1. Data Plots, Graphic Analysis and Modeling
Air Bag Deployment Evaluation Example

2. Bred Technology Inc. develops air bags and is evaluating a new propellant.
A technician has developed a test stand to measure the distance the front of an air bag moves away from the dash board after the propellant has been ignited.
This presentation reviews the thought process, graphic plotting, analysis, and modeling procedures this technician does during the study of this new propellant.

3. A technician has developed a test stand to measure the distance the front of an air bag moves away from the dash board after the propellant has been ignited.
Distance

4. arranged as ordered pairs
an experiment is run
data is collected
arranged as ordered pairs
time
distance
(ms)
(inches) 10 5 30 15 50 25
and then graphed to facilitate analysis and modeling and/or predictive tasks.

5. Air Bag Radial Distance Deployment from Dash Board
time
distance
(ms)
inches 10 5 30 15 50 25
Air Bag Radial Distance Deployment from Dash Board
Air Bag moves out from the dash board 10 20 30 40 50 5 15 60 70 80
Time (milliseconds)
Distance (inches)

6. Concepts remembered and understood
time
distance ms
inches 10 5 30 15 50 25
Concepts remembered and understood X 1 2 Y
Slope of a line =
Change in the Y value
Change in the X value t 1 2 d
Speed (velocity) of an object =
Change in the distance
Change in the time
acceleration of an object t 1 2 v =
Change in the velocity
Change in the time

7. Possible Speed (velocity) calculations
time
distance ms
inches 10 5 30 15 50 25
Possible Speed (velocity) calculations
velocity of an object d 2 d 1
Change in the distance = = t 2 t 1
Change in the time
( 5 inches – 0 inches)
(10 ms – 0 ms) v 1 =
(15 inches – 5 inches)
(30 ms – 10 ms) 2
(25 inches – 15 inches)
(50 ms – 30 ms) 3

8. 10 5 30 15 50 25 0.5 time distance velocity ( 5 inches – 0 inches)ms
inches 10 5 30 15 50 25
Possible Speed (velocity) calculations
( 5 inches – 0 inches)
(10 ms – 0 ms) v 1 = 5 10
0.5 ms
inches
(15 inches – 5 inches)
(30 ms – 10 ms) v 2 = 10 20
0.5 ms
inches
(25 inches – 15 inches)
(50 ms – 30 ms) v 3 = 10 20
0.5
inches per millisecond ms
inches 10 5 30 15 50 25
inches/ms
0.5
time
distance
velocity

9. Possible acceleration calculations
time
distance ms
inches 10 5 30 15 50 25
velocity
inches/ms
0.5 v 1 = 5 10
0.5 ms
inches v 2 = 10 20
0.5 ms
inches v 3 = 10 20
0.5 ms
inches
Possible acceleration calculations v 1 2 =
change in the velocity
change in the time a
delta t v 2 3 =
change in the velocity
change in the time a t
note:
change in time = delta t = t

10. [ ] ? Possible acceleration calculations 0.5 v 1 = 5 10 0.5 v 2 = 10
time
distance ms
inches 10 5 30 15 50 25
velocity
inches/ms
0.5 v 1 = 5 10
0.5 ms
inches v 2 = 10 20
0.5 ms
inches v 3 = 10 20
0.5 ms
inches
Possible acceleration calculations t 1 2 v
acceleration of an object =
change in the velocity
change in the time [
inches ms
inches ms ]
(change in the time) a 1
0.5 = ? a 1 =

11. [ ] time distance 10 5 30 15 50 25 0.5 acceleration velocity ms inches
0.5 a v t d 10 5 30 15 50 25
0.5 a v t 1 2 v
acceleration of an object =
change in the velocity
change in the time a 1
inches ms
0.5 [ ] =
(change in the time)
time
distance ms
inches 10 5 30 15 50 25
inches/ms
0.5
acceleration
velocity

12. Air Bag Radial Distance Deployment from Dash Board10 5 30 15 50 25
0.5 a v
Air Bag Radial Distance Deployment from Dash Board 40
Value of the slope of this line is the velocity of the moving front wall of the air bag during deployment 30
Distance (inches) 20 15 10 5 1 2 3 4 5 6 7 8
Time (seconds)
Air Bag moves out from the dash board at a constant speed.

13. y = m·x + b y = 0.5·x + 0 Model for Air Bag behaviort d 10 5 30 15 50 25
0.5 a v
Model for Air Bag behavior
Once the data has been plotted and analyzed, technicians, engineers and scientists try to find an equation that describes the data so that everyone can easily use the data.
In the case of this air bag experiment, the technician sees that the data seems to fall on a line that has a slope of 0.5 and crosses the y axis at the value y =0.
y = m·x + b
Where the slope is the letter “m” and the letter “b” is the value of y where the line crosses the y axis, (the y intercept).
y = 0.5·x + 0

14. y = m·x + b y2 = 0.5· x2 + b 5 = 0.5·(10) + b 5 = 5 + bt d 10 5 30 15 50 25
0.5 a v
Model for Air Bag behavior
y = m·x + b
m = 0.5 (the slope)
b = 0 (the intercept)
Where:
To check the model, we can use the second ordered pair, x2, y2, to see if the data fits the equation.
y2 = 0.5· x2 + b
x2 = 10, y2= 0.5
5 = 0.5·(10) + b
5 = 5 + b
The only time that the number on both sides of this equation is the same is when b equals zero.

15. Difference Table for the Air Bag Experiment
One easy and simple way to make sure you have completed all of the possible calculations needed before the data is analyzed is to just make and then fill in a difference table.
Difference Table for the Air Bag Experiment
acceleration
time
distance ms
inches 10 5 30 15 50 25
inches/ms 2
0.5 = m
velocity 3 1
0 = a

16. General Format for a Difference Table
Difference Tables
General Format for a Difference Table
Independent variable
Dependent variable
1st
2nd
3rd
difference
difference
difference 1 x y 1 1 m 1 x 2 y 2 1 a 2 m 1 c 1 x 3 y 3 2 a 3 m 2 c 1 x 4 y 4 3 a 4 m 3 c 1 x 5 y 5 4 a 5 m 1 x 6 y 6
Note:
Most of the time, people only use information from the first 3 difference columns.