Pilot's Handbook of Aeronautical Knowledge
Preface
Acknowledgements
Table of Contents
Chapter 1, Introduction To Flying
Chapter 2, Aircraft Structure
Chapter 3, Principles of Flight
Chapter 4, Aerodynamics of Flight
Chapter 5,
Flight Controls
Chapter 6,
Aircraft Systems
Chapter 7,
Flight Instruments
Chapter 8, Flight Manuals and Other Documents
Chapter 9,
Weight and Balance
Chapter 10, Aircraft Performance
Chapter 11, Weather Theory
Chapter 12,
Aviation Weather Services
Chapter 13,
Airport Operation
Chapter 14,
Airspace
Chapter 15, Navigation
Chapter 16, Aeromedical Factors
Chapter 17, Aeronautical Decision Making
Appendix
Glossary
Index 
Computations With a Negative Arm
Figure 910 is a sample of weight and balance computation
using an airplane with a negative arm. It is important to
remember that a positive times a negative equals a negative,
and a negative would be subtracted from the total moments.
Figure 910. Sample weight and balance using a negative.
Computations With Zero Fuel Weight
Figure 911 is a sample of weight and balance computation
using an aircraft with a zero fuel weight. In this example,
the total weight of the aircraft less fuel is 4,240 pounds,
which is under the zero fuel weight of 4,400 pounds. If the
total weight of the aircraft without fuel had exceeded 4,400
pounds, passengers or cargo would have needed to be reduced
to bring the weight at or below the max zero fuel weight.
.
Figure 911. Sample weight and balance using an aircraft with a
published zero fuel weight. 
Shifting, Adding, and Removing Weight
A pilot must be able to solve any problems accurately that
involve the shift, addition, or removal of weight. For example,
the pilot may load the aircraft within the allowable takeoff
weight limit, then find a CG limit has been exceeded. The
most satisfactory solution to this problem is to shift baggage,
passengers, or both. The pilot should be able to determine
the minimum load shift needed to make the aircraft safe for
flight Pilots should be able to determine if shifting a load to
a new location will correct an outoflimit condition. There
are some standardized calculations that can help make these
determinations.
Weight Shifting
When weight is shifted from one location to another, the
total weight of the aircraft is unchanged. The total moments,
however, do change in relation and proportion to the
direction and distance the weight is moved. When weight is
moved forward, the total moments decrease; when weight
is moved aft, total moments increase. The moment change
is proportional to the amount of weight moved. Since many
aircraft have forward and aft baggage compartments, weight
may be shifted from one to the other to change the CG. If
starting with a known aircraft weight, CG, and total moments,
calculate the new CG (after the weight shift) by dividing the
new total moments by the total aircraft weight.
To determine the new total moments, find out how many
moments are gained or lost when the weight is shifted.
Assume that 100 pounds has been shifted from station 30 to
station 150. This movement increases the total moments of
the aircraft by 12,000 inlb.
Moment when
at station 150 = 100 lb x 150 in = 15,000 inlb
Moment when
at station 30 = 100 lb x 30 in = 3,000 inlb
Moment change = [15,000  3,000] = 12,000 inlb
By adding the moment change to the original moment (or
subtracting if the weight has been moved forward instead of
aft), the new total moments are obtained. Then determine the
new CG by dividing the new moments by the total weight:
Total moments =
616,000 inlb + 12,000 inlb = 628,000 inlb
CG = 628,000 inlb = 78.5 in
8,000 lb
The shift has caused the CG to shift to station 78.5. 
