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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. |
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