MergingLanes

The Physics Behind…

http://www.aaroads.com/west/oregon005/i-005_nb_exit_299_04.jpgOctober 16, 2010

http://www.drivingschoolireland.com/regulatory-signs.htmlOctober 16, 2010

http://www.drivingschoolireland.com/regulatory-signs.htmlOctober 16, 2010

http://www.gribblenation.com/ncpics/raleigh/i440-exit1-curley.jpg October 16, 2010

• Based on the acceleration of cars, and the acceleration necessary to change speeds on varying acceleration and de-acceleration lanes, is it possible to scientifically calculate the distance required for a car to safely accelerate to the correct speed within these merging lanes?

Problem

• Using data found such as time taken to get from 0-100 km/h and from 100-0km/h, and the change of speed limits going onto or coming off a highway, we can calculate the acceleration of each car. With this information we will be able to calculate the minimum distance that is required for a car to have enough time and space to safely achieve the necessary speed limit. Each car will have a different acceleration rate, and this information will come into account when determining the length of a merging lane. We will be able to calculate this because we have all the velocity and acceleration equations that we need to calculate this data.

Hypothesis

Car Facts

Honda Pilot0.00-100 km/h in 9.70 seconds (http

://www.insideline.com/mazda/cx-9/2008/2009-honda-pilot-vs-2008-mazda-cx-9-vs-2008-toyota-highlander.html

October 12, 2010)100-0.00 km/h in 3.27 seconds (

http://www.insideline.com/mazda/cx-9/2008/2009-honda-pilot-vs-2008-mazda-cx-9-vs-2008-toyota-highlander.html

October 12, 2010)

Smart Fortwo0.00-100 km/h in 14.3 seconds

(http://blogs.insideline.com/straightline/2009/08/il-track-tested-2008-smart-fortwo-brabus.html

October 12, 2010)100-0.00 km/h in 2.70 seconds

(http://blogs.insideline.com/straightline/2009/08/il-track-tested-2008-smart-fortwo-brabus.html

October 12, 2010)

Bugatti Veyron 0.00-100 km/h in 2.50 seconds (

http://www.thesupercars.org/fastest-cars/fastest-cars-in-the-world-top-10-list/

October 16, 2010)100-0.00 km/h in 2.30 seconds (

http://www.bugatti.com/en/veyron-16.4/technology/deceleration.html

October 16, 2010)

http://tysongamblin.files.wordpress.com/2009/11/bugatti-veyron.jpgOctober 16, 2010

https://wiki-land.wikispaces.com/file/view/2008-smart-fortwo-pure.jpg/53660430/2008-smart-fortwo-pure.jpgOctober 16, 2010

http://www.automedia.com/New_Cars/honda_pilot_2008_photos_SUV_Exterior_2008-Honda-Pilot-ext-1.jpgOctober 16, 2010

We chose these three cars for their varying degrees of acceleration.

Positive Accelerating Merging Lanes

Highway onto Ramp64.0 km/h-120km/h

(http://maps.google.ca/maps?hl=en&tab=wlOctober 16, 2010)

All speeds chosen at random from actual places in Canada and the United States and are direct examples from the road that is shown in the pictures

Highway onto Cloverleaf 40.0 km/h-100 km/h

(http://maps.google.ca/maps?hl=en&tab=wlOctober 16, 2010)

http://www.inside-lane.com/wp-content/uploads/2009/08/I-270-at-Vasquez.jpgOctober 16, 2010

http://maps.google.ca/maps?hl=en&tab=wlOctober 18, 2010

Negative Accelerating Merging Lane

The cloverleaf going off a highway is of the same speed as the cloverleaf going onto a highway, except negative, so we are only doing one negative accelerating Merging Lane

Highway onto Ramp100 km/h-70km/h

(http://maps.google.ca/maps?hl=en&tab=wlOctober 16, 2010)

http://www.drivingschoolireland.com/regulatory-signs.htmlOctober 16, 2010

• First, we look at our givens:• Vi , or initial speed equals the speed the car is traveling at before the

acceleration/de-acceleration lane. We convert this to m/s so it will be usable in our equation.

• (e.g. For cloverleaf, 40.0 km/h. (forward) Is converted to 11.1 m/s (forward) )

• Vf , or final velocity, equals what speed the car will be traveling at the end of the acceleration/de-acceleration lane. We convert this to m/s so it will be usable in our equation.

• (e.g. For cloverleaf, 100 km/h. (forward) , which we convert to 27.8m/s (forward) )

Finding Final Velocity (V f) and Initial Velocity (V i)

• a= Δv/Δt = a= (Vf-Vi)/Δ t

• First, to get the Vf and Vi we translate the units given to us (km/h.) into m/s (x1000 to get from km to m, /3600 to get from hours to seconds) this will give us Vf and Vi, which we can place properly in our equation

• (E.g. for Bugatti Veyron, 0-100 km/h. (forward) converts into 0-27.8 m/s (forward) )

• Then, we divide by the time (Δt) by which it takes these cars to go from 0-100 km/h (forward)

• E.g. : for Bugatti Veyron:• a= Δv/Δt • a= (Vf - Vi)/Δt• a= (27.8m/s -0 m/s) / 2.50seconds• a= 11.1 m/s2 (forward)• Now that we have solved for acceleration, lets find out the maximum acceleration

of the three cars.

How to Find +Acceleration

Car: Bugatti Veyron Honda Pilot Smart Fortwo How we did this...

0-100 km/h equals...

0m/s-27.7m/sVf =27.7 m/s (forward)

Vi = 0 m/s (forward)

X1000 to get meters/3600 to get seconds

Time it takes from 0-100

2.50 seconds 9.70 seconds 14.3 seconds See slide with information about cars.

Equation used a= (vf-vi)/Δt = See previous slide

Therefore... a= (27.8m/s-0m/s)/2.50 seconds

a= (27.8m/s-0m/s)/ 9.70 seconds

a= (27.8m/s-0m/s)/14.3 seconds

Using the givens from the acceleration of the car, and the time it take the car to travel that fast, we can fill in the equation.

Acceleration 11.1 m/s2

(forward) 2.87 m/s2

(forward) 1.94m/s2

(forward) Solve equations

Calculating Positive Acceleration for All 3 Cars

• The steps to find acceleration and negative acceleration are the same, except we will now get a negative answer.

• a= Δv/Δt = a= (vf-vi)/ Δt• First, we translate the units given to us (km/h.) into m/s (x1000 to get from km to

m, /3600 to get from hours to seconds) this will give us V f and Vi, which we can place properly in our equation

• (E.g. All cars, 100-0.00 km/h. equals into 27.8-0.00 m/s)

• Then, we divide by the time by which it takes these cars to go from 100-0 km/h. (or 27.8- 0.00 m/s.)

• E.g.: for Bugatti Veyron:• a= Δv/ Δt• a= (Vf -Vi)/Δt • a= (0m/s- 27.8m/s) / 2.30 seconds• a= -12.1 m/s2 (forward)

How to Find -Acceleration

Car: Bugatti Veyron Honda Pilot Smart Fortwo How we did this...

100-0km/hequals...

27.8- 0.00 m/sVi =27.7 m/s (forward)

Vf = 0 m/s (forward)

X1000 to get meters/3600 to get seconds

Time it takes from 100-0

2.30 seconds 3.27 seconds 2.70 seconds See slide with information about cars.

Equation used a= (Vf -Vi)/Δt = See previous slide

Therefore... a= (0-27.777 m/s) /2.3 seconds

a= (0-27.777 m/s) /3.27 seconds

a= (0-27.777 m/s) /2.7 seconds

Using the givens from the acceleration of the car, and the time it takes the car to travel that fast, we can fill in the equation.

Acceleration -12.1 m/s2

(forward) -8.50 m/s2

(forward) -10.3m/s2

(forward) Solve equations

Calculating Negative Acceleration for All 3 Cars

• Now that we have solved acceleration, we now have all of our necessary givens.

• Initial velocity, or Vi ,equals the speed the car is traveling at before the acceleration/de-acceleration lane.

• Final velocity, or Vf , equals what speed the car will be traveling at the end of the acceleration/de-acceleration lane.

• Acceleration, a, is dependant on how fast the car goes from 0-100 km/h., or rather 0-27.8 m/s, as we have seen in the last three slides.

• Distance, or Δd, is what we are trying to solve, using these givens. This is the total distance the acceleration or de-acceleration lane will need to be.

• With all these givens, and the unknown, we can use the equation Vf2=Vi

2+2aΔd, and rearrange it, to look like (Vf

2-Vi2)2a=Δd

How to Find Distance

http://tysongamblin.files.wordpress.com/2009/11/bugatti-veyron.jpgOctober 16, 2010

We have everything necessary, we can go

through the three types of acceleration/ de-acceleration lanes,

and see how long each one would have to be as a minimum distance, enabling

each car drive safely and properly.

And Now…

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http://www.drivearabia.com/news/wp-content/uploads/2008/11/2009-honda-pilot-dubai-13.jpgOctober 16, 2010

Type of acceleration / de acceleration lane

Bugatti Veyron

Honda Pilot Smart Fortwo How we did it

velocityVi= 40.0 km/h.= 11.1m/s (forward) Vf = 100km/h.= 27.8 m/s (forward)

See slide 7

Acceleration a=11.1 m/s2

(forward) a=2.86 m/s2

(forward) a=1.94m/s2

(forward) See slides 8 and 9

Equation to find Δd

(vf2-vi

2)/(2a)= Δd See slide 12

Filled out (27.82 -11.12)/(2 x11.1)

(27.82 -11.12)/(2x2.87)

(27.82 -11.12)/(2x1.94)

Filled out previous equation

Answer/distance needed

29.3m 113m 167m Solve equation

Cloverleaf onto Highway(40km/h-100km/h)

Type of acceleration / de acceleration lane

Bugatti Veyron

Honda Pilot Smart Fortwo How we did it

velocityVi= 64.0 km/h.= 17.8m/s (forward) Vf= 120 km/h.= 33.3 m/s (forward)

See slide 7

Acceleration a=11.1 m/s2

(forward) a=2.86 m/s2

(forward) a=1.94m/s2

(forward) See slides 8 and 9

Equation to find d (vf2-vi

2)/2a= Δd See slide 12

Filled out (33.32 -17.82)/(2 x11.1)

(33.32 -17.82)/(2 x2.87)

(33.32 -17.82)/(2 x1.94)

Filled out previous equation

Answer/distance needed

35.7m 138m 204m Solve equation

Merging Lane onto Highway(64km/h-120km/h)

Type of acceleration / de acceleration lane

Bugatti Veyron Honda Pilot Smart Fortwo How we did it

velocityVi= 100km/h.= 27.8 m/s (forward) Vf= 70km/h.= 19.4m/s (forward)

See slide 7

Acceleration a=-12.1 m/s2

(forward) a=-8.50 m/s2

(forward) a= -10.3m/s2

(forward) See slides 8 and 9

Equation to find d

(vf2-vi

2)2a=Δd See slide 12

Filled out (19.42 -27.82)/(2 x-12.1 m/s2)

(19.42 -27.82)/(2 x -8.50m/s2)

(19.42 -27.82)/(2x-10.3m/s2)

Filled out previous equation

Answer/distance needed

16.4m 23.3m 19.2m Solve equation

Merging Lane off of Highway(100km/h-70km/h)

Car: Cloverleaf (40km/h.-100 km/h.)

Merging lane in united states(64km/h.-120km/h.)

Ramp(100km/h.-70km/h.)

Bugatti Veyron 29.3m 35.7m 16.4m

Honda Pilot 113m 138m 23.3m

Smart Fortwo 167m 204m 19.2m

In bold, we see the highest result for each type of acceleration/de-acceleration ramp. This is the minimum length that a acceleration/ de-acceleration lane can be built, because although faster cars may be able to travel safely on these lengths of lanes, slower cars need this length as a minimum. If it were any less, they could not drive safely. The car accelerating at its fastest would need this much space to change to the new proper speed limit, and if not, slow down traffic dramatically.

Final Conclusions

We can calculate the distance that is required for a car to accelerate (positively

or negatively) from one speed limit to another. But we are not taking into

account any factors that may or may not increase or decrease the length of a

merging lane. Therefore it is impossible to determine the maximum length of a

turning lane.

Something to Consider…

Some Factors That Would Affect the Length of a

Merging LaneOn average, the factors that affect the length of a merging lane could be more or less….

Busy EmptyVS WetVSDry

http://media.canada.com/d2ab0b62-0cf1-4ff2-b5d2-35b7f81fc208/210highway.jpgOctober 17, 2010

http://www.chinadaily.com.cn/english/doc/2005-09/24/xin_1909022415361082954314.jpg October 17, 2010

http://farm5.static.flickr.com/4010/4454418474_2a82578162.jpg October 17, 2010

http://geoffreymcallister.com/%20a021008_14.jpg October 17, 2010

http://us.123rf.com/400wm/400/400/leaf/leaf0804/leaf080400263/2948079.jpg October 17, 2010 Final SpeedInitial Speed VS

http://kereta.info/wp-content/uploads/2010/01/CAR-RPM-METER-READING-AT-100110-KMH-SPEEDOMETER-READING-2.jpg October 17, 2010

http://electronicpro.org/wp-content/uploads/7%20crash%20car%20video.jpg October 17, 2010 No reaction time VS

http://www.comparecheapinsurance.com/car-insurance/images/car-insurance-policy.jpg October 17, 2010

Lots of Reaction time

Follow Up• In the heart of any major city there are merging lanes that would not

necessarily be found in a minor city or rural town. This is because the traffic volume is not as great as the traffic volume in a large city; merging lanes in a big city cause the traffic to flow a lot easier and more fluid.

• Arizona has a drier climate than Florida; therefore Arizona’s merging lanes don’t necessarily need to be as long as Florida’s wet roads.

• Depending on the speed at which you are accelerating from to speed the speed you are trying to achieve also determines the length of a merging lane. The greater the difference between final and initial speed, the longer the merging lane has to be for a car to accelerate safely onto the required speed.

• When designing a merging lane, any unforeseen events must be taken into account so that the drivers have time and room to react to the situation. Not enough room or time to react, you get a car crash; too much room and you simply get people having more time to accelerate.

Following Up That Follow Up…

• These factors are averages, and should only be taken into account only if the climate of the area is a factor listed (there are other factors, these are just the some of the bigger ones).

• Therefore, we can not accurately calculate the length of a merging lane, but we can hope that engineers take these factors into account when designing a merging lane onto any street.

• Some streets and roads do not contain any merging lanes because they are either not used often, or the speed limit is low enough that any car can get up to speed in a safe time and distance.

• The majority of the merging lanes are found on highways, interstates, and busy roads. Merging lanes give drivers the ability to safely enter and exit these roads without causing chaos, or accidents.

• Based on the previous slides, we have seen that these distances are the final answer. However, we must remember that these are the minimum distances only, because the car accelerating at its fasted would need this much space to change to the new proper speed limit.

• Thanks to kinematics, we have a better understanding of the world around us. By looking at everyday actions, such as driving, and applying physics to it, we see science behind life. In this project, we learn that the length of certain merging lanes are crucial to peoples safety. Should we be driving a smart car, and come across a Cloverleaf which is only 100 m in length, we would be in danger because we would not have the proper time to accelerate, even at our fastest acceleration rate. The truth is, through our study of sciences, we save many lives.

Thanks To Kinematics…

Half of our marks should be based on how awesome this next transition of

slides is….click

!MR. DICKIE!

http://upload.moldova.org/auto/Smart/Smart-Fortwo_LE_One_1.jpg

All references were verified as of October 19,

2010

http://www.diseno-art.com/images/Bugatti-Veyron-driving.jpg

http://www.deweytube.com/used%20Honda%20Pilot.jpg

ReferencesData Sources

• http://www.thesupercars.org/fastest-cars/fastest-cars-in-the-world-top-10-list/

• http://www.bugatti.com/en/veyron-16.4/technology/deceleration.html

• http://www.insideline.com/mazda/cx-9/2008/2009-honda-pilot-vs-2008-mazda-cx-9-vs-2008-toyota-highlander.html

• http://blogs.insideline.com/straightline/2009/08/il-track-tested-2008-smart-fortwo-brabus.html

• http://maps.google.ca/maps?hl=en&tab=

• http://winewriter.files.wordpress.com/2008/09/bugatti-veyron.gif• http://spbcar.ru/news/en/i/2006-12-30/veyron_sport_rumor.jpg• http://tysongamblin.files.wordpress.com/2009/11/bugatti-veyron.jpg• http://www.diseno-art.com/images/Bugatti-Veyron-driving.jpg• http://

www.automedia.com/New_Cars/honda_pilot_2008_photos_SUV_Exterior_2008-Honda-Pilot-ext-1.jpg

• http://www.drivearabia.com/news/wp-content/uploads/2008/11/2009-honda-pilot-dubai-13.jpg

• http://www.deweytube.com/used%20Honda%20Pilot.jpg• https://

wiki-land.wikispaces.com/file/view/2008-smart-fortwo-pure.jpg/53660430/2008-smart-fortwo-pure.jpg

• http://upload.moldova.org/auto/Smart/Smart-Fortwo_LE_One_1.jpg• http://pictures.topspeed.com/IMG/crop/200912/smart-fortwo-electri-20_460x0w.jpg• http

://photos-e.ak.fbcdn.net/hphotos-ak-snc3/hs472.snc3/25887_382104579172_138573714172_3484229_6874735_a.jpg

Car Pictures

• http://www.drivingschoolireland.com/regulatory-signs.html• http://www.inside-lane.com/wp-content/uploads/2009/08/I-270-at-Vasquez.jpg• http://media.canada.com/d2ab0b62-0cf1-4ff2-b5d2-35b7f81fc208/210highway.jpg• http://

www.chinadaily.com.cn/english/doc/2005-09/24/xin_1909022415361082954314.jpg• http://geoffreymcallister.com/%20a021008_14.jpg• http://farm5.static.flickr.com/4010/4454418474_2a82578162.jpg• http://www.aaroads.com/west/oregon005/i-005_nb_exit_299_04.jpg• http://www.gribblenation.com/ncpics/raleigh/i440-exit1-curley.jpg• http://us.123rf.com/400wm/400/400/leaf/leaf0804/leaf080400263/2948079.jpg • http://electronicpro.org/wp-content/uploads/7%20crash%20car%20video.jpg • http://www.comparecheapinsurance.com/car-insurance/images/car-insurance-policy.jpg

Road and Merging Lane Pictures