Recently, SAS announced that:

Withdrawing tax-free sales will reduce the overall weight of the aircraft, which in turn will reduce fuel consumption and emissions.

I could buy that this might be a polite way to say "we don't make any sales, consequently, the trolley with the items is just ballast; throw it away". It's not the first time that I hear it though: some time ago I remember an article in Aegean's Blue magazine about saving 15 tons of CO₂ in one year just by replacing the pilots' flight bags with the electronic equivalent (EFBs). Unfortunately I don't remember in which issue was that.

Now assuming that a trolley weights approximately 25kg empty so let's say 30kg with the merchandise. The L/D ratio of a an Airbus A320 is 16,3 and thus a 30kg reduction in the weight will result in approximately 18,05N reduction in drag and and an equal reduction in the thrust required to maintain the same speed.

Compared to the ~150kN that 2 CFM56-5B4 produce in cruise, the 0,00012% reduction in required thrust seems like a drop in the ocean. Can this make a difference measurable by an airline company at the end of the month/semester/year/century?

Well, any reduction in Basic Operating Weight, which eliminating the trolley achieves, is an increase in efficiency, because anything not humans and their bags paying money, or kerosene, and not essential to getting from A to B, is ballast. So there is value in forgoing 65lb of ballast and whatever cash income it brings in (I suspect the real reason is it doesn't bring in enough cash flow to be worth the hassle of administration) in the accumulated savings over many years.

You can be sure that the financial and operations organization of SAS did a business case on whether to keep it on or get rid of it. Clearly the business case favoured the get-rid-of-it option.

And you always have to stick the word "emissions" in there because that gives you extra moral weight to prevent anyone from accusing you of a simple economic decision to cancel the service.

I paid for a flight Amsterdam to Accra this afternoon.

I selected the option to "Benefit from CO2-neutral travel".

fly CO2 neutral

Contribute directly to reforestation and conservation of tropical forest in Panama: this project promotes the restoration of ecosystems and biodiversity, and supports local development.

CO2 compensation for your flight costs:

GBP 5.80 [why in GPB, I don't know, I paid for the flight in Euros]

How did we get to this amount?

The calculation goes like this: by burning 1 kg (2 lbs) of fuel, 3.157 kg (6.959 lbs) of CO2 is emitted. So we start by determining the fuel consumption for your flight. This depends on the type of aircraft, distance flown, and number of passengers. Then, we calculate the average CO2 emission per passenger over a period of 3 months. This is how we calculate the amount you will have to pay to compensate for your share.

Now, flying my ~70 kg body plus ~10 kg of luggage to Accra and back consumes an additional X kg of fuel, and therefore emits about 3.157 * X kg of CO2.

The amount of extra fuel it costs may be relatively small, and it may well be a rounding error in each particular flight (a tailwind, or a couple of circuits of a holding pattern, may far outweigh any difference I could make), but it's a determinate and well-known amount (well-known by the airlines, that's for sure), and it corresponds to a determinate quantity of CO2 emissions.

Yes, the removal of payload will result in a measurable reduction in emissions.

First, I have to correct some math: the engines don't run at 150 kN in cruise - that would indicate a L/D ratio of only 4-5, since a typical A320 weighs around 60 tons mid-flight (give or take 10). Fuel consumption is roughly proportional to weight, so 30 kg out of roughly 60,000 kg is a 0.05% reduction, not a 0.00012% one.

As to whether one would be able to move the throttle down exactly 0.05% to benefit from the reduced weight and leave everything else equal, no, not even the autothrottle is so precise.

But that doesn't mean fuel consumption is unaffected: the balance of an aircraft's weight, lift, drag and thrust always affects its energy. At the exact same throttle setting, the aircraft will climb a fraction of a percent faster, and so finish its climb and go to lower fuel burn at cruise a few seconds sooner. In cruise, at the same flight level, it will average a bit lower trim, also arriving a few seconds sooner.

That may not change how much fuel is pumped into the tanks that particular day, but the effect is cumulative and persistent through the variations from other sources. Overall the effect of weight on fuel burn is proportionate. Depending on the distance, everything aboard an aircraft can consume 10% to 50% of its weight in fuel.

As an aside, in-flight sales of random junk really serve the airline, not the passengers. The profit margin on them is up to 100 times the profit margin on economy tickets themselves. With airports packed full of duty-free shops, there's no shortage of shopping opportunities on an air trip. Cramped and burning fuel for every item on board, whether it sells or not, aircraft don't make for a very efficient or practical storefront. Airlines only make up for this inefficiency by exploiting their cabin crews as free salesmen.

Of course, airlines' environmental consciousness tends to correlate strongly with the price of jet fuel, so it may well be that the sales profit no longer covers the extra burn.

When American Airlines switched from paper to iPad for the pilots, they saved 40 lbs (18 kg). This translated to "$1.2 million of fuel annually". (forbes.com; 2013)

Of course this is across AA's fleet, which is big. 963 planes as of writing this.

I don't know how to check the historic fleet size, especially that the merger with US Airways was around 2013 (also big fleet). So let's do it another way.

Medium and long-range planes (combined) make an average of 2.95 flights per day. And according to Simon Weselby, a Fuel and Emissions Performance Manager at Airbus, to carry 1,000 kg of [additional] fuel, requires an additional 150 kg of fuel to be burned.

Using this ratio, we're looking at saving 4.5 kg of fuel per fight for not carrying a 30 kg trolley.

That's ~4,800 kg of fuel annually per plane. Or ~$3,000 worth of jet fuel. (IATA Jet Fuel Price Monitor; 31 May 2019)

Back to AA in 2013, using the 2012 peak jet fuel price per barrel of $129.5, which translates to ~$1 per kg (1 barrel = 159 liters at 0.804 kg/l), means AA's fleet back in 2013 must have been ~410 planes. (No wait, that wasn't your question, go back one paragraph.)