Fuselage length vs wing location vs wingspan

[Litvyak]

I've started working on my De Havilland BC Trident variants, with the first part being working out interior floor plans/maximum seats (which has led me to learning about FAR stuff about exit limits), and as I was working on a seat map for a stretched version I looked at the position of the overwing exits, which prompted me to wonder what sort of engineering factors determine the location of the wings relative to the length of the fuselage.

Looking at the DC-9/MD-80/MD-90/717 family, I noticed that that there is some variation in the positioning of the wings in the MD-80/MD-90 variants, which all use a 107' 8" span wing:



My question then would be, is there a simple(ish) calculation to determine where on a fuselage of a given length the wings need to be positioned? I don't need anything super accurate since I'm not actually building something to fly, just something that's close enough that discrepancies could be explained away as "small error made by the drafter".

From there the question of wingspan entered my mind, too: what determines the necessary wingspan for a fuselage of a given length? The MD-80 family and the MD-90 all use wings with a 107' 8" span, with fuselage lengths ranging from 130' 5" (MD-87) to 152' 6" (MD-90) - that's a 22 foot range... whereas the DC-9/717 variants get more complex:

DC-9-21 -- span 93' 3.6" -- length 104' 4.8"
DC-9-32 -- span 93' 3.6" -- length 119' 3.6"
DC-9-41 -- span 93' 3.6" -- length 125' 7'2"
DC-9-51 -- span 93' 4.2" -- length 133' 7"
B 717 -- span 93' 4.2" -- length 124'0 "

Again I'm absolutely not an aero engineer, but I'd guess that that 6/10 inch difference in span between the two wings isn't something related to the length of the fuselage (if there's a relation there at all?), which guess is based on the fact that the 717 which uses the longer wing is a little shorter than the -41 which uses the shorter wing...

What complicates this further is that the DC-9-15 has the same length as the -21, but has a wingspan of only 89' 4.8"; I know the -15 is the only DC-9 without leading-edge slats... but can the addition of slats increase the span of the wings by nearly four feet?

I'd *almost* start thinking I can figure something out based on this data, but then I look at the values for the HS Trident:

Trident 1C -- span 89' 10" -- length 114' 9"
Trident 1E -- span 95' 0" -- length 114' 9"
Trident 2E -- span 98' 0" -- length 114' 9"
Trident 3B -- span 98' 0" -- length 131' 2"

... and then nothing makes sense anymore.

Rephrasing all of this in a different way better expressing my purposes:

Is there a way to easily figure out the maximum length of the fuselage forward of the forward edge of wing root for a given length of the fuselage aft of the aft edge of the wing root? Or does it matter, since although the Douglas designs have the wings aftwards of centre, looking at the 727 and Tu-154 the offset appears much smaller (though still aft of centre)? Does the planform of the wing play a role in this?

And a sudden thought: is the height of the vertical stabiliser going to be affected by the fuselage length/positioning of the wings?

[Litvyak]

Corollary question: is there a maximum the fuselage length can be for a given wingspan? E.g. if we're using the 95' span wings of the Trident 1E, what's the longest the fuselage can be overall (assuming here the wings are in the correct position for the fuselage)?

[Old Wombat]

The leverage (or "moment") of the mass distribution plays a significant part in determining where the wings are positioned, not just the centre of mass, which is particularly important in rear-engined aircraft like the DC/MD series & the Trident, as the mass of the engines is a considerable percentage of the total mass of the rear of the aircraft & it is all at the furthest point from the centre of mass.

The greater length of the wings in the listed variants probably has more to do with extending the range of the aircraft for the same fuel load (more lift for same thrust / same lift for less thrust).



Probably more than you want/need to know but; moment = https://web.mit.edu/4.441/1_lectures/1_lecture5/1_lecture5.html

[kitnut617]

If you look at the Bombardier CRJ's, they were extended along the same lines as the DC-9. In all cases it got a fuselage stretch, but I've read that each one got a different wing (and engines). Looking at my 1/72 Challenger and comparing it to my 1/72 CRJ-200 (which is a Challenger with a 20 foot stretch) the wing is quite a bit larger. I'll try to take some photos of the two for you to see as I think the DC-9 series also had different wings.

[Litvyak]

Okay, so... I gather that if I can do some calculations to see approximate wing positioning in relation to fuselage length of the 727 and Tu-154 variants (perhaps Dassault Falcon too - since I'm working with a trijet here), then using similar relationships should produce a "close enough" value for my purposes?

If they're all rather different then I'll probably use the Tu-154M values, since the dry weight of the Soloviev D-30 is closer to that of the RR Medway derivative on the BC Tridents than is that of the JT8D... should get something looking reasonable enough for my purposes, I think.

I'll use this same approach but with DC-9/MD-80 variants when I work on the twin-engine Kehloke.

[kitnut617]

Here's the difference between the CL-600 and the CRJ-200 wings to give you an idea. This might explain the difference between a CRJ-100 and the CRJ-200 too, the -200 being the longer range variant, the fuselages for these two being the same.

[jcf]

The "wing position" doesn't change, that wing/fuselage interface is the core structure of the aircraft.
When they do a stretch plugs are added, fore and aft of the wings, to lengthen the fuselage, the length
of those plugs varies by how great a stretch is wanted and, along with increasing capacity, the aft plugs
serve to move the tail aft in relation to the wing to balance the length added forward and maintain
CG relationships etc. Everything is done in relation to the wing box and main landing gear well, which
don't change location. This is one of the major advantages of the tubular fuselage, it's relatively easy
to change the length.

Perhaps this drawing will help, 777-200 compared to stretched 777-300, the plugs are 210" added to
Section 43 fwd. of the wing-box/mlg (Section 44-upper lobe and Section 45-lower lobe) and a 189"
plug added into Section 46 aft of the wing.



The drawing of the DC-9 family is misleading, lining the profiles up by the aft point of the tail does not
show the actual relationship between the various types. They need to be aligned based on the main
landing gear position.

[kitnut617]

Here's the difference between the CL-600 and the CRJ-200 wings to give you an idea. This might explain the difference between a CRJ-100 and the CRJ-200 too, the -200 being the longer range variant, the fuselages for these two being the same.

I was giving the wings another look yesterday, it appears that the only difference with these two wings is the wing tip extension on the CRJ-200 wing (resin)