Regarding the figures: The CFM56 on the 340 is 4 tonnes dry weight. And by looking at a 3-view drawing it's more like 15 m not 10 m (each wing is ~27 m).

I measured the wing and 10m is correct. The distance between engines is about a third of a wing. I looked at the wrong cfm56, will fix.

I've created this image if you want to use it in the question body. Original source: Wikipedia.

@ymb1 nice picture

Anytime :) With each wing ~27 m from the root, it does look more than 10 m to me.

@ymb1 Wings are measured to center of fuselage

@Pilothead then it's even more than ~15

wingspan is 60.30 m tip to tip

minus fuselage width gives each each from root ~27 m

so the outboard ones are definitely more than 10 m just by looking at it

distance from root that is, which is the bending moment the article speaks of, not from tip

Get a ruler. The wingspan is 60m and you'll see the distance between engines is about a sixth.

not between, but from outboard to root

engine weight vector down times distance to root is the bending moment

which counters the upward bending from lift (higher weight, higher bending)

I'll try to measure it in pixels instead, i'll need 5 minutes

We are talking about different distances. Bending relief is moving weight outboard, so from the 330 engine location to the outboard 340 engine location. It is not bending moment which is relative to wing center point, or installed at wing root.

The distance you are talking about is at least 15m.

but the a330 still have inboard engines

each 5 tonnes btw en.wikipedia.org/wiki/General_Electric_CF6#Specifications

so you added 4 tonnes outboard times distance to root

by pixel accuracy it's 17 meters

from root to outboard engine on A340

correction: 16.51 m

minus 1 tonne from inboard to root

This is the misunderstanding. Bending relief is the difference between the cases. Bending moment is the absolute location of the weight. So the relief distance is 10m and the moment distance is 17m.

...between the two cases we are considering...

ok, I'll breakdown the first sentence, let you know how I understand it:

> Because of bending relief from the weight of its outboard engines [relief for lift due to the bigger moment arm], the bending moment [of the wing due to lift] of a four-engined aircraft is substantially lower than it is for a twin at the same maximum take-off weight

the bits in the brackets are my understanding

* by moment arm I mean engine location to root

*understand. Relief is not moment. Relief is differential.

In either case, the question states 4t weight is moved outboard from a330 engine location to a340 engine location, which is 10m.

I think the question conveys the correct meaning, whether or not we have the same understanding of terminology.

if distance between engines on each wing then yes it's 10 m

higher MTOW causes bigger wing bending upwards right? the relief here is outboard engine countering this bending, that's why I said to wing root

Yes, but that is moment

the engine's moment relieves the bending (?) :D

Do you agree the question is ok? I don't think any terminology problem ruins it

I liked "the engine's moment relieves the bending (?) :D"

:D question is fine -- it's just the 10 m thing confused me and I thought it was an error, because of the way I see it (moment to root relieves)

@Pilothead cleared my comments and +1'ed, you missed a comment btw on my answer :D feel free to leave the link to chat though

less clutter

agree and done