Expert: James Bell - 9/25/2007

Question
Hello James,
I am very impressed about your wide knowledge about all these different subjects. I was wondering if you could help me with some formulas used regarding weight and balance. Anything will help since I am about to take the big jump into the Herc-world!! Thanks in advance
Best regards Belinda

Answer
Greetings Belinda -

I had to look back through previous answers, as I had a nice one with math formulas.  It was posted on May 5, 2006 to Michael.  Anyway, here you go ...

I'll give you the basic formula that will guide ALL your weight and balance lessons (referred to as the WAM formula): W*A=M.  W is weight.  A is arm (a specified distance).  M is moment.  Weight, times a distance, will generate a moment.  Think of it as similar to foot pounds of torque.

Quick example -

You have a board resting on a pivot point (like a teeter totter).  On one end you place a 10 pound weight, 30 inches from the balance point.  How far would you need to place a 5 pound weight on the other side to balance the beam?

10 pounds * 30 inches = 300 moments.  So you need to have a 5 pound weight generate 300 moments on the other side.  300 / 5 = 60.  So, a 5 pound weight placed 60 inches from the balance point will equal the force generated by a 10 pound weight placed 30 inches in the opposite direction.

Airplanes aren't balanced from a central point, but from what's call an RDL (reference datum line).  This is a point in front of the aircraft from which all distances are measured.  These distances are often referred to as stations.  Station 500 would be 500 inches from the reference datum line.

Another example: You have a two axled vehicle that weighs 5000 pounds.  The front axle weighs 3000 pounds and the rear axle weighs 2000 pounds.  The wheelbase of the vehicle is 100 inches, and the RDL is 25 inches in front of the front axle.  Where is the center of gravity (CG) of the vehicle?

Moments for the front axle -
25 * 3000 = 75000

Moments for the rear axle -
Distance from RDL to rear axle = 25 + 100 = 125
125 * 2000 = 250000

Total moments = 325000

Now you run the WAM formula in reverse.  You need to find out the arm for the CG.  You know the moments and weight, now find the arm ... 325000 / 5000 = 65

The center of gravity of the vehicle is 65 inches from the RDL, or 40 inches behind the front wheel, and 60 inches in front of the rear wheel.

General information about cargo aircraft.  A basic C-5 weighs 350,000 lbs.  A C-130 weighs 150,000 lbs.  A KC-10 weighs 250,000 lbs.  Because weights that huge over such long distances generate HUGE moments, we use what's called SIMPLIFIED moments.  The C-5 simplified its moments by 100,000.  This means you simply lop off the last five digits of the moments.

A 2500 pound pallet at station 1428 generates 3570000 moments, or 35.7 simplified moments.

And the lesson can go on and on.  But, I've given you an idea of what you are getting into.  Believe me, it gets easy with a little practice and it will be second nature to you in just a few short months of training.  I haven't done serious loadmaster work since 1987, but it came back to me with a little thought.

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Here is one for you to figure out:  You have a three axled vehicle.

RDL is 55 inches from the front axle
Distance between first (front) and second axle is 180 inches.
Distance between second and third axle is 45 inches.
Each axle weighs 2500 pounds.
How far is the center of gravity from the RDL?

Sincerely,
James Bell
(who isn't going to tell you the answer is 190)