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The arm is the distance from the
reference datum to the area in
question, such as a passenger seat or
the fuel tank. It may be measured in
Imperial or Metric units, and you
must use the same ones (the word
station may also be used). To get the
C of G of an aircraft, you multiply
160 Canadian Private Pilot Studies
the weight of each item in it by the
arm to get the moment, or the amount
of leverage that item contributes.
The aircraft itself will have an arm
and a moment from when it was last
weighed, and this is where you start.
You can find it in the weight and
balance schedule (usually in the flight
manual), and it may be varied if you
add or take off various items of
equipment, such as the hook or hoist
in a helicopter.
Because you might end up using very
long numbers, sometimes you use a
moment index, the result of dividing
the moment by 1,000 to make the
figures more manageable. Here is a
simplified typical calculation for a
Bell 206 helicopter (the principles
are the same for larger machines):
Item Wt Arm Moment
Aircraft 1881 116.5 219137
Front pax 185 65 13000
Rear Pax 185 104 19240
Baggage 50 147.50 7375
Fuel 310 110.7 34273
Total 2611 112.22 293025
The total C of G for takeoff is
112.22, obtained by dividing the total
moment figure (293025) by the total
weight (2611). This particular
machine's fuel has a variable CG
range, meaning that it has one all on
its own (that is, the arm will change
with the weight), so the figure of
110.7 will change with the amount,
for which check the flight manual.
The procedure is therefore to
multiply the weights by the arms to
get the moments, and divide the
total moments by the total weights
to get the C of G. Then you refer to
the flight manual to see if the figure
fits into the authorised range.
Look for a graph like this:
Simply take the all-up weight you
end up with, and the final C of G,
and line them up horizontally and
vertically. If they are inside the
envelope, you are OK, but don't
forget you have to land again! Your
C of G may well be fine for takeoff,
but check again after the fuel has
been used!
Lateral C of G works the same way,
except the figures are smaller and
easier to work with. In fact, they may
even be zeroed if the items are in the
centre, as the fuel tank might be.
Items left of the centreline have a
negative sign, and those on the right
are positive, so the lateral moments
for the front doors on a 206 would
be –12 for the left and +12 for the
right. Here’s an example lateral C of
G for the 206:
Item Wt Arm Moment
Aircraft 1881 .41 773
Pilot 185 14 2590
Front pax 185 -11 -2035
Left Rear Pax 185 -16 -2960
Centre Rear Pax 185 0 0
Right Rear Pax 185 16 2960
Baggage 50 147.50 7375
Fuel 310 0 0
Total 3166 2.75 8703
Flight Planning 161
Again, there will be a chart in the
Flight Manual to show you where
your plot lies. Fortunately, most of
the time it is something that only
helicopter pilots need to bother
about, which is why it's mentioned.
Flight Manuals often have helpful
charts with precalculated moment
figures for fuel and baggage (the arm
figures will be excluded). They are
quite simple to use, except that the
exam will require you to interpolate
here and there. However, you should
watch for special conditions, as with
any chart, especially for maximum
weights in particular locations. There
may also be a plan view of the
aircraft with the arms displayed next
to the locations they refer to.
Performance
The take-off and landing phases are
the most critical, demanding the
highest skills from crews and placing
the most strain on the aircraft.
Because of this, strict regulations
govern the information used for
calculating take-off or landing
performance. Of course, in the old
days (say during the war, or when
the trains ran on time), having
enough engines to lift the load was
all that mattered and no priority was
given to reserves of power and the
like. Now it's different, and
performance requirements will be
worked out before a C of A is
issued, over a wide range of
conditions. They are subsequently
incorporated in the Flight Manual,
which actually forms part of the C of
A. In addition, CARs require you to
ensure that your aircraft has
adequate performance for any
proposed flight.
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