The Nature of Engineering Knowledge September 29, 2010

Grand Unified Theory

Consider an architect’s model of a building; the building and the model are geometrically similar, but different sizes 100 m1 m

Measurements on the model can be translated to measurements on the building via scale factors: 100 m1 m QuantityScale Factor Length of water pipe Floor Area Enclosed Volume Weight Ratio of Study space to Travel space

FwFw FrFr FgFg fwfw fgfg frfr

The Froude Number Fr = V 2 /Lg If the Froude number is the same for a ship and its model, both will behave the same way (e.g., capsize and sink)

Catamaran model in a towing tank

Reynolds Number At a critical value of Reynolds number, flow changes from laminar to turbulent Re = Inertial Forces Viscous Forces = ρvl μ

Reynolds’s Experiment

Karman Vortex Street Characteristic of turbulent flow

The Mach Number M = v/c If the Mach number is the same for an aeroplane and its model, both will be in the same sonic regime (e.g., both supersonic)

NASA’s Supersonic wind tunnel at Glenn Research Center

Weber Number Indicates the ratio between inertial forces and surface-tension forces (this is why you can’t design bugs with a towing tank) We = ρV 2 l σ

Water strider on a pond

Detailed attention to non-dimensional numbers made pre-CGI monster movies more realistic

Usefulness of the Non- Dimensional Numbers Fluid friction in a pipe is affected by its diameter, and by the fluid’s speed and viscosity. Using Reynolds number, we can investigate all these in one series of experiments.

Why aren’t there any non-dimensional numbers in electrical engineering?

Laplace’s Equation …applies to heat conduction and electrostatics. So an electrostatic problem can model a thermal problem. Δ 2 Φ = 0 d 2 φ dx 2 d 2 φ dy 2 d 2 φ dz 2 ++= 0

Teledeltos paper

Finite-Element Analysis

Accuracy Number of elements Error in Computer Simulations

Fuzzy Control Fuzzy logic employs models of systems that are deliberately imprecise: for example, a car may be modelled as having three possible speeds, `too slow’, `OK’, `too fast’. This can yield simple, robust control algorithms.

Qualitative Physics In making predictions about the world, we employ mental models. These are neither exact nor numerical, but they work. Qualitative physics attempts to get computers to do the same thing.

Example: what happens if I knock over this glass of water?

Conclusions Engineering has a range of strategies, not limited to the application of scientific knowledge New non-scientific strategies are continuing to be developed, and may be used in preference to older, more scientific methods.