$1.$ A sag curve needs to be designed under a railway bridge with the following conditions:

Centreline station of bridge: $12+452$

Elevation of underside of bridge: $890\mathrm{.}22$

PVI @ $12+380\mathrm{.}37$

Bridge width: $15\mathrm{.}24$

Minimum clearance under bridge: Per BC Supplement to CHBDC $($

G$1$: $-3\mathrm{.}96\%$

G$2$: $4\mathrm{.}17\%$

Design the curve so the length of curve provides the minimum vertical clearance under the bridge. Determine stations and elevations for all critical curve locations.