A perennial favourite argument on cycling forums is the cost-benefit of choosing a wheelset with superior aerodynamics vs a wheelset that is lighter (or an aero vs a lighter frame).

It is of course a false dichotomy that one must chose only one or the other. But that does not stop people having fun arguing the merits of each, or of holding onto beliefs/myths/folklore handed down through the generations. Of course there are a multitude of things that go into what is a suitable choice of wheels, and I'm not going to delve into those, suffice to say they involve a range of factors aside from aerodynamics and mass, including, inter alia (and not in any particular order):

- strength
- durability
- ability to stay round and true
- lateral stiffness
- cost
- repair-ability and service cost
- suitability for the purpose/race/riding situation
- braking demands
- handling characteristics
- available tyre choices
- bearing and freehub quality etc
- rules of competition
- suitability for the bike (e.g. will it fit?)
- sex appeal / bling factor
- and so on.....

*if for instance we could assume that all other factors between two wheel sets were identical*.

####
**So, back to weight v aero - the classic prize fight.**

*relative*energy demands of the various resistance forces encountered when cycling, primarily:

- air resistance (bike and rider's aerodynamics, speed and wind)
- gravity (weight of bike and rider, and gradient)
- rolling resistance (tyres and road surface)
- drive-train friction losses
- changes in kinetic energy (accelerations)

*almost*linearly proportional to our power to mass ratio. Hence why weight is a primary consideration when the road tilts upwards. Lose 2% mass for same power, as you'll go nearly 2% faster. Pretty simple.

*cubic*relationship with relative air speed, meaning that to sustain a speed that's 2% faster (1.02 times), you'll need

*nearly*

** when you really account for all the forces correctly, then the increase in power demand for an increase in sustained speed from say 40.0 to 40.8km/h (a 2% speed increase) is more like 5.5%, and you can use a exponent of 2.7 rather than 3 as a slightly better ROT.*

#### But what about accelerations?

Some of you might recognise a few of the author's names. In summary, the equations look like this (as per a slide from one of Dr Coggan's powerpoint presentations):

*forward integration*- which is a way of being able to predict the second by second speed of a rider if we know their second by second power, and a handful of key variables like their aerodynamic drag coefficient, weight, tyre rolling resistance, gradient, wind and so on.

**Scenario 1:**

A rider accelerates from a standing start with an average power of 1000 watts for 10 seconds.A rider accelerates from a standing start with an average power of 1000 watts for 10 seconds.

**Scenario 2:**

A rider accelerates from 30km/h with an average power of 1000 watts for 10 seconds.A rider accelerates from 30km/h with an average power of 1000 watts for 10 seconds.

*Bike set up A: CdA of 0.320m^2 and mass of 80.0kg (lighter but less aero)*

*Bike set up B: CdA of 0.297m^2 and mass of 80.5kg (heavier but better aero)**But does that mean they are ahead?*If they were initially slower in the early phases of the acceleration, will they catch up? Well to examine that, we simply inspect the difference in cumulative distance travelled at each time point:

For my next trick, I will examine the shape of a typical power curve during such accelerations, and apply that variable power supply to the models, since nobody really accelerates with a flat power curve. Look out for Part II.

## 4 comments:

Slight correction I think in the discussion on power speed relationship n the flat. In a cunic relationship to go 2x faster you need 8x the power but to go 2% faster you need 1.02 cubed or 6% more power - not 8%. Or did I miss something?

Hi Ken, nope, you're right. I'll amend that bit, thanks.

In real life when you account for all the forces on flat windless ground, it's more like an increase in power of 5.5% to sustain a 2% increase in speed from say 40.0 to 40.8 km/h.

The cube is just a rule of thumb.

Hi. So I'm watching a MythBusters and they explain how a dimpled golf ball goes further than smooth due to the dimples reducing net drag

http://math.ucr.edu/home/baez/physics/General/golf.html

So... should TT / Tri frames be dimpled?

Unlikely that dimples on a frame will make sense (but you don't rule it out unless tested).

Golf balls are (i) a different shape and size, (ii) are spinning, and (iii) travelling at a far greater velocity, and so the Reynolds numbers are significantly different to that representing air flow around a bike frame.

Bike frames are made with aerofoil shapes - which are exceptionally slippery - far more aerodynamic than a cylinder or a sphere ever will be.

There is some merit in the idea of strategically placed trips on certain components or parts of the body (e.g. upper arms, lower legs), so that the boundary layer remains attached for longer and reduces the for-aft pressure differential but such things on clothing are not permitted under UCI rules.

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