Aerodynamics of time trialling bikes

This morning I had an email from a cousin in London, and because I haven't blogged for weeks I am usefully padding out my Internet contributions with the conceit of a) thinking I know what I'm talking about and b) thinking anyone's still reading and c) imagining someone's int'rested in my vastly sagacious advice and d) hoping that no-one will write a Comment proving my ignorance and mathematickal stupidity. - Here goes. -

http://www.bicycling.com/bikes-gear/bikes-and-gear-features/revenge-nerds

So I had given thought to forking out for a pair of zipp (or equivalent) aero racing wheels as I want to better my 1:06 time for 25 miles (as done at last year's North Norfolk Triathlon)…….
But then I read the blog or message board entry above which suggests I'd be better off buying an aero helmet instead!!!
As a man much versed in all things aero and wind (no pun intended), what is your opinion?
D 

I just read your link, and every single thing they say is correct, *everything*. Baggy clothing will add 30% to your drag - we've know it for ages, and all the MIT people are doing is methodically testing everything else and putting numbers on it all. Bear in mind that David Gordon Wilson who wrote Bicycling Science and was one of the four founder members of the Human Power Association was a professor of engineering at MIT. They have a superb record in the bicycling science field. They're the best in the world. (MIT is the world's top engineering university, bar none.)

And it's dead true about calculating beforehand how fast a machine will go. Remember the Jason Queally attempt in 2001, where he got a Formula One racing car team to build him a bike? http://www.speed101.com/now/fastest_0908_2.htm  All the HPV crowd examined the dimensions beforehand, and the physicists  and engineers all calculated that he'd do between 63 and 65 mph, and no more. They were sufficiently confident to put their calculations and predictions on the IHPVA discussion list which I used to subscribe to, and I remember reading it there. Result? He did 64.34mph. The same event that year, Sam Whittingham did 79.79mph.

That sort of prediction sounds too accurate to be plausible, but of course the speed you attain is proportional to the cube of your power output, and that's an incredibly steep part of the graph. To go twice as fast you need to put in eight times as much power. Again, how does that work? Well the physics is the telling thing.

If you can remember any physics from school, force = mass times acceleration. Acceleration is metres per second, per second. So that's already the square of your speed. Anything travelling twice as fast, has four times as much energy.

A cubic metre of air weighs about a kilogram. When you ride through the air, you catch up a cubic metre of completely stationary air in the wind-bucket of your arms and legs and chest, and accelerate it from completely still to the same speed that your bike is going. Then it all slips out of the gaps under your arms and  swirls around behind you.

Accelerating something - even a cubic metre of air - takes a huge amount of energy. And if you're accelerating it to an even higher speed - which is what you are trying to do if you're going to improve your times of course - then that kilogram of air is also going to suck the square of the *extra* speed out of your leg-power. And even worse than that, because you are going faster, in any one second of pedalling, you're going through an even longer chunk of air - catching it up in your arms, accelerating it from standstill to 22.7272 mph-plus-the-extra-bit-of-speed.

So in going faster, you're catching a bigger kilogram of air, and accelerating it to a higher speed. (Can you have bigger kilograms?) More mass, and accelerating it to a higher velocity. So mass goes up, and velocity squared goes up too, and you're multiplying them together. *ucking impossible to do, which is why every cyclist 'hits the wall' and why you can do precise calculations.

Which means that yes, definitely, anything at all that allows you to knife your way through the air rather than catch it up and accelerate it, is a Fantastic'ly Good Thing.

With the aero wheels thing, yes they're definitely an advantage because spoked wheels contribute 10 % - 15%  to your air drag. http://www.analyticcycling.com/WheelsConcept_Disc.html

However the spokes at the bottom are not moving at all. The bottom of a wheel is stationary. (Unless your wheel's skidding.) The top of the same wheel, however, is going forward at twice the velocity that you're going. And this is why spoked wheels are a Bad Thing.

But the other However bit is this - the top spokes are within the aerodynamic mess that is created by your front forks, your legs, pedals, bike frame, back forks and of course back wheel. Each bit of this needs tidying up, which is where they come up with the idea of tucking the water bottle on the seat tube, where it helps to create a slightly wide nose-fairing for the back end of the bike. On the down-tube it has only air behind it, rather than the gubbins of a seat-tube-and-back-wheel which make it more like a nice tear-drop shape.

And the helmet thing is very significant. Your head is a big round unnecessary object and if it weren't for the fact that there are collateral disadvantages I would say cut it off and leave it at home. Most bike helmets are a mess of holes and gashes and stylish shapes and whatnot, and their contribution to drag is colossal. I notice when I tuck my head right down into my shoulders and ride looking straight down at the road, that my speed will pick up by easily a mile an hour.  If I then ride into a lamp-post I lose that advantage, so an aero helmet is a seriously good plan.

By way of illustrating the aerodynamics, I can tell you what I do here, where my lunchtime daily ride up the west bank road of the Motueka river, crossing the bridge at Alexander Bluffs, and coming back through town, covers 18.55 miles. On my racing bike my best times are about ten seconds under the hour. It's a 531 steel bike, weighing about 22 lbs, so it's much heavier than your exquisite carbon-fibre affair of today. 

However I also have a home-made recumbent, which weighs 44lbs because I can only weld mild steel. And on the same ride my best recumbent times are fifty-four minutes. That's six minutes faster. The road is undulating but otherwise reasonably flat, so I don't pay much of a weight penalty for riding a machine with twice the mass. But I get a massive aerodynamic benefit from having a much smaller frontal area.

R