Vehicle Problem

Stephen MooreME270

Prof. GrandaOctober 30, 2007

Vehicle Problem

• Car impacting a wall at various speeds

• Car driven at 25, 40, and 55 mph

Parameters given

• Mass of the car- 1500kg• Mass of the driver- 100kg• Spring constants of the bumper- 300,000 N/m• Resistance of the bumper- 80,000 N-s/m• Spring constants of the seatbelts- 10,000 N/m• Resistance of the seatbelts- 500 N-s/m• Masses stay the same, the spring constants and the

resistances change

R1

1

R1

0

1

0

1

11

Cb

Sf w

C1 C1

Id

Rb

Ic

Bondgraph model

Element Definition Value

Sfw Source of flow, wall Sfw = 0

Rb Resistance of the bumper Varies

Cb Capacitance of the bumper Varies

R1 (2 each) Resistance of the seat belt and shoulder belt

Varies

C1 (2 each) Capacitance of the seat belt and shoulder belt

Varies

Id Mass of the driver 100 kg

Ic Mass of the car 1500 kg

Design Criteria

1. Driver does not hit the windshield at 25 and 55 mph

2. Forces on driver at 25 and 55 mph

3. Critical maximum velocity

4. Traveling without a seatbelt, how long does it take to hit the windshield?

#1. Driver does not hit the windshield at 25 and 55 mph

• After running the models in Campg and running Matlab programs, the acceptable criteria are shown in table below.

Design Criteria

Vel. (mph)

# belts

k1 (N/m)

R1 (N-s/m)

k2 (kN/m)

R2 (kN-s/m)

Force on the driver (N)

Displacement of the driver (m) Notes

1 25 2 9000 600 350 100 12860 0.501

Max force w/ two belts is 13340 N

  55 2 9000 600 350 100 28200 1.000

Max force w/ two belts is 13340 N

Displacement of the driver

0 0.5 1 1.5-1.5

-1

-0.5

0

0.5Head displacement (m) (stored in column 1),color blue

disp

lace

men

t (m

)

Time (seconds)

0 0.5 1 1.5-1.5

-1

-0.5

0

0.5 Waist displacement (m) (stored in column 2), color magenta

disp

lace

men

t (m

)

Time (seconds)

Displacement the driver experiences at 25 mph.

0 0.5 1 1.5-0.6

-0.4

-0.2

0

0.2Head displacement (m) (stored in column 1),color blue

disp

lace

men

t (m

)

Time (seconds)

0 0.5 1 1.5-0.6

-0.4

-0.2

0

0.2 Waist displacement (m) (stored in column 2), color magenta

disp

lace

men

t (m

)

Time (seconds)

Displacement the driver experiences at 55 mph.

#2. Forces the driver experiences upon impact

Design Criteria

Velocity (mph)

# of belts

k1 (N/m)

R1 (N-s/m)

k2 (kN/m)

R2 (kN-s/m)

Force on the driver (N)

Displacement of the driver (m) Notes

2 

25 2 9000 600 350 100 12860 0.501Max force w/ two belts is 13340 N

55 2 9000 600 350 100 28200 1.000Max force w/ two belts is 13340 N

  

Max force w/ one belt is 6670 N

2555

11

90009000

600600

350350

100100

1664019930

0.5011.000

Max force w/ one belt is 6670 N

#2 Forces the driver experiences

0 0.5 1 1.5-3

-2

-1

0

1x 10

4 Effort variable of Force on the driver (N)" stored in column 2

For

ce o

n dr

iver

(N

)

time(s)

0 0.5 1 1.5-10

0

10

20

30 Flow variable of velocity of the driver (m/s)" stored in column 3

Vel

ocity

of

driv

er (

m/s

)

time(s)

The figure is the force the driver experiences at 55 mph.

0 0.5 1 1.5-0.6

-0.4

-0.2

0

0.2Head displacement (m) (stored in column 1),color blue

disp

lace

men

t (m

)

Time (seconds)

0 0.5 1 1.5-0.6

-0.4

-0.2

0

0.2 Waist displacement (m) (stored in column 2), color magenta

disp

lace

men

t (m

)

Time (seconds)

The figure is the force the driver experiences at 25 mph.

#3. Critical maximum velocity

Design Criteria

Velocity (mph)

# of belts

k1 (N/m)

R1 (N-s/m) k2 (kN/m)

R2 (kN-s/m)

Force on the driver (N)

3 26.04 2 9000 600 350 100 13340

#4. Traveling without a seat belt, how long does it take the driver to hit the windshield?

Design Criteria

Velocity (mph) # of belts

Delta time (ms) Notes

4 25 0  0.105  

  

40 0  0.073  

55 0  0.057