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Positioning cargo such that the center of gravity of the plane is within a certain range is essential, but is there any advantage to having the center of gravity closer to some ideal point within the acceptable envelope?

Would additional control surface drag be caused by cargo loaded right on the edge of operating standards?

Would finding an optimal loading be computationally complex? How many cargo pallets/containers fit in a large cargo aircraft?

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Positioning cargo such that the center of gravity of the plane is within a certain range is essential, but is there any advantage to having the center of gravity closer to some ideal point within the acceptable envelope?

There is no one ideal point for all large cargo aircraft as defined by a center of gravity (cg) expressed as the percent of the mean aerodynamic chord (%mac). There are a lot of aircraft model and operational variations. The general idea for large aircraft like the 747 is to put the c.g. as far aft as possible while keeping undesirable operational characteristics within reason. The farther aft the c.g. is the lower the fuel burn because as you move the c.g. aft (toward the center of lift of the wing), the pitch down moment of the wing lift decreases and thus the tailplane has to supply less downward force, which means there will be less overall drag and fuel efficiency goes up (the aerodynamicists here can probably say that more succinctly).

The operating envelopes of the airplane define how far aft you are allowed to put the c.g. There are multiple constraints insofar as determining the aft most limit. Two obvious ones are controllability in engine-out situations and in turbulence.

One doesn't always try to put the c.g. just forward of the aft limit, though. There can be other considerations. For example, on 747-100/200/400 aircraft at typical weights, the aft c.g. limit is 33.0%mac, but a common aiming point for the zero fuel weight c.g. is 26.6%mac. While I don't know all the reasons for using 26.6%, one is that that is the location of the wing gear, so if for some reason you couldn't extend the body gear, the aircraft might sit on its tail when landing depending on how much fuel you had left and how far aft of 26.6% you are.

Loadmasters for a given aircraft are a good source for what the usual aiming point is for the c.g.

Would additional control surface drag be caused by cargo loaded right on the edge of operating standards?

Yes, if you had the c.g. up against the forward limit, the tailplane would have to generate a greater downward force than otherwise, and that would mean more drag. Also, on wide-body aircraft, if you were up against the maximum lateral imbalance moment, you're going to have aileron drag that you otherwise would not have.

Would finding an optimal loading be computationally complex?

Not really, especially if its the case that all pallets/containers are going to be off-loaded at a single destination. If there's more than one off-loading destination it gets more complicated since you'd want those pallets getting off first to be positioned such that you could move them to the cargo door without having to move pallets not getting off.

There might be other constraints as well. For example, let's say you had a 30,000 lb pallet to be put aboard a 747-100/200/400. The only area that can take that kind of weight in a single size M pallet is over the wing box. That limits you to using one side of three side-by-side position pairs. Let's say you put that pallet on the left side of the aft most side-by-side position pair. That's fine, but you have now limited the right side to a max of 6250 lb.

You also have to ensure that you don't violate cumulative loading limits from the front of the aircraft to the middle and from the aft to the middle, and a few other things besides.

Computer programs for doing weight & balance for large cargo aircraft have been able to handle all of these things since the 1980s. I wrote a DOS application in 1988 that did all these things and was eventually used by three cargo carriers. It was finally phased out in 2016.

The algorithm it used was straight forward. Sort the pallets by weight and allocate from heaviest to lightest. Put the heaviest in the position closest to the target c.g. Then put the next pallet either aft or forward of the previous depending on which will produce a c.g. closest to the target, and so forth. After each position allocation, it checked to see if any limitation had been violated. If so, it reallocated until there were no violations. Even on slow computers of the DOS era, it never took more than a few seconds to complete.

How many cargo pallets/containers fit in a large cargo aircraft?

Depends on the size of the containers and the size of the aircraft. There are a lot of choices. Go to this ULD sizes page to see common sizes. For 747s carrying civilian cargo, size code M is probably the most used on the main deck, with either 29 or 30 positions. For military cargo size code B was that size I mostly saw on the 747 main deck, usually with 33 aboard.

The lower holds on 747s had a lot of variability insofar as the ULDs used down there.

If you want to explore 747 cargo position configurations, go to this 747 weight & balance page. The POSITION CONFIG menu will allow you to select different configurations between 30, 29, and 33 main deck positions. After selecting a configuration, you can scroll down to see the arrangement (or press F6, either the key of the left nav button).

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  • $\begingroup$ The question was supposed to read, "Would finding an optimal loading be complex?" A brute force algorithm checking every permutation of container locations would require O(n!) which would be intractable for n=33... Would a program like JWB ever attempt to offer better container locations (for example, on the 747 placing the CG closer to mid-line/rear limit)? $\endgroup$ – user9394 Nov 2 '17 at 6:49
  • $\begingroup$ @BaileyS I edited the answer to include the info about optimal loading complexity. Maybe I'll even get around to finally adding that feature to JWB. $\endgroup$ – Terry Nov 2 '17 at 20:40
  • $\begingroup$ @CGCampbell Concerning your edits to the answer, no problem except for one minor point. You chose to use "The operating envelope of the airplane defines" rather than the plural I had used, "envelopes of the airplane define." I used the plural because there are multiple envelopes. In the case of the 747 there are, at a minimum, different envelopes for taxi, takeoff, zero fuel, and landing. As it happens the aft limit c.g. is typically the same for all envelopes with one notable exception, the aft limit for takeoff with a light load is considerably farther forward than for the other envelopes. $\endgroup$ – Terry Dec 19 '17 at 19:32
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The accepted answer does a great job of describing this from an operational standpoint, which is perhaps the answer you were looking for. But let me address this from perhaps a more fundamental flight mechanics / aerodynamics point of few: Yes, loading certainly affects the efficiency of an aircraft.

The fundamental principle by which it does so is through trim drag: the induced drag caused as a consequence of the force (typically downwards) produced by the horizontal tail to balance the aircraft.

Aerodynamic efficiency, which can be described by the ratio of lift to drag $$\frac{L}{D} \: ,$$ is directly proportional to fuel efficiency. If total drag increases for a fixed lift (read fixed aircraft weight), aerodynamic and thus fuel efficiency decreases.

The main purposes of the horizontal tail is longitudinal control, damping and trim. In order to trim the aircraft, the horizontal tail needs to apply a force $F_{ht}$ to ensure that the total moment about the center of gravity of the aircraft is zero, i.e. that it flies at a fixed angle of attack. As with all lifting surfaces the price to pay for this lifting force (be it upwards or downwards) is induced drag: $$D_i \: .$$ The horizontal trim force required to balance the aircraft can be quite substantial and the induced drag of the horizontal tail scales with the tail force squared: $$D_i\propto F_{ht}^2 \: ,$$ so an increase in the force leads to a higher than proportional increase in drag.

To bring this back to your question: If the cargo is located such that the center of gravity of the aircraft is too far fore of the neutral point of the entire aircraft (i.e. a large static margin), the horizontal tail force required to balance the aircraft can be substantial and thus even more so the induced drag of the tail that scales with the force squared.

The chain of causality is something like $$\text{Too fore cargo loading} \rightarrow \text{Large static margin} \rightarrow \text{Large trim force} \rightarrow \text{Larger trim drag} \rightarrow \text{Decreased} \: \frac{L}{D} \rightarrow \text{Increased fuel burn}$$

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In laymans terms...

A plane needs to be at a certain angle to its flight path. In order to achieve this the centre of gravity (CG) will be in the exact place it needs to be to achieve this angle and fuel efficiency will be optimum.

In actual fact, the CG will have to be corrected by 'trimming' ie by setting the horizontal stabilizers to achieve the desired pitch angle. This however creates drag and increases fuel consumption. When fuel efficiency became a priority for the customers, the designers hit upon a great idea! By having fuel in the horizontal stabilizers (HS), you can manage the CG in flight to achieve the desired pitch. This eliminates additional drag and the HS can be set at a minimal drag setting.

The actual CG does not remain constant throughout the flight, as fuel is burnt the CG will shift as the fuel tanks are not a constant size and have a different value (CG wise) at different levels of fuel. By having a tail-tank, the fuel in tanks is managed to achieve best efficiency.

While this is pretty neat stuff, it is nothing new. Back in the late sixties the Concorde used fuel distribution to manage the pitch as it did not have horizontal stabilizers.

Airlines have long recognized that trimming does indeed affect efficiency. A certain Middle-east airline had a 'target' MACTOW for the load-sheet. While not always possible to achieve it was something to aim for. Similarly a European airline I worked for had an 'optimum value' in the loadsheet software so you were constantly aware of the best place to have the CG (this was in the 90s!). For a 10-11hr flight there would be decent savings!

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