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Power Models  :  Acceleration and Wheel Inertia
Rider & Bike
Rider Weight (kg)
Bike Weight (kg) inc wheels
Front Wheel Weight (grams)
Rear Wheel Weight (grams)
Front Wheel Type (700c) & Inertial Constant
Rear Wheel Type (700c) & Inertial Constant
Wheelset Inertia (kg/m^2)
s - b
Required Energy (Joules)
Cost In Watts
Due to Wheels
Kinetic Energy (Joules)
Cost In Watts
Rotational Inertia Joules
Cost In Watts
Much of the cycling related modelling that we do is what’s called “steady state” which means that the rider is assumed to be travelling at a constant speed or power output. This sort of modelling is exactly what’s needed to answer questions such as “what is the aerodynamic saving of wheel X over wheel Y at a constant 50kph?” or “what power output achieves a VAM of 1800 metres/hour on Alp d’Huez?" But there are times when it’s NOT what you want, usually when considering a rider who is momentarily or frequently accelerating.
Acceleration features in cycling during at least 3 activities. First, towards the back of a road race riders experience constant demands to accelerate as the bunch “concertinas” into and out of corners. Second, tight criterium circuits demand frequent accelerations of riders anywhere in the bunch. Third, the “kick” that initiates a sprint effort is largely an effort to accelerate the rider and bike, in spite of the high aerodynamic power demands at speeds of 50-80kph.
In every case the power required to accelerate is determined by the combined weight of the rider and bike with the weight of the wheels, a mass whose rotation must be accelerated, having particular importance. In the terminology of physics we can say that power is required to increase the kinetic energy of the rider and bike and separately to add rotational inertia into the wheels. This model simply applies the relevant physics to help the interested cyclist answer questions concerning the relative advantages of weight savings, especially in the contexts of sprint execution and wheel choice.
Repeated Accelerations and Sprinting
Use this aspect of the model to evaluate the power demands of an acceleration between two specified speeds given a certain rider and bike weight. You can think of this power demand in terms of the overall addition to a riders power requirements for example when a rider has to accelerate every X seconds, such as in a criterium, or as a once-only impact on sprint performance. Either way the lessoon is clear - a lighter rider or bike is less damanging in terms of performance.
Use this aspect of the model to study the power impact of alternative wheel choices under conditions of acceleration. Once again lighter wheels are generally better though what really matters is a wheel's coefficient of inertia multiplied by it's weight. Evaluating the coefficient of inertia of a wheel is somewhat tricky so we provide some standard, experimentally determined coefficients covering the range of wheel types. "Standard" wheels, having most of the weight in the rim, tend to display a coefficient close to 1. Disc wheels perform more like a flywheel with weight evenly distributed between the center of rotation (hub) and rim so the coefficient is a little lower.
Rider Weight (kg): Input a rider weight in kilos for the Baseline &/or Scenario.
Bike Weight (kg): Input a bike weight in kilos for the Baseline &/or Scenario.
Front & Rear Wheel Weight (Grams): Input for the Baseline &/or Scenario.
Wheel Types: Choose suitable wheel types - their combined coefficient of inertia will be calculated.
From Kph: Input a start velocity from which the rider is assumed to be accelerating.
To Kph: Input a final velocity to which the rider is assumed to be accelerating.
Over Seconds: Input the duration of the acceleration between the From and To velocities. Less time requires more power.
Total Acceleration - Required Energy (Joules) & Cost In Watts: The energy required for the acceleration, including all factors, also expressed in watts.
Due to Wheels - Kinetic Energy (Joules) & Cost In Watts: The energy required to accelerate the wheels forward on the road, also expressed in watts.
Due to Wheels - Rotational Inertia (Joules) & Cost In Watts: The energy required to accelerate speed of rotation of the wheels, also expressed in watts.
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