Is have a jacket that flaps loudly when I ride. Aside from the sound being annoying, I’m wondering if the noise means it’s less aero. Is there a direct correlation between noise and aerodynamics?
Yup
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If something is flapping, that means the air is pushing against extra surface area which, indeed, means less aero.
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Sort of. More noise = more drag (sound waves carry energy, and that energy has to come from somewhere). But just because something’s quiet doesn’t necessarily mean that it’s aero.
I’d expect the drag from vortex shedding behind a rigid object to be fairly quiet but it can be non trivial (~1-2% of total drag from having someone sitting on your wheel and smoothing out your wake). Not sure how you’d really measure the acoustics of that aside from perhaps measuring the sound on a team pursuit by position.
TL:DR Aerodynamics 101
I was a bit terse there… I should state that a long time ago in a galaxy far far away, I was an aerodynamicist. I am stuck waiting for a phone call so I can bore you to tears with this stuff…So anyone more recent feel free to critique. If you desire a nosebleed and headache and want to read about the physics involved and get some google tags to pull on then read on.
Back at the dawn of the age of reason we started trying to seriously get our heads around how fluids moved. Newton thought that they just hit the front of the surface and moved around it then left at the back. Think about a ball moving through the air. That means the pressure from the speeding air pressing on ball is at a maximum as the fast air hits it on the front. It drops as you go around the ball. It hits its minimum at the top of the ball when the air is moving parallel with the local surface so it isn’t really pressing on it any more. So what happens next? Well if you followed Newtons model then the air springs back and the pressure started to increase back up to the maximum at the back where it came off.
If Newton’s model was correct then if you throw a ball straight up on a windy day it should come straight back down again. There would be no drag. This is known as D’Alembert’s paradox, google ain’t got it alas.
The guys who sorted this were the Bernouilli brothers; Swiss contemporaries of Newton.
Drag is due to a few things and classified in many ways but essentially it is all down to the fact that air, thin as it is, still has viscosity. So right next to the ball the air doesn’t move at all. It drags the bit next to it back a bit which in turn drags the next bit out and so on. This leads to the concept of the boundary layer. The layer close to the surface that is affected by all this. Self evidently it grows thicker with time. In fact it can grow so thick that it can tear itself off the surface and create a horrible mess of roiling air behind it that is a serious impediment to progress. Drag has many little contributors but that is the biggest.
Your clothes flapping in the wind is just that. The flow separates causing the cloth to flap one way then attaching and causing the cloth to flap the other. There is a similar cyclical flow phenomena that has bitten the arse of many an engineer over the years. It is a Karman Vortex Street (never understood why it was call a street). It is the reason why chimneys have those spiral tabs around them. Another fine example of this phenomena is the Tacoma Narrows Bridge: a horror movie shown to baby engineers. All this stuff implies energy being dissipated and hence excess drag.
You can trick this by using a key feature of this boundary layer. The boundary layer starts out in this simple layered structure and then it degrades to a turbulent mess. The weird thing is it is easy to separate the simpler structure from the surface; leading to higher drag. It is much harder to separate the turbulent version, by dint of the fact that there is a lot of cross flow movement. It still happens but much later and with a significantly lower overall drag, even though the local drag is higher (because of all that cross flow motion). That’s why you have dimples in golf balls, Zipp wheels, skinsuits and trip strips on some aero frames. To trip the boundary layer from the simple structure into the turbulent one and get it to stick on the surface for longer…
If you read this far then god bless you and Merry Xmas…
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So what you’re really saying is due to boundary layer dynamics a flapping jacket that flaps just enough to delay flow separation is in fact faster than no flapping jacket. Proving that more noise to a point is faster than no noise. 
Ok, so flapping does mean less aero. Any ballpark idea how much of a difference it makes? In the context of a person on a bike, the flapping fabric of a zipped-up and form-fitting jacket seems like it would be a relatively minor part of the overall drag (but maybe not). The noise is irritating, but I’m wondering if it’s worth it to buy a new jacket.
note the emoji’s…=joking. Forums are so great.
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Any excuse for new kit works for me.
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There’s various clothing related specialized win tunnel episodes here where they test stuff like that iirc. It’s been awhile since I’ve watched them, though.
Personally, I’d probably lose some watts just from being continuously annoyed by the sound, but that’s just me.
Thank you Simon for the memories of my heat transfer and fluid mechanics classes.
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one more thing to consider… if it makes noise then that takes energy, anything that can be quiet is better. So if you have clothing that is close to your body and does not flap and make noise then it is best, if it is an undulating surface but does not make noise it is worse aerodynamically and the worse still is flapping and noise because that noise is energy that you are wasting. Same goes for your chain, the noisier the less efficient. That is a probably pretty simplistic way to see it.
A working parachute is quiet, a flapping parachute not so much. Noise is extra work done if all things are equal, but because there is noise, then all things are not equal.
Mostly. The actual amount of energy in sound waves is fairly small (at the decibels we’re talking about, at least). It’s possible to have scenarios where non audible drag is reduced but something is noisier. The two examples that come to mind are disc/deep section wheels and possibly some aero helmets (I’m hypothesizing more on the latter, based on the source of the noise being right by your ear).
Also depends on the frequency of the noise… just to make things more 
the sound from the flapping is your kinetic energy being transferred into sound energy, so yes, it is less aero if you have something flapping