Landing on a sloping runway with different wind velocities

"Peter Duniho" wrote in message
...
"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).

Me too (on motivation), and I'm supposedly qualified to work
it out for myself, but was wondering if anyone had done it before!

Thinking about it after posting, in practice I think it might get even
more complicated. Ever worked out how accurately you can "spot"
a landing? I think of myself as a pretty average sort of private pilot,
and I'd guess I can pick a touchdown point to around +- 200 feet
or so on a good day. But I know I can do much better (calm wind)
on an upslope runway than a downslope one -- I suppose it is because
with an approximate 6 degree descent path, after factoring in the
runway slope (lets say 2 degrees) any deviation in approach angle
gets magnified by 2 (6+2=8 degree intercept vs. 6-2=4 degrees).
So, the actual "rollout" distance isn't really the thing to look at --
one ought to factor in your own personal "uncertainty" in
touchdown point too and look for the minimum runway length
(rollout + anticipated touchdown point uncertainty) that you'll
use for landing. This would bias in favour of the uphill approach,
regardless of other factors. (Probably. Air speed affects
approach angle too!)

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

I'd like to be definitive, but my airport guide is in the plane,
and I don't seem to be able to find the info through google.
I *thought* it was 3 degrees (and I really ought to know,
having been based there 6 years), but I may be wrong. Anyway,
3% works out as 2 degrees. It's our crosswind runway at
61B (Boulder City, Nevada) if you have a book to hand.
Another local airport is 3.5 units (degrees or grade) at
Temple Bar (U30) which is a wonderful destination if you're
in the area. Wish I had my damn book!! Regardless, these
grades make a substantial difference to one's decision. The
runways, at 3500' or so, leave little room to be sloppy if you're
in a Mooney and landing when the DA is over 5000'.


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).

I've heard that too, and Sedona airport (KSEZ) goes as far
as to mandate which runway to use depending on wind (I think
they have a slope of 1.5 *units*, but their runway is so long it
hardly makes a difference to us little guys).

I think the takeoff calculation ought to be more straightforward.
You can use the whole runway, for a start, and all one needs
to do is to work out how much acceleration you sacrifice by
running up the grade. Clearly, braking effects are irrelevant.
Still, it'd take a bit to figure the math.


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.

I just feel more comfortable landing uphill. Perhaps its because
on approach you have a bigger target to hit!


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.

Me too, with my mother on board as well. Quite a
wake-up call.