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V-n diagram, Vs (stall speed) Va (maneuvering point)

in my textbook and apparently everywhere online I have found that Va or cornering velocity is defined to be the point of intersection where the stall line and the limit load factor line meet. Apparently, it also states that this Va is the lowest airspeed at which load factor can be reached and any speed below that cannot exceed the limit load factor because the airplane will stall first.

Ok, I see that. If I so horizontally to the left from Va (around 120kts) yes, the plane will stall first. however, it seems to be that this speed is not the lowest airspeed to reach that load factor. isn't the lowest airspeed around 80kts? which is at the bottom part of the intersection around when negative Gs (between -1 and -2gs)are experienced.

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Because it is unlikely that you fly upside down for an extended period.

You are right that it is possible to exceed the negative limit by aerodynamic means below v$_A$ but that does not mean that the structure will fail immediately. Normally, the maximum positive and negative structural load factors are about equal; the biggest exception occurs with wooden spars (wood is stronger in tension than in compression) or if buckling limits the compression load of the spar. Note that aerobatic airplanes typically have the same value of load factor in both directions.

The low negative limit is used because more is not needed and some things become easier with a lower load factor, especially for the airplane systems (engine, instruments, controls).

The next reason are gust load factors. Starting from 1 in level flight, an upward gust will cause a load factor 2 gs higher than a negative gust of the same magnitude. Since it is assumed that you fly right side up in gusty weather, the lower limit can be 2 gs smaller (in absolute terms) than the upper limit.

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I'm not sure I follow your reasoning (at 80kt, the aircraft would stall at either $\approx$ 1.6g or $\approx$-1.3g, both smaller than the limit load factors +3.8g and -1.5g), but it's just a definition. You could define a "negative manoeuvring speed" and take the negative limit load, but the consensus for manoeuvring speed is taking the positive one.

While flying, we usually experience more positive load factors (e.g. turns, flaring out,...) than negative ones. Therefore, I am not surprised to see the positive load being used for the definition.

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Because under normal flight conditions (for non-acrobatic activities), we fly at or around 1 G. So deviations caused by updrafts, down drafts turbulence, etc. that might cause airframe overstress are much more likely to occur in the positive G direction than in the negative G direction. Since "maneuvering speed" in General Aviation is defined in order to give pilots an idea as to what speed puts them at risk of overstressing the airframe due to these deviations, it is the positive G inflection point that is most relevant.

But you are right, if a string enough downdraft occurred (near a thunderstorm or in heavy turbulence, for example), it could cause an overstress if you are faster than the indicated/calibrated airspeed at the lower negative G inflections point.

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