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A 707 being a much older plane with relatively stiff wings compared to the 787. What percentage would the g forces be reduced on a 787 given its wing flex?

And yes, I mean if the 707 and 787 were flying through the exact same turbulence at the same time.

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    $\begingroup$ The B787 has a gust alleviation system that likely has a much greater impact than the wing flexibility. Related: Does the 787 gust alleviation system make a more comfortable ride or for a more stable aircraft? $\endgroup$
    – Gerry
    May 17, 2019 at 12:30
  • $\begingroup$ @Gerry is there any data on what % turbulence g factor would be reduced? Ie if it went through the same turbulence as the hypothetical 707 in my post title. $\endgroup$
    – Warden
    May 17, 2019 at 13:38
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    $\begingroup$ I expect that Boeing's flight controls group may have access to the raw data needed to make the comparison. That doesn't mean they've actually compared the two platforms. It's also unlikely that any significant data has been published outside Boeing as it would be considered proprietary. $\endgroup$
    – Gerry
    May 17, 2019 at 16:59

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Gust is an impulse load on an aircraft: a sudden change in force, which distorts the previous equilibrium. Upon a vertical gust, the aircraft will respond with a second order response: vertical acceleration, damped by the air resistance.

The factors for accelerations due to gusts of a certain intensity and duration, as per this answer:

  • Elasticity of the wing construction material acts like a spring. Load it with a vertical gust, and it will bend upwards, then spring back.
  • The wing bending experiences damping forces from the surrounding air, proportional to bending velocity.
  • The wing sweep angle spreads out the gust: not all of the wing is accelerated upwards immediately.

When comparing the two planes (from the wiki pages):

  • Faster planes are less impacted by a gust load - the B707 cruised at 1,000 km/h, the 787 at 900 km/h, so this is in favour of the 707.
  • Wing sweep is comparable, 35° for the 707 and 32.2° for the 787
  • Higher wing loading is favourable: 151,300/283 = 535kg/m$^2$ for the 707-320; 254,011/377 = 674 kg/m$^2$ for the 787-10, the 787 wins
  • Higher aspect ratio is favourable: A = 7 for the 707-320, 9.59 for the 787: it wins

Simple observation as a passenger reveals that the carbon-fibre composite wing of the B787 flexes up-and-down a lot, so the spring-mass-damper response of the B787 would be slower, despite its 10% lower cruise speed.

enter image description hereScreenshot from this video

The active gust alleviation system of the B787 deflects the inboard flaperons as a function of detected vertical acceleration, which indeed helps in comforting out the ride.

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The 787 will not experience lower G-forces, but it will smooth out short spikes. If a 707 experiences +5G for 200ms, a 787 might ride over it and not feel much. If a 707 experiences +5G for 2s, so will the 787.

What percentage would the g forces be reduced on a 787 given its wing flex?

You cannot give a percentage of reduction. If the updraft persists for long enough, both aircraft will feel the same G-forces. If anything, you can give a maximum gust duration that can be smoothed out.

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    $\begingroup$ Since G-force is an acceleration, I do not think this answer can be right. The root of the wing will start to produce lift instantaneously on both aircraft. On a 707 the tip will also produce lift very quickly. on a 787 the flex of the wing will distribute the force output over time, thus expanding the exertion of the force over a longer period -> Z less G-force. $\endgroup$
    – Jpe61
    Jan 12 at 14:25
  • $\begingroup$ @Jpe61 - Your comment is correct, but I cannot see where it disagrees with my answer or what point you are trying to make. A floppy wing does not reduce G-forces in general, but it does average out short spikes. That's what my answer says and that's what your comment says. OP was asking for a "percentage of reduction" and that doesn't exist. If anything, you can state the "maximum gust duration" that will be averaged out (longer on a 787 than on a 707). Longer gusts will always produce full G-forces, on both aircraft. $\endgroup$
    – Rainer P.
    Jan 12 at 14:39
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    $\begingroup$ Gust by definition is a brief change in wind. During this brief period the gust will load the wing of 787 gradually bwcause of the elasticity, so the effect of the gust force is spread over a longer period of time resulting in lower vertical acceleration of the airframe (m/s^2). Think of it this way: you have two equal weights on table, attached to the edge of the table, one with a rubber band, one with a chain, both of equal length. Now push both over the edge of the table. Which one of the weights will experience higher g-forces as comes to a stop? $\endgroup$
    – Jpe61
    Jan 12 at 20:16
  • $\begingroup$ @RainerP. You are conflating the cumulative force delivered to the aircraft by a gust with the number of Gs that the aircraft experiences. If I experience 2Gs for 3 seconds, or 3Gs for 2 seconds, it may seem like I have experienced the same amount of cumulative force. But in the first example I experienced 2 Gs, and in the second I experienced 3 Gs. $\endgroup$
    – Max R
    Jan 17 at 1:12
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G-forces caused by turbulence are instantaneous. The wings will not "cushion" the aircraft to mitigate the force of the turbulence. The additional flexibility of the wings means that they will absorb more energy and dissipate them without damage to the structure.

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