Quantum Racing: Engaging Students with the Physics of Motorsports
Author list: Hodek, Hann, Van Hook, Kane, Meinecke, Miller, Schall, Welch, Zeiter
Matt Hodek was the President of the BGSU SPS and the Crew Chief for the Quantum
Racing team. He is now a graduate student in physics at Michigan State University.
Alex Hann is the laboratory machinist for the BGSU Department of Physics &
Astronomy and was the 2007 Chair of the BG Grand Prix Committee. adhann@bgsu.edu
Stephen J. Van Hook is an Assistant Professor in physics & astronomy at BGSU.
Jackie Kane is a physics teacher at St. Ursula Academy in Toledo, OH.
Ken Meinecke is a physics teacher at Maumee Valley Country Day School in Toledo,
OH.
Vicki Miller is a physics teacher at Waite High School in Toledo, OH.
Jim Schall is a physics teacher at ??? (Springfield Local)
Patrick Welch is a science teacher at Polly Fox Academy in Toledo, OH.
Sarah Zeiter is a math and science teacher at Anthony Wayne Junior High in Whitehouse,
OH.
http://physics.bgsu.edu/Quantum_Racing
Acknowledgments:
We wish to thank the Department of Physics & Astronomy at BGSU for their support and
all of our sponsors for the funding of the Quantum Racing team.
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NOTE: 2000 words or less.
Figures:
Jackie Kane activity
Gear ratio activity (car underside)
Organization of Paper
1.
2.
3.
4.
Introduction (general ideas and goals)
Undergraduate students’ experiences
Physics of Racing and with activities developed by teachers
Momentum Racing
Cornering
Gear ratio & torque
Friction circle
Coasting friction
General conclusions about how wonderful racing is for teaching physics
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Quantum Racing: Engaging Students with the Physics of Motorsports
Introduction
Racing is one of the most popular sports world wide with many different forms of racing
creating a broad fan base. What many people don't know, however, is that racing involves
many different aspects of physics – from kinematics to pressure to torque. A lot of the
physics involved is within the scope of high school or introductory college physics
students.
Quantum Racing is a part of the BGSU Society of Physics Students and was formed as
the first entrant in the Inaugural Grand Prix of BG held April 22, 2006. The Quantum
Racing team was created by the Society of Physics Students and the Department of
Physics and Astronomy at Bowling Green State University to engage undergraduate
students in physics through racing and as a way to reach out to local schools using the
physics of racing.
This paper describes the experiences of some of the undergraduate physics students and
some hands-on classroom activities developed by high school physics teachers in
collaboration with the Quantum Racing team.
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Undergraduate Student Experiences
Physics is an invaluable tool when it comes to racing. Quantum Racing team member
Randy Patton stated “While it may not be necessary to have a thorough understanding of
physics to participate in a race team; knowing the ‘why’ of your actions leads to a much
more fulfilling experience and allows you to make better decisions when changes need to
be made.” This extends from introductory physics concepts to complex multi-system
interactions.
Figure 1: People working on car
Jen Bradley, Quantum Racing driver for the 2006 and 2007 race seasons, says that she
had to learn about how to drive the kart through turns to get the most speed going in and
coming out of turns. Simple kinematics equations such as
v2 = vo2 + 2a x
can teach a driver an important lesson. This equation shows that a small advantage in
speed at the beginning of a straightaway, can lead to a large advantage in speed and in
elapsed time at the end for a given acceleration. With the low power to weight ratio that
Grand Prix of BG karts have, and hence the low acceleration rates, it is very important for
the drivers to take full advantage of this concept to be competitive. This type of driving is
known as ‘momentum driving’. This gives a reason as to why drivers need to conserve
momentum, but how do they do that? An activity later in the article explores the physics
of making a turn will explain one such way.
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Figure 2: Jen Bradley driving the Quantum Racing kart around the course.
The team also provides an environment for more advanced projects in the form of
independent studies with faculty members. These projects allows students to get hands on
experience in experimental and theoretical physics of a real world situation. Working
with the kart can provide many difficult issues to study needing complex real world
methods, but it does so in a small enough setting as to be manageable by an
undergraduate student. There have been studies on the dynamics of the chassis and plans
are being made for more studies in the future. Papers and write-ups of these studies can
be found on the Quantum Racing website.
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Physics of Racing with Activities
The Quantum Racing team collaborated with several local science teachers to develop
activities that could be used in high schools that highlight the physics of racing. We
discuss some of these below: taking a turn, gear ratios, and rolling friction. The
discussion here is meant only as an overview. Full descriptions and lesson plans can be
found on the Quantum Racing website under research.
A. What’s the best way to take a turn? (The driving line)
Determining the best way to take a turn is critical to winning a race and it involves
finding the right speed and path to take. Hugging the inside of the turn involves the
shortest distance to travel, but also requires the driver to slow down so that friction (FFr)
between the wheels and the ground is sufficient to provide the centripetal force (mv2/R)
required to keep the car from skidding, that is
FFr = mv2/R,
where v is the speed of the car and R is the radius of the curve. Following the outside
curve allows the driver to go faster (larger R), but the driver still must slow down
somewhat and has to take a longer path. The purpose of an ‘apexed’ line (Figure 4) is to
make the turn radius as large at possible. That means that the kart can go as fast as
possible with the friction available. This path is a good balance between distance to travel
and speed (Figure 5). Since these karts have low acceleration, it is particularly important
to avoid braking around curves.
Figure 4. The three basic driving lines and their associated radii.
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Figure 5. Calculated corner times as a function of radius assuming a 1.1g turn
An activity to convey to concept of centripetal acceleration in going around curves was
developed for the classroom. This demonstration illustrates some of the physics
principles involved in cornering.
Radius vs Acceleration Activty: In this activity students explore the relationship between
turn radius and the centripital acceleration going around that corner.
Method: This activity requries some advanced preperation and fine tuning. In
general a small toy car is given a constant velocity and the students must
find the proper force, and therfore centripital acceleration, needed for the
car to maintain a given turn radius. The car is given a constant velocity by
using a suspended hammer raised to a certain hight that strikes the car.
This or a similar setup is important to the activity in order remove the
velocity dependence and isolate the radius vs. acceleration component of
the problem. The force/centripital acceleration is provided by a weight
hanging on a string attatched to the car. In the tested setup pennies were
added to a plastic bag suspended on a fine fishing line. The line was strung
though a straw attached to the edge of the table at the turn’s center. A
piece of paper was layed out on the table with different radius circles
inscribed on it to ensure the car was traveling along a constant radius
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Figure 6: Driving line experimental setup.
Results: With a given speed, a car needs more centripital acceleration and thus for
to mantian a smaller radus as opposed to a larger radius.
Applicaion: Knowing that a car has a limited amount of avalible friction puts a
limit on the smallest radius turn a car can take a certain speed.
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B. Gear Ratio: Torque vs Speed
In a racecar, a very important use of mechanical advantage is found in the gears that
transfer power from the engine to the axle that the racecars wheels are attached to. The
gear ratio effects how fast a vehicle accelerates and the top speed the vehicle can achieve.
Making the gear ratio numerically smaller (e.g.. subtracting teeth from the rear sprocket)
will increase the top end speed for a given RPM. Making the gear ratio numerically larger
(e.g.. Adding teeth to the rear sprocket) will increase the amount of torque and therefore
the acceleration. Instead of mechanical advantage, racecar mechanics call this “Gear
Ratio”. The gear ratio is defined as the ratio of the number of teeth on the output gear as
compared to the number of teeth on the input (drive) gear. For example, if our motor is
attached to a gear with 10 teeth and this gear is then attached to a gear with 20 teeth that
drives the wheels, our gear ratio is 20/10, or more accurately 2.0
Gear Ratio = # teeth on axle sprocket / # teeth on clutch sprocket
The nomenclature used in racing can be confusing since a numerically large gear ratio is
called a low gear ratio (what is called low gear on a bicycle or car); a numerically small
gear ratio is called a high gear ratio (high gear on a bicycle or car).
chain
16
32
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et
Figure 7. tee
Gear Ratios
th
h
A classroom activity can demonstrate the importance of gear ratio by demonstrating with
Axle sprocket
(attached to wheels)
Clutch sprocket
(attached to engine)
a toy battery-powered car with a variable gear ratio (Figure 8). We bought a cheap plastic
toy car from a local discount store, hot-glued a 3.6 V DC motor to its underside to drive
the axle. We used duct tape to change the thicknesses of the two ends of the axle –
making one thicker than the other. A rubber band wrapped around the axle and the motor
shaft acted as the chain. When the rubber band was wrapped around the thicker part of
the axle, the car was in low gear and had greater acceleration. When the rubber band was
wrapped around the thinner part of the axle, the car was in high gear and had less
acceleration but under good conditions could attain a higher maximum velocity.
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Figure 8. Top and bottom views of the variable gear ratio car. A gear at the end of the
motor shaft is used to keep the rubber band onto the motor shaft.
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C. Friction and Drag Forces
There are several resistive forces that act upon a car as it moves around the race track,
even when it is coasting along a straight line. One such force is the rolling friction
between the tires and the ground that act to slow down the car. In addition, air resistance
(drag) provides an additional force to slow down the car as well as friction in the axel
bearings. These forces may depend on the speed the car is traveling, too, as well as issues
such as the temperature of the tires and conditions of the road.
In this experiment, we will investigate what are the effects of the total forces of friction
for a car and does it change significantly with speed? To determine the total forces of
friction we will use the equation, V2 = Vo2 + 2ax to determine the acceleration of the car
where V= velocity, a = acceleration, and x = the distance traveled. Newton’s law tells us
that force is equal to the mass of the object multiplied by its acceleration which is also
equal to the coefficient of friction multiplied by the mass of the object multiplied by the
acceleration due to gravity or or 9.8 m/s2. (F = ma = mg) In these two equations, the
mass cancels out so we end up with  = a/g.
Equipment:
 toy match box cars
 flexible race car track
 a meter stick
 a digital video camera
Experimental procedure:
1. On a flat surface, lay out two to three meters of track
2. Mark two 10 centimeter sections of the track with one meter space between the
two sections.
10 cm
1 meter between each 10 cm
section
10 cm
3. At one end, attach additional flexible track to serve as a launch ramp with variable
height. (Stacks of books or ring stands work well)
4. Set up the video camera to view the horizontal portion of the ramp and begin the
camera as the car is released.
5. Release the car from various heights to obtain different initial velocities. The
height doesn’t really matter as long as your car travels the whole length of the
track.
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Data Analysis:
1. Using a computer, analyze the video to determine the average speed of the car at
the beginning of the horizontal motion and at the end of the horizontal motion. (S
= d/t) d = to 10 cm, t = # of frames the car traveled divided by 30.
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References [Annotated Bibliography]
Beckman, Brian. "Physics of Racing, Part 18: "Slow in, Fast Out!" or, Advanced Racing
Line, Continued." Aug. 2000. 22 Apr. 2007
<http://www.miata.net/sport/Physics/Part18.html>. This is the most topic specific
and complete reference site on the web about the physics racing. This section
explains turns.
Beckman, Brian. "The Physics of Racing, Part 4: There is No Such Thing as Centrifugal
Force." HSPN Reviews. 29 Apr. 2006. 22 Apr. 2007
<http://reviews.hspn.com/articles/121/1/The-Physics-of-Racing-Part-4-There-IsNo-Such-Thing-as-Centrifugal-Force/Page1.html>. Are your students confused
about the term, centrifugal? This site explains it in easy to understand examples. It
is one of many sections about the physics of car racing.
"Circular Motion and Planetary Motion." The Physics Classroom. 2004. StudyWorks!
Online. 22 Apr. 2007
<http://www.physicsclassroom.com/Class/circles/circtoc.html>. This is one of
the best sites available to learn about centripetal motion both mathematically and
conceptionally. It has animated links and study questions and answers.
Franklin, George B. "The Late Apex Turn." The Physics Teacher 28 (1990): 68. This
author is a teacher who responds to Richard A. Hewko's article,” The racing Car
turn" [Phys. Teach. 26, 436 (1998), by pointing out that the best path is the largest
radius turn. This article should be read along with the original article.
Hewko, Richard A. "The Racing Car Turn." The Physics Teacher 26 (1988): 436-437.
This article is written by a teacher who mathematically discusses the better of two
paths for a racing car to take around a turn, an inner or outer radius turn. He
shows how the best path depends on whether a 90 or 180 turn is made. See letter
response in The Physics Teacher, Feb 1990, vol. 28, pp 68, for discussion of the
largest radius turn.
Stanbrough, Jr. "Turning a Car." BHS Physics. 27 Dec. 2005. Batesville High School. 22
Apr. 2007
<http://www.batesville.k12.in.us/physics/PHYNET/Mechanics/Circular%20Moti
on/turning_a_car.htm>. This is an outstanding high school physics teacher's site
on driving around a turn. A must see.
"Unit VIII: Central Force Particle Model." Modeling Workshop Project 2002. 2002. 22
Apr. 2007 <http://modeling.asu.edu/Modeling-pub/Mechanics_curriculum/8UCM/01_U8%20Teachernotes.pdf>. This excellent site explains how to teach
centripetal force through the modeling technique.
Zibell, John. "Much Ado About Cornering." Moto Guzzi National Owners Club. 22 Apr.
2007 <http://www.mgnoc.com/article_much_ado_about_cornering.html>.
Although this site describes how to take a corner in a motorcycle, it covers many
different types of turning situation complete with diagrams and explanations. It is
short, concise and is an "easy read".
Web Sites on friction:
http://www.newi.ac.uk/buckleyc/forces2.htm
http://www.reachoutmichigan.org/funexperiments/quick/dirtmeister/friction.html
http://www.school-for-champions.com/science/frictionrolling_tires.htm
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