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

2. Air Bag Deployment Study 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. Air Bag Deployment Study 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. Air Bag Deployment Study 4 an experiment is run arranged as ordered pairs data is collected timedistance (ms)(inches) 105 30 15 50 25 00 and then graphed to facilitate analysis and modeling and/or predictive tasks.

5. Air Bag Deployment Study 5 Air Bag Radial Distance Deployment from Dash Board timedistance (ms)inches 105 30 15 50 25 00 Air Bag moves out from the dash board 1020304050 30 5 10 15 20 40 607080 Time (milliseconds) Distance (inches)

6. Air Bag Deployment Study 6 Concepts remembered and understood X 1 X 2 Y 1 Y 2 Slope of a line = Change in the Y value = Change in the X value t 1 t 2 d 1 d 2 Speed (velocity) of an object = Change in the distance = Change in the time acceleration of an object t 1 t 2 v 1 v 2 = Change in the velocity = Change in the time timedistance msinches 105 3015 5025 00

7. Air Bag Deployment Study 7 t 1 t 2 d 1 d 2 velocity of an object = Change in the distance = Change in the time Possible Speed (velocity) calculations timedistance msinches 105 30 15 50 25 00 ( 5 inches – 0 inches) (10 ms – 0 ms) v 1 = (15 inches – 5 inches) (30 ms – 10 ms) v 2 = (25 inches – 15 inches) (50 ms – 30 ms) v 3 =

8. Air Bag Deployment Study 8 Possible Speed (velocity) calculations (25 inches – 15 inches) (50 ms – 30 ms) v 3 = v 3 = 10 20 = 0.5 inches per millisecond ( 5 inches – 0 inches) (10 ms – 0 ms) v 1 = v 1 = 5 10 = 0.5 ms inches (15 inches – 5 inches) (30 ms – 10 ms) v 2 = v 2 = 10 20 = 0.5 ms inches msinches 105 3015 5025 00 inches/ms 0.5 timedistancevelocity timedistance msinches 105 30 15 50 25 00

9. Air Bag Deployment Study 9 timedistance msinches 105 3015 5025 00 velocity inches/ms 0.5 Possible acceleration calculations v 2 = 10 20 = 0.5 ms inches v 3 = 10 20 = 0.5 ms inches v 1 = 510 = 0.5 ms inches v 1 v 2 = change in the velocity = change in the time a 1 delta t v 2 v 3 = change in the velocity = change in the time a 2 t note: change in time = delta t =  t 

10. Air Bag Deployment Study 10 Possible acceleration calculations t 1 t 2 v 1 v 2 acceleration of an object = change in the velocity = change in the time v 2 = 10 20 = 0.5 ms inches v 3 = 10 20 = 0.5 ms inches v 1 = 5 10 = 0.5 ms inches ms inches ms [ ] ? a 1= (change in the time) a 1 0.5 = (change in the time) 0 = timedistance msinches 105 3015 5025 00 velocity inches/ms 0.5

11. Air Bag Deployment Study 11 a 1 inches ms 0.5 inches ms 0.5 [] = (change in the time) 0 = t 1 t 2 v 1 v 2 acceleration of an object = change in the velocity = change in the time td 105 3015 5025 0 0 0.5 av 0 0 timedistance msinches 105 3015 5025 0 0 inches/ms 0.5 accelerationvelocity inches/ms 0 0 td 105 3015 5025 0 0 0.5 av 0 0

12. Air Bag Deployment Study 12 Distance (inches) 12345 30 5 10 15 20 40 678 Air Bag Radial Distance Deployment from Dash Board Time (seconds) Air Bag moves out from the dash board at a constant speed. Value of the slope of this line is the velocity of the moving front wall of the air bag during deployment td 105 3015 5025 0 0 0.5 av 0 0

13. Air Bag Deployment Study 13 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 td 105 3015 5025 0 0 0.5 av 0 0

14. Air Bag Deployment Study 14 Model for Air Bag behavior y = m  x + b x 2 = 10, y 2 = 0.5 5 = 0.5  (10) + b To check the model, we can use the second ordered pair, x 2, y 2, to see if the data fits the equation. 5 = 5 + b The only time that the number on both sides of this equation is the same is when b equals zero. m = 0.5 (the slope) b = 0 (the intercept) Where: td 105 3015 5025 0 0 0.5 av 0 0 y 2 = 0.5  x 2 + b

15. Air Bag Deployment Study 15 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 Difference Table for the Air Bag Experiment accelerationtimedistance msinches 105 3015 5025 0 inches/ms 2 0.5 = m velocity inches/ms 0 3 0.5 = m 1 1 0 = a 2

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

17. Air Bag Deployment Study 17