The Black Bird

Anthony GarzonEryn Richardson

Paul QuarlesBlake Vaughn

Constants and DesignConstants and DesignConstraintsConstraints

Maximum design Maximum design velocity: 120 ft/svelocity: 120 ft/s

g – acceleration of g – acceleration of Earth’s gravityEarth’s gravity

1g = 32.2 ft/s1g = 32.2 ft/s22

Maximum g force – Maximum g force – 3g’s or 96.6 ft/s3g’s or 96.6 ft/s22

Car DesignCar Design

• Take Shape of SR-71 Black Bird Supersonic AircraftTake Shape of SR-71 Black Bird Supersonic Aircraft

• Dimensions of SR-71 were scaled down to fit a 4 ft. track widthDimensions of SR-71 were scaled down to fit a 4 ft. track width

• Height: 4.33 ft.Height: 4.33 ft.

• Width: 4 ft.Width: 4 ft.

• Car Length 8ft.Car Length 8ft.

• Frontal Surface Area used for Drag Calculations: 17.33 ft2Frontal Surface Area used for Drag Calculations: 17.33 ft2

Vehicle DesignVehicle Design

Accordion joints – ascetic appealAccordion joints – ascetic appeal Total allowable passenger weight 6000 lbsTotal allowable passenger weight 6000 lbs Total vehicle weight 10,200 lbsTotal vehicle weight 10,200 lbs Diametrically opposed BlackbirdsDiametrically opposed Blackbirds

Track DesignTrack Design

Housing Dimensions will be approximately Housing Dimensions will be approximately 50x10 square feet50x10 square feet

Track width: 4 ft. Total track length: Track width: 4 ft. Total track length: 2013.625 ft2013.625 ft

Braking track will run between 2 main rails, Braking track will run between 2 main rails, a friction brake will be employed in tandem a friction brake will be employed in tandem with halting power toward forward motion.with halting power toward forward motion.

Starting DistanceStarting Distance• Distance based on a maximum acceleration Distance based on a maximum acceleration

of 3g’s or 96.6 ft/s2of 3g’s or 96.6 ft/s2• A maximum velocity of 120 ft/s wanted to be A maximum velocity of 120 ft/s wanted to be

reached over this section of trackreached over this section of track• The distance calculated was 74.5 ft. using The distance calculated was 74.5 ft. using

the following equation:the following equation:

dstart

sftv 1202 01 v

)(222ifif xxavv

Drag Force CalculationDrag Force Calculation

DAVGSCVD 2

2

1

DC

D = Drag (95.83 lbs)

= rho (0.00237 slugs/ft3)

VAVG = Average Velocity (96.6 ft/s)

S = Surface Area (17.33 ft2)

=drag coefficient (0.5)

Friction ForceFriction Force

Coefficient of Friction: 0.03Coefficient of Friction: 0.03 F=Force of FrictionF=Force of Friction W=WeightW=Weight N=Normal ForceN=Normal Force W-N=0W-N=0 W=NW=N W=mgW=mg F = 126 lbsF = 126 lbs

W

N

F

mgWNFf mgFf

Loop DesignLoop Design

Keep Normal Acceleration Keep Normal Acceleration Approximately 3’gApproximately 3’g

-need to find R-need to find R

na

VR

2

R

Van

2

298.1 ft

Max AccelerationMax Acceleration

Max acceleration will occur Max acceleration will occur in start of loop where the in start of loop where the velocity is a maximum.velocity is a maximum.

The max g force is a The max g force is a function of normal and function of normal and tangential accelerations.tangential accelerations.

The max g force The max g force experienced in the ride experienced in the ride was found to be 3.02 g’s or was found to be 3.02 g’s or 97.24 ft/s97.24 ft/s22

22222

Rv

tvaaa ntTOT

t

vat

R

van

2

`tana

R

Work-Energy MethodsWork-Energy Methods

Work-Energy methods were used to Work-Energy methods were used to calculate parameters throughout the track.calculate parameters throughout the track.

General EquationGeneral Equation

Work-Energy Equation when Applied to the Work-Energy Equation when Applied to the Roller Coaster ProblemRoller Coaster Problem

2211 PEKEPEKE

2221

21 2

1

2

1mghmVdFdFdFdFmghmV SSBBDDff

Force to Accelerate Vehicle Force to Accelerate Vehicle to 120 ft/s over 74.5 ft to 120 ft/s over 74.5 ft

Work-Energy Equation Work-Energy Equation

Starting Force: 30,820 lbsStarting Force: 30,820 lbs

222

1mVdFdFdF DDFFSS

s

sDsf

s d

dFdFmVF

222

1

74.5 ft

sftv 1202 01 v dstart

Loop CalculationsLoop Calculations

To insure that we made it through the loop, we To insure that we made it through the loop, we used Work-Energy Methods to calculate the used Work-Energy Methods to calculate the vehicles velocity of the top of the loop.vehicles velocity of the top of the loop.

Minimum Loop Velocity: 64.36 ft/sMinimum Loop Velocity: 64.36 ft/s Loop Exit Velocity: 114.40 ft/sLoop Exit Velocity: 114.40 ft/s

1

2

1

212

22mV F d F d mVd f `

exitv

R

minv

Straight AwayStraight Away

• A 150 ft. section of track added before inclineA 150 ft. section of track added before incline

• This section of track adds time to the ride This section of track adds time to the ride making it more excitingmaking it more exciting

•Exit Velocity of Straight Section: 113.48 ft/sExit Velocity of Straight Section: 113.48 ft/s

sftv 48.1132

150 ft

40.1141 v

V mV F F dmd f2 1

21

2

2 [ ( ( ) * )( )]

Incline OneIncline One

Incline Design Height is 223.6 ftIncline Design Height is 223.6 ft The Max Height was found using a velocity of 120 The Max Height was found using a velocity of 120

ft/s for safety and a load of 2g’s on the body.ft/s for safety and a load of 2g’s on the body. HeightHeightCoasterCoaster<Height<HeightInclineIncline

Again using WE methods, the max height of the Again using WE methods, the max height of the coaster was found to be 192.33 ftcoaster was found to be 192.33 ft

hmV V SC mg

r

m g

NG d

2

12 21

2

1

2 2 ( ) *

Reverse CalculationsReverse Calculations• Calculating vehicle characteristics in Calculating vehicle characteristics in reverse uses the same method as forwardreverse uses the same method as forward

• Reverse Loop Exit Velocity: 103.31 ft/sReverse Loop Exit Velocity: 103.31 ft/s

• Max Height of Incline Two: 158.16 ftMax Height of Incline Two: 158.16 ft

• Incline Two Exit Velocity: 99.16 ft/sIncline Two Exit Velocity: 99.16 ft/s

Braking SectionBraking Section

Vehicle must come to rest from 99.16 ft/s over a Vehicle must come to rest from 99.16 ft/s over a 150 ft section of track150 ft section of track

Total Braking Force: 10,160 lbsTotal Braking Force: 10,160 lbs

02

1 21 BBDDFF dFdFdFmV

B

BDBf

B d

dFdFmVF

212

1

150 ft

02 vsftv 16.991 dbrake

Results and ConclusionsResults and Conclusions

Design ConstraintsDesign Constraints– Max g Loading: 3g’sMax g Loading: 3g’s– Max Velocity: 120 ft/sMax Velocity: 120 ft/s

Dynamics, Aerodynamics, and Work-Energy Dynamics, Aerodynamics, and Work-Energy Methods were used to calculate all Methods were used to calculate all parameters of the roller coaster.parameters of the roller coaster.

The Blackbird will be an exciting ride The Blackbird will be an exciting ride pushing the human body to 3g’s while pushing the human body to 3g’s while obtaining altitudes close to 300 ft.obtaining altitudes close to 300 ft.