Recently, Tony Cox posted:

Here's a problem which seems to have a non-trivial solution.
At least, I've not been able to find a definitive answer to it, but
what do I know??

Suppose one wishes to land at an airport with a runway
that slopes at X degrees. The wind -- assumed to be directly
aligned with the runway -- is Y knots from the "high" end of
the runway.

Clearly, if Y is positive, one should try to land in the
"up-slope" direction to minimize one's ground roll. One
will be landing "up" and into a headwind. But what if
Y is negative? Clearly, if Y is just a few knots neg, one would
still land "up-slope", because the braking effect of rolling
out up-hill more than compensates for the higher landing
speed due to the tail wind.

If Y is negative and more substantial, which way should
one land? At some point, it makes sense to switch to the
other end of the runway -- landing downhill -- to take advantage
of the (now) headwind. But how does one establish which way
to land, assuming no clues from other traffic in the pattern? The
aim is to select a direction, given X and Y, which would result
in the smaller ground roll.

Rule of thumb responses are interesting, but better would be
a full mathematical treatment. Presumably, a proper treatment
would need to include touch-down speed too, and perhaps
gross weight as well.

Its more than an academic question for me. My home airport
has a 3 degree runway, and some local airports are even
steeper.

Having done that (Jaffrey Airport, NH), all I can suggest is that you go
with the head wind, whichever way that is. My first approach was to land
going "uphill", but on final the wind shifted to a tailwind and it made
things pretty dicey. So, I went around and landed downhill. The roll-out
was a quite bit longer than I'm accustomed to, but other than that it was
uneventful. When I left a couple of days later, the wind favored taking
off "uphill", and that was an experience, as well. It gave the folks at
the ice cream stand about 500' off the departure end something to gawk at.

Neil