# Weight and Balance Curtailment

# Flight Engineering

Do you use "standard weights" when figuring your aircraft's weight and balance? If so, and if you are operating under 14 CFR 135, you will need OpSpec A097 and must have a method of making standard weights work for you. Even if you are operating under 14 CFR 91, you should still understand how to make standard weights work.

It isn't as simple as figuring what the average man, woman, and child weigh. You have to take your normal weight and balance envelope, and shrink it a bit to allow for inevitable variations. You only have to do the hard part once, but you do have to do it.

### The Problem

Before you proceed, however, it may be helpful to understand exactly how the aircraft's center of gravity is computed: Weight and Balance Principles.

Then you should also understand what the aft and forward limits mean: Weight and Balance, A Sensual Approach.

And once you've done that, you can better visualize what a weight and balance graph is telling you and how to narrow (curtail) the limits to allow for the variations in passenger weights and seating that you are sure to see.

How can things go wrong?

- Wrong Weights — Let's say you planned on a 175 pound passenger seating in the most desirable seat and some ape shows up who is easily twice that weight.
- Too Far Forward — Let's say the passenger(s) decide they would all rather sit up front. Will you have the elevator authority to rotate during takeoff?
- Too Far Aft — Let's say the passenger(s) want to sit as far aft as possible. Will you be able to delay rotation to the correct speed? Once you rotate, will you be able to keep the rotation under control and prevent a stall?

I tend to use the Gulfstream G450 for a lot of examples to explain principles because it is very simple in most respects. The problem with using the G450 for weight and balance is that once you've covered the principles you are hard pressed to illustrate problems. The G450 is "CG Insensitive," in that it is very hard to get the airplane outside of its center of gravity envelope. I can, however, show a real world example of how your decision making can make the difference between a flyable airplane and one that is doomed to end up a smoldering wreck at the end of the runway, using a Challenger 605 Example.

There are two possible solutions:

- Weigh everyone and everything, insist they stay there for takeoff and landing (and presumably for the entire flight).
- Narrow the forward and aft limits of your center of gravity chart to allow for expected variations. If you are operating commercially, you will need OpsSpec approval to do this.

I once flew for a management company that insisted on option one and we weigh everything and ask every passenger their weight. I've flown for several operators that used the curtailment method. You end up with a curtailed CG that makes life so much better.

The Operations Specification isn't too hard to get, you just need to do that math once per airplane. I'll show you how: How to Curtail your CG.

### The Center of Gravity Chart — What it Really Means

We are tempted to look at our center of gravity charts and think they are massive. In the example G450 chart we have from 36 percent all the way up to 45 percent! But that is a percentage of the mean aerodynamic chord. A Gulfstream G450 is 89 feet 3 inches long (1,071 inches) but the mean aerodynamic chord is only 166 inches, so we are only talking 15 inches between the forward and aft CG limits. On many other business jets the margin is even smaller. More about this: Weight and Balance: A Sensual Approach.

This particular manufacturer has certified the airplane as flight worthy based on zero fuel weight; no variation in fuel quantity can throw the airplane outside of center of gravity limits so long as it was loaded correctly before fueling. So as long as you start out inside the forward and aft limits of the chart, you are good to go. But if you don't weigh everyone and everything precisely, how can you really be sure?

### Problem: Wrong Weights

So let's say you are flying a charter and figured on 16 passengers each weighing 175 pounds, but then a load of monkeys show up each clocking in at 250 pounds. So you have an extra 1200 pounds of weight. If you simply add the weight and realize you are still below your maximums, are you good to go?

#### More than expected weight

If in our example you started out at 46,000 lbs and 42% MAC and all that you did was add 75 lbs per passenger, you will end up beyond the aft limits of the aircraft's center of gravity.

If your CG is too far aft, the airplane may rotate prematurely on you or you could find yourself out of trim and be unable to control your takeoff pitch.

#### Less than expected weight

I once flew an airplane with ballast under the nose because the CG was too far aft under any condition. I also flew a business jet that required the passengers be seated in the front seats under some fuel conditions. You really need to explore your aircraft's center of gravity characteristics under all possible fuel, cargo, and passenger loading conditions.

### Problem: Too Far Forward

Our G450 is a forgiving airplane in many respects and the center of gravity of something we don't have to worry about much. But having a passenger pick a different seat than expected can impact your CG.

A passenger who for some reason wants to sits as far forward as possible on our airplane will shift the center of gravity by 0.7% MAC as opposed to as far aft as possible, so there is an impact.

### Problem: Too Far Aft

### A Real World Example of Weight and Balance Decision Making in Action

The Challenger 605 has several fuel tanks that move the aircraft's center of gravity forward at first, then aft, and then forward again. To make matters worse, its total envelope is only 9 inches long. Both factors mean Challenger pilots need to be keenly aware of the impacts of changing fuel loads and passenger seating. I hear from Challenger pilots now and then that tell me this isn't covered in adequate detail during initial or recurrent training. Let's fix that.

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 due to center of gravity, so it bears looking into. (See CL-600 N370V.)

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:

- The first 9,720 lbs will fill the left and right wing tanks.
- 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.
- 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.

I use to fly the version of Challenger that preceded this one (The Challenger 604) and have had this exact scenario more than a few times.) 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.

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?

The six passengers seated full forward shifted your entire curve forward and now you are well beyond your forward CG limit. Takeoff rotation is doubtful!

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.)

### The Solution: A Curtailed Center of Gravity Chart

A simple, common sense solution is to add a safety margin to those forward and aft limits, but how much of a safety margin? The FAA has provided a method to do this, and we will get to that below.

Once you have this safety margin figured out, you only have one change to your day-to-day operations. You simply compute your weight and balance as before, using estimated weights. But you compare the computed % MAC value to the forward and aft limits reduced by the safety margin. If you are inside the curtailed limits, you are good to go. Otherwise, you know you will have to get more precise data and be more specific about who sits where.

### How to Curtail Your Center of Gravity Chart (You only have to do this once)

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?

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?

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.

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 under-seat 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.

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

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:

- If your passengers and baggage appear to be "about standard," compute your %MAC for each flight using standard weights.
- Plot your %MAC against the curtailed chart.
- If the result is inside your curtailed chart, you are good to go.
- 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