Power to weight cost for criteriums of 2.5 watts / kg

Looking at new wheels is a bit of a mine field in terms of the different benefits that are listed with the list that I have seen in various adverts indicating different characteristics with the main three being weight, aerodynamic drag and stiffness.

Thinking about weight and the cost of this over either a time trial or creiterium and the weight characteristic is split into three elements. Horizontal energy expelled lifting a mass is not fully recoverable in cycling as the down hill speed is not necessarily recoverable in the same degree as the speed is higher and therefore more aerodynamic drag as a whole is increased.

When you take a 1kg mass and lift it 300 meters you would need to input 2940 joules of energy or an average of 0.817 watts over an hour. For a typical crit, which lasts just under an hour you could approximate this to around 1 Watt per kg of weight you are carrying around, on average.
So, if your on a heavier bike, heavier body and lugging 2 water bottles around you could need an extra 10 watts more than the next person.

Accelleration and inertia are the next element to evaluate, in terms of the constant accelleration and decelleration during a crit. Suppose the riders mass is 80kg (inc bike) and is accelerating from zero to 22.4mph in the space of 30 seconds, which would require 133 watts input (excluding drag, rolling resistance, etc.) just to accelerate the mass. The cost of an extra 1kg in mass would equate to an extra 1.7 watts over the 30 seconds.
The typical crit could involve 3 accelerations per lap of 10mph average increase in speed and over 30 laps this would equate to an average energy requirement of 100 watts if the event lasted 45 minutes. So, add and extra 1 kg into the pot and this equates to 1.25 watts per kg average.

Rim weight is the next interesting one as the acceleration of the bike, effectively includes the energy required to accelerate the rim weight to an average speed of the bike but the rim is travelling between zero and twice the speed of the bike as you move. As the potential energy includes the square of the velocity this makes the rim more critical and the hub can be ignored. The energy input for the rim is therefore double that of a mass attached to the bike, so your extra 500g on the rim could equates to approximately an extra 1 watt over the duration of a crit.

Drag is the last one to add could be anywhere depending upon your bike position and choice of wheels the easiest options to change, for this example we will assume the bike position is un changed and the wheels equate to a 10 watt difference in drag (approximation for medium carbon rims and a reasonable alloy race wheel)

So, summary so far is you require an extra 2.25 watts per kg for a crit to cover just the kinetic and potential energy of the mass, if it where attached to the bike (not the rotating mass of the wheels). If you were a 77kg rider on a 8.2kg bike racing against a rider on a 7kg bike and weighed 73kg you would need an extra 11.7 watts just to compensate for the kinetic and potential of the mass.
Add in an extra 1 watt due to the heavier rims and then throw in the extra 10 watts for the arodynamics and you end up with a 22.7 watts difference in energy requirement for the two riders.