Table 1 |
Figure 1 |
Figure 2 |
I have two sculptures that I intend to convert to kinetic sculptures Skin and Bones. To do so, I need to determine the specifications of the motors needed for this task. To begin, I set up a pulley system so that I could observe how fast various weights accelerate the sculptures as well as the rotation rate that is the most aesthetically pleasing. These experiments are shown in the videos below.
I collect data on acceleration and rotation speed for four different weights or forces. By calculating the difference between theoretical speed and observed experimental speed for the various weights, one should be able to estimate the amount of friction on the shaft bearings and pulleys. See friction problem below.
A big snow storm in February 2010 provided a nice opportunity to extend the problem. By observing the differences in acceleration and speed caused by the same force, one should be able to calculate the total weight of the snow on the sculpture. See snow weight problem below.
Next, I purchased a small gearmotor with a nameplate torque capability of 7.5 in-lbs. Once this motor is set up, I will record the velocity and acceleration that it is able to achieve. It will be interesting to see the difference between the predicted and actual capability.
Ultimately, an interactive website and live streaming webcam will be set up that will enable a viewer to see the sculpture, initiate the motor and start the sculptures spinning. Once a maximum rotation speed is obtained, the force from the motor would be removed and the sculptures would spin freely until they stop.
This project seems to offer a nice opportunity to apply basic physics and mechanical engineering concepts. Below I have documented as best I can calculations related to torque, as well as measures of velocity and acceleration obtained from some preliminary experiments. The underlying data is provided for your use below. Any comments, corrections and suggestions are greatly welcomed. You can email me here. Thanks in advance for looking into this project.
Skin with 40 lb MassTrial #1 February 8, 2010 | |
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Data from the experiments shown in the videos was collected. The video was recorded at 30 frames per second. This fact provided the measure of time. The number of frames per 1/5th revolution are counted - QuickTime provided that capability. (Note: after analyzing the data recorded at 30 frames per second it became clear that the fins on the sculpture are not exactly the same distance apart. Consequently, velocity calculated between each fin as the sculpture rotates is quite volatile. To account for this, my calculations below are based on the same fin-to-fin comparison, that is, the time it take to make six full revolutions, not 1/5th of a revolution. ) The data is available here. Regression analysis is used to estimate a log-log specification as shown in Table 1. Note: This specification may not directly conform to standard physics formulas, i.e., V = Vf*(1-exp(-kt)). I will be looking into this further; comments and suggestions would be helpful here. Nonetheless, the log-log specification gives a good prediction as shown in Figure 1 below. Based on these predicted results velocity in terms of RPM can be computed as shown in Figure 2.
| Table 1 |
| Figure 1 |
| Figure 2 |
T = d * F = (2 in.) * (10 lbs.) = 20 in-lbs. = 1.67 ft-lbs.
T = d * F = (2 in.) * (20 lbs.) = 40 in-lbs. = 3.33 ft-lbs.
T = d * F = (2 in.) * (30 lbs.) = 60 in-lbs. = 5.00 ft-lbs.
T = d * F = (2 in.) * (40 lbs.) = 80 in-lbs. = 6.67 ft-lbs.
1. Snow. Assume a 7 foot spherical kinetic sculpture rotates on a vertical shaft with a 2" radius. A 40 lb weight is attached to the shaft by a rope which then passes through two pulleys. The rope is wrapped around the shaft six times. When the sculpture is released it takes 30 seconds to spin 6 complete revolutions. However, after a big snow storm it takes 40 seconds to make the same 6 revolutions. Assume that most of the snow is distributed between 2.5 and 3.5 feet from the center of the sculpture. Estimate how much the snow weighs.
(Apply moments of inertia?)
J (g*m^2)=M^2/2 *(Rinside^2+Routside^2)
(Apply Torque required to accelerate inertial load ?)
T (mN*m) = J alpha
Where:
T = Torque (nM*m)
J = Inertia in grams*meter^2
alpha = acceleration in radians/second^2
2. Friction. Assume a 7 foot spherical kinetic sculpture rotates on a vertical shaft with a 2" radius. A 40 lb weight is attached to the shaft by a rope which then passes through two pulleys. The rope is wrapped around the shaft six times. When the sculpture is released it takes 30 seconds to spin 6 complete revolutions. (a) Assuming there is no friction on the shaft or with the pulleys, how fast would the six rotations theoretically take with a (30/50) lbs weight? (b) When a (30/50) lbs weight it applied the six rotations take (45/25) seconds. Based on this experimental information, calculate the total amount of friction from the shaft and pulleys.