There is an old saying that “You can’t compare apples to oranges”; but frequently as an engineer, one of our jobs is to compare apples to oranges. Why and what does that mean?
Frequently, when systems are built the actual system does not yet exist. As a result, we need to draw analogies between the two items. So if we are going to compare apples and oranges how do we “juice” them for the correct data?
The mapping between objects: first principals
One objective with these mappings is to reduce the volume of first principals modeling that needs to be done; e.g. instead of building up a complex system of equations, use a modified data reduction of an existing system modified for the new system. However, to do that, we must first validate that the fundamental behavior of the systems scale between each other. For example, scaling a 4 cylinder 1.8L engine to a 2.1L engine is straight forward. To go from a 4 cylinder to an 8 cylinder is also straightforward if a slightly different problem.
What is the same? What is different?
You selected the reference model because there are things that they share in common. At the same time, there will be things that are different. In our example of the 4 cylinder to the 8 cylinder engine, there are differences in total displacement (an easy mapping) torque output excetra. The thing that may not be easy to map is the change to the in the vibrational aspects of the engine. The questions to ask are
- What physical aspects of the system am I concerned with?
- Torque
- Fuel consumption
- Max rpm
- …
- What aspects am I not concerned with?
- Vibration
- Heat transfer
- ….
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