Imagine it's the stereotypical hot summer day at a mountain airport where the weather isn't all that bad, but it's not quite good enough to comfortably depart under VFR and pick up your clearance in the air. That means you'll need to make an instrument departure. Being the proficient IFR pilot that you are, you first consult the relevant takeoff minimums, only to find that your old 182 loaded up with people, bags and gas, isn't going to be able to meet the required climb gradient on this warm, high-density-altitude day.
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