Transcript Sport Pilot Training Program

Post-Solo Training Module
Flight Briefing: Lesson 12
Weight and Balance
In cooperation with AvSport of Lock Haven ,
Piper Memorial Airport, Lock Haven PA
(by H. Paul Shuch, Chief Flight Instructor)
Lesson 12 Objectives
Upon completion of this module, you will:
 Define datum, station, arm, moment, and CG
 Perform calculations of total weight and center of
gravity for a Light Sport aircraft
 Explain the importance of proper aircraft loading
 Understand why CG varies throughout flight
 Ensure that the aircraft is always being operated
within its proper loading envelope
Flight Briefing: Lesson 12
Definition of Terms
On the pages that follow, we will define the
following terms, which will be used throughout
this lesson:








Datum
Weight
Arm
Moment
Center of Lift
Center of Gravity
Envelope
Mean Aerodynamic Chord
Flight Briefing: Lesson 12
Definition of Terms


Datum: an arbitrary reference point, with respect to
which locations and distances on the aircraft are
measured. The datum can be defined as the firewall,
instrument panel, leading edge of the wing, tip of the
propeller spinner, baggage compartment bulkhead, or
any other convenient, identifiable location that the
manufacturer specifies.
Note: Different aircraft may well use different references.
For consistency, you must always measure every
location on a given aircraft with respect to the same
specified datum.
Flight Briefing: Lesson 12
Definition of Terms

Weight: actually, we have several different ones to
be concerned with.




Maximum Gross Weight, set by the manufacturer (and
limited by the Light Sport Aircraft rules) includes the aircraft,
occupants, fuel, and baggage. For LSA airplanes, it cannot
exceed 1320 pounds. (Caution: it may be less!)
Empty Weight typically includes the aircraft, installed
equipment, engine oil, and unusable fuel.
Useful Load is the difference between the two above
figures, i.e., Maximum Gross Weight minus Empty Weight.
Payload is what you can transport, assuming full tanks. So,
it equals useful load minus the weight of maximum usable
fuel.
Flight Briefing: Lesson 12
Definition of Terms

Arm: The location of a specific point on the aircraft (for
example, the center of the seat, baggage compartment,
or a fuel tank), expressed with respect to the Datum.

Note: measured arms can be to locations either ahead of, or
behind, the specified datum. We specify arms as distances
in inches forward of, or aft of, the datum respectively. The
arm for a location forward of the datum is typically given a
negative sign, while one aft of datum would be expressed as
a positive number.
Flight Briefing: Lesson 12
Definition of Terms

Moment: Consider the forces exerted with respect to the
datum by both the aircraft itself and its various contents.
Moment is a torque being exerted, and is related to both
the weight and the location of a given object. It is found
by multiplying the weight of the item (empty airframe,
quantity of fuel, pilot, passenger, or baggage item) by its
arm (distance forward or aft of datum). If we measure
arm in inches, and weight in pounds, then moment is
expressed in inch-pounds (a familiar torque wrench unit).

Note: moment can be positive or negative, depending upon the sign
of the arm (positive for objects aft of datum, and negative for objects
ahead of datum).
Flight Briefing: Lesson 12
Definition of Terms


Center of Lift: We know that the lift of an airfoil
is what supports the aircraft in flight. It can be
regarded as a force acting perpendicular to the
surface of the wing. If we consider total lift to be
a vector emanating from a particular point on the
wing, its point of origin would be called Center of
Lift (CL).
Note: on a typical airfoil, CL is typically located
near the thickest part of the wing.
Flight Briefing: Lesson 12
Definition of Terms

Center of Gravity: In unaccelerated level flight,
the upward force of lift exactly counterbalances
the downward force of gravity. Center of Gravity
(CG) is the point of origin of the gravity vector.
For lift and gravity to balance, one would expect
CG to be somewhat close to the Center of Lift.

Note: in the real world, planes (especially those with
engines up front) tend to be nose-heavy. Thus, CG tends
to fall ahead of CL. The exact location of CG varies with
aircraft loading (and in this lesson you will learn how to
calculate it precisely).
Flight Briefing: Lesson 12
A Problem!

Question: But, if the CG is ahead of the CL, how
can the plane ever possibly fly level?

Answer: So far, we’ve been talking only about the Center
of Lift of the wing (an airfoil). But, the horizontal tail is
also an airfoil, with lift in the down direction. It is the
downward lift of the tail that counteracts the downward
force of gravity acting on the forward CG. This balances
the aircraft for level flight. The amount of downward lift
exerted by the tail is controlled with elevator (and
elevator trim keeps it where you want it).
Flight Briefing: Lesson 12
Definition of Terms

Envelope: For every aircraft, there are limits to
where the CG must fall for safety and stability.
These limits vary with Gross Weight. A loading
envelope is a diagram that shows the range of
acceptable CG values, as the loaded Gross
Weight changes.

Note: an aircraft loaded out of the safety envelope is an
accident waiting to happen! Thus, we calculate weight
and CG before every flight, and plot them on an
envelope diagram.
Flight Briefing: Lesson 12
Definition of Terms

Mean Aerodynamic Chord: Thus far, we have assumed
CG would be described in inches fore (or aft) of datum.
Since for safe operation the CG will always fall somewhere
along the chord line of the wing, we could also describe CG
as a point a certain percentage along the chord line (with
0% MAC indicating the leading edge of the wing, and 100%
MAC referring to the trailing edge).

Note: For a straight, symmetrical (“Hershey Bar”) wing, the chord is
the same all the way from wing root to wing tip. If the wing is swept
or tapered, the chord changes along its length. We would then have
to compute the average (“mean”) chord, and express CG as a
percentage of Mean (average) Aerodynamic Chord, or MAC.
Flight Briefing: Lesson 12
Determining Empty Weight




After all standard equipment has been installed, all usable fuel is drained. The plane
is placed on scales, and its total empty weight is measured directly.
This is done by the manufacturer before the plane receives its airworthiness
certificate, and is recorded on the aircraft’s official Weight and Balance form.
The plane must be reweighed any time equipment is added or removed.
Alternatively, weights of any equipment items or accessories added or removed can
be used to recompute a new empty weight. The W/B form must then be updated.
Flight Briefing: Lesson 12
Determining Total Weight



Before any flight, the weight of pilot, passengers,
fuel, and baggage is added to the empty weight
of the aircraft (obtained from the W/B records).
The sum of these weights must be below the
aircraft’s specified maximum gross weight.
Exceeding maximum gross weight will result in
increased takeoff roll and stall speed, reduced
climb performance, and possible overstressing of
the airframe.
Flight Briefing: Lesson 12
Determining Total Weight (Example)








Empty weight =
Pilot =
Passenger =
Baggage =
Fuel = 30 gal x 6#/gal =
Total takeoff weight =
Maximum Gross Wt =
Weight margin =
750 pounds
+170 pounds
+150 pounds
+ 35 pounds
+180 pounds
1285 pounds
1320 pounds
35 # below max
Flight Briefing: Lesson 12
Total Weight Shortcut (example #1)
If you happen to know your aircraft’s useful load (which you
should):
 Maximum Gross Wt =
1320 pounds
 Empty weight =
- 750 pounds
 Useful load =
570 pounds
All you need do before flight is add pilot, passenger, fuel,
and baggage weights, and ensure they fall below that
figure.
[170 + 150 + 180 + 35 = 535 < 570]
Flight Briefing: Lesson 12
Total Weight Shortcut (example #2)
If you happen to know your aircraft’s payload
(which you also should):
 Useful load =
570 pounds
 Full fuel = 30 gal x 6#/gal =
- 180 pounds
 Payload =
390 pounds
And, if you plan to take off with full fuel,
All you need do before is add pilot, passenger, and
baggage weights, and ensure they fall below that figure.
[170 + 150 + 35 = 355 < 390]
Flight Briefing: Lesson 12
Using a Wt/Bal Worksheet (1)



Here is a typical loading chart for a Light Sport Aircraft.
For now, you can ignore the columns marked Arm and Moment.
The Weight indicated next to “Plane” is its measured empty weight.
Flight Briefing: Lesson 12
Using a Wt/Bal Worksheet (2)




Under the “Weight” column, write the weights of the occupants, fuel, and baggage.
Remember that each gallon of AvGas weighs six pounds.
Add up all the figures in the Weight column to get total weight.
(We’ll come back to this worksheet later.)
170
150
180
35.5
1281
Flight Briefing: Lesson 12
Adjusting Total Weight




Should the aircraft’s specified maximum gross takeoff
weight be exceeded, the pilot must remove baggage,
passengers, or fuel, to bring total weight within limits.
If fuel is reduced, the range of the aircraft must be
recomputed, and leg lengths adjusted (or fuel stops
added to the trip, as required).
Taking off over-gross is not just contrary to FARs; it is
also unsafe!
Remember that stall speed increases with weight.
Above 1320#, an LSA may stall at above 45 KCAS.
Flight Briefing: Lesson 12
Determining Empty Weight CG (1)

I suppose we could place the empty aircraft on a teeter-totter (the
child’s playground toy consisting of a plank, pivot, and fulcrum), and
slide the plane back and forth until it is exactly balanced (level).
Where the fulcrum ended up with respect to the airframe would then
be the EWCG. We could specify its location in inches fore or aft of
datum.
Flight Briefing: Lesson 12
Determining Empty Weight CG (2)

But wait! Remember that the manufacturer already placed calibrated
scales under each of the plane’s wheels, when reading total weight.
If the plane was level during weighing, and if we know the exact
location of the three wheels relative to the selected datum, it’s now
possible to compute EWCG. (Fear not, the manufacturer of your
aircraft has already done this for you! Check your wt/bal documents.)
Flight Briefing: Lesson 12
Determining Empty Weight CG (3)

Here’s an example of a full
aircraft weighing experiment,
including all the calculations.
The CG has been computed
both in inches aft of datum, and
also as a percentage of mean
aerodynamic chord (MAC). Your
actual wt/bal documents may
show one, or the other, or both.
Flight Briefing: Lesson 12
Determining Object Arms





The location of each area in the airplane to which weight
can be added is called a Station.
Locations of Stations are typically measured in inches
forward or aft of the specified Datum.
You will need to determine the Station for each of the
seats, fuel tanks, and baggage compartments in your
aircraft.
Your Aircraft Operating Instructions (or Pilot’s Operating
Handbook) should list stations for the pilot, passenger,
baggage, and fuel.
The distance from the Datum to any specified Station is
called its Arm.
Flight Briefing: Lesson 12
Determining Object Arms (2)


Here is a typical loading chart we introduced earlier. Note that all
Arms are specified in inches aft of Datum.
For now, you can ignore the column marked Moment.
170
150
180
35.5
1281
Flight Briefing: Lesson 12
Determining Object Arms (3)




Remember, the Station labeled “Plane” represents the empty aircraft.
The Weight shown next to “Plane” is still the measured aircraft empty weight.
The Arm shown next to “Plane” is actually the computed or measured EWCG.
All of the other Arm values come from the POH or AOI.
170
150
180
35.5
1281
Flight Briefing: Lesson 12
Computing Individual Moments (1)


We’ll come back to this worksheet in a moment.
Before we can tackle the third column, we need to talk a bit
about Moment.
170
150
180
35.5
1281
Flight Briefing: Lesson 12
Computing Individual Moments (2)



Recall that Moment is simply a measure of Torque, the result of a
turning Force being applied at a specified Distance.
Consider a 24 inch torque wrench, being used to tighten a bolt. If we
pull with 10 pounds of force, at a distance of 24 inches from the
fastener, we have applied a torque of [24 inches x 10 pounds = 240
inch pounds].
Moments are calculated similarly, by a multiplying force (in this case,
weight) by a distance (in this case, arm). So, moment is measured in
inch pounds.
Flight Briefing: Lesson 12
Computing Individual Moments (3)


Here, the torque (moment) of the empty aircraft has already been computed for
you. We multiplied its empty weight (745.5 pounds) by its EWCG of 10.16”
You can now calculate the remaining moments, by multiplying across.
170
150
180
35.5
1281
Flight Briefing: Lesson 12
Computing Individual Moments (4)

If you came up with something like this, you’re
getting the hang of computing moments!
170
3646.5
150
3217.5
180
4815
35.5
1514.1
1281
Flight Briefing: Lesson 12
Computing Total Moment


Bear with me, we’re getting there! We now have moments in inch lbs.
The total torque acting on the loaded CG is now found by simply
adding up the individual moments (right column).
170
3646.5
150
3217.5
180
4815
35.5
1514.1
1281
20767.4
Flight Briefing: Lesson 12
Computing Loaded CG (1)

Remember the torque wrench equation?
Torque (inch pounds) = distance (inches) x force (pounds)


If we use a little algebra, rearrange and we can solve for distance:
Distance (inches) = torque (inch pounds) / force (pounds)
Which is the same as saying:
CG (inches) = moment (inch pounds) / weight (pounds)
Flight Briefing: Lesson 12
Computing Loaded CG (2)

Well, we already have total weight and total moment.
So, to find CG, all we have to do is divide:
170
3646.5
150
3217.5
180
4815
35.5
1514.1
1281
20767.4
16.2”
Flight Briefing: Lesson 12
Computing Loaded CG (3)

Remember, we got here from the Torque Wrench
Equation:
CG (inches) = moment (inch pounds) / weight (pounds)
We now know the Center of Gravity of the loaded airplane!
But, is that a safe CG? To find out, we need to use a Loading Envelope.
Flight Briefing: Lesson 12
Computing Loaded CG (4)

There are computer spreadsheets available
to help expedite the computation of weight
and balance, but officially, this is how you
determine the location of the CG.
Flight Briefing: Lesson 12
Loading for Longitudinal Stability
Let’s take a look at a typical airplane in level flight:
Notice that the loaded CG is ahead of the wing’s
Center of Lift. In other words, the plane is
deliberately nose-heavy. Why is this important?
Flight Briefing: Lesson 12
Loading for Longitudinal Stability (2)
Recall that the wing and the tail are both airfoils.
The wing has lift in the up direction.
The tail has lift in the down direction.
Because the plane is nose-heavy, between the three forces,
the plane exactly balances. Flight Briefing: Lesson 12
Loading for Longitudinal Stability (3)
Let’s assume the plane speeds up for some reason.
More airflow across the wing increases lift; the plane climbs.
But more airflow across the tail increases its down lift. The
nose pitches up. Since pitch controls airspeed, this slows
down the plane, decreasing lift and restoring level flight.
Flight Briefing: Lesson 12
Loading for Longitudinal Stability (4)
Now assume the plane slows down for some reason.
Less airflow across the wing decreases lift; the plane descends.
But less airflow across the tail reduces its down lift. The nose
pitches down. Since pitch controls airspeed, this speeds up
the plane, increasing lift and restoring level flight.
Flight Briefing: Lesson 12
Loading for Longitudinal Stability (5)
Thus, when properly trimmed, the plane maintains a
constant airspeed.
We use the elevator to compensate for small deviations from
stable, unaccelerated flight (and then use trim to reduce the
amount of stick or yoke pressure necessary to achieve this
goal).
Flight Briefing: Lesson 12
Stability and Stall Recovery

Several factors affect how an airplane will
stall, especially weight and balance.
If the center of gravity moves
forward, the down force required by
the tail is increased (airplane needs
higher angle of attack). With a
forward CG, the airplane will stall at
a faster speed, but it will be more
difficult to stall and easier to
recover. Forward CG also gives the
tail more leverage, and increased
control effectiveness.
Flight Briefing: Lesson 12
Stability and Stall Recovery
Let’s assume the wing exceeds its critical angle of
attack, inducing a stall.
Because the CG is ahead of the center of lift, the plane pitches
down. Since pitch controls airspeed, the plane accelerates,
providing more airflow across the wing, restoring lift and thus
breaking the stall.
Flight Briefing: Lesson 12
Stability and Stall Recovery
Of course, improper pilot actions can hamper stall
recovery.
Holding back-pressure on the stick or yoke increases the
downward lift of the elevator, possibly keeping the angle of
attack above critical. This is why we relax elevator backpressure when recovering from a stall.
Flight Briefing: Lesson 12
Stability and Stall Recovery



It is very important that the airplane be
properly loaded, with the CG within the
acceptable limits.
To calculate where the CG is, use the
information in the Pilot’s Operating Handbook
(POH) or the Airplane Operating Instructions
(AOI).
The empty weight data must come from the
documents specific to that airplane. These
documents are required to be onboard the
aircraft during all flights.
Flight Briefing: Lesson 12
CG Loading Limitations
Just how far ahead of the wing’s center of lift should
the loaded CG be?
That depends upon the downward lift available from the tail at
various elevator deflections. For any plane, there are limits on
how far forward, or back, the CG needs to be, and these vary
with weight. A loading envelope helps keep us safe.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (1)
Here is a typical weight and balance envelope. It comes from the approved flight
manual (POH or AOI).

Note that it lists weight along the vertical axis, and CG along the horizontal.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (2)

The red polygon represents the range of acceptable values within
which the total weight and CG must fall.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (3)

First find the total weight on the vertical scale, and plot a horizontal
line through it.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (3)

Next, find the CG on the horizontal scale, and plot a vertical line
through it.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (4)

The intersection of these two lines represents the loading of your
aircraft. It must fall within the red polygon representing safe values.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (5)

Now, calculate the weight and CG for the end of the flight (fuel
burned off), and repeat the process.
Flight Briefing: Lesson 12
Plotting on the Envelope Diagram (6)

Notice that the wt/CG dot has moved down and to the left. But, for a
well-designed aircraft, the dot should still remain within the envelope.
Flight Briefing: Lesson 12
What Happens In Flight?

Throughout a flight, the CG and weight constantly change. You must
ensure that at no time do they go outside of the loading envelope.
Flight Briefing: Lesson 12
Review Questions
1.
In what unit are each of the following quantities expressed?
a.
b.
c.
d.
e.
f.
g.
2.
3.
4.
5.
Arm
Moment
Center of gravity
Empty weight
Payload
Datum
CG ref. MAC
To determine moment, multiply ____________ by _____________
To determine CG, divide ______________ by ________________
What happens to weight and CG during flight?
When may the wt/bal dot extend outside the envelope?
Write down your answers before
continuing to next slide
Flight Briefing: Lesson 12
Review Answers
1.
In what unit are each of the following quantities expressed?
a.
b.
c.
d.
e.
f.
g.
2.
3.
4.
5.
Arm
Moment
Center of gravity
Empty weight
Payload
Datum
CG ref. MAC
inches
inch pounds
inches
pounds
pounds
unitless location
%
To determine moment, multiply _weight__ by ____arm____
To determine CG, divide _total moment_ by _total weight_
What happens to weight and CG during flight? weight decreases,
CG moves forward
When may the wt/bal dot extend outside the envelope? NEVER!
Review any missed questions before
continuing to today’s flight.
Flight Briefing: Lesson 12
Before Today’s Flight








Determine your weight, and your instructor’s
Measure fuel quantity and calculate fuel weight
Weigh whatever’s in the baggage compartments
Do a full Wt/Bal calculation, at takeoff weight
Estimate flight duration and fuel burn
Do another Wt/Bal calculation, at landing weight
Go over these figures with your instructor
Repeat before every Cross Country flight.
Flight Briefing: Lesson 12