### High Jump

Our project idea is high jump. We are testing how much acceleration is needed for the jumper to clear specific amounts of height. Since we cannot use the force plate (i.e. it’ll break if someone tries to jump on it), we will test the acceleration of the jumper from the time he/she leaves the ground to the time until they land on the mat. Based on this timeframe and knowing this acceleration, we can then calculate the theoretical maximum height the jumper can jump, if they have perfect form. Our most important factor is detecting our person’s center of mass, in order to see where he/she needs to place this mass in order to attain the proper height needed to get over the bar.

Variables to test:

-acceleration of jumper to get over heights between 4’0” to 5’0”
-location of the center of mass
Materials:

Accelerometer
Video Camera (high speed)
High jump mat/bar
Jumper

Procedure:

1) Attach the accelerometer to the person

2) Record the person jumping without the bar

3) Start the stopwatch when the person begins their jump, and stop it when the person ends their jump.

4) Repeat this process seven times.

5) Calculate the average acceleration needed for a person to attain the maximum height they can.

6) Then, repeat the process again, except with the bar, and see if they can manage to jump that maximum height.

Data:

At take-off during the jump:

Eric's mass = 80.9 kg

Vertical Y-Velocity once in air = 0.144 m/s

Time of impulse for jump (frames 120-161) = 41 frames at 0.004 s per frame =  0.164 s

Force applied to ground = 71.0341 kg*m/s^2

Impulse= Momentum= MV= 80.9 kg x 0.144 m/s= 11.6 kg m/s

Acceleration during jump = change in velocity / change in time = (0.144 - 0.0) / (0.164) = 0.8780487804 m/s^2

Picture: Y-Position of body parts and center of mass over time. Different peaks correspond to different moments crossing the bar.

During the high jump, Eric's right foot is always slightly higher than his left foot. The right foot clears the bar at about 0.042 seconds while the left foot doesn't clear the bar until 0.052 seconds. This can be justified because when looking at the video, he lifts his right leg as he pushes off with his left leg. The right leg is used to give himself more momentum as he pushes off with the other leg. Both legs do not come to the same level until both legs have cleared the bar. Continuing, his head lifts higher than the bar just after he jumps, and then it levels with the bar from 0.03 to 0.04 seconds as his feet swing over the bar. From there, his head drops as gravity takes control. Eric's chest acts in a similar fashion. At the very beginning of the jump, his chest is below the bar because he is crouched in order to give more thrust when he jumps. His chest gets high enough to clear the bar, then gets level to it so his feet can swing over.  Then, his chest falls as gravity brings him down onto the mat. Lastly, the pelvis is crouched low as he begins the jump because he knees and hips are flexed. As both the knees and hips extend, the pelvis's resembles the expected parabolic shape. At 0.05 seconds, the pelvis is at its highest position and it falls from there.

Picture: Tracker 2.5 plotting the trajectories of the Center of Mass, head, chest, and pelvis. Legs not shown for clarity.

Picture: Graph of the Y-Position of the Center of Mass
Picture: Graph of the Y-Velocity of the Center of Mass

In order to get lift off the ground and get enough momentum to propel over the bar, the pelvis is most important in placing the center of mass. We can infer this because the center of mass line most closely follows the position line made by the pelvis. The makes sense because by looking at the video, Eric's pelvis and torso must be thrust over the bar first before lifting his legs over.

Conclusion:

This was a neat project to do since it isn't often that we get to play with high speed cameras and other cool equipment. We learned that the general path the high jumper takes is parabolic just like the "throwing up" problems we did., but because of a human's irregular shape and flexibility, none of the body parts fit a perfect graph. As one can see in the picture above, the center of mass, does appear to follow a mainly predictable parabola. The more force you can apply when pushing off the ground and the more one flexes the hip and knees, the more one can get more momentum and achieve enough upward velocity and acceleration to lift over the bar.

Comments