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Weight and Balance

Weight and balance is something critical to airplane flight. Weight is pretty obvious – if you’re too heavy you may not get off the ground, or if you do you may find that you exceed the structural capabilities of the aircraft once you start flying.

Balance is equally important. The aircraft has a natural center of gravity. If you add a weight aft of the CG the tail will drop. If you add weight ahead of the CG, the nose will drop. This matters when flying. Nose low will mean more work when landing, while tail heavy could result in little room for the flare.

Additionally, balance factors in because 20 lbs. loaded at the center of gravity doesn’t weigh as much as 20 lbs. placed 45 inches aft of the CG once the plane starts climbing, banking and descending (think of holding a pail of water in one hand at your side, and then imagine holding it straight out from your body. The weight doesn’t change, but one way sure feels heavier than the other, right?

Every plane has a designated center of gravity, center of gravity arm, or station (they’re all the same thing). In my plane, a C-150L, the station is located at the firewall. They are measured in inches back (of forward, in the case of the oil) from the firewall. Loading Arrangements Cessna C-150L

Its easy to see in the diagram that the CG Arm for the pilot/passenger, for example, is on average 39, but can range from 35 to 41. Shorter legs, smaller Arm, longer legs, longer Arm. Similarly, baggage in Area 2 has an Arm of 84.

For the C-150 I use the Owner’s Manual and its weight and balance section. This approach actually ignores Arm altogether by plotting the weights on a chart that will then give you the moment. Moment at each station is what we want in order to calculate the W&B.
Weight and Balance Sample Problem Cessna C-150L

The sample loading problem shows the math. The licensed empty weight of the plane is 1,069 lbs. This figure is on the official W&B sheet (it starts at the factory and then is changed from time to time as equipment is added or taken out and the plane is re-weighed. My plane, for example, now weighs 1107.9 empty. Don’t use the sample weight. use your correct weight). The moment comes from the same sheet.

Oil weighs 11 lbs for 6 quarts, and because its forward of the CG it is assumed to have an arm of -0.1. The same thing happens with fuel. Because its always in the same station we can just take the number of gallons, multiply it by 6lbs for the weight, and use an arm of 5.7.

Those are the first three rows of the W&B worked out. Now comes the work. In the sample problem the pilot and passenger are assumed to weigh 340 lbs. In your case you can easily figure out the weight. What, however, is the arm, and what is the moment?

The C-150 POH has a handy graph to bypass the arm/moment calculation:
Weight and Balance Loading graph Cessna C-150

Follow the solid black line to the point where the 340 lb. weight line crosses it, and then go down to find the moment, which is 13.3. Simple, right?

What if you don’t have the graph, or, if you want to adjust the arm, as Note 1 suggests is possible? Simple. The relation between weight, arm and moment is (weight x arm)/ 1000. So, for the example weight you would multiply 340 by an arm of 39 (the center of the pilot/passenger area from the Loading Arrangements diagram) for 13,260, which you then divide by 1,000 to get 13.26 (which the POH rounds up to 13.3).

This would allow you to use a smaller arm if you were short, or a longer one if you were tall. You could customize your W&B for more accuracy. You could do it on a simple Excel spreadsheet, an iPhone app or on paper.

Once you’ve figured out the weight and moments for each station you can plot the Center of Gravity Moment for the full weight.
Weight and Balance Center of Gravity Moment Chart Cessna C-150

The sample problem weights total 1600 lbs. That’s max for this type of airplane, and note that you add, and do not subtract, the weight of the oil even though it has a -arm). Totaling the moments gives you 56.7. Those two co-ordinates are right on the envelope line, so we’re ok to fly at this weight (we’re within limits, as they say).

Next, we have to figure empty weight. That’s simple. Assume that you have no fuel and subtract that weight and that moment from the equation. The empty weight would now be 1,465 lbs. The moment would be 51. Again, those two co-ordinates put us right where we need to be.

Strictly speaking, you should calculate some residual fuel weight to be really accurate. Even if you ran dry of fuel in flight you wouldn’t get rid of all the fuel in the tanks, so you’d still be a bit heavier. Of course, you’d still be within limits.

What happens if you aren’t within limits? That depends on where you fall on the chart. Some planes have utility and normal categories, meaning that the CofG Moment Envelope has two areas – a narrower “utility” envelope and a wider “normal” envelope. If you are within the normal envelope but not inside the utility envelope you can still fly, but you are restricted in what sorts of manouvres you can do (no spins, for example). Some planes, however (like mine) have identical normal and utility envelopes. In this case, if you’re outside of the envelope you have to either reduce weight or move it around. In other words, if you’re too heavy you can reduce fuel (sometimes you’re just over, by say 6 pounds, and you can conclude that you’ll use a gallon of fuel in run up and taxiing), or reduce baggage. If your CoG is too far forward or too far aft you can move weght around. What you can’t do is fly outside the envelope for your plane.

My name is Rob Chipman and I’m a realtor, pilot and all around goof off based in Vancouver, BC. I really enjoy flying, real estate and the Chilcotin.¬† My company is¬†Coronet Realty Ltd., located at 3582 East Hastings Street, Vancouver, BC, V5K 2A7. I have a C-150L that I own with two other pilots, based out of Pitt Meadows. Do not hesitate to contact me by email if I can help you do anything, especially if its likely to be interesting.

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