"Tony Cox" wrote in message
ups.com...
[...]
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.

I have occasionally thought about trying to treat the problem
mathematically, but so far haven't had enough motivation to do so. It's a
very complicated problem, mathematically speaking (assuming you're not
someone who does this sort of math on a daily basis, and I'm not). I
suspect that in addition to looking at touch-down speed and gross-weight,
along with runway slope and wind velocity, you would also have to include
some measure of braking performance (maybe this is somehow derivable from
the POH roll-out distances).

A 3 degree slope sounds pretty steep to me. Are you sure it's not 3%?

As far as general rules of thumb go, the one I've heard is that 1% of slope
is worth about 10 knots of headwind *for a takeoff*. This is not
necessarily applicable to the landing case, which is what you're asking
about, but it's at least related. In this rule of thumb, take the runway
slope in percent, multiply that by 10, and if you've got a headwind less
than that, operating downslope is better for a takeoff (upslope for a
landing, if you apply the same rule of thumb).

Personally, that rule of thumb seems optimistic to me, but I don't have any
good justification for doubting it. Still, it's worth considering the fact
that a headwind or tailwind affects the takeoff or landing differently than
slope. That is, the wind speed affects the total velocity change required,
while the slope affects the acceleration available. Even if you take off
uphill but upwind, while the acceleration will be less, so may the runway
used since you need a lower total velocity change to reach takeoff speed.
Likewise, landing downhill but upwind, yes your deceleration is less but you
also need less reduction in speed to come to a stop.

More importantly, the change in acceleration or deceleration is linear,
while the difference in total speed change is exponential.

To me, that suggests that if you're going to err, it's better to choose the
headwind over slope when in doubt, since a good headwind is beneficial to
the exponentially related parameter, while the slope is only beneficial to
the linearly related parameter.

That said, like I said I haven't taken the time to look at any of this in a
rigorous mathematical way, so I might have made a mistake in some
assumptions. Still, I have to say that the one time I ever took off
downwind but downslope, I sure used a lot more runway than I thought I was
going to.

Pete