Calc

# The mathematics of airline baggage

Article Category: Units  |

This one started with one of those email forwards derived from someone’s flippant Facebook or Twitter posting. It featured a photo like the one above and a caption that (stripping out the swear words) read:

“This plane is carrying a ************* spaceship. Why do I have a 50 lb. limit on my ******* suitcase?”

This set us to thinking: are aviation baggage limits actually linked to aircraft capacity or are they just a useful extra revenue earner for airlines?

Well, we’ve done the calculations and the results are quite surprising - even a little disturbing. They perhaps back up Samoa Air's decision to be the first airline in the world to charge customers by body weight as well as luggage weight in 2013. Some industry sources claim this concept could be the future for air fares. Time will tell.

## Carrying a space shuttle

Let’s start with that Shuttle Orbiter, whose dry weight is around 78,000 kilos (Like most airlines, we’ll keep all the numbers metric: it makes life a lot easier).

The carrier aircraft is a Boeing 747 SCA (Shuttle Carrier Aircraft), modified from a standard Boeing 747-100. To equip the aircraft for its new role, Boeing stripped out most of the main cabin fixtures and insulation (though keeping a few first class seats for NASA passengers), added some mounting struts and beefed up the fuselage.

They also added some extra vertical stabilizers to keep the thing flying straight with the Orbiter on top, as well as some more powerful engines. They even added an escape tunnel system for the flight crew (although they had to remove it later, after it became clear that the escape trajectory was unlikely to take the hopeful parachutist much further than the fan blades of one of the inboard engines).

Plainly (planely?) these modifications were sufficient to allow a Boeing 747 to carry a 78-tonne spaceship, implying that the basic aircraft could so so as well.

## Aircraft fuel calculations

So let’s look at the basic data for a Boeing 747-100 in airline service.

Maximum takeoff weight is 333,390 kilograms. That’s the total weight that the wings and engines can lug into the air. But the airframe weight in airline trim is 162,400 kg. so the net lifting capacity is 170,990 kg - still enough to carry almost three Orbiters!

But that’s before you’ve added fuel. Jet aircraft are incredibly thirsty and therefore require huge amounts of fuel. The 747-100B had maximum fuel capacity of 183,380 liters (enough to give it a range of 5,300 nautical miles (6,100 miles or 9,800 kilometers).

In order to calculate the weight of a maximum fuel load, we need to find out what kind of fuel was used and then apply a conversion factor. Your basic common or garden jet fuel is Jet A or Jet A1, with a density on the ground of 0.804 kg per liter. Thus the weight of a full fuel load is just under 147.5 tonnes. Suddenly, that lifting capacity isn’t looking so generous after all. Now we’re left with actual carrying capacity of a mere 23,552 kilos. You can deduct a further 240 kilos for the weight of a three man flight crew (though a three woman flight crew would only weigh 175 kilos).

All of which explains why even the stripped out SCA had a very short range, having to go coast to coast in hops of little more than 1,000 miles at a time with the shuttle on top.

And how does that net payload of 23.5 metric tonnes cope with long haul airline service? The short answer is - it doesn’t.

Say 16 crew (5 flight + 11 cabin) with 50/40 male/female distribution wearing winter clothing (6.4 kg each). That’s 1,200 kilos. An average 40,000 items of inflight catering and other supplies: 6,000 more kilos gone.

With just 16.3 tonnes left in hand, we’re finally ready to start loading passengers and baggage for our notional flight from London Heathrow to Los Angeles LAX (5,440 miles), for which we’re going to require almost full fuel load.

Airlines don’t like to make passengers get on the scales at the Check In Desk, so they work to a basic rule of thumb of 79 kg per male and 57.6 kg per female, adding 3.6 kg clothing weight to each person in summer and 6.4 kg each when wrapped up for winter. Children up to 12 are counted as 34 kilos each all year round.

In airline trim, the 747-100B could carry 412 passengers in two classes or 266 in three classes. Plainly that first configuration isn’t going to work for London to LA, with a basic passenger weight (assuming 220 male, 175 female, 32 minors) of more than 28 tonnes, even in short sleeved shirts and summer frocks.

In three class configuration, we might have better luck. Now the weight of passengers comes down to just over 17 tonnes (130 male, 110 female and 26 minors) but we’re still a little over maximum takeoff weight - with everyone bare-ass naked and without their luggage.

Quite apart from preserving decency, that’s a major problem because the baggage also weighs a lot. Each passenger and crew member has a carry on bag weighing an average 7 kilos: for our flight that comes out at 1,975 kilos - nearly two tonnes!

Then you have the hold bags. If you allow each of the 200 Economy passengers one suicase at 30 kg and 66 First Class/Club Class given two hold bags at 50 kg each, that would weigh in at a grand total of 12.6 tonnes. We’re now around 16 tonnes over weight and will have to offload close to 20,000 liters of fuel to get airborne. Forget LA - we might make Chicago O’Hare.

On the next page we look at the baggage capacity of modern aircraft and safety calculations to conclude whether baggage weight matters.