# By Mark O. Worthington

Posting date August 5, 2004

# The Physical Length of the CD, DVD Spiral

An expression can be resolved by converting the polar representation of the Spiral of Archamedes equation to rectangular coordinates.

For a spiral of constant thickness or pitch – Length = Pi * R^2/ T

For the donut geometry of an optical disc we can approximate;

Length = Pi * ( R(outer) ^2 – R(inner) ^2 )

# Track Pitch

CD Path Length;

Router = 59.mm

## Rinner = 24.8mm

TP = 1.5 – 1.7 um

Length = Pi * (3481 – 615)/ .0015    =                     6,002,536 mm

So,

1 mile = 1,604,344 mm ,                (CD Track Length =     3.7414 Miles)

Pit/Land Lengths are 3..11 clock cycles or (0.8-3.0 ums) with an average     length of 2 um.

Modulated marks on a CD =        6,002,536 mm  / 2.0um = 3,001,268,000

For DDCD;

For DDCD      TP = 1.2

## Length = Pi * (3481-615)/ .0012=7,503,170 mm

(DDCD Track Length =    4.6767 Miles)

## Modulated marks on a DDCD = 7,503,170 mm / 2.0 um  =3,751,585,227

DVD Path Length;       *** (Opposite Track Path discs may have a smaller outer diameter)

For DVD-5;

Router = 59 mm

Rinner = 23.6 mm

TP= 0.73 – 0.75 um

Length = Pi * (3481-557) / .00073              =                     12,583,585 mm

So,

(DVD-5 Track Length =  7.8434 Miles)

Pits and Lands on a DVD are 3…11 clock cycles (14T for sync) or 0.4 – 1.84 ums. Average Length is approx ~ 0.72um

Modulated marks on a DVD-5 = 12,583,585 mm / 0.72 um = 17, 477,201,390

For DVD– 9/10,     2 X Physical Density of DVD-5 (Parallel Track Path) ***

Length =                                                                                   25, 167,170 mm

So,

DVD-9/10 Track Length = 15.6868 Miles

Pits and Lands on a DVD-9/10 are ~ 0.44 – 2.0 um. Average Length ~ 0.78

Modulated marks on a DVD-9/10 = 25, 167,170 mm / 0.78 um = 32,265,602,560

For DVD-18 ,          2X Physical Density of DVD-9/10 (Parallel Track Path)***

Length =                                                                                   50,334,340 mm

So,

DVD-18 Track Length =  31.3736 Miles

Modulated marks on a DVD-18 = 50,334,340 mm/ 0.78um = 64,531,205,130