 

Transportation Challenge (the 2005 concept)

 

How can we most quickly save lives with Guardian car technology?  The technology needs a lot of time and miles in real-life situations to debug and become idiot proof.  As of 2005, researchers at the University of California PATH believed $1 to $2 billion would be needed to make the technology much more robust and reliable that human drivers (See Economic Analysis below.).  And then the technology must be desired by drivers.  

 

As of January 2008, it is evident manufacturer's have been making that investment.  The challenge has become unnecessary.

 

Order of Magnitude Great Investment

Summary - The United States total monetary benefits are on the order of $4 trillion over ten years after an investment of $100 billion.  (California, with the 8th largest global economy,could run the challenge without waiting for the Feds.  Total benefits and costs would be about 1/10th.  Per-person benefits and costs would be about the same.)  An investment of $300 per person, yields a return of about $6,000 per person.  While every investment has some uncertainty, this investment has one heck of a high payoff.  One of our first efforts should be a rigorous economic analysis because that will provide clues for how to reach our goals most cost efficiently.  However, the “napkin” analysis below is useful for recognizing the challenge is a good investment.

Researchers with the UC Berkeley PATH program and past attempts to produce automated highways point out that it won’t be easy to refine the existing technology for the robust reliability of our goal.  They estimate a $1 to $2 billion investment over ten years.

If we assume new cars will all be “ready” for the technology with drive-by-wire features, the main expense will be for a device, perhaps cell phone size, that plugs into motor vehicles and is carried by bicyclists and pedestrians.  In 2005, General Motors researcher’s suggested the extra cost for their V2V program might be $200 per vehicle.  It seems reasonable to project each device would cost less than $200 in a production run of 300 million.  A device for every American man, woman, and child would cost us collectively about $60 billion.

The challenge may discover roadside appurtenances are essential for robust precision of the devices or for areas not reached by GPS satellite signals.  (See the Science Sidebar.)    The typical GPS base station covers 100 square miles with a signal making GPS accurate within inches.  $40 billion should be plenty to cover the 3 million square miles of theUnited States with the necessary base stations and other roadside appurtenances.

Our total costs, in round numbers, would be on the order of $100 billion (or about $300 per person).  The up-front cost for the initial trials, testing, and refining is very small.  The larger costs are 5 to 10 years from now, which virtually guarantees they will be much less because electronic devices continue to become smaller and less expensive, with better performance.  When considering the time-value of money, the cost of deploying the technology happens nearly simultaneous with the benefits.

One big savings would be for auto insurance.  Typical auto insurance inCalifornia is $1,000 per vehicle per year.  If technology reduces accidents to one-fourth of the current rate and that reduces auto insurance rates to one-half of current rates, every private, business, non-profit, and government vehicle owner will save $500 per year on vehicle insurance.  With on the order of 300 million vehicles, that is a collective $100 billion per year.  Ten years’ savings would be $1 trillion.  Note that the auto insurance savings would phase in gradually.  Savings would starting no sooner than 5 years from now, and take perhaps 20 years to reach maximum benefit.

A discussion of auto insurance doesn’t begin to address the emotional benefits of fewer accidents.  What is the life of a loved one worth to you?

A second big savings would be avoiding the cost of new roads or transit systems.  This is particularly hard to peg because many roads are already congested and it is hard to find estimates for the cost of nearly eliminating congestion.  Californians spend on the order of 80 hours per year in congested traffic.  In January 2006, Governor Schwarzenegger suggested a $109 billion bond to reduce congestion (using 20th Century technology) to 65 hours per year.  California represents about a tenth of theUnited States’ population.  TheUnited States might expect to spend ten times the $100 billion of Governor Schwarzenegger’s suggestion, or $1 trillion.  (That would be to reduce congestion to 80% of current levels.)

A third large savings would be time.  The averageCalifornia driver loses on the order of 80 hours per year to traffic congestion.  Let’s round down to 50 hours per year for the average of 300,000,000 Americans.  Let’s guess our time is worth only $10 per hour.  The value of lost time would be $150 million per year, or $1.5 trillion over ten years.

DARPA spent about $20 million staging its Grand Challenge.  Grand Challenge contestants provided about $100 million of effort.  (Mark Twain’s Tom Sawyer fence painting effect.) 

January 2006 news accounts of Governor Schwartzenegger's 20th Century approach to traffic congestion indicated $107 billion for no real safety improvement and 20% traffic congestion reduction (say from 100 hours per year to 80 hours per year).  With Guardian technology, Californian’s spend $1 billion of public funds on the Transportation Challenge and perhaps $10 billion in private funds at $200 per car.  But the Guardian technology could save thousands of lives, billions of dollars (from accidents), and drops congestion toward 10 hours per year.

 

Per Engineering News Record, November 14, 2005, Page 61 a report by Cambridge Systematics indicates the Highway Trust Fund annual revenue will be $23 billion short of what’s needed to maintain current road and transit conditions and $48 billion short for federal system improvements.  View the report at www.uschamber.com/ncf/publications/default.

Mass produced electronics (like cell phones with Global Positioning Systems) keep decreasing in size and price.  Cars are already becoming drive-by-wire for active cruise control, anti-flip steering, anti-lock breaks, etc.  General Motors V2V team estimated the incremental cost for Guardian technology in 2007 at about $200 per car.  This is roughly in agreement with the projected costs for navigation equipped cell phones.  www.Neimanmarcus.com is selling a dog collar that will phone your cell phone, if the dog wanders beyond set boundaries for $350.

 

Computer Traffic Capacity Calculations

 

Guardian technology would not allow 10,000 vehicles per hour (vph) per traffic lane immediately.  Rather the combination of the Transportation Challenge and congestion relief incentives would evolve higher vph as needed.  Transportation agencies should recognize the addition of three more tools for congestion prevention – 1. a challenge; 2. Guardian technology; and 3. vehicle demand incentives.

 

Calculations:

The calculations are rounded off to single digits for ease of understanding and to make more clear the results are not sensitive to minor variations in the assumptions.

 

2005 – Non-Guardian Condition:  If drivers' followed the California Drivers' Handbook, cars would be at least 3 seconds apart.  Or longer, if the weather wasn't perfect, visibility unimpaired, or a host of conditions affecting human reaction time and vehicle stopping distance.  Therefore, if everyone were a safe driver, cars would be passing no more than one every three seconds which gives a maximum of 1,200 vph per lane, regardless of how fast, or how slow, the vehicles are moving. Most everyone follows too close, nearly doubling the actual California freeway lane capacity to about 2,000 vph. (2,000 vph per lane is a real-world lane capacity verified with actual vehicle counts. Craming more cars per lane usually triggers a sudden speed drop from 60 - 70 mph to 0 - 30 mph.)

 

You may have the perception of somewhat higher capacity.  At 70 mph, you cover 100 feet in a second.  It seems like you have been in groups of cars with only 20 - 30 feet (0.2 - 0.3 seconds) between cars.  Four perception distortions are at work.  1. You notice and remember the higher danger situations, the closest cars.  2. The foreshortened viewing angles make the cars appear closer than they are.  3. Those high density groups only persit over a fraction of a mile (less than a minute) because someone will tap their brakes.  4. You are moving, and cannot assess the average lane capacity in one spot over an hour. Now recall, how often does the situation you perceive as more than 2,000 vph (average follow distance less than 200 feet at 70 mph) suddenly transition to 0 - 30 mph?  Not every time, but a lot more often than when follow distances are more than 200 feet.

 

We need the Transportation Challenge to establish the safe following distances for Guardian technology.  That is a few years of rigorous racing to learn if car groups should be two or ten, if distances within groups should be 2 feet or twenty feet, if distances between groups should be 1 second or 4 seconds. I estimate the technology will be safe for the 2015 and 2020 situations below.

 

2015 – Guardian Situation, only 2005 size cars:  Suppose an average speed over 3 lanes of 70 mph (100 feet/second, fps).  Perhaps the average 2015 vehicle is nearly 20 feet long. The vehicles travel in groups of five with 10 feet bumper-to-bumper. A group of five vehicles is about 140 feet (or about 1.4 seconds) long.  The distance between groups is Drivers' Handbook recommended 3 seconds.  Therefore, five cars pass every 4.4 seconds per lane or 4,000 vph per lane. (The technology will need a reaction time of less than 0.05 seconds to maintain plus or minus five feet of separation during hard braking or accelerating.  Generally, simple computations and radio communications react in a few 0.000001 of a second.)

 

2020 – Guardian Situation, 2015 sized cars:  Suppose an average speed over 3 lanes of 70 mph (100 feet/second, fps).  In 2015, the average vehicle is 10 feet long, because many “commuter specials” are 10 feet long and 3 feet wide traveling side-by-side in the same lane space.  The vehicles travel in groups of five with 2.5 feet bumper-to-bumper.  A group of five is 60 feet long (or about half a second).  The Challenge will have improved the safe following distance between groups to about 1.5 seconds.  Therefore, five cars per lane every 2 seconds sums to 9,000 vph per lane.

 

 

 


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