# Acceleration Perturbations of Daily Living

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A "g" is a unit used to measure acceleration due to gravity; one g is approximately 9.81 m/s2. Amusements rides such as rollercoasters are known to have a high acceleration. But what many do not realize is that everyday activities "create a far greater gravitational pull than that of any amusement park ride," stated in a study by Murray Allen, MD, Ian Weir-Jones, P. Eng, Ph.D. et al. (Spine November 1994). In his research the following values were measured:

Everyday Accelerations (in g's)
Sneeze 2.9
Cough 3.5
Crowd jostle 3.6
Slap on back 4.1
Hop off step 8.1
Plop down in chair 10.1

In our experiment, we attempted to recreate the values that were found in his study. An accelerometer was used to measure the acceleration of the forces. It is a device for measuring acceleration and the effects of gravity. Low-g accelerometers are ideal for studying one-dimensional motion of elevators, amusement park rides, cars, etc. In our experiment, three accelerometers were placed on the head in such a way that one read the acceleration going left and right, the other forward and backward, and the third up and down.

Our Results:

An example of a graph; the test subject: Jenny Hua:

Plop Down on Chair

Since, we measured the accelerations in three different orientations, we had to calculate the acceleration because it is a vector. The equation used was:

Acceleration = sqrt((Accelerationx2)+(Accelerationy2)+(Accelerationz2))

The directions are as follows:

Where

x - up and down
y - forward and backward
z - left and right

The acceleration is the orange line. The peak of the acceleration is indicated by the arrow. The value was 57.703 m/s2. That is approximately 5.89 g's. Compared to Dr. Allen's results, ours is 58% of his value.

We took measurements with three different subjects; they are Stephanie Ma (5'0'' or 152.4 cm and 105 lbs or 47.6 kg), Jenny Hua (5'6'' or 167.64 cm and 125 lbs or 56.7 kg), and Matthew Grabczynski (6'2'' or 187.96 cm and 165 lbs or 74.8 kg) to see if there is a significant difference in our results with height and weight.

Everyday Accelerations (in g's)

Jenny Hua Matthew Grabczynski Stephanie Ma Average
Sneeze 2.189 1.800 0.957 1.649
Cough 1.790 0.899 0.957 1.215
Slap on Back 1.287 1.956 1.524 1.589
Hop off step 6.902 4.796 4.715 5.471
Plop down on chair 5.888 4.377 4.610 4.958
Crowd jostle N/A N/A N/A N/A

Compare to Dr. Allen's we have:

Dr. Allen's Our Average Value % of our value to Dr. Allen's
Sneeze 2.9 1.649 57%
Cough 3.5 1.215 35%
Slap on back 4.1 1.589 39%
Hop off step 8.1 5.471 68%
Plop down on chair 10.1 4.958 49%

From the values, height and weight do not seem to be a factor with the amount of acceleration on a person. Our value compared to Dr. Allen's seem to be roughly 50%. Thus, it appears that Dr. Allen exaggerated his values as a way to encourage people to ride on rollercoasters without fear.

Gary Louie, Michelle Fung, Jenny Hua, Stephanie Ma -- 2005

## Hey. There's more!

Haven't had enough of this topic? Check out the the 2006 follow up to Acceleration Perturbations of Everyday Living.