Transcript Equation of Maximum Velocity

The Degrees of Racing
Created by
Keith Johnson, Alan Riley, and Brandon Sasser
The History Of NASCAR






1936 Daytona Begins the Dream
The Sacrifice of War
1948 The Birth of National Association for Stock Car
Auto Racing (NASCAR)
Bill France, Founder of NASCAR and International
Speedway Corporation (ISC)
1971 Winston Cup Series Begins
2004 Nextel Cup Series Begins
The Southern Sport Goes National
•
•
•
NASCAR becomes #1
spectator sport in 2000.
Eighty million television
viewers in 2000
3 divisions of NASCAR
•
•
•
Winston Cup Series
Busch Series
Craftsman Truck Series
Banking On The Turn
Design Speed Equation
(vmax )  (tan  ) gr
2
Equation of Maximum Velocity





(Vmax)2 = [(sin + scos) / (cos - ssin)]gr
 is equal to the degree of banking of the particular
turn
s is the coefficient of static friction between the
track and the tires
g is acceleration due to gravity
r is the radius of the particular turn
Derivation of Maximum
Velocity Equation
F
y
 FN cos  mg  f s sin   ma y  0
FN cos    s FN sin   mg
FN  mg /(cos    s sin  )
f s   s FN
2
F

F
sin


f
cos


ma

m
(
v
)
/r
 x N
s
x
max
[mg sin  /(cos    s sin  )]  [  s mg cos  /(cos    s sin  )]  m(vmax ) 2 / r
(vmax )  [(sin    s cos  ) /(cos    s sin  )] gr
2
(vmax )  (tan  ) gr
2
Darlington Raceway
1.366-Mile Egg-shaped Oval
Backstretch
Length: 1,229 Ft
Width: 90 Ft
Banking: 2°
Turns 3 & 4
Turns 1 & 2
Banking: 23°
Width: 62 Ft
Radius: 525 Ft
Banking: 25°
Width: 79 Ft
Radius: 600 Ft
Frontstretch
Length: 1,229 Ft
Width: 90 Ft
Banking: 3°
Qualifying Record: 173.797 mph
Finding the Coefficient of Static
Friction
(138) 2  [(sin 23   s cos 23) /(cos 23   s sin 23)] gr
 s  .98
Talladega Superspeedway
Turns
Length: 3,750 Ft
2.66-Mile Trioval
48 Ft wide
Frontstretch
Chute: 2,150 Ft
18°
Radius: 1,100 Ft
Total: 4,300 Ft
33°
33°
4,000 Ft
2003 Pole Speed: 189.943 mph
Talladega Super Speedway

Turns are banked 33 degrees
 Radius of turns is 1100 feet
Vmax  [(sin 33  .98 cos 33) /(cos 33  .98 sin 33)](78967)(.2083)
2
Vmax  271.5
Daytona International Speedway
2.5-Mile Trioval
3,000 Ft.
40 Ft wide
31°
31°
Turns
Frontstretch
Length: 3,000 Ft
Radius: 1,000 Ft
18°
Chute: 1,900 Ft
Total: 3,800 Ft
2003 Pole Speed: 184.752 mph
Daytona Super Speedway

31 degree banking in turns
 Turns have 1000 foot radius
Vmax  [(sin 31  .98 cos 31) /(cos 31  .98 sin 31)](78967)(.1894)
2
Vmax  239.8
Bristol Motor Speedway
.533-Mile Concrete Oval
40 Ft Wide
Turns- 36°
Straightaways
Length: 650 Ft
Banking: 16°
Bristol Motor Speedway

Corners are banked at 36 degrees
 Radius is 241 feet
Vmax  [(sin 36  .98 cos 36) /(cos 36  .98 sin 36)](78967)(.0457)
2
Vmax  146.2
Lowe’s Motor Speedway
1.5-Mile Quad-oval
Backstretch: 1,360 Ft
Banking: 5°
Turns
Banking: 24°
Frontstretch: 1,952 Ft
Banking: 5°
Qualifying Record: 186.657 mph
Lowe’s Motor Speedway
Vmax  [(sin 24  .98 cos 24) /(cos 24  .98 sin 24)](78967)(.1389)
2
Vmax  166.5
Sources
Nascar.com
Darlingtonraceway.com
Quicktv.net
Bristolmotorspeedway.com
National Broadcasting Corporation
Talladegasuperspeedway.com
Nascar-info.net
Daytonainternationalspeedway.com
Findarticles.com
Physics.bu.com