Wednesday, November 26, 2008

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.

Dispatcher said...

Looking forward to the coming post on balance.

I deal with some Canadian airlines in work, one in particular has standard summer and winter weights for passengers of Canadian origin, but also another year round standard for UK passengers although the standard bag weight is the same.

Anonymous said...

Having been on a lot of commercial/charter flights in the past, I have a hard time imagining how they came up with the 187lb standard male figure. Seems like all you'd need to get is a few guys carrying around the last few cases of beer they drank (or worse) and that'd be woefully inadequate. Maybe that's just in the US though. ;-)

How do large commercial carriers do it? If you have 200-300 pax on a plane, how can you know in advance how much they'll weigh aside from guessing? Does the gear have some functionality built in to give the pilot a heads up so that he can have the ground crew shift/remove cargo to account for an unusually large number of unusually large people sitting in the aft? Or are the tolerances on large turbine aircraft loose enough that they can wing it with an estimate? (no pun intended)

This is very interesting though - thanks for posting it. I read a lot of NTSB reports and it's amazing how often W&B (or lack thereof) kills people. An entire family died in a GA accident a few years back about five miles from where I live in part due to a lack of planning in that respect (many other things also went wrong as is often the case).

hawk205 said...

you did not mention the A/C empty weight and CG for US registered A/C should be be found on the latest 337 form.

Aviatrix said...

Anon 08:29 PM: Passenger weight numbers actually used by various airlines depend on their individual agreements between the airlines and their respective transport authorities. An airline operating solely on the BC coast gets permission to use summer weights year round, because who wears a parka and heavy boots in Nanaimo? Some US airlines use a single standard passenger weight for males and females. I think JetBlue has their own weight based on a survey of their own passengers. E-mail me what you do for passenger weights at your airline and I'll collect them up and do a post on that.

hawk205: that's because this is a Canadian blog, and I fly Canadian registered aircraft that have W&B documents, not 337 forms.

Christopher said...

Here are some links to Canadian guidance documents and safety board information:

A04H0001 - Interim Aviation Safety Recommendations
Standard Passenger Weights - Use and Validity of Standard Values

AC 0235R - Air Operator Weight and Balance Control Procedures
Subparts 703/704/705 of the Canadian Aviation Regulations

Also, there are proposed changes to the regulations in the works to address the issue of adequate W&B calcuations following a number of accidents. Here is the proposal for the Canadian air taxi segment of the industry (703 of the CARs):

NPA 2008-058 - Weight and Balance Control (Aeroplanes)

Aviatrix said...

The first two documents Christopher mentions were mostly superseded by the CARs when the proposals were implemented, but the third introduces a new idea. It's not the sort of calculation you want to be doing on the back of your OFP during boarding, but it's interesting. I'll have to read it over a couple of times and perhaps blog on it after I've digested it.

Anonymous said...

All passengers were weighed on Maverick Helicopters Grand Canyon tours last June...I suspect this is quite standard for helicopter tours.
Also the last arriving passengers were weighed for Air Tahiti's flight from Bora Bora to Papeete last week. Air Tahiti used a
ATR 72-500 on this route.

Jim said...

After a Beech 1900 went down in the US (dual causes - CoG was aft, and the elevator cables were mis-adjusted so full nose-up authority was not available), the TSB recommended a re-evaluation of standard weights used. Among other research, the report noted that some 5,000+ individuals were weighed at Heathrow, as well as their gender and category (adult/child/infant). The standard weights in use in the USA were low.

Also, as Dave (Fl390) notes - sometimes they count bodies, sometimes (when near the limit) they count men, women and children separately.

Anon 8:29 - It's all done with averages, hopefully intelligently applied ones (see comment wrt football teams). Statistically, the more individuals you have in your aircraft, the better the averages work. If your sample size is small (4 people in a C172), then a variance in one indivual has a much larger effect on the overall calculation.

Airplanes will fly when our of range on CoG, or when over-weight. It isn't legal when you fly them that way, things can go horribly wrong if you get towards the edges of the flight envelope, recovery is not assured in upset situations, and performance will not be as good... but it isn't like you're 10 pounds overweight and then the wings fall off and the undercarriage comes up through the floorboards.

Unknown said...

Dear Sir / Ms,

My company submitted a PCT patent application related to accurate preflight determination of passenger's weight in civil aviation (PCT Patent Application No. PCT/IL2009/000463, Based on Provisional Application filed in the U.S.A No. 61/050,258 filed on 5 May, 2008)

filed in the U.S.A No. 12/434,692 on 4 May, 2009). This system and method integrates the following advantages:

Increasing airline profits

1. Quantity of fuel loaded on an aircraft essentially derives from its overall weight. Accurate determination of passenger's weight allows decreasing this quantity whenever the passenger's actual weight is lower than the predicted average. The resultants weight reduction decreases fuel consumption during the flight.

2. Processing passenger's weight prior to flight enables to control their sitting distribution / location, controls the desired center of gravity (C.G). Controlling C.G improves aircraft range and endurance performance.

3. In flights when passenger's actual weight is lower than the predicted average, alternative freight or mail could be carried by the airline, allowing increased profit.

Safety improvement

4. Accurate determination of both weight and C.G improves crew and aircraft performance on diverse emergencies.

We apply for a patent related to any weight of passengers information being electronically transferred (via internet / travel offices, ext).
Entering the "weight" value is a must precondition / will allow ticket to be issued (failing to do so may prevent insurance...safety issue).
Real measuring / validation may be required from a time to time - to fortify the data collected
Lots of business potential!. It is estimate that the combination of optimizing aft C.G location (derived from knowing who will seat were) & decreasing fuel quantities carried + carrying fright (when passengers weight is lower than average) reveals xxx\$ to xxxx\$ increase profit in every single large jet flight.

My company intends to commercialize the technology and the patents.

Sincerely yours,

FAR Technologies Ltd.

Israel
Mobile: 972-54-2512138
E-mail: info@fartechnologies.com
WebSite: http://www.fartechnologies.com

Unknown said...

Dear Sir / Ms,

My company submitted a PCT patent application related to accurate preflight determination of passenger's weight in civil aviation (PCT/IL2009/000463 ) . The application was published on 5 November, 2009, and was assigned publication number US 2009-0276267 A1 .

This system and method integrates the following advantages:

Increasing airline profits

1. Quantity of fuel loaded on an aircraft essentially derives from its overall weight. Accurate determination of passenger's weight allows decreasing this quantity whenever the passenger's actual weight is lower than the predicted average. The resultants weight reduction decreases fuel consumption during the flight.

2. Processing passenger's weight prior to flight enables to control their sitting distribution / location, controls the desired center of gravity (C.G). Controlling C.G improves aircraft range and endurance performance.

3. In flights when passenger's actual weight is lower than the predicted average, alternative freight or mail could be carried by the airline, allowing increased profit.

Safety improvement

4. Accurate determination of both weight and C.G improves crew and aircraft performance on diverse emergencies.

We apply for a patent related to any weight of passengers information being electronically transferred (via internet / travel offices, ext).
Entering the "weight" value is a must precondition / will allow ticket to be issued (failing to do so may prevent insurance...safety issue).
Real measuring / validation may be required from a time to time - to fortify the data collected
Lots of business potential!. It is estimate that the combination of optimizing aft C.G location (derived from knowing who will seat were) & decreasing fuel quantities carried + carrying fright (when passengers weight is lower than average) reveals xxx\$ to xxxx\$ increase profit in every single large jet flight.

My company intends to commercialize the technology and the patents.

Sincerely yours,