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How to interpret the term "standard" which is found in FAA's Obstacle Departure Procedures (ODP) and Standard Instrument Departure Procedures (SID)?

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This might be obvious, but I find it difficult to interpret correctly the term "standard", when it refers to the takeoff phase of the flight.

Take, for example, the takeoff minimums for the La Guardia airport, page L16. For Runway 13, it states 400' ceiling height and 2¼ statute (I think) miles visibility but it does not mention any climb gradient. Is it implied that it follows the "standard" climb gradient of 200 feet per nautical mile? Next, it states that alternatively one can takeoff with the "standard" visibility rules, but only with a climb gradient of at least 280 FPNM until it reaches to 500 feet altitude. Which exactly are these standard visibility rules? The only source I remember finding states a requirement for 1 statute mile visibility for 1-2 engines aircrafts and 1/2 statute mile visibility for aircrafts with more than two engines, but no requirement for ceiling height.

Another example can be found by looking at this SID. Its takeoff minimums description states that for runway 4 "Standard" takeoff minimums apply. In addition, for runway 13, it states "400-2 or Standard with minimum climb of 280' per NM to 500." Does this mean that for "400 feet ceiling height - 2 statute miles visibility" the "standard" 200' per NM climb gradient applies, while for "standard" visibility a 280' per NM climb gradient is required?

I would be really grateful if someone could help me clarify the above rules.


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