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# Understanding the Physics of Anti-Lock Brakes

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## Pamela Morton

on 6 August 2015

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#### Transcript of Understanding the Physics of Anti-Lock Brakes

Introduction
Many of us rarely stop and think about the advancements in technology that help to make our lives a little bit easier. One form of technology that we take for granted often is the car. Physics is a form of science that has not only made it possible for us to drive around in motorized vehicles, but it has allowed us to do it safely. One of the car’s features that provides extra safety for drivers is the anti-lock braking system (ABS).
Introduction
The anti-lock braking system is an example of how we have been able to overcome limitations by physics. Much of the physics of a car's movement on a surface is based on the frictional forces developed between the car's tire and the surface. Therefore, the rate at which a car can decelerate is limited by the maximum frictional force between the tire and the surface.
Introduction
Introduction
So far, it would seem like there is no potential for problems with the movement and stopping of the car. However, variations in the road surface, along with other factors, affect the maximum amount of static friction force that can be developed. Hence, the coefficient of static friction may change as a vehicle encounters different road conditions(i.e. dry to wet, wet to icy, etc.). The vehicle's ABS can sense wheel slip and adjust the braking force applied so that the force the vehicle exerts on the roadway does not exceed the maximum force of static friction available for a particular condition.
Introduction
When the force needed to stop the moving car exceeds the available force due to static friction, the wheels lock up and stop moving.
The car is no longer in control. The car is basically moving along the road much like a box would if a person pushed it across a surface. A five-pound box sliding aimlessly across a floor may not be too bad, but a 4,000-pound car sliding aimlessly across a freeway is dangerous.
Introduction
Fortunately for us, physicists and engineers have found a way to keep this from happening. The anti-lock braking system does just that – it keeps the wheels from locking up, which stops the car from sliding on the road. The system pumps the brakes and handles the wheels individually, which makes it more efficient. It pumps the brakes when the wheels are just shy of the threshold between static friction and kinetic friction, ensures that the wheels do not exceed the static friction, and keeps the car and the driver in control.
Real World Application
The anti-lock braking system works automatically. Instead of the driver having to manually gauge when the tires are approaching the limits of static friction and pumping them individually, they can rely on the physics of the anti-lock brakes to do that for them. The anti-lock braking system is significant from a physics standpoint because it is an innovation that has allowed physicists to better handle the limitations of force and friction. It is significant from a real world standpoint because it is an innovation that helps keep people safe. ABS is an example of the ultimate benefit of physicists applying their work to the real world and using those results as fuel for advancement and improvement, making what they do worth the while for us all.

Modeling Vehicle Stopping Distance with and without ABS
The following calculations are based upon the following:
Wfriction = -μmgd = -1/2mVo^2

GOAL!
Understanding the Physics of

Anti-Lock Brakes

Modeling

Our test vehicle, a 2006 BMW M3, was used to demonstrate the effectiveness of Anti-lock Braking Systems (ABS). Based on the “Braking 60-0 mph” instrumented test data available from
Motor Trend
, our group estimated the coefficient of static friction between the tires and the road surface as follows:
μs = Vo^2/2gd = 1.1

Where:
Vo= 60 mph = 88 ft/s
g=32 ft/s2
d=111 ft (Given from Motor Trend data)

Modeling
The coefficient of static friction determined (μs), was used to estimate our test vehicle’s stopping distance. For safety, the initial velocity (Vo) used in our test was 35 mph (51 ft/s). This initial velocity was verified by the “
Speedometer – Free – Speed Limiter
…”, Version 1.5.4 for iPhone app. Our estimated stopping distance was calculated as follows:
d
estimated
= Vo^2/2μg = 37 ft

Experimental Data
The experiment consisted of four runs at the speed noted above. The driver of the test vehicle accelerated to a speed programmed into the vehicle’s cruise control system (this speed was verified by the app noted previously). The driver of the test vehicle drove towards a line on the road surface, and the driver applied full braking force (engaging the vehicle’s ABS) just as the front tires of the vehicle crossed the line.
Experimental Data
Experimental Data
The average μs based on this data is 1.2, which is slightly higher than the expected μs of 1.1. This data is within 10% of the expected value of μs and is considered to be acceptable based on the methods used in this experiment.
Experimental Data
Based on information obtained from
Engineer’s Handbook
, the coefficient of kinetic friction μk for rubber on dry asphalt (our test surface) is between 0.5 and 0.8. Using μk = 0.5, the estimated stopping distance for a sliding (brakes are “locked”) vehicle traveling at 35 mph is calculated as follows:
d = Vo^2/2μg = 82 ft

* Due to the hazards involved with disabling a vehicle’s ABS, no experimental data was collected to validate the stopping distance required for a sliding condition.
Kinetic Friction
Experimental Data
Conclusion

The stopping distances reported for static friction versus kinetic friction are synonymous to the stopping distances required for a vehicle with and without an anti-lock braking system. ABS prevents the vehicle’s wheels from locking during a severe braking event, which allows the vehicle to fully stop without sliding. The data shows that a vehicle traveling 35 mph can stop completely within about 35 feet, while the same vehicle without ABS would stop in about 82 feet.
Cars can decelerate due to the force that the braking system can apply on the road. Thus, the more force the braking system applies to the wheel, the more frictional force is applied between the road and the tire (during straight-line deceleration, the friction force is in the opposite direction of the car's motion). Since the static frictional force is much greater that the force of kinetic friction, the purpose of the anti-lock braking system is to keep the wheels from "locking up" during braking. Also, it keeps the frictional force between the tire and the surface maximized.
Sources
“Coefficient of Friction”. Engineers Handbook. 2006. Web. 3 Aug. 2015.
http://www.engineershandbook.com/Tables/frictioncoefficients.htm.

Clench, Courtney. “How Anti-Lock Brakes Work”. MIT. 1999. Web. 1 Aug. 2015.
http://web.mit.edu/2.972/www/reports/anti_lock_brakes/anti_lock_brakes.html

Evans, Scott. “The BMW M3 at 25. Dial M for Magnificent: We Look Back at BMW’s
Performance Icon”. Motor Trend. 20 Jul. 2010. Web. 3 Aug. 2015.
http://www.motortrend.com/features/consumer/1007_the_bmw_m3_at_25/viewall.html

Maggie F. “Physics of Anti-Lock Brakes and How ABS Works”. Car Safety-Physics. Weebly. 29 May
2103. Web. 1 Aug. 2015. http://carsafetyphysics.weebly.com/physics-of-anti-lock-brakes--how- they-work.htm

Nice, Karim. “How Anti-Lock Brakes Work”. How Stuff Works. Web. 27 Jul. 2015.
http://auto.howstuffworks.com.auto-parts/brakes/brake-types/anti-lock-brake.htm

Owens, Derek. “Physical Science 2.5d- Car Braking and ABS”. Online Video Clip. YouTube. 28 Jun.
2011. Web. 28 Jul. 2015. http://youtu.be/32xK-AaJnKg.
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