for climbing steeply, any weight reduction can be felt directly. E.g., a reduction of 10% of the total system weight (bicycle, rider, and luggage combined) will save nearly 10% power. A reduced mass is also directly felt when accelerating. For example, the Analytic Cycling calculator gives a time/distance advantage of 0.16 s/188 cm for a sprinter with 500 g lighter wheels. In a criterium race, if a rider has to brake entering each corner, then this is wasted as heat. For a flat criterium at 40 km/h, 1 km circuit, 4 corners per lap, 10 km/h speed loss at each corner, one hour duration, there would be 160 corner "jumps". For 90 kg rider and bike, this adds roughly one third effort compared to the same ride at a steady speed, and a mass reduction of 10% of the total system weight (bicycle, rider, and luggage combined) could thus give about a 3% advantage. Advantages of light wheels The mass of tires and rims must be accelerated linearly and rotationally. It can be shown that the effect of rim and tire mass of typical spoked wheels is effectively doubled. Reducing their mass is thus especially noticeable in the case of sprints and corner "jumps" in a criterium. Power required Heated debates over the relative importance of weight saving and optimization of tires and aerodynamics are common in cycling. By calculating the power requirements for moving a bike and rider, one can evaluate the relative energy costs of air resistance, rolling resistance, slope resistance and acceleration. There are well-known equations that give the power required to overcome the various resistances mainly as a function of speed: Air drag The power needed to overcome air drag or resistance is: in still air, or in a headwind, where is the air density, which is about 1.225 kg/m^3 at sea level and 15 deg. C. is the speed relative to the road, is the apparent headwind, and is a characteristic area times its associated drag coefficient. The concept of apparent wind is only directly applicable here if it comes from a true headwind or tailwind. Then is the scalar sum of and the headwind or the difference between and the tailwind. If this difference is negative, must be regarded as assistance rather than resistance. If however the wind has a sideways component, the apparent wind must be calculated with a vector sum and, especially