As a pilot you should always expect change. Change can often occur prior to your flight even beginning. I’ve been in situations before where I have completed my entire cross country flight plan and weight and balance only to find out another friend wants to come along for the ride. Before doing another entire weight and balance problem you should know about a few quick tricks.
Find a few more of these types of tricks in Mental Math for Pilots, and an example of fuel planning can be found in Mental Math for Pilots: Fuel Planning Made Easy.
Weight Shift
Whenever weight is either added to or subtracted from a loaded airplane, both the gross weight and the center of gravity (CG) location will change. The solution to such a calculation is really a simplified loading problem. Instead of calculating a weight and moment for every section of the aircraft, it is only necessary to compute the original weight and moment—then, the effect of the change in weight.
For example, if an aircraft’s total weight was 8,600 pounds, and you shifted 100 pounds from station (or, arm) 100 to arm 150, a simple weight shift formula can be applied:
This is solved easily by cross-multiplying: 50 x 100 ÷ 8,600 = .06 inches. Therefore, the CG shifts .06 inches aft.
Weight Change
Use the following formula to find the change in CG, if weight has been added or subtracted. The amount of weight changed and the new total weight must be known, in addition to the distance between the original CG and the point where the weight is being added or subtracted.
You can also use this formula to determine your new CG after fuel burn. Here is an example.
Problem:
Determine the new CG location after 1 hour 45 minutes of flight time, given the following:
Total weight: 4,037 lbs
CG location Station: 67.8
Fuel consumption: 14.7 GPH
Fuel CG Station: 68.0
Solution:
- Find the amount of weight change. The aircraft has consumed 14.7 GPH for 1 hour 45 minutes. The total fuel consumed is:
14.7 GPH x 1.75 hr = 25.7 gal
Which weighs:
25.7 gal x 6 lbs/gal = 154 lbs
- Determine the new total weight by subtracting the weight of the fuel consumed (154 lbs) from the total weight (4,037 lbs):
4,037 – 154 = 3,883 lbs new total weight
- Find the distance between the original CG (67.8) and the point weight removed (fuel CG = 68.0):
68.0 – 67.8 = 0.2 inches
- Place the three known values into the formula:
154 lbs. / 3,883 lbs. = Change in CG / 0.2 in
Change in CG = 154 lbs. x 0.2 in / 3,883 lbs. = 0.01 in
- The CG was found to shift approximately 0.01 in. Since the weight was removed aft (68.0 in) of the CG (67.8 in), the CG shifted forward 0.01 in.
67.80 (original CG) – 0.01 (forward shift) = 67.79 (new CG)
