Suposing that your SID has a climb gradient you can not comply with , your operator must have an EOSID available for the EO case.
The implication that a SID can provide protection for performance losses with one engine inop is not always correct.
SID's do not take into account low, close-in obstacles in the Initial Climb Area. Those obstacles may be a threat to a WAT-limited airplane with one engine inop.
The case of low, close-in obstacles is one of the reasons that paragraph 7 of
AC 120-91 states:
...Further, compliance with TERPS all-engines-operating climb gradient requirements does not necessarily assure that one-engine-inoperative obstacle clearance requirements are met.
Procedure designers also have options to publish ceiling and visibility minimums for the purpose of avoiding obstacles within 3 miles of the departure end of the runway.
However, the operating rules (14 CFR 121.189 and equivalent) make no exceptions for weather conditions.
Thus, reliance on a SID or published (all engines) Obstacle Departure Procedure may not adequately protect for the loss of an engine during takeoff.
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