Ground/Air Nautical Miles

Actually, in the world of digital computers, infinity *is* a finite
number.

No. The real "infinity" is the number of bugs in Microsoft programs. The "finite, computer infinity" is the number of bugs they will fix.

Jose
--
Freedom. It seemed like a good idea at the time.
for Email, make the obvious change in the address.

On Sun, 07 Nov 2004 00:47:22 GMT, David CL Francis
wrote:

On Sat, 6 Nov 2004 at 22:00:32 in message
, Stealth Pilot
wrote:

So at a TAS of 110k you travel a ground distance of 100nm against a wind
of 10k and surprise, surprise you than fly 110 'air' nm

More or less self evident so I am unclear what that achieves?

You're wrong, here's why:

you're still wrong and that is why you're not achieving anything.
in the real world your cruise speed remains constant so what happens
is that the 110 nautical miles that the wind makes the 100 miles seem
like, takes longer to fly. engine running for longer equals more fuel
burn from the fixed tankage in the aircraft hence the need to pre calc
the usage and plan for it.


No one disputes that statement of the obvious I would guess. Anyway as
far as I know you slightly adjust your cruise speed according to the
situation. That wasn't what anyone was discussing as far as I can see.
Perhaps you could tell me what I was trying to achieve as you seem to
know better than I do? On second thoughts don't bother.

if you are actually a pilot you are an accident waiting to happen.
Stealth Pilot

I'm not, just an elderly aeronautical engineer, so that's all right
then!

thats ok, you make comments which one becomes attuned to over the
years as indicating a lack of knowledge at the level expected for
licencing. there was a question in my mind as to what your background
was. (at least you arent a precocious 14 yr old :-) )

you dont slightly adjust your cruise speed as you suggest. in the real
world you are cruising at the maximum continuous rpm that the engine
is capable of, that pretty well defines your cruise speed.

the navigation problem is caused by the wind is in two parts.
first: how much angle do you need to lay off into wind so that you get
blown off course by the wind back on to your intended track.
(otherwise you would never reach your destination) you solve this with
the speed vectors triangle on the graphical side of the E6B whiz
wheel.
Second: you determine the effect on your speed over the ground that
any headwind or tailwind component has, then from the resultant ground
speed and the actual distance you work out how long it will take to
fly the leg. your fuel consumption at cruise is a simple litres per
hour figure. litres per hour times the time aloft gives you the fuel
requirement. you work out the ground speed as part of the speed
vectors triangle then you take the value derived and use it on the
slide rule side of the E6B to work out time and then fuel needed in 2
calcs.

when you sit an exam on navigation quite often the question is simply
how much fuel will the flight take given a wind of XX knots from
XXXdegrees, cruise speed is XXX knots with a fuel flow of XX litres
per hour. takeoff from A, tracking via waypoints B and C to
destination D as marked on the map.
it is a sucker question :-) because you can only give the answer by
fully calculating the effect of wind on each individual leg.

btw I *have* tried to increase straight and level cruise on one
occasion by firewalling the throttle for over half an hour. I ended up
still being the original calculation past last light. the difference
was imperceptible.

Stealth (ask away on the nav questions) Pilot

On Mon, 8 Nov 2004 at 23:02:55 in message
, Stealth Pilot
wrote:

thats ok, you make comments which one becomes attuned to over the
years as indicating a lack of knowledge at the level expected for
licencing. there was a question in my mind as to what your background
was. (at least you arent a precocious 14 yr old :-) )

LOL

you dont slightly adjust your cruise speed as you suggest. in the real
world you are cruising at the maximum continuous rpm that the engine
is capable of, that pretty well defines your cruise speed.

You surprise me. Is that why ranges and fuel consumption are quoted for
different cruise power settings for many aircraft?

Lets take a review of the Diamond DA42 Twin Star

Cruise 90% @ 12,500ft 201 knots
Cruise 75% @ 10,000ft 181 knots

Range 60% standard tanks 1.061 nm
Range super long at 110 knots 2,063 nm

Seems that planning your cruise power might be rather important to
whether or not you make it. Adjustment for wind showed also be in order.
The report does not mention the likely range at 201 knots but I have a
*feeling* it will be even less.

Endurance is, naturally, even more sensitive to cruise power.

[Snip load of stuff that is teaching your grandmother to suck eggs]

Stealth (ask away on the nav questions) Pilot

I don't think I will, thank you all the same. You know next to nothing
about me and if you assume that non pilots always know little about
aviation you are gravely mistaken. I have the greatest respect for many
pilots and I have known and still know a few whose words I hang on. That
does not mean that all pilots know more than I do about every subject.
--
David CL Francis

On Mon, 8 Nov 2004 at 01:40:02 in message
, Jose
wrote:
That was fascinating and I enjoyed it but I do have trouble with
the concept of different 'sizes' of infinity although I feel sure they
exist. 0r do they? What do I mean by 'exist' anyway? :-)

Infinities (it works for finites too) are compared by attempting a one
to one comparison between their elements. If one can achieve this,
then they are the same "size". If it is impossible to achieve this,
then one of them is "bigger".

The number of errors that can be made is bigger than the number of people.
The number of ways to skin a cat is bigger than the number of cats.


I like it but neither the number of cats nor the number of people is
infinite! :-)

There are actually an infinite number of sizes of infinity. The best
way to think of an infinity is that it's the size of a set that
contains all the elements. For example, the "size" (quantity of
elements) that a set containing all the integers is infinite. It is
however smaller than the set of real numbers between zero and one, as
shown in my original post. More generally, the quantity of subsets of
an infinite set is bigger than the set being subsetted (to coin a
word). (a subset is a set which contains "some" of the elements of the
original set, and no other elements, where "some" could be "all" or
could be "none". Sets are designated (sometimes) by listing their
elements inside curly braces; a few (i'll show three) subsets of the
days of the week are {sunday} and {tuesday, thursday, friday} and {}
(that last one being the empty, or "null" set).

So, the set of positive integers ( {1,2,3,4,...} ) is not as large as
the set of subsets of the positive integers ( {}, {1}, {2}, {1,2},
{1,2,3,4}, {8, 9, 423}, {500}, ... )
Note that it is perfectly fine for a set to contain sets as elements.
Don't confuse a set with an element however: 1 is different from {1}.
"Monday" is different from "the SET of days between Sunday and
Tuesday". A car (something you can drive) is different from "car" (the
word describing something you can drive).

Ceci n'est pas une pipe.

Is that Maigret?

I think I've got it! By George I think I've got it Professor Higgins!
Once again where does it rain? No sorry that's not it. But there are
more raindrops than clouds and there is an infinite number of shapes and
sizes of clouds?

I do now understand the point that where you can map an infinite number
of sub objects to each integer it implies some substantial difference in
kind (scale? extent? Infinity? Whatever).

I liked the skinning a cat one!

Seriously thanks very much - I have made a step forward I think. However
what use you can make out of two sets where one of them is infinitely
greater than the 'smaller' infinite set escapes me at the moment.

Will it help with my dabbling in aerodynamics I wonder?
--
David CL Francis

I haven't been following this exchange closely, but one thing does stick
out...

"David CL Francis" wrote in message
...
you dont slightly adjust your cruise speed as you suggest. in the real
world you are cruising at the maximum continuous rpm that the engine
is capable of, that pretty well defines your cruise speed.

You surprise me. Is that why ranges and fuel consumption are quoted for
different cruise power settings for many aircraft?

While it is true that the most efficient speed (and thus best range) depends
on headwind or tailwind (fly faster in a headwind, slower in a tailwind, for
best economy), in practice pilots mostly ignore that. They aren't usually
flying at the best economy power setting, but rather are looking for best
speed and the power setting for best speed doesn't depend on winds aloft.

Of course, a concession is made to fuel economy, in that we rarely use the
true "best speed" power setting (which would be maximum continuous power).
That would use so much fuel as to generally be impractical.

But neither do we usually adjust the power setting (and thus cruise speed)
based on winds aloft. We just pick the power setting at the high end of the
published cruise power settings, and go with that. Alternatively, when
we're not in a hurry and we'd like to save on gas (applies only to owners
and those who rent "dry"), we'll select a lower power setting. But even
there, the winds aloft don't come into the equation for selecting the power
setting.

Mr. Pilot's response was entirely accurate, and no amount of poring through
aircraft manuals on your part will change that.

What your comment about "teaching your grandmother to suck eggs" means, I
have no idea. In the US, "go suck an egg" (and its variants) isn't a
friendly statement, and I didn't see anything in Mr. Pilot's post that would
have justified such a response. But who knows? Maybe in the UK, a
statement like that is considered harmless, for all I know. If not, it sure
seems out of character for you.

Pete

"Todd Pattist" wrote in message
news
It looks to me like Mr. Francis was "entirely accurate" and
Mr. Pilot wrong. I don't run my engine at the "maximum
continuous rpm that the engine is capable of."

Your operations are not relevant for what "most pilots" do. One sample does
not make any sort of generalization. The fact remains that most pilots use
the maximum cruise power setting for most operations. Mr. Pilot's statement
was certainly closer to the truth than any statement that claims pilots take
into account the wind when choosing their power setting (which was what
David said).

None of that has anything to do with wind, but Mr. Francis
is also right even if he was thinking of wind. Since my
airplane is about as slow as they come, I sometimes choose
speed during a headwind leg and efficiency during a downwind
leg. The slower your cruise speed, the more it makes sense
to do this. That's point 2.

"Sometimes"? Or "always"? I never said, nor do I believe Mr. Pilot
intended to say, that no one ever worries about fuel economy. The question
is what a typical operation is. And again, the typical operation does not
correlate wind, power setting, and fuel economy.

I'd give Mr. Francis the nod for both points.

If you like.

Pete

Ceci n'est pas une pipe.

Is that Maigret?

Oui.

But there are more raindrops than clouds and there is an infinite number of shapes and sizes of clouds?

Yes, and yes. And, oddly, there are (theoretically) more cloud shapes than there are real numbers. (the cardinality of the (which means, roughly, "number of") functions of real numbers is greater than the cardinality of the real numbers themselves.
A function is a set of real number pairs (+). Each such set is a subset of the real numbers. So the set of possible functions is essentially the set of subsets of real numbers. This has greater cardinality. ("There are more of them.") Which is
what you realize below when you say:

I do now understand the point that where you can map an infinite number of sub objects to each integer it implies some substantial difference in kind (scale? extent? Infinity? Whatever).

It has a greater cardinality. But I'm talking about the case where the "map" is done by considering the set of subsets. Not every infinite map will give a greater cardinality. There are an infinite number of fractions with any given integer in the
numerator, but the number of fractions ("rational numbers") has the same cardinality as the integers ("there are just as many of them, no more, no less")

Will it help with my dabbling in aerodynamics I wonder?

No. But it will help pass the time if you get bored with it.

Jose

(+) ok, they are ordered pairs such that the first element can only occur once in the set. For example:
{(2,4) , (3,5) , (4,5) } (the set containing the three ordered pairs (2,3), (3,5), and (4,5)) is a function, but
{(2,4) , (2,5) , (4,5) } (the set containing the three ordered pairs (2,3), (2,5), and (4,5)) is not. (It's a relation though)
Essentially, for each and every first element, there can only be one second element associated with it. Therefore, the cardinality of the function is equal to the cardinality of the first elements of the function. (there are exactly as many ordered
pairs in the function as there are distinct first elements in the function.)

--
Freedom. It seemed like a good idea at the time.
for Email, make the obvious change in the address.

On Tue, 9 Nov 2004 13:37:00 -0800, "Peter Duniho"
wrote:


intended to say, that no one ever worries about fuel economy. The question
is what a typical operation is. And again, the typical operation does not
correlate wind, power setting, and fuel economy.

I'd give Mr. Francis the nod for both points.

If you like.

Pete

It depends entirely on the engine Pete.
I fly an O-200 in a homebuilt wittman W8 tailwind.
a very simple setup that obeys Lear's admonition.
.....and one that I wouldnt swap for a mooney :-)
Stealth Pilot

On Tue, 09 Nov 2004 18:20:48 GMT, David CL Francis
wrote:



I don't think I will, thank you all the same. You know next to nothing
about me and if you assume that non pilots always know little about
aviation you are gravely mistaken. I have the greatest respect for many
pilots and I have known and still know a few whose words I hang on. That
does not mean that all pilots know more than I do about every subject.

what non pilots can never do is get the real relative importances of
each item sorted out. it is very often never written about because the
law actually isnt flexible enough that you can be honest at times.
by all means read all the theory but do try to get involved hands on
in the aviation environment so that you have a chance to develop some
practical experience and expertise.
you sound like the sort of guy who would enjoy the EAA chapter
environment.

come back to your writings and thoughts with some practical hands on
experience and you will surprise yourself at how subtly your writing
has changed because of that experience.

Stealth (get involved it will add years of pleasure to your life)
Pilot

"Stealth Pilot" wrote


It depends entirely on the engine Pete.
I fly an O-200 in a homebuilt wittman W8 tailwind.
a very simple setup that obeys Lear's admonition.
....and one that I wouldnt swap for a mooney :-)
Stealth Pilot

What are your real world figures for empty weight, and gross for your W8?
It seems the figures I have seen place it ever so close to sport plane
status, except for the speed, but that could be taken care of with a climb
prop, I think.
--
Jim in NC


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