Weight Calculations

This is the first of a two-part post on calculating weight and balance of a loaded aircraft, as eighty percent of private pilots are purported not to know how to do. I promised a while ago to explain, and it turns out that a post a few days hence requires some understanding of the subject, so now is the perfect time. Today I'll look at weight, the easy part. Tomorrow's post will look at balance, which really isn't all that complicated. I just got carried away and wrote too much to swallow in one bite.

Aircraft have published maximum weights. There may be a separate maximum ramp weight (how much the loaded airplane may weigh just to sit there on its wheels and taxi around), maximum take-off weight (what it says), maximum zero fuel weight (effectively requiring a certain proportion of the weight to be in the fuel tanks, bending the wings down, as opposed to being in the fuselage, where it bends the wings up), and maximum landing weight (what it says). Depending on the type of operation, those weights may change depending on the temperature and available runway. For safe, legal flight the airplane must be under each of these weight requirements for the appropriate stage of flight.

To find the total weight, you must know the weights of the various components. One of the documents belonging to an individual airplane will state how much the airplane alone weighs. Yep, someone had to weigh it. When they add or change equipment they don't have to re-weigh it, though. They can just do the math. So if you take out a basic 20 lb seat and replace it with a deluxe 35 pound seat, you increase the basic empty weight by fifteen pounds. The BEW includes the airplane, the engines, the seats, the avionics, everything that is installed in the airplane and also full hydraulic fluid and the like. It usually includes full oil but there are exceptions, so you need to examine your paperwork carefully. It even includes what's called the unusable fuel: the fuel that could be left sloshing around in the bottom of the tanks if you were to run the engine until it stopped from fuel starvation, in some reasonable flight attitude. You read the empty weight of the airplane off the weight and balance (W&B) document, make any adjustments written in the journey log, and write down that number.

A commercial airplane may be dispatched with a Standard Operating Weight, which is the basic empty weight of the airplane plus the weight of the crew and their personal equipment. Sometimes the SOW is calculated and written in the journey log book as if the crew are both males, so that when one of more of the crew is female, the weight can be adjusted, to carry an extra thirty pounds of fuel. If the airplane doesn't list a standard operating weight, the crew and their gear are counted along with the passengers. It doesn't matter which way, so long as it adds up, and complies with what the regulatory authorities have approved if it's a commercial operation.

Next you add fuel. The usable fuel is the fuel the manufacturer says is available for your use in all normal flight attitudes. Avgas weighs six pounds per U.S. gallon and jet fuel weighs about seven. These weights vary with the temperature and exact grade, and you can use a table to work out the weight for the volume of fuel you will have in the tanks. (The numbers I'm quoting are in American units because the airplanes I fly were built in the US and so the operating manual lists weights and fuel volumes that way. If you buy a new Airbus (or even Boeing for delivery outside the US) I'm sure you can get the documentation in kilograms and litres.

The remaining weight on board will be cargo and passengers. Cargo is weighed, as you know from checking baggage at the airport. Some charter operations have a big floor scale and simply ask all the passengers to stand on it with their cargo. "You're 200 lbs over," the boss says. It's up to the customer to decide whom or what to leave behind. In a remote charter operation, the pilot may estimate and mentally sum the weights of articles loaded. I've also done it by standing on a bathroom scale as I lifted each bag and subtracting my weight from each reading in order to add up the total weight on board. Some pilots carry a handheld spring-based scale, which works if every article has a handle or other point that the scale can hook onto. You lift the scale with the hook holding the item, and extension of the spring moves a pointer indicating the weight of the item.

Passengers are rarely physically weighed but may be asked for their weights, estimated by the pilot or dispatcher, or counted at standard weights, depending on the operation. In Canada, standard weights count clothed females at 165 lbs and males at 200 lbs each. Everyone is assumed to weigh six pounds more in the winter, and the weights include a 13 lb carry on. A charter operator that weighs all baggage as cargo, and thus has no uncounted carryons can count men at 187 lbs, but a pilot flying a charter for the Toronto Argonauts football team is expected to apply reasonable weights for football players, not just use the defaults.

Once numbers for the airplane, people, bags and fuel have been obtained, you just add them up. If the total is over the maximum then you can load less fuel (but not less than the legal minimum), or leave passengers or cargo behind. Once the weight is within limits, so far so good, but you must make sure that the airplane will also be loaded within balance limits. That's tomorrow's posting. Because, as I mentioned, I got carried away.