On Bicycles, and.... what else is there?

In my last post on the subject of barometric altimetry, it was discussed that a moving altimeter may report a lower altitude than a stationary one, due to the dynamic pressure of the air piling up in front of the moving cyclist. The amount of this altitude increase is determined by a coefficient between zero and one relating the effective wind speed to the cyclist speed. Before that, I described how I'd combine a barometric altitude signal with a GPS signal to get the best of both: the short-term responsiveness and reliability of the barometric altimeter with the general accuracy of the GPS (at least when there's a signal). I'd applied this to randomly generated data , which were derived using a simple pacing model with the bike power-speed equations. The effect of dynamic pressure on measured altitude is simply derived from Bernoulli's equation : Δz = ‒½ ( k dp v )² / g, where Δz is the error in altitude, v is the speed relative to the wind, k dp is the coeffici...

I never could wrap my head around this stuff. Bernoulli's_principle basically says that when an incompressible fluid is moving more rapidly, the pressure drops. Air is obviously included in the list of incompressible fluids, leading to all the activity at SFO not so far south of where I live. In some physics class in my distant pass, the professor justified this by launching into a set of differential equations . You stare at the equations, one after another, and sure enough it's hard to dispute any one of the steps, but that doesn't mean the result actually makes any sense . Differential equations, after all, are just a model. There's no physics in differential equations. The physics is in particles bouncing around: scattering elastically and inelastically, transferring momentum, transferring energy. Scattering, if anything, is the heart of physics. So I envision gas molecules bouncing around, energy scattering between various degrees of freedom, minding their...