# Bjorn’s Corner: After weight or fuel limited we examine weight or volume limited

By Bjorn Fehrm

31 July 2015, ©. Leeham Co: Last week we explained what fuel limited meant and how that differs from an aircraft that has big enough fuel tanks so it can operate weight limited for its missions.

This was for fuel and it dictates to a large degree how the aircraft will behave on long range missions. When we block off seats to fly further, is it to allow more fuel in our tanks or is it to make the aircraft lighter to fly further with tanks already filled to the brim.

A similar phenomenon appears when we load the aircraft with its payload; an aircraft can take-off volume or weight limited.  Here is how it works.

Once again the best way to understand how it works is to take a practical example and work through it, explaining as we go. To make things easy, we stay with our aircraft from last week, Boeing’s Ultra Long Hauler 777-200LR.

The Payload-Range chart in Figure 1 gives us the payload the aircraft can haul for different transportation distances. Once again, this is taken from the Airplane Characteristics for Airport Planning document (ACAP) that Boeing issues for the 777-200LR and their other aircraft.

Figure 1. Payload/Range chart for Boeing’s 777-200LR. Source: Boeing. Click on chart to see better.

As before, it is a good chart. Boeing is giving the aircraft’s combined empty weight+payload on the Y axis. It thereby circumvents the problem of making several charts for different empty weight configurations.  The aircraft’s payload range performance sees the aircraft’s total weight as important; it determines the amount of drag that develops based on the aircraft’s total weight at each point on the route flown.  Other OEMs give the chart as Payload versus range and assume a fixed empty weight.

As before, we assume an Operational Empty Weight (OEW) of 155t. To this we can add a maximum of 54 tonnes of payload before we reach the aircraft’s Maximum Zero Fuel Weight (MZFW) of 461,000lb/209,106kg.

The aircraft we are flying today’s mission with has 300 seats. Let’s assume it is our airline’s best route and we happen to have a load-factor of 100% for the day. This means we can board 300 passengers with their bags. When OEMs do their standard maximum range calculation for their long range brochure numbers, they use 210lb as the weight for passenger with his bags. This equates to 95kg and is a bit low for operational airline use.

We will use 100kg per passenger with bags. We create our operational procedures and rules (OPS rules), which is what airlines do as well. With a 100% load factor and 300 seats, we have 30 tonnes of passenger with bags payload. With that we could be satisfied; we could fill the tanks with our trip fuel+reserves and go. This is not good enough for the companies’ bean counters, however. They want to maximize earnings for every flight we do. Therefore they require us to look at the payload range/diagram and tell how many tonnes of additional cargo we could load on the trip.

Cargo is worth about one fifth of a paying economy passenger in terms of revenue but is pays for the additional fuel we need to take on-board for the extra weight of cargo and then some and therefore we need to find out how much cargo we can load.  Let’s say that today’s trip requires us to plan with the flying time equivalent to 8,000nm to reach our destination. As an 777-200LR is flying close to 500nm per hour on such a trip we are talking about 16 hours plus some margin for take-off and landing procedures, so a 17 hour long haul trip.

Now we can enter the diagram from the X axis 8,000nm marker. We go up from our empty weight of 155t and first pass the red line at 155+30=185t. This means we can have all passengers with us on the flight, no need to block seats. Then we can see that the MTOW line passes our 8,000nm at around 203t empty weight+payload. This means we can add 203-185=18 tonnes of cargo on the trip. Our fuel load for the trip is now the MTOW minus our Zero Fuel Weight (ZFW), which is 347t minus our 203t we have used for empty weight+payload, i.e., we are carrying 144 tonnes of fuel on the trip.

We will not consume all this fuel. Around 10% is for our different reserves stipulated by FAA but also by our company OPS rules. If our mission was a normal one, these reserves would still be in our tanks when we have landed. Company and FAA rules allow that taxiing in to the gate can be done on these reserves; we have landed and don’t need the reserves any longer.

Weight or volume limited

So we could bring 18 tonnes of cargo with us on the trip? Not so fast! We have not checked if we have room for 18 tonnes of cargo. If we have room we are weight limited. If we don’t we will take-off volume limited. Here is how we can check what it will be.

First we need to know how many of our 32 LD3 container positions are taken by LD3s, which have passenger bags in them. We would have 23 LD3 positions left after the bag containers are loaded. Now it is all about how much the cargo weighs per m3 or cubic ft. Average values for the industry are 7lb per cubic ft or 112kg/m3. In this case, each LD3 would take 500kg of cargo and add 90 kilos of tare own weight to that.

To take on our 18 tonnes of additional weight, we need to divide with 590kg for each LD3 position. It equates to 31 LD3 containers that can be loaded before we reach MTOW for the aircraft. But we have only 23 left! Therefore we are volume limited. We can load 23 containers each holding on average 0.5t of cargo, i.e., we can get revenue for 11.5t of cargo, not 15.5t (we have to deduct the container’s empty weight) which would have been possible have we had space.

Would we have flown longer or with an aircraft which is less of a heavy lifter than the 777-200LR, we would have found that we would take-off with empty space in the cargo pit. We would have reached the aircraft’s weight limit for the trip before we ran out of space; we would have been space or volume limited instead of weight limited.

An aircraft which is loaded full is always taking off weight or volume limited; it is all about weight margins versus space margins.