Interrelations can be established between MRS or ASA and ORS or between ORS and NRS systems and vice versa.

RAKE FACE ANGLES.

CASE 1.

Given bake rake angle and side rake angle in ASA.

Find inclination angle and orthogonal rake in ORS system.

Assume either $\varphi$ or $\varphi_s$ is known

$tanY_o = tanY_xSin \varphi+ tanY_yCos \varphi$

$tan \lambda = -tanY_x Cos \varphi + tanY_ySin \varphi$

NOTE

$\phi$ (in ORS) = 90° - $\phi_S$ (in ASA)

$\phi_1$ (in ORS) = $\phi_e$ (in ASA)

CASE 2.

Given inclination angle and orthogonal rake in ORS.

Find back rake and side rake angle of ASA system.

Assume $\varphi_s$ is known

$tanY_x = tanY_o Sin \varphi - tan \lambda \varphi$

$ tanY_y = tanY_o Cos \varphi + tan \lambda sin \varphi$

CASE 3.

Given inclination angle and orthogonal rake in ORS.

Find normal rake angle in NRS system.

$ tan \gamma_n = tan \gamma_o cos \lambda$

CASE 4.

Given, inclination angle and orthogonal clearance in ORS.

Find normal clearance angle.

$cot \alpha_n = cot \alpha_o cos \lambda$

Clearance angles.

Given orthogonal clearance and inclination angle of ORS.

Find front clearance and side clearance angle of ARS system.

Assume $\varphi$ is known.

$cot \alpha_X = Cot \alpha_O sin \varphi – tan \lambda cos \varphi$

$cot \alpha_Y = cot \alpha_o cos \varphi + tan \lambda sin \varphi$

Alternatively we can write

$cot \alpha_O = cot \alpha_X sin \varphi + cot\alpha_Y cos \varphi$

$tan \lambda = - cot \alpha_X cos \varphi + cot \alpha_Y sin \varphi$