Transcript Aerospace Presentation 2006

Anthony Garzon
Eryn Richardson
Paul Quarles
Blake Vaughn
Constants and Design
Constraints
 Maximum design
velocity: 120 ft/s
 g – acceleration of
Earth’s gravity
 1g = 32.2 ft/s2
 Maximum g force –
3g’s or 96.6 ft/s2
Car Design
• Take Shape of SR-71 Black Bird Supersonic Aircraft
• Dimensions of SR-71 were scaled down to fit a 4 ft. track width
• Height: 4.33 ft.
• Width: 4 ft.
• Car Length 8ft.
• Frontal Surface Area used for Drag Calculations: 17.33 ft2
Vehicle Design




Accordion joints – ascetic appeal
Total allowable passenger weight 6000 lbs
Total vehicle weight 10,200 lbs
Diametrically opposed Blackbirds
Track Design
 Housing Dimensions will be approximately
50x10 square feet
 Track width: 4 ft. Total track length:
2013.625 ft
 Braking track will run between 2 main rails,
a friction brake will be employed in tandem
with halting power toward forward motion.
Starting Distance
• Distance based on a maximum acceleration
of 3g’s or 96.6 ft/s2
• A maximum velocity of 120 ft/s wanted to be
reached over this section of track
• The distance calculated was 74.5 ft. using
the following equation:
v  v  2a( x f  xi )
2
f
2
i
v2  120 ft
v1  0
dstart
s
Drag Force Calculation
1
2
D  VAVG
SC D
2
D = Drag (95.83 lbs)
 = rho (0.00237 slugs/ft3)
VAVG = Average Velocity (96.6 ft/s)
S = Surface Area (17.33 ft2)
C D =drag coefficient (0.5)
Friction Force
 Coefficient of Friction: 0.03
 F=Force of Friction
 W=Weight
 N=Normal Force
 W-N=0
 W=N
 W=mg
  Ff N  W  mg

 Ff mg
 F = 126 lbs
W
F
N
Loop Design
 Keep Normal Acceleration
Approximately 3’g
2
V
 an 
R
 R  V 2 -need to find R
an
298.1 ft
Max Acceleration
2
v
at 
t
v
an 
R
 Max acceleration will occur
in start of loop where the
velocity is a maximum.
2
2
2
2
2

v
v
 R
aTOT  at  an  
t
 The max g force is a
function of normal and
tangential accelerations.
 The max g force
R
experienced in the ride
was found to be 3.02 g’s or
at
a
n
97.24 ft/s2
 
`
Work-Energy Methods
 Work-Energy methods were used to
calculate parameters throughout the track.
 General Equation
KE1  PE1  KE2  PE2
 Work-Energy Equation when Applied to the
Roller Coaster Problem
1
1
2
mV1  mgh1  F f d f  FD d D  FB d B  FS d S  mV22  mgh2
2
2
Force to Accelerate Vehicle
to 120 ft/s over 74.5 ft
 Work-Energy Equation
FS d S  FF d F  FD d D 
1
mV22
2
 Starting Force: 30,820 lbs
1
mV22  F f d s  FD d s
Fs  2
ds
v1  0
dstart
74.5 ft
v2  120 ft
s
Loop Calculations
 To insure that we made it through the loop, we
used Work-Energy Methods to calculate the
vehicles velocity of the top of the loop.
 Minimum Loop Velocity: 64.36 ft/s
vmin
 Loop Exit Velocity: 114.40 ft/s
1
1
2
2
mV1  Fd d  F f d  mV2
2
2
`
R
vexit
Straight Away
• A 150 ft. section of track added before incline
• This section of track adds time to the ride
making it more exciting
•Exit Velocity of Straight Section: 113.48 ft/s
1
2
2
V2  [( mV1  ( Fd  F f ) * d )( )]
2
m
v2  113.48 ft
v1  114.40
150 ft
s
Incline One
 Incline Design Height is 223.6 ft
 The Max Height was found using a velocity of 120
ft/s for safety and a load of 2g’s on the body.
 HeightCoaster<HeightIncline
 Again using WE methods, the max height of the
coaster was found to be 192.33 ft
1
1
r
2
2
mV1  ( VNG SCd  mg ) *
2
2
h2  2
mg
Reverse Calculations
• Calculating vehicle characteristics in
reverse uses the same method as forward
• Reverse Loop Exit Velocity: 103.31 ft/s
• Max Height of Incline Two: 158.16 ft
• Incline Two Exit Velocity: 99.16 ft/s
Braking Section
 Vehicle must come to rest from 99.16 ft/s over a
150 ft section of track
 Total Braking Force: 10,160 lbs
1
mV12  FF d F  FD d D  FB d B  0
2
1
mV12  F f d B  FD d B
FB  2
dB
v1  99.16 ft
s
dbrake
150 ft
v2  0
Results and Conclusions
 Design Constraints
– Max g Loading: 3g’s
– Max Velocity: 120 ft/s
 Dynamics, Aerodynamics, and Work-Energy
Methods were used to calculate all
parameters of the roller coaster.
 The Blackbird will be an exciting ride
pushing the human body to 3g’s while
obtaining altitudes close to 300 ft.