WEIGHT AND BALANCE CALCULATIONS FOR
PHANTOM X-1 AND X-1E
Figure 1 – Side View of the Ultralight
WARNING: Do not use the exact numbers
calculated here. Each aircraft is different depending on the location
instruments, parachute, and other items that are selected by the builder. A
customized weight and balance table should be implemented for each individual aircraft.
STEP 1 – Calculation of
the Aircraft Empty Weight and Empty Weight Moment Arm
The first step in calculating the weight and balance for your aircraft is determining the empty weight and empty weight moment arm. You will need a tape measure, a roll of masking tape, a plumb bob and a scale to measure the weight of your aircraft. Three scales are ideal; however this can be completed with one scale and pieces of wood that are exactly the same height as the scale. First measure the distance ‘A’ shown in Figure 1. This is the distance from the nose of the aircraft (datum) to the axle on the front nose gear. This is the moment arm for the nose gear. Next measure the distance ‘B’ shown in Figure 1. This is the distance from the datum to the axle on the main gear. Next measure the distance ‘C’ shown in Figure 1. This is the distance from the datum to the leading edge of the wing. Finally measure the distance ‘D’ shown in Figure 1. This is the chord length of the wing and is typically 64” for the Phantom X-1 and X-1E. To make measuring these distances easy the plumb bob is used to transfer the location of the nose leading edge, front axle, main axle and wing leading edge to the floor of your hangar. Mark the location of these on a piece of masking tape attached to the floor and measure the distance between the marks on the floor. All measurements should be made in inches.
Next measure the weight of the aircraft. First place the scales under each wheel and record the weight at each wheel. If you have only one scale you will need to move the scale around to obtain the weight at each wheel. Make sure that you put your pieces of wood under the wheels without the scale to keep the aircraft level. The measurements will be incorrect if the aircraft is not level. These measurements should be taken without the pilot or fuel in the aircraft.
Next calculate the Empty Weight of the aircraft:
Empty Weight = Nose Gear Weight + Left Main Weight + Right Main Weight
Next calculate the Moment Arm (MA):
MA = 
Typically the moment arm is referenced to the leading edge of the wing. A good center of gravity location is at 25% of chord of the wing. To determine the Empty Weight Moment Arm (EWMA) from the leading edge of the wing use the following formula:
EWMA = MA – Distance C
To determine the % location of the wing chord use the following formula:
CG % Wing Chord = 
A sample Calculation Table is shown below.
The Empty Weight Moment Arm and the Empty Weight are the important numbers to record and remember from this calculation.
STEP
2 – Calculation of the Pilot Moment Arm
You will need the Empty Weight, Empty Weight Moment Arm, Distances A, B, and C.
First measure the weight of the pilot using the scale.
Next have the pilot sit in the aircraft and measure the weight of the aircraft at the nose gear and each of the main gear just as you had before. Record these new weights and use them in the equation below calculate the pilots moment arm.
Moment Arm =
Pilot Moment Arm = Moment Arm - C
STEP
3 – Calculation of the Fuel Moment Arm
You will need the Empty Weight, Empty Weight Moment Arm, Distances A, B, and C.
First calculate the weight of the fuel. Fuel weighs 6 pound per gallon, thus a 5 gallon tank of fuel weighs 30 pounds. Fill the fuel tanks.
Next measure the weight of the aircraft at the nose gear and each of the main gear just as you had before. Record these new weights and use them in the equation below calculate the fuel moment arm.
Moment Arm =
Fuel Moment Arm = Moment Arm – C
You are now ready to calculate the flying configuration weight and balance.
STEP 4 – Overall Weight
and Balance
The aircraft weight and balance should be calculated every flight to ensure that it is in the proper location. If the center of gravity is to far forward the elevator stick forces can be high and it may be impossible to properly flare the aircraft in landing. It may also be impossible to get the aircraft off the ground. If the center of gravity is to far back the stick forces will be very light and the aircraft will be very sensitive to the control inputs. It will be very easy to lose control of the aircraft. The wing may stall and could put the aircraft in an uncontrollable spin.
Aircraft Center of Gravity = Total Moment / Gross Weight
The aircraft CG
should fall between 18.0625 inches and 26.0625 inches.
SAMPLE WEIGHT AND BALANCE TABLE
|
ITEM |
MOMENT ARM |
WEIGHT |
MOMENT |
|
Empty Aircraft |
16.82 inches |
250 lbs |
4205 in - lbs |
|
Pilot |
21 inches |
180 lbs |
3780 in - lbs |
|
Fuel |
22.9 inches |
30 lbs (5 gallons) |
687 in – lbs |
|
|
|
450 lbs |
8672 in – lbs |
|
|
|
GROSS WEIGHT |
TOTAL MOMENT |
|
|
|
|
|
|
AIRCRAFT CG |
18.85 inches |
|
|
WARNING: Do not use the numbers calculated here. Each
aircraft is different depending on the location instruments, parachute, and
other items that are selected by the builder. A customized weight and balance
table should be implemented for each aircraft.
WEIGHT AND BALANCE
Aircraft _____________________ Date _____________________
Pilot Name _____________________ Pilot Weight _____________________
|
ITEM |
MOMENT ARM |
WEIGHT |
MOMENT |
|
Empty Aircraft |
|
|
|
|
Pilot |
|
|
|
|
Fuel |
|
|
|
|
|
|
|
|
|
|
|
GROSS WEIGHT |
TOTAL MOMENT |
|
|
|
|
|
|
AIRCRAFT CG |
|
|
|
CG Limits: Forward Limit = 18.0625inches; Aft Limit = 26.0625 inches
Maximum Gross Weight = 570 pounds