A First Course in Dimensional Analysis: Simplifying Complex Phenomena Using Physical Insight (Mit Press)

Needs an errata so one doesn't have to be on guard for errors. But I would buy it again if I gave my copy away.

I was introduced to rudiments of dimensional analysis back in high school (you can't add meters to grams, for example). but was not aware of the depth of insight the technique can offer. Santiago goes even further than my baby-steps introduction, and paints the world in abstract units of length, mass, time, and temperature, irrespective of any particular system of concrete units. In other words, he exposes the raw core of the physical phenomena in terms of raw physical dimensions. From this, he explains weight categories of power-lifters, Kepler's laws of motion, the flight of mosquitoes and passenger aircraft, and lots more.Even this stripped-down system, the analyst can get at least a general idea of what happens as time periods or distances become very small or very large, can identify measurements that cannot be mathematically relevant, and can get a good idea of which measurements need to be combined - for example, when considering a system in time, speed, and acceleration, it's clear that you must combine speed or acceleration with time, to get the two into compatible dimensioned units (not that that's the only valid algebraic move you can use). Finally, Santiago requires real experimentation to determine the dimensionless constants that characterize the system, and that might show ranges where the initial assumptions break down.I note two major omissions in this book, neither of which I consider flaws. Santiago confines himself to basic dimensions of time, distance, mass, and temperature (with a brief mention of mole quantity of substance). In my field, Dennard scaling and voltage-frequency scaling have huge industrial importance. But, since they deal in units including capacitance, resistance or conductance, they would have required an additional fundamental unit: electrical current, in the SI convention. This would have added an additional kind of unit ("the curse of dimensionality"), and would have required uncommonly-held intuitions about current and derived units. The omission loses nothing in basic concept, but keeps the discussion more approachable.The second omission can be readily added by the analyst: conversions between concrete units of measurement, e.g. inches and meters. In the abstract, L/L units cancel each other, leaving a dimensionless conversion constant. In practice, treating "inch" and "meter" as algebraic units helps ensure correct results: inches * (meters/inch) algebraically gives meters. An easy mistake would have been inches * (inches/meter), but holding onto the concrete units shows the error quickly. As an example, the Mars Polar Orbiter unintentionally become the Mars Polar Lander when ground control ordered thrust in newton-meters and the satellite executed that abstract number as foot-pounds. The abstract dimensions line up just fine, but one newton-meter is nothing like one foot-pound in the concrete world.As I said, adding in these discussions would have lost the intuitive clarity of the discussion and blunted its important points. I consider this a valuable introduction for anyone trying to understand the essence of complex physical systems.-- wiredweird