## History of The Banked Turn Edit

It's hard to say when and where the banked turn was invented and utilized being that the banked turn is a naturally occuring topiographic feature. But we can assume that the true utility of the banked turn was discovered upon the building of the first race tracks that utilized banked turns. The first race track with banked turns was built in 1903, in Boston, and called the Readville Race track. This track used a few banked turns, and allowed cars to travel around these turns at higher speeds.

## Banked Turns in Automobiles Edit

What keeps an object making a turn from cotinuing on its path and flying off its path? The answer is Centripetal force. Centripetal Forceis what pulls an object towards the center of a circle during a turn keeping it from flying off its circular path.

There are three different scenarios when making a turn where the centripetal force is supplied by different sources. The first and most common scenario is driving a car on a flat surface. During this scenario all the centripetal force is supplied by friction. Due to the laws of friction, we know that as speed increases, the friction need to make a turn also increases. Some tires with lower coefficents of friction are not able to supply enough friction for a tire to make at certain speeds; the car will skid out of the turn.

The second scenario is the banked turn friction combination. The banked turn redirects the normal force supplied by the ground to keep the car from falling through the ground, toward the center of the circle. The angle of incline determines just how much horizontal force is provided by the normal force. The horizontal component of the the normal force is pointed toward the center, and centripetal force is supplied. Therefore cars can achieve higher speeds because the friction created by the tire is not soley responsible for creating the centripetal force that the car needs to stay in the circle. As the angle of incline increases, the horizontal component of the normal force increases, and the less friction is needed to keep the car in the turn. The opposite is true when the angle of incline decreases.

The third type of turn is the turn that only uses the bank to create centripetal force. In this scenario there is an abscene of friction. This scenario is not very applicable in real life driving.** **

http://www.nyclabschool.net/physics/alex/force1.jpg

## Absence of Friction Edit

In some cases, there exist no friciton to provide centirpetal force, so how is a car to make a turn? The answer is by the normal foce created by the angle of incline. To create horizontal force from the normal force excerted by the ground, oneIn tilts the ground a car is driving on to a certain angle, which in turn tilts the normal force toward the center of the circle, pushing the car to the center of the circle, and providing centirpetal force for the car. The following is an equation generated by setting centirpetal force equal to the normal force generated by the angle of incline.

http://upload.wikimedia.org/math/e/7/0/e708a22c46301abdbb1565549a425b4d.png

Since there is no vertical motion, the sum of all vertical forces must be zero. Because of this we set the vertical component of the car's normal force equal to its weight. The following is the equation yielded after taking the considerations above::

http://upload.wikimedia.org/math/2/4/3/243dce2d1227eb88d978b1038b223a64.png

When solving for velocity we get:

http://upload.wikimedia.org/math/a/1/d/a1d6850832b5d1a7e4b08e17bef474bc.png

**Practice Problem: What speed must a car be traveling at if it is on a frictionless ice path with a radius of 200 feet, and an angle of incident of 80 degrees?**

Solution: First we must identify all of our variables. Angle of incidence is equal to 80 Radius is equal to 200

Plug the variables into the equation The soulution is 105.4 Meters per Second

## Combination of Friction and Banked Turn Edit

Here is the most applicable case of the banked turn. This is the banked turn used by the nascar racer displayed above. In order to derive the equation for centripetal force, we must recognize that the centripetal force is the sum of the friction caused by the tires added to the normal force created by the banked turn (see below):

http://upload.wikimedia.org/math/f/b/d/fbd77d304da03668bee96f583b824b72.png

Through out this page, one must realize that the equations for solving for velocity differ between solving for the minimum velocity and the maximum velocity when friction is involved. When solving for the maximum velocity, one must recognize that when a car is reaching its maximum speed, the force of friction points inward, and the force of the car points outward. When solving for the minimum speed the opposite is true. As shown below we can solve for maximum velocity by using the equation above (see below):

http://upload.wikimedia.org/math/a/8/3/a8328f54722fc5097490140261d0bb98.png

Becuase of the difference described above about the direction of friciton when we are dealing with minimum velocity, the eqations for mminimum veloicty is different. below, the equation for solving for maximum velocity is shown:

http://upload.wikimedia.org/math/c/d/5/cd509673a3647f41f6677a34ca518d97.png

The equation solving for velocity for minimum velocity is shown below.

http://upload.wikimedia.org/math/c/9/3/c93c3704a46920f279ca4d90f20a58a3.png

**Practice problem: Ford is creating a new race track for a big race to be held in 2008. Ford wants to create a track that will allow their car to drive the fastest. If fords car has tires with a coefficent of friction of .7, and the tracks two turns must have a radius of 150 feet, what speed can Ford expect their car to achieve if the angle of incline is 45 degrees? And will their car beat Toyotas car which can travel 50 Meters per second on this track?**
Solution
Identify the varaibles
Angle is 45
Radius is 150
Coefficent of friction is .7

Plug the variables into the equation and find that the speed the car will achieve is 39.3 meters per second. Better luck next year ford! When you watch your basic Nascar race on Televsion, the turns the cars make are a combination of friction and banked turn. But sometimes a driver overestimates the coefficent of friction of his tire, or the angle of incidence of the bank, and the following happens.

Car Crash Video [[1]]

## Friction only (the turn you usually make) Edit

Friction is the force that allows us to make turns in everyday life. When your getting off the highway, changing lanes, or parking a car, it is fricition that allows us to redirect our vehicles (to turn). As we increase our velocity, we need our tires to produce more and more friction in order to allows us to turn. There is a point however, due to the coefficent of friction of one's cars's tires, that the car cannot supply enough friction, and the car gives out. We can calculate the maximum amount of friciton a car can generate by determining the coefficent of friciton of its tires, and the cars weight. After we determine the maximum friction, we have to determine the amount of force a tire must supply by determining the radius of the turn, and the speed of the vehicle. Using all this information, we can determine the maximum speed a car with certain tires can take a turn with a certian raidus. We set the two equations abouve equal to each other, and solve for velocity:

http://upload.wikimedia.org/math/9/5/a/95ac8f8280308865ef11fe938d7a94f7.png

The following is the same equation simplified to find velocity:

http://upload.wikimedia.org/math/9/8/e/98e708776511f3d0207bfba21219622a.png

As stated before, one must acknowledge that there is a difference in the direction in which the force pushes when a car is achieving a maximum speed versus a minimum speed. This is applicable in all cases where friction is involved.**Practice Problem: An axe murder has just managed to break out of a high security prision and steal a 8000 pound police bus which has tires with coefficents of friction of .4. the murderer must make a turn onto the highway so he can get across the border out of the country. If the raidus of the turn is 50 feet, what is the maximum speed the murder can take the turn at so that he does not end up back in jail and with a broken bus on his concious?**

Solution: The first step is to identify our variables. Radius: 50 Mu: .4

We plug the variables into the equation and yeild : 14 Meters per second

## Resources Edit

Barron's Review Course Series: Physics- The Physical Setting by Miriam A. Lazar Barron's Educational Series, Inc. 2004

Physics: Principles and Problems by Paul W. Zitzewitz The McGraw-Hill Companies, Inc. 1999

The nascar website www.nascar.com

A banked turn with friction (basic information adn a great photo0 http://www.batesville.k12.in.us/physics/phynet/mechanics/Circular%20Motion/banked_with_friction.htm

Another excellent site with good visuals, and worked equations http://spiff.rit.edu/classes/phys311.old/lectures/bank/bank.html

## Images Edit

Green Race Car Turning http://www.weblogsinc.com/common/images/5573671824745669.JPG?0.09672112633687113

Car Crash Video
http://video.google.com/videoplay?docid=-6289950699679944532&q=Nascar+crash

Hand Made Drawing Alex Rich's computer

## References Edit

Centripetal Force http://en.wikipedia.org/wiki/Centripetal_Force

Normal Force http://en.wikipedia.org/wiki/Normal_Forcetle