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Calculation of turn table diameter

A calculation of table diameter Diameter of D and 2r (Fig.1) can take measuements with a rule.

　We can calculate n and ｄfrom measured D and r using following equations.

r : radius of core [mm]

d: thickness of paper [mm]

L: Total Length of the tape

n: Number of winding

L=2 π r+2 π (r+d)+2 π (r+2d)+2 π (r+3d)+ ...+2 π {r +(n-1)d}

=n [2 π r+2 π {r+ (n-1) d }]/2

= (n/2) {4 π r+2 π (n-1) d}

= π d+2 π rn-n π d・・・・(1 )

For a sample tape,which have length L, we can measure the D,

πDn+2πrn-πD-L=0

n=（L+πD）/(πD+2πr)

d=D/n

from eq(1) then measured D=nd.

Use this d,and n, and L=46km, we can get D.

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