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Weight and Balance (A Sensual Approach)

Flight Engineering

Weight and balance tends to be a math intensive subject and you should understand the principles: Weight and Balance Principles. Because some airplanes are more sensitive than others and even those that are center-of-gravity-sensitive tend to be okay most of the time, we tend to let our guards down on this subject. That is too bad, because getting weight and balance wrong can be deadly. (See CL-600 N370V.)

Even if you aren't a math wizard, having a "feel" for weight and balance can come in handy. If you can visualize where on your airplane the center of gravity resides, the forward and aft limits of your center of gravity, and how the seats and fuel tanks all relate to those points, you will have the skills you need to approach your weight and balance sensually. Sensually? Yes: weight and balance by feel.


 

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Photo: The center of gravity on Eddie's aircraft.
Do you know where your CG resides?

  • Balance — Center of gravity management is all about keeping the airplane in balance. If you think of balancing the airplane on a pyramid, you will know what you need to know about what comes next.
  • Limits — The limits of your longitudinal center of gravity are determined by where exactly the airplane's center of lift resides and how much elevator authority you really have. The manufacturer gives these numbers to you in terms of a percentage of the mean aerodynamic chord, but what does that really mean? There is an easier way.
  • Sensitivity — Not all airplanes are created equal and when it comes to weight and balance, you have to worry more about some than others. Knowing your airplane's "center-of-gravity-sensitivity" will help you focus on the most important issues.
  • Impacts — Your center of gravity will be impacted by where on the aircraft you have stored fuel, cargo (baggage), and people. When these things move around, so does the center of gravity. Understanding where the CG moves is key to having a feel for your airplane's weight and balance.
  • Legal Issues — You need to know what the Fed has to say about this, it could affect your license.

Balance

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If you could place the airplane on a point so that it remains level, you will have found the center of gravity for that airplane as currently loaded.

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With any kind of relative wind over the wing you will have an aerodynamic force which can be broken into two components. The component that operates perpendicular to the relative wind is known as lift. Just as you can visualize the airplane's center of gravity going through one point along the fuselage, you can also visualize all of the lift generated in an upward direction as the "center of lift." An airplane with a conventional layout — wing in the middle, tail in the back — the center of lift will be behind the center of gravity.

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Of course having the center of lift behind the center of gravity induces a pitch down moment. We counteract that moment with a downward force from the tail. You might think the ideal arrangement would be to have the center of lift precisely over the center of gravity and have no tail at all. This would work in theory until any kind of movement within the aircraft moves the center of gravity. The tail is necessary to compensate for these movements and to give the pilot some pitch control over the airplane.

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If we replace our balancing pyramid with a graphical representation of our center of gravity, we will have the classic illustration of the weight and balance problem. Our task as pilots is to always keep the center of gravity forward of the center of lift, but not so far forward that we overwhelm the amount of downward force available from the tail.

In the example center of gravity chart, we see our G450 has an aft limit of 45% MAC and a forward limit of 36% MAC. In the case of a takeoff problem, we know that too far aft will mean the nose will rotate on its own and we won't be able to keep the airplane from pitching up regardless of our inputs, and too far forward we won't be able to rotate at all. But where exactly are these points?

Limits

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The limits of your longitudinal center of gravity are determined by where exactly the airplane's center of lift resides and how much elevator authority you really have. The manufacturer gives these numbers to you in terms of a percentage of the mean aerodynamic chord, but what does that really mean?

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The MAC is the "Mean Aerodynamic Chord" of the wing. The chord is simply a line drawn from the leading edge of the wing to the trailing edge. Of course most aircraft have wings that change shape from the fuselage outward to the wing tip. The mean aerodynamic chord is an average of all the chord lines from root to tip.

For more about this, see Lift.

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We can better visualize the limits of our center of gravity by looking at a bird's eye view of the aircraft.

Gulfstream chose a reference point 4" forward of the nose and all manufacturing measurements take place from this imaginary point. They then drew a horizontal reference datum 72" behind that. In the case of our G450:

  • The Leading Edge of the Mean Aerodynamic Chord (LEMAC) is 387.7" aft of the horizontal datum.
  • The Trailing Edge of the Mean Aerodynamic Chord (TEMAC) is 166.22" aft of the LEMAC.
  • The forward limit of our CG is 36% of the MAC, or 59.84" behind LEMAC.
  • The aft limit of our CG is 45% of the MAC, or 74.80" behind LEMAC.
  • The distance between the forward and aft limit is 74.80 - 59.84 = 14.96".
  • Our CG must reside within those meager 15".

This may not seem like much, but this Gulfstream's fuel tanks are all in the wings and the airplane is certified to allow C.G. computations without regard to fuel. Even without the first drop of fuel on board the airplane weighs nearly 43,000 lbs. So getting outside this 15" when you are dealing with 14 people who weigh on average only 200 lbs will take some doing.

Sensitivity

Not all airplanes are created equal and when it comes to weight and balance, you have to worry more about some than others.

CG-Insensitive

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In the case of our G450, a typical airplane with a 42% basic %MAC can load 900 lbs of baggage in the furthest aft location and still be okay. From that point passengers can be loaded aft-to-front or front-to-aft and the airplane will still be within tolerances. (The furthest aft seat is still forward of the center of gravity, so any passenger at all brings this CG forward.

Note: A G450 with a forward galley may run into forward CG issues.

This particular center of gravity chart is used for takeoff computations and does not include fuel. Gulfstream found that the wing-only fuel arrangement will not put the airplane out of CG no matter the quantity of fuel, and was able to certify it this way. While fuel loading does impact takeoff trim, it can never place the airplane in an unacceptable CG range.

This particular G450 can be said to be "CG-insensitive," it can tolerate wide movements of passengers, baggage, and fuel and still be within CG limits. It is helpful to know how sensitive your airplane is.

CG-Sensitive

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A Challenger 605 can be said to be "CG-sensitive." While it can tolerate movements of passengers, baggage, and fuel and still be within CG limits, it can also find itself out of limits without too much effort. With fuel distributed from nose to tail those 605's with forward galleys tend to be nose heavy. Fuel mismanagement can also jeopardize a safe balance:

  • In a typical 600-series Challenger, about half the seats are forward of the CG, half are aft. Where you seat passengers matters.
  • Fueling the wings only will start to move the CG forward but at about the halfway point moves it aft.
  • After the wings are full, fuel should be computer controlled to distribute between the auxiliary and aft-auxiliary tanks in a 2.65 to 1 ratio. That generally moves the CG forward.
  • After the auxiliary tank is full, the rest of the fuel goes to the aft-auxiliary tank and then to the saddle and tail cone tanks. All of that tends to move the CG aft.

This is a lot to consider when you are making changes. Most of these airplanes have forward galleys and tend to be nose heavy until they become very heavy. This airplane is CG-sensitive.

Impacts

Your center of gravity will be impacted by where on the aircraft you have stored fuel, cargo (baggage), and people. When these things move around, so does the center of gravity. Understanding where the CG moves is key to having a feel for your airplane's weight and balance.

CG-insensitive Example (G450)

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Photo: The CG Envelope on a G450 (Those 36% and 45% markers are both aft of the aft-most passenger seat), from Eddie's aircraft.

In the case of our example CG-insensitive G450:

  • The LEMAC is 387.7" behind the horizontal datum.
  • The forward-most center of gravity allowed is 36% of MAC (166.22") which comes to 59.8". That means the forward-most center of gravity allowed is 387.7 + 59.8 = 447.5" aft of the horizontal datum.
  • The aft-most center of gravity allowed is 45% of MAC (166.22") which comes to 74.8". That means the aft-most center of gravity allowed is 387.7 + 74.8 = 462.5" aft of the horizontal datum.
  • The aft-most seat on a typical G450 is 426" behind the horizontal datum.
  • The cabin door in front of the aft baggage compartment is 555" behind the horizontal datum.

So what does this mean to us as pilots? Simply, for this example G450, any aft baggage moves the C.G. aft and any passenger moves the C.G. forward. You might be alarmed that the distance from one limit to the other is only 15" but don't be. The airplane weighs 43,000 pounds before you add any fuel and you would need to move a lot of passengers and cargo to get the C.G. out of that range.

CG-sensitive Example (Challenger 605)

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Unlike the G450, visualizing the center of gravity on a Challenger 605 does not yield easily discernible results. The range is still pretty narrow but the range moves with weight. You can still profit from knowing exactly where on the airplane that range resides, so you can better understand the impacts of moving people, bags, and fuel.

If everything is working by the book, the airplane's center of gravity should not be a problem. But there has been at least one Challenger 600 series crash so it bears looking into. (See CL-600 N370V.)

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Let's say you are flying without passengers on a leg requiring 15,000 lbs of fuel. Your aircraft has a fully stocked galley and is generally nose heavy as Challengers go. Your Zero Fuel Weight (ZFW) comes to 30,000 lbs and 28% MAC. This is a pretty normal condition for you without passengers.

A 15,000 fuel load should automatically distribute itself thusly:

  1. The first 9,720 lbs will fill the left and right wing tanks.
  2. The remaining fuel should distribute itself in a 2.65 to 1 ratio between the auxiliary and aft-auxiliary tanks: 3,384 lbs auxiliary and 1,446 lbs aft-auxiliary.
  3. This airplane can have fuel system problems if the fuel pressure is interrupted which is what happens just as the aft-auxiliary gets to 1,000 lbs. At that point it stops accepting fuel and the remaining 446 lbs all ends up in the auxiliary tank.

So you've had a very minor glitch but your margin of safety was wide enough so the airplane is still within acceptable center of gravity limits for your planned takeoff. It is highly unlikely you would notice the fuel glitch. The information of fuel distribution is available, but few pilots would notice 446 lbs in the wrong place. If, on the other hand, you computed your resulting weight and balance and center of gravity, you would be aware that you are very close to your forward limit.

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Now let's say you are fully loaded and about ready to depart when your phone rings. Your charter company found six passengers with 200 lbs of baggage wanting to fly the exact city pair so it is an easy revenue pick up. You gladly accept the six male passengers who climb on to the airplane and take the first six seats, all forward.

If you hadn't bothered with the weight and balance routine you wouldn't have realized just how far forward your center of gravity is. It was okay before, but now?

Now you are well beyond your forward CG limit. Takeoff rotation is doubtful!

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If, on the other hand, you were aware of your starting weight and balance issue you would have been forewarned. Simply placing your passengers in the aft-most seats keeps you within your authorized limits, though just barely. (You might want to consider burning off some fuel before takeoff.)

You need to know what the Fed has to say about this, it could affect your license. Besides, if you have a center-of-gravity-sensitive airplane, it will help you understand . . .

Certification

Transport category aircraft must be built with published center of gravity limits established.

[14 CFR 25, §25.23(a)] Ranges of weights and centers of gravity within which the airplane may be safely operated must be established. If a weight and center of gravity combination is allowable only within certain load distribution limits (such as spanwise) that could be inadvertently exceeded, these limits and the corresponding weight and center of gravity combinations must be established.

[14 CFR 25, §25.27] The extreme forward and the extreme aft center of gravity limitations must be established for each practicably separable operating condition. No such limit may lie beyond — (a) The extremes selected by the applicant; (b) The extremes within which the structure is proven; or (c) The extremes within which compliance with each applicable flight requirement is shown.

There isn't anything regulatory that says a general aviation pilot must compute weight and balance data, however . . .

[14 CFR 91, §91.7 (b)] The pilot in command of a civil aircraft is responsible for determining whether that aircraft is in condition for safe flight. The pilot in command shall discontinue the flight when unairworthy mechanical, electrical, or structural conditions occur.

[14 CFR 91, §91.9 (a)] no person may operate a civil aircraft without complying with the operating limitations specified in the approved Airplane...Flight Manual, markings, and placards.

These are the citations you will see on the accident report if you fail to compute a weight and balance for every takeoff. Besides . . .

[FAA-H-8083-1A, pg. 1-1] The pilot in command of the aircraft has the responsibility on every flight to know the maximum allowable weight of the aircraft and its CG limits. This allows the pilot to determine on the preflight inspection that the aircraft is loaded in such a way that the CG is within the allowable limits.

Manifest

If you are flying commercially, or if you want to employ best practices . . .

[14 CFR 135, §135.63]

For multiengine aircraft, each certificate holder is responsible for the preparation and accuracy of a load manifest in duplicate containing information concerning the loading of the aircraft. The manifest must be prepared before each takeoff and must include:

1) The number of passengers;

2) The total weight of the loaded aircraft;

3) The maximum allowable takeoff weight for that flight;

4) The center of gravity limits;

5) The center of gravity of the loaded aircraft, ...

(d) The pilot in command of an aircraft for which a load manifest must be prepared shall carry a copy of the completed load manifest in the aircraft to its destination. The certificate holder shall keep copies of completed load manifests for at least 30 days...

Weight and balance control program

[AC 120-27E, ¶5.a] This document provides guidance to both passenger and cargo operators that are either required to have an approved weight and balance control program under parts 121 and 125, or choose to use actual or average aircraft, passenger, or baggage weights when operating under part 91, subpart K of part 91, or part 135. The guidance in this AC is useful for anyone involved in developing or implementing a weight and balance control program.

Standard Average Weights

[AC 120-27E, ¶5.b.] As shown in Table 1, the FAA has divided aircraft into three categories for this AC to provide guidance appropriate to the size of the aircraft.

For this AC, an aircraft originally type-certificated with— Is considered—
71 or more passenger seats A large-cabin aircraft.
30 to 70 passenger seats A medium-cabin aircraft.
5 to 29 passenger seats A small-cabin aircraft.

NOTE: Aircraft with fewer than five passenger seats must use actual passenger and baggage weights.

[AC 120-27E, ¶6.] Who can use standard average or segmented weights?

  1. Standard Average Weights. Use of standard average weights is limited to operators of multiengine turbine-powered aircraft originally type-certificated for five or more passenger seats who hold a letter of authorization (LOA), OpSpecs, or MSpecs, as applicable, and were certificated under 14 CFR part 25, 29, or part 23 commuter category or the operator and manufacturer is able to prove that the aircraft can meet the performance requirements prescribed by part 23 commuter category aircraft. Single-engine and multiengine turbine Emergency Medical Service Helicopter (EMS/H) operators may use standard average weights for EMS operations, provided they have received an LOA.
  2. Segmented Weights. Segmented weights are provided for, but not limited to those aircraft that are multiengine turbine-powered aircraft originally type-certificated for five or more passenger seats and that do not meet the performance requirements of part 23 commuter category aircraft or part 29.
  3. A segmented weight program is simply a standard average weight program with a statistical pad added to each weight.

  4. The FAA’s recommendations and advice on the safe use of standard average weights and segmented weights are contained in this document. In the FAA’s view, it would be unsafe for an aircraft operator to use standard average weights or segmented weights in any of the following aircraft:
    1. All single-engine piston-powered aircraft.
    2. All multiengine piston-powered aircraft.
    3. All turbine-powered single-engine aircraft.
    4. NOTE: All multiengine turbine-powered aircraft certificated under part 23, except for commuter category aircraft, may only use an actual weight or segmented weight program. Operators that elect to use a segmented weight program must meet the requirements in paragraph 6b and curtail the CG envelope as specified in Appendix 3, 4, and 5. Commuter category aircraft may use standard average weights and should refer to paragraph 200f for further guidance.

Most of us in the transport category aircraft world use "standard average weights" when computing our weight and balance. You might say, for example, that a typical adult male passenger weighs 175 lbs, a typical female adult passenger weighs 150 lbs, and so on. That usually works in the airline world because they are dealing with large cabins and have the necessary regulatory requirements met. But it more than likely is the wrong approach in the 14 CFR 135 business jet world and could get your operator into some trouble if caught. Moreover, it is the wrong thing to do in a 14 CFR 91 operation too, just because it could be dangerous.

Actual Weights

So if you don't use standard average weights what is the alternative? If you have fewer than five passengers seats you don't have much choice, you have to use the actual weights of your passengers and baggage. (That means you either weigh them or ask them, "how much do you weigh?")

[AC 120-27E, Chapter 2, §5]

An operator may determine the actual weight of passengers by—

  1. Weighing each passenger on a scale before boarding the aircraft (types of weight scales and scale tolerances will be defined in the operator’s approved weight and balance control program); or
  2. Asking each passenger his or her weight. An operator should add to this asked (volunteered) weight at least 10 pounds to account for clothing. An operator may increase this allowance for clothing on certain routes or during certain seasons, if appropriate.
  3. NOTE: If an operator believes that the weight volunteered by a passenger is understated, the operator should make a reasonable estimate of the passenger’s actual weight and add 10 pounds.

To determine the actual weight of a personal item, carry-on bag, checked bag, plane-side loaded bag, or a heavy bag, an operator should weigh the item on a scale.

If you have more than five passenger seats you have another option: you can curtail your center of gravity envelope and then use standard average weights. Setting up a curtailment program can take a little brain power, and if you are operating under 14 CFR 135 it will also require Operation Specification A097 (or equivalent). But once that is done there is very little to worry about other than watching out for unusual passenger loads. If, for example, you are flying the front line of the New England Patriots, you might want to increase your standard weights.

More about this . . .

Curtailment

WARNING

Before you skim down and look at all the tables and math and decide to go back to the way you've been doing things, take a breath and relax. It isn't that hard, you only have to do this once per airplane, and once you've done it, you can use standard passenger weights with a clear conscious. If you are operating under 14 CFR 135 you will need an OpSpec, but I've applied for and got OpSpec A097 without too much fuss in the past. If you can run through these numbers below and adjust them for your airplane, you will know more about this than the FAA inspector.

What?

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Figure: Center of gravity curtailment example, from AC 120-27E, Appendix 3, Figure 3-6.

[AC 120-27E, Appendix 1, ¶6.] Curtailment. Creating an operational loading envelope that is more restrictive than the manufacturers’ CG envelope, to assure the aircraft will be operated within limits during all phases of flight. Curtailment typically accounts for, but is not limited to, in-flight movement, gear and flap movement, cargo variation, fuel density, fuel burn-off, and seating variation.

Curtailing your center of gravity envelope means you shrink it inward by a computed amount, thereby increasing your margin for error. You can curtail your C.G. envelope to account for variations of passenger weights from whatever standard you are using, movement of passengers within the cabin, variations in the weight of luggage, and fuel burn off.

If you are lucky, you will have a clear statement in your aircraft documentation that clearly states you don't need to worry about passenger movement during flight or fuel burn off. For example:

[Bombardier CL-605 Weight and Balance Manual, §01-40-40, ¶3.] With the weight and CG limits met with the aircraft on the ground, safe limits in flight are achieved. This is with the conditions that follow:

  • Landing gear retracted
  • Crew and passengers are allowed normal movement in flight.

If that is true, we can focus our curtailment efforts on variations in passenger weights. It will be to your advantage to curtail your center of gravity envelope for variations in passenger weights from standard.

Why?

You may be legally required to curtail your center of gravity envelope, see Legal Issues, above. If you are flying a business jet with 5 to 29 passenger seats, it probably makes "statistical sense" to curtail your center of gravity envelope . . .

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If you are flying a Boeing 737 with a hundred people on board and about ten percent of them are much heavier than your standard weight, chances are another ten percent will be much lighter than standard so it all evens out. With that many people you are likely to have what a statistician calls "data smoothing" and your likelihood of being off your calculated weight is relatively low.

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If, on the other hand, you are flying a Citation X with four passengers the chance of error is much higher. Lets say two of the passengers are male and they weigh 180 and 320 lbs. If your standard weight for a male is 175 lbs. you will be off by 43 percent! You should not use standard weights.

How — Step 1: Determine Standard Average Weights

[AC 120-27E, Chapter 2, §2, ¶201.]

a. The standard average passenger weights provided in Table 2-1 were established based on data from U.S. Government health agency surveys. For more background information on the source of these weights, refer to Appendix 2.

If you have an approved carry-on baggage program. . .

b. The standard average passenger weights in Table 2-1 include 5 pounds for summer clothing, 10 pounds for winter clothing, and a 16-pound allowance for personal items and carry-on bags. Where no gender is given, the standard average passenger weights are based on the assumption that 50 percent of passengers are male and 50 percent of passengers are female.

Standard Average Passenger Weight Weight Per Passenger
Summer Weights
Average adult passenger weight 190 lb
Average adult male passenger weight 200 lb
Average adult female passenger weight 179 lb
Child weight (2 years to less than 13 years of age) 82 lb
Standard Average Passenger Weight Weight Per Passenger
Winter Weights
Average adult passenger weight 195 lb
Average adult male passenger weight 205 lb
Average adult female passenger weight 184 lb
Child weight (2 years to less than 13 years of age) 87 lb

c. An operator may use summer weights from May 1 to October 31 and winter weights from November 1 to April 30. However, these dates may not be appropriate for all routes or operators. For routes with no seasonal variation, an operator may use the average weights appropriate to the climate. Use of year-round average weights for operators with seasonal variation should avoid using an average weight that falls between the summer and winter average weights. Operators with seasonal variation that elect to use a year-round average weight should use the winter average weight. Use of seasonal dates, other than those listed above, will be entered as nonstandard text and approved through the operator’s OpSpec, MSpec, or LOA, as applicable.

All that is based on having an approved carry-on baggage program and that a portion of passengers will be carrying a 15-pound personal item. For more about this see Advisory Circular 121-29. It gets even more complicated when you start considering a standard checked bag is supposed to be 30 pounds, heavy bags are any over 100 pounds, and there are entire categories devoted to plane-side baggage and "non-luggage" bags. You can dive into this in Chapter 2 of AC 120-27E. Most of us will be in the "no-carry program" where we don't have underseat or overhead bin accommodations for baggage.

[AC 120-27E, Chapter 2, §2, ¶205.]

a. An operator with a no-carry-on bag program may allow passengers to carry only personal items aboard the aircraft. Because these passengers do not have carry-on bags, an operator may use standard average passenger weights that are 6 pounds lighter than those for an operator with an approved carry-on bag program. See Table 2-2.

Standard Average Passenger Weight Weight Per Passenger
Summer Weights
Average adult passenger weight 184 lb
Average adult male passenger weight 194lb
Average adult female passenger weight 173 lb
Child weight (2 years to less than 13 years of age) 76 lb
Standard Average Passenger Weight Weight Per Passenger
Winter Weights
Average adult passenger weight 189 lb
Average adult male passenger weight 199 lb
Average adult female passenger weight 178 lb
Child weight (2 years to less than 13 years of age) 81 lb

[AC 120-27E, Chapter 2, §2, ¶206.]

a. An operator may choose to use the standard crewmember weights shown in Table 2-3 or conduct a survey to establish average crewmember weights appropriate for its operation.

Crewmember Average Weight Average Weight with Bags
Flight Crewmember 190 lb 240 lb
Flight attendant 170 lb 210 lb
Male flight attendant 180 lb 220 lb
Female flight attendant 160 lb 200 lb
Crewmember roller bag 30 lb NA
Pilot flight bag 20 lb NA
Flight attendant kit 20 lb NA

You also have the option of conducting surveys to derive your own set of standard weights. For information on how to do this, see AC 120-27E, Chapter 2, §3.

How — Step 2: Determine Average Weights Standard Deviation

This may seem like a bit of extra bother but it is needed when figuring out by how much your C.G. envelope is going to shrink. Standard deviation is a measure of how far a set of data points varies from the average, squared. Simply put, the smaller the standard deviation the more homogeneous the data. Conversely, large standard deviations means the data points are pretty diverse. Fortunately you don't need to be a statistician to curtail your C.G. You only need to know what the standard deviation is for the source data used to compute your standard weights. If you use the standard weights shown here, the answer is given to you:

[AC 120-27E, Appendix 2, ¶1.b.] The standard deviation of the sample was 47 pounds.

How — Step 3: Determine Curtailment Row Factor

[AC 120-27E, Appendix 4, ¶a.] The use of average weights for small cabin aircraft requires consideration of an additional curtailment to the center of gravity (CG) envelope for passenger weight variations and male/female passenger ratio.

(1) Passenger weight variation is determined by multiplying the standard deviation (from the source of the average passenger weight used) by the row factor from Table 4-1. The following table is a statistical measure that ensures a 95-percent confidence level of passenger weight variation, using the window-aisle-remaining seating method.

No. of Rows 2-abreast 3-abreast 4-abreast
2 2.96 2.73 2.63
3 2.41 2.31 2.26
4 2.15 2.09 2.06
5 2.00 1.95 1.93
6 1.89 1.86 1.84
7 1.81 1.79 1.77
8 1.75 1.73 1.69
9 1.70 1.68 1.65
10 1.66 1.65 1.62
11 1.63 1.59 1.59
12 1.60 1.57 1.57
13 1.57 1.54 1.54
14 1.55 1.52 1.52
15 1.53 1.51 1.51
16 1.49 1.49 1.49
17 1.48 1.48 1.48
18 1.46 1.46 1.46

(2) Protect against the possibility of an all-male flight by subtracting the difference between the male and average passenger weight.

If you use the standard weight data presented in the AC, that will always be 10 pounds.

(3) The sum of these two provides an additional weight to be used for CG curtailment, similar to the way in which passenger seating variation is calculated.

They wrote this to confuse you . . . here is the formula derived from their text and example:

Weight for Additional Curtailment = (Standard Deviation) (Row Factor) + (Male - Average Weight)

If you are using the standard data:

Weight for Additional Curtailment = (47) (Row Factor) + 10

How — Step 4: Determine Weight for Additional Curtailment

[AC 120-27E, Appendix 4, ¶a.] Calculation of the curtailment passenger weight variation is decided by multiplying the standard deviation by the correction factor and adding the difference between the average all-male and average passenger weight.

Easy! Well the AC can be confusing at this point. We'll use my airplane as an example to work this through. You will need to rethink how you categorize rows to do this. My aircraft has 16 passenger seats spread across two divans and eight individual seats. For each of these we will need the seat centroid (location of the center of the seat) and the curtailment row factor from the previous step.

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Using their definition of rows and numbers abreast, our example airplane has 10 rows, 2-abreast. That means we have a row factor of 1.66 and that means:

Weight for Additional Curtailment = (47) (1.66) + 10 = 88 lb

Now you need to dig out your aircraft's weight and balance manual to find the seat centroid (the location of each seat in terms of its distance from the aircraft datum, also known as its "arm"). For my airplane they are as follows:

Row (Seat) Centroid (Arm)
Row 1 (1) 226
Row 1 (2) 226
Row 2 (3) 243
Row 3 (4) 260
Row 4 (5) 277
Row 4 (6) 277
Row 5 (7) 311
Row 5 (8) 311
Row 6 (9) 362
Row 6 (10) 362
Row 7 (11) 398
Row 7 (12) 398
Row 8 (13) 414
Row 9 (14) 439
Row 10 (15) 446
Row 10 (16) 446

How — Step 5: Determine Curtailment for Passenger Weight Variation

Now we need to construct two tables, one assuming your passengers load front-to-back and the other back-to-front. We need to find the highest moment deviation. So let's do this step by step.

Row (Seat) Draw a table where the left column is the row/seat

Centroid The second is the corresponding centroid.

Seat Moment In the third column enter the product of the seat centroid and the weight for additional curtailment (88 in our example).

Total Seat Moments In the fourth column total the previous column.

Total Additional Weight (TAW) In the fifth column enter the weight for additional curtailment (88 in our example) multiplied by the number of seats so far.

Determine the cabin's centroid (the middle of the cabin). You might find this in your weight and balance manual or you might just take the lowest seat arm, add that to the highest, and then divide by two. For our example airplane we'll say:

Cabin Centroid = (226 + 446) / 2 = 336.0 inches

TAW x Cabin Centroid In the sixth column enter the product of the total additional weight times the cabin centroid (this yields the moment arm if everyone was in the cabin center).

Moment Deviation In the last column enter the difference between the Total Seat Moments and the TAW X Cabin Centroid. This will show you the highest deviation when loading from the forward to the aft of the aircraft.

Forward Seating

Row (Seat) Centroid (Arm) Seat Moment Total Seat Moments Total additional weight (TAW) TAW x Cabin Centroid Moment Deviation
Row 1 (1) 226 19,888 19,888 88 29,568 -9,680
Row 1 (2) 226 19,888 39,776 176 59,136 -19,360
Row 2 (3) 243 21,384 61,160 264 88,704 -27,544
Row 3 (4) 260 22,880 84,040 352 118,272 -34,232
Row 4 (5) 277 24,376 108,416 440 147,840 -39,424
Row 4 (6) 277 24,376 132,792 528 177,408 -44,616
Row 5 (7) 311 27,368 160,160 616 206,976 -46,816
Row 5 (8) 311 27,368 187,528 704 236,544 -49,016
Row 6 (9) 362 31,856 219,384 792 266,112 -46,728
Row 6 (10) 362 31,856 251,240 880 295,680 -44,440
Row 7 (11) 398 35,024 286,264 968 325,248 -38,984
Row 7 (12) 398 35,024 321,288 1056 354,816 -33,528
Row 8 (13) 414 36,432 357,720 1144 384,384 -26,664
Row 9 (14) 439 38,632 396,352 1232 413,952 -17,600
Row 10 (15) 446 39,248 435,600 1320 443,520 -7,920
Row 10 (16) 446 39,248 474,848 1408 473,088 -1,760

In the case of our example G450, the highest deviation when loading forward-to-aft is 49,016 inch-lbs. Now we have to repeat the process when loading aft-to-forward.

Aft Seating

Row (Seat) Centroid (Arm) Seat Moment Total Seat Moments Total additional weight (TAW) TAW x Cabin Centroid Moment Deviation
Row 10 (16) 446 39,248 39,248 88 29,568 9,680
Row 10 (15) 446 39,248 78,496 176 59,136 19,360
Row 9 (14) 439 38,632 117,128 264 88,704 28,424
Row 8 (13) 414 36,432 153,560 352 118,272 35,288
Row 7 (12) 398 35,024 188,584 440 147,840 40,744
Row 7 (11) 398 35,024 223,608 528 177,408 46,200
Row 6 (10) 362 31,856 255,464 616 206,976 48,488
Row 6 (9) 362 31,856 287,320 704 236,544 50,776
Row 5 (8) 311 27,368 314,688 792 266,112 48,576
Row 5 (7) 311 27,368 342,056 880 295,680 46,376
Row 4 (6) 277 24,376 369,432 968 325,248 44,184
Row 4 (5) 277 24,376 393,808 1056 354,816 38,992
Row 3 (4) 260 22,880 416,688 1144 384,384 32,304
Row 2 (3) 243 21,384 438,072 1232 413,952 24,120
Row 1 (2) 226 19,888 457,960 1320 443,520 14,440
Row 1 (1) 226 19,888 477,048 1408 473,088 3,960

In the case of our example G450, the highest deviation when loading aft-to-forward is 50,776 inch-lbs, and that is worse than the previous forward-to-aft scenario. So we will curtail our C.G. envelope by 50,776 inch-lbs. To do this, we need to compute the %MAC change for each "inflection point" of the existing chart.

How - Step 6: Curtail Center of Gravity Chart

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An inflection point is simply a position along the edges of the limit where things change. In our G450 example we see six of them. We divide our curtailment (50,776 inch-lbs in our example) by the weight at each point to determine how much to curtail that point inward by inches. Since the chart is drawn in %MAC, we need to convert the inches to %MAC. 100% MAC for the G450 is 166.22 inches. In our example aircraft:

  • 49,000 lbs, 36%, — 1.04 inches (0.63% MAC)
  • 46,500 lbs, 36%, — 0.92 inches (0.55% MAC)
  • 39,800 lbs, 38%, — 0.78 inches (0.47% MAC)
  • 38,400 lbs, 45%, — 0.76 inches (0.46% MAC)
  • 44,000 lbs, 45%, — 0.87 inches (0.52% MAC)
  • 49,000 lbs, 39.75%, — 1.04 inches (0.63% MAC)

Now we simply draw new limits inside the manufacturer's limits by the margins computed. With the appropriate Operations Specification we can use standard weights legally. As general aviation operators, we can compute weight and balance using standard weights with a higher degree of confidence that we will still be within the manufacturer's limits had we weighed every passenger and bag.

How - Step 7 : Use!

At this point you are done with curtailment and all you need to do is:

  1. If your passengers and baggage appear to be "about standard," compute your %MAC for each flight using standard weights.
  2. Plot your %MAC against the curtailed chart.
  3. If the result is inside your curtailed chart, you are good to go.
  4. If the result is outside your curtailed chart, revert to actual weights against the manufacturer's chart.

References

14 CFR 25, Title 14: Aeronautics and Space, Airworthiness Standards: Transport Category Airplanes, Federal Aviation Administration, Department of Transportation

14 CFR 135, Title 14: Aeronautics and Space, Operating Requirements: Commuter and On Demand Operations and Rules Governing Persons on Board Such Aircraft, Federal Aviation Administration, Department of Transportation

Advisory Circular 120-27E, Aircraft Weight and Balance Control, 6/10/05, U.S. Department of Transportation

Advisory Circular 121-29B, Carry-on Baggage, 7/24/00, U.S. Department of Transportation

Air Force Manual (AFM) 51-9, Aircraft Performance, 7 September 1990

Bombardier Challenger 605 Weight and Balance Manual, A/C 5701 and subs, Publication No. CH 605 WBM, Feb 01/2010.

FAA-H-8083-1A, Aircraft Weight and Balance Handbook, U.S. Department of Transportation, Flight Standards Service, 2007

Gulfstream G450 Maintenance Manual, Revision 18, Dec 12, 2013

Gulfstream G450 Weight and Balance Manual, Revision 3, March 2008

Revision: 20160601
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