## ZF 9HP 9-Speed Automatic Transmission Interactive Nomogram

If the geometric figure does not appear, click in the center !

Please enable Java for an interactive construction (with Cinderella).

Magenta Lines = 1st Gearsets Pair | Cyan Lines = 2nd Gearsets Pair (Simpson)

This interactive nomogram is a real geometric calculator exactly representing the rotational speeds of the transmission's 3x4 = 12 internal shafts for each of its 9 ratios (+ reverse), grouped according to their 4 permanent coupling on 4 joint ordinates and 3 independent ordinates. These ordinates are positioned on the abscissa in strict accordance with the proportions of the sun gears' teeth numbers relative to those of their rings. Consequently, the output ratios on the ordinate c4 (carrier of the last planetary gearset) follows closely those of the actual transmission. This advantageous geometric construction sets us free from Willis' famous and tedious formula, because all calculations are determined exclusively by lengths ratios, respectively teeth numbers on the abscissa for the 4 epicyclic ratios Re, and of rotational speeds on the c4 ordinate for the 10 gear ratios.

Observe the effect of resizing each of the 4 planetary gears sets on this geometric figure:
- Drag the C dot (C brake) to change the mechanical dimension of the first planetary gearset Re1.
- Drag the D dot (D brake) to modify the mechanical dimension of the second planetary gearset Re2.
- Drag the third green dot to change the mechanical dimension of the fourth planetary gearset Re4.
- Simultaneously (shift+click) drag the dots C+D+3+5, or 4+6+A, to modify the mechanical dimension of the third planetary gearset Re3.

Legend:
A dot: Dog Brake (blocks s3+s4 sun gears)
B dot: Clutch (couples s1 with input shaft)
C dot: Brake (blocks s1 sun gear)
D dot: Brake (blocks r2 ring gear)
E dot: Clutch (couples c3+r4 with input shaft)
F dot: Dog Clutch (couples r1+s2 with input shaft)

Warning:
- The red dots on the abscissa modify simultaneously more than one gearset !