# Why would a stretch variant need a larger horizontal stabilizer?

### Update and accept reason

The reason for asking why would as opposed to why does is I was not aware of any previous [jetliner] stretch requiring a larger horizontal stabilizer. For example, all the DC-8's from shortest to longest (almost the same stretch as the 787-10) retained the horizontal stabilizer throughout:

(Great Airliners) Click to view.

But then I finally recalled a situation where it has happened, the 737 Classic, and the reason given is the "fore-and-aft loading flexibility", in other words the cg range, and that's why I'm accepting @jwzumwalt's answer.

With the 787-10 stretch, Vedad Mahmulyin (a Boeing engineer) saved the company millions by implementing a software solution that negated the need to enlarge the horizontal stabilizer.*

When a plane is shrunk, that is usually the case because of the reduced moment arm. When it is stretched, the tail volume is retained if I understand this comment about the DC-10/MD-11 stretch correctly:

Isn't the tail of the MD-11 smaller because it has a longer lever arm? The tail volume of both aircraft should be quite the same. Also, any FCS cannot help to trim the aircraft over a wide range of cg positions, and it is this trim range which drives tail surface volume. @PeterKämpf

• Why would a stretch variant need a larger horizontal stabilizer?

From an interview with Mahmulyin:

Mahmulyin figured out he could use software to tell the wings and the stabilizers how to fly together, "As opposed to having to produce all new horizontal and vertical stabilizers," he said.

• What does 'flying together' mean? (This is an optional question and does not involve proprietary information.)

* Flight International (27 Mar 2018) confirms the horizontal stabilizer size issue:

Software again proved useful with the sizing of the horizontal tails. As a stretch of the 787-9, textbook aircraft design would suggest the 787-10 would need larger horizontal stabilisers, offsetting the effect of the longer fuselage on pitch control. Instead, Boeing engineer Vedad Mahmulyin used software to increase the effectiveness of the existing stabilisers. Boeing gave Mahmulyin an internal engineering award for solving the problem.

• According to this it is not about avoiding a larger tail but avoiding a stronger tail. The patent is about limiting tail loads at high dynamic pressure differently when the gust alleviation system is engaged. – Peter Kämpf Apr 4 '18 at 21:06
• @PeterKämpf - I also checked your conversation with DL. An excellent find. I agree the coverage of Flight was better in the past decades and there was little to go on by. I might end up asking a tie-in question. Thank you for taking it further. – ymb1 Apr 5 '18 at 8:20
• The issue why a stretched plane would need a larger tail was too astounding for me to be left alone. – Peter Kämpf Apr 5 '18 at 12:26
• The first 737 classic model (the -300) had a larger tail than the -200 from which it was derived, but this was generational not due to stretch. The -500 which directly replaced the -200 had a -300 sized tail. – Pilothead Apr 16 '18 at 20:47

1. The primary reason is probably because a larger tail increases the CG range. It does not make sense to stretch an aircraft without increasing the CG range. calculating tail volume
2. Often the horz stab is used for the extra fuel capacity needed for stretch models (i.e MD11 and B747). "...the tail fuel tank will provide added range and improve the aircraft’s performance"
3. Part of the stretch is forward of the CG (and wings) and therefore counteract the tails effectiveness. (float planes often suffer the same adverse weather cocking problem and so extra vertical surface is sometimes added below the fuslage.)
4. The stretch will have higher gross weight and the tail surfaces will have to overcome greater inertia. Per @DeltaLima moment of inertia math shown below.
• I think your 1. and 3. contradict eachother? If I add one section in front of the cg and and one section behind the cg, and both fill them up with the same weight, the cg will not change? Also, I don't understand why you mention the tail volume at 1., if anything, the stretched version would have a larger distance to the AC, therefore permitting a smaller tail. – ROIMaison Apr 4 '18 at 9:05
• 1) The primary cg range is controlled by wing MAC (~15-30%) and the original wing is sized for cg extremes. When you stretch, the cg range increases (arm * weight) and changing the wing chord is impractical. To adjust for the new cg range extremes the tail is enlarged. 3) Any surface ahead of the cg creates adverse weather cocking. A float plane CG does not change but the added float surface ahead of cg often require increase tail surface such as the vertical surface seen added below the fuselage. – jwzumwalt Apr 4 '18 at 9:28
• But usually a stretch adds sections in front and after the wing, so the cg range does not increase? See for example this image where more sections are added in front of the wing than after for A321 – ROIMaison Apr 4 '18 at 9:34
• If your reason 1 were correct we would see larger tails on all stretched aircraft, but this is a rarity. If anything, reason 2 (for trim, not range) is the means by which manufacturers avoid needing to do your reason 1. – Pilothead Apr 16 '18 at 20:28

When the fuselage is stretched, the arm of the horizontal stabiliser is increased, and hence it's effectiveness increases linearly with the fuselage length.

However, because the mass is distributed further away from the centre of gravity, the pitch moment of inertia increases too.

If the fuselage would be modelled as a uniform rod, the moment of inertia in pitch would be $\frac{1}{12}mL^2$, with mass $m$ and length $L$.

source: hyperphysics.phy-astr.gsu.edu

You see that the moment of inertia increase with the square of the fuselage length, while the effectiveness of the elevator increase linearly with fuselage length. The nett result is that the pitch response of a longer fuselage with the same horizontal stabiliser/elevator is reduced.

In addition to the change of inertia, the heavier aircraft needs more powerful flaps (double-slotter vs single slot before) which causes a bigger pitch moment change.

Therefore a stretched aircraft needs a more effective elevator.

As for the meaning of "flying together" I assume that this means that the software solution for the 787-10 controls the pitch moment of the aircraft not only by changing the elevator angle, but also uses control surfaces on the wing.

• Not to forget that a stretch, being heavier, needs more powerful flaps (double-slotted when single-slot sufficed before) which cause a bigger pitch moment change. That is at least as likely as the inertia increase to drive elevator size. – Peter Kämpf Apr 4 '18 at 6:37
• Morgen @PeterKämpf. Thanks for the comment, I'll work that into the answer. Is there a rule of thumb to quantify the change in pitch moment? – DeltaLima Apr 4 '18 at 6:45
• Oh boy, not that I know one. I would also argue that normally a stretched variant needs the same or a smaller tail (see the increased vertical of the A318 for the opposite situation). I would expect that the bigger tail is driven by the desire for a wider cg margin. What happened in case of the 787 and the software fix is unknown to me. I'm now researching this – Peter Kämpf Apr 4 '18 at 20:32
• The patents are about elevator loads, not size. It seems that the trick is to limit the elevator deflection differently when speed brakes or a load alleviation system is engaged. A look-up table controls variable elevator deflection limits depending on dynamic pressure and stabilizer angle, but that is not exactly new. Looks like I read the wrong patents, or Flight did not get their facts straight (also not exactly new). – Peter Kämpf Apr 4 '18 at 20:57
• It think the patents you found are right, Flight is probably slightly off. Rethinking it, it makes sense that the stabilizer size shouldn't change, or may even be smaller, when the fuselage length increases. In the static situation, the increased arm increases the moment. In the dynamic situation, a pitching motion will cause higher vertical velocity of the tail and hence the change in local angle of attack of the horizontal stabilizer due to pitch rate increases with fuselage length. The pitch dampening is therefore probably more effective on longer fuselages. – DeltaLima Apr 4 '18 at 21:14

A stretch variant doesn't need a larger tail, due to increased arm. If you want to muck with the CG or whatever that is independent of a stretch. The classic counter example is the 747SP, a shorter variant with a gigantic tail, due to reduced arm.