# Type "Lanchester" Central element of this design is a differential put on end. Compared to the generic design, wheel 6 is "left hand side (2)", wheel 9 is "right hand side (1)" and wheel 8 is the "difference (4)". The adapted equation reads
 (a:) n9 * rot9 + n6 * rot6 - (n9 + n6) * rot8 = 0
The other constraints are straight forward
 (b:) rot1 = rot2 (c:) rot3 = rot4 (d:) rot11 = rot12 (e:) rot13 = rot14 (f:) n2 * rot2 + n3 * rot3 = 0 (g:) n4 * rot4 + n5 * rot5 = 0 (h:) n10 * rot10 + n11 * rot11 = 0 (i:) n12 * rot12 + n13 * rot13 = 0
Composition (POV is from top respectively from far right):
 (j:) rot6 = rot5 = (-1) * (n4 / n5) * rot4 = (-1) * (n4 / n5) * rot3 = (-1) * (n4 / n5) * (n2 / n3) * rot2 = (-1) * (n4 / n5) * (n2 / n3) * rot1 (k:) rot9 = rot10 = (-1) * (n11 / n10) * rot11 = (-1) * (n11 / n10) * rot12 = (n11 / n10) * (n13 / n12) * rot13 = (n11 / n10) * (n13 / n12) * rot14

To make it "south-pointing" requires, that if rot14 is held 0, rot8 has to be exactly one turn when wheel 1 of diameter d1 covered one full circle (centre at wheel 14's contact to the ground, radius equal to track width t):

 (l:) d1 * rot1 * PI = 2 * t * PI (m:) rot8 = 1 (n:) rot14 = 0 (k=>) rot9 = 0 (a=>) n9 * 0 + n6 * rot6 - (n9 + n6) * 1 = 0 (=>o:) rot6 = (n6 + n9) / n6 (j=>) rot1 = (-1) * (n5 / n4) * (n3 / n2) * (n6 + n9) / n6 (l=>) | d1 | = 2 * t * (n4 / n5) * (n2 / n3) * (n6 / (n6 + n9))

The same method can be applied to calculate the required size for wheel 14: If rot1 is held 0, rot8 has to be exactly one turn when wheel 14 of diameter d14 covered one full circle (this time centre at wheel 1's contact to the ground, radius equal to track width t):

 (p:) d14 * rot14 * PI = 2 * t * PI (q:) rot1 = 0 (j=>) rot6 = 0 (a=>) n9 * rot9 + n6 * 0 - (n9 + n6) * 1 = 0 (=>r:) rot9 = (n6 + n9) / n9 (k=>) rot14 = (n10 / n11) * (n12 / n13) * (n6 + n9) / n9 (p=>) d14 = 2 * t * (n11 / n10) * (n13 / n12) * (n9 / (n6 + n9))

## Given Parameters (Your choice !)

 Reference Size Description 2 n2 = [teeth] Bevel gear, fixed to wheel 1 3 n3 = [teeth] Bevel gear, freerunning on vertical shaft 4 n4 = [teeth] Spur gear, fixed to wheel 4 5 n5 = [teeth] Spur gear, freerunning on central vertical shaft 6 n6 = [teeth] Bevel gear, fixed to wheel 5 7 n7 = [teeth] Bevel gear, freerunning on short shaft, which in turn is fixed to central vertical shaft 8 - Platform, fixed to central vertical shaft 9 n9 = [teeth] Bevel gear, freerunning on central vertical shaft 10 n10 = [teeth] Spur gear, fixed to wheel 9 11 n11 = [teeth] Spur gear, freerunning on vertical shaft 12 n12 = [teeth] Bevel gear, fixed to wheel 11 13 n13 = [teeth] Bevel gear, fixed to wheel 14 T t = [length units] Track width

## Derived Parameters

 Reference Size Description 1 d1 = [units of t] Roadwheel, freerunning on axle 14 d14 = [units of t] Roadwheel, freerunning on axle