Clock Timing Analysis
Avoiding Mistakes in Engineering Analysis is Critical
Mistakes can cost money, hurt careers, and result in injury or lost lives.
We want a systematic approach to analysis that will catch errors.
See consequence of unit conversion error of the Gimli Glider
See consequence of miscommunication and unit error in Mars Climate Orbiter that was lost.
To avoid mistakes we will use 3 approaches described below in the Clock Timing Analysis, and these same methods should be used whenever possible for all important analyses
Clock Timing Analysis
The challenge of the clock timing analysis is to predict how fast your clock will tick before you actually measure it (each pendulum will tick at a different speed due to the shape variations amount pendulums). In real-world design projects, the cost of building a device is typically high, so it is essential that analysis is correct. Therefore we will emphasize use of the following analytical approaches to catch errors and should be used in all design projects:
1) Clear Documentation:
All values should be shown with units, and unit conversions should be clearly done (see unit conversion tips). Show only the proper number of significant digits in results and not more than warranted by accuracy of your measurements. Clear documentation is essential in design projects so that team members can check one's work. In the clock project we will use an Excel spreadsheet to perform an analysis and use a method of naming cells so that the equations, values, and units can be printed out for the clock report.
2) Multiple Methods of Analysis:
Calculate results using different approaches to see if both methods yield similar results. Approximate estimations complement more accurate calculation methods, since they allow one to find large errors. In the clock project we will use both the point-mass and rigid-body methods to calculate the natural frequency of the pendulum.
3) Intermediate Verification:
One would always like to catch any error early on when it is less expensive to fix. Whenever one can measure an intermediate result, this is a very valuable way to validate the analysis. In the clock project we use intermediate verification by:
Weighing the pendulum after it is cut (before and after adding bolts)
Balancing it on our finger to get an approximate center of mass (before and after adding bolts)
Natural Frequency of a Point-Mass Pendulum
The first step in analysis is often to consider a simplified case that can be easily verified. For the pendulum analysis we initially assume that the mass of the pendulum is concentrated at a point.
Deliverables:
Problem Description
Objectives
Assumptions
Free Body Diagram
Basic Equations
Center of Mass Analysis for Pendulum without Bolts
Intermediate Analysis and Verification
Center of Mass Analysis for Pendulum with Bolts
Intermediate Analysis and Verification
Point Mass Pendulum Frequency Calculation
Comparison of Calculated Time to Actual Time
Natural Frequency of a Rigid Body Pendulum
A more accurate method for calculating the natural frequency of a pendulum is to consider the whole body of the pendulum and include the effect of the rotational inertia. The rotational inertia cannot be as easily verified as the center of mass, but it is more accurate.
Deliverables:
Problem Description
Objectives
Assumptions
Free Body Diagram
Basic Equations
Center of Mass Analysis for Pendulum without Bolts
Intermediate Analysis and Verification
Center of Mass Analysis for Pendulum with Bolts
Intermediate Analysis and Verification
Rotational Inertia Analysis for Pendulum without Bolts
Rotational Inertia Analysis for Pendulum with Bolts
Rigid Body Pendulum Frequency Calculation
Comparison of Calculated Time to Actual Time
