Introduction
Almost all weight and balance problems involve only simple
math. This allows slide rules and hand-held electronic
calculators to relieve much of the tedium involved with these
problems. This chapter compares the methods of determining
the center of gravity (CG) of an airplane while it is being
weighed. First, it shows how to determine the CG using a
simple electronic calculator, then solves the same problem
using an E6-B flight computer. Finally, it shows how to solve
it using a dedicated electronic flight computer
Use of Computer for Weight
and Balance Computations
Chapter 10
Figure 10-2. Weight and balance data of a typical nosewheel
airplane.
Weighing Point Weight (lb) Arm (in)
0
0
–78
830
836
340
2,006
Right side
Left side
Nose
Total
Figure 10-1. A typical electronic calculator is useful for solving
most types of weight and balance problems.
Examples of typical weight and balance problems (solved
with an electronic calculator) that pilots and airframe and
powerplant (A&P) maintenance technicians encounter
throughout their aviation endeavors are shown later in this
chapter.
Electronic Calculator
Determining the CG of an airplane in inches for the main-
wheel weighing points can be done with any simple electronic
calculator that has addition (+), subtraction (–), multiplication
(×), and division (÷) functions. [Figure 10-1] Scientifi
calculators with such additional functions as memory (M),
parentheses (( )), plus or minus (+/–), exponential (y x),
reciprocal (1/x), and percentage (%) functions allow more
complex problems to be solved or simple problems to be
solved using fewer steps.
According to Figure 10-2, the weight of the nosewheel (F) is
340 pounds, the distance between main wheels and nosewheel
(L) is –78 inches, and the total weight (W) of the airplane is
2,006 pounds. L is negative because the nosewheel is ahead
of the main wheels.
To determine the CG, use this formula:
CG = F × L
W
= 340 × –78
2,006
Key the data into the calculator and press the equal (=) key.
The answer should read as follows:
(340)(×)(78)(+/–)(÷)(2006)(=) –13.2
The arm of the nosewheel is negative, so the CG is –13.2 or
13.2 inches ahead of the main wheel weighing points.
E6-B Flight Computer
The E6-B uses a special kind of slide rule. Instead of its scales
going from 1 to 10, as on a normal slide rule, both scales
go from 10 to 100. The E6-B cannot be used for addition or
subtraction, but it is useful for making calculations involving
multiplication and division. Its accuracy is limited, but it is
sufficiently accurate for most weight and balance problems.
The same problem that was just solved with the electronic
calculator can be solved on an E6-B by following these steps:
CG = F × L
W
= 340 × –78
2,006
First, multiply 340 by 78 (disregard the minus sign)
[Figure 10-3]:
• Step 1—place 10 on the inner scale (this is the index
opposite 34 on the outer scale that represents 340).
• Step 2—opposite 78 on the inner scale, read 26.5 on
the outer scale.
Determine the value of these digits by estimating:
300 × 80 = 24,000, so 340 × 78 = 26,500.
Then, divide 26,500 by 2,006 [Figure 10-4]:
Figure 10-3. E6-B computer set up to multiply 340 by 78.
Figure 10-4. E6-B computer set up to divide 26,500 by 2,006.
Step 2
Step 1
Step 4
Step 3
Figure 10-5. Dedicated electronic flight computers are programmed
to solve weight and balance problems, as well as flight problems.
• Step 3—on the inner scale, place 20, which represents
2,006 opposite 26.5 on the outer scale (26.5 represents
26,500).
• Step 4—opposite the index, 10, on the inner scale read
13.2 on the outer scale.
Determine the value of 13.2 by estimating:
20,000 ÷ 2000 = 10, so 26,500 ÷ 2,006 = 13.2.
The arm (–78) is negative, so the CG is also negative.
The CG is –13.2 inches or 13.2 inches ahead of the datum.
Dedicated Electronic Flight Computer
Dedicated electronic flight computers, like the one in
Figure 10-5, are programmed to solve many flight problems
such as wind correction, heading and ground speed,
endurance, and true airspeed (TAS), as well as weight and
balance problems.
The problem just solved with an electronic calculator and
an E6-B can also be solved with a dedicated flight computer
using the information shown in Figure 10-2 . Each fligh
computer handles the problems in a slightly different way,
but all are programmed with prompts that solicit the required
data to be inputted so there is no need to memorize any
formulas. Weight and arms are inputted as called for, and a
running total of the weight, moment, and CG are displayed.
Typical Weight and Balance Problems
A hand-held electronic calculator like the one in Figure 10-5
is a valuable tool for solving weight and balance problems. It
can be used for a variety of problems and has a high degree
of accuracy. The examples given here are solved with a
calculator using only the (×),(÷),(+),( – ), and (+/–) functions.
If other functions are available on your calculator, some of
the steps may be simplified
Determining CG in Inches From the Datum
This type of problem is solved by firs determining the
location of the CG in inches from the main wheel weighing
points, then measuring this location in inches from the datum.
There are four types of problems involving the location of
the CG relative to the datum.
Nosewheel Airplane With Datum Ahead of the
Main Wheels
The datum (D) is 128 inches ahead of the main wheel
weighing points; the weight of the nosewheel (F) is 340
pounds, and the distance between main wheels and nosewheel
(L) is 78 inches. The total weight (W) of the airplane is 2,006
pounds. Refer to Figure 3-5 on page 3-5.
Use this formula:
CG = D – F × L
W
1. Determine the CG in inches from the main wheel:
(340)(×)(78)(÷)(2006)(=) 13.2
2. Determine the CG in inches form the datum:
(128)(–)(13.2)(=) 114.8
The CG is 114.8 inches behind the datum.
Nosewheel Airplane With Datum Behind the Main
Wheels
The datum (D) is 75 inches behind the main wheel weighing
points, the weight of the nosewheel (F) is 340 pounds, and
the distance between main wheels and nosewheel (L) is 78
inches. The total weight (W) of the airplane is 2,006 pounds.
Refer to Figure 3-6 on page 3-5.
Use this formula:
CG = – D + F × L
W
1. Determine the CG in inches from the main wheels:
(340)(×)(78)(÷)(2006)(=) 13.2
2. Determine the CG in inches from the datum:
(75)(+)(13.2)(=) 88.2
The minus sign before the parenthesis in the formula
means the answer is negative. The CG is 88.2 inches
ahead of the datum (–88.2).
Tailwheel Airplane With Datum Ahead of the Main
Wheels
The datum (D) is 7.5 inches ahead of the main wheel
weighing points, the weight of the tailwheel (R) is 67 pounds,
and the distance between main wheels and tailwheel (L) is
222 inches. The total weight (W) of the airplane is 1,218
pounds. Refer to Figure 3-7 on page 3-6.
Use this formula:
CG = D + R × L
W
1. Determine the CG in inches from the main wheels.
(67)(×)(222)(÷)(1218)(=) 12.2
2. Determine the CG in inches from the datum:
(7.5)(+)(12.2)(=) 19.7
The CG is 19.7 inches behind the datum.
Tailwheel Airplane With Datum Behind the Main
Wheels
The datum (D) is 80 inches behind the main wheel weighing
points, the weight of the tailwheel (R) is 67 pounds, and the
distance between main wheels and tailwheel (L) is 222 inches.
The total weight (W) of the airplane is 1,218 pounds. Refer
to Figure 3-8 on page 3-6.
Use this formula:
CG = –D + R × L
W
1. Determine the CG in inches from the main wheels:
(67)(×)(222)(÷)(1218)(=) 12.2
2. Determine the CG in inches from the datum:
(80)(+/–)(+)(12.2)(=) –67.8
The CG is 67.8 inches ahead of the datum.
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