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## Directory:Bedini SG:Calculations:Deceleration

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'Deceleration Calculations for John Bedini's "Directory:Bedini SG"'

Calculating Frictional Lossess from Deceleration Data.

#### Preface

Supposedly you can take wheel deceleration data (plotting the curve of decay) and derive a rough estimate of the frictional losses in the rotating system.

#### Equation Explanation

Oct. 14, 2004

The essence is that the quantity Q is a useful measure in considering any

oscillator. It is defined as the energy stored divided by the energy lost

per cycle. For an angular momentum device, like a bicycle wheel, the energy

stored, W = 1/2 I omega squared. Working through the equations one gets

that Q = -1/2 omega/y-dot, where y-dot is the time derivative of the

fractional frequency acceleration of the rotating device. This is what one

can easily measure, then use this equation to calculate the energy lost per

cycle.

It is energy, not power, lost per cycle, which is like a power loss. As you

will see in the equations sent, the model is that of an exponential decay.

As you know, this is very typical for decay processes. When you write the

energy stored as a function of time, it is an exponential with a time

constant tau_sub_e of 1/(2y-dot). The fractional frequency is just y =

(f(t) - fo)/fo, where fo is the nominal frequency -- in Sterling's case

about 115 rpm. The symbol y-dot denotes the time derivative of y, and it

will be negative because of the resistive slow down of the bicycle wheel.

You can see all of this in the equations excuse the rough form of them.

These were for my own notes as I was writing them up in a LaTex file, which

I have not compiled yet, or I would send you that. It has all the words

wrapped around the equations. If you can read LaTex, I could send that to

you.

#### Specific Data

Sterling's Deleration data for his 22 (xml) Decelerating from 109 rpm. If any of you can combine this information provided on this page to supply a frictional loss calculation for my wheel, I would appreciate it.

Directory:Bedini SG:Data

Directory:Bedini SG:Theory

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