Hello,
First of all, sorry to disappoint, but the normal law in pitch is not an Nz law. It's a C* law, where C*=Nz+Veq*q/g
Where Veq is a speed around 210-220 kt depending on airbus models, V is IAS, q is pitch rate (it's the letter usually used in France to describe an airplane pitch rate), Nz is indeed the load factor.
At very high speed, you require little q to have a big Nz, your C* law is closer to an Nz law. At lower speeds, the q term is more noticeable.
Boeing has the same law on the 777 except it adds a speed stability term C* = Nz + Veq*q/g + k*(V-Vtrim)
By the way if anyone knows where to see this Vtrim speed (trim reference speed) in the cockpit, I'd be amazed.
Imagine you're asking for more lift. You're asking for C* = 0.2g. The airplane has q=0, so it translates at first with Nz = 0.2. It starts pitching up. You're having some positive q that will appear. This term will damp the Nz demand.
Conversely, if you're stable in level flight, and decide to decelerate. You're asking 0g (of variation), so when reducing speed, at first the airplane will have to have some positive q. Since you still want a null sum, the Nz will become slightly negative. It will damp the q, the q will stabilize at 0 again, but with a very shallow descent.
Knowing more than this would require to have in depth knowledge of the design office.
However I'm not inventing anything as you can see here :
https://www.engineeringpilot.com/pos...n-unknown-star
For the roll axis it's a completely different story. The flight control law will have you control a roll rate. If your stick is neutral, you're asking for 0 roll rate. So the aircraft will damp any roll rate. But the resulting roll won't be corrected.
A technique that I found useful when flying the bus was to consider doing a half correction of the gusts.
- When you correct for a gust, on a conventional airplane :
You counter the roll rate (p = roll rate), by applying some ailerons (p' = roll rate rate) for a certain time. Let say dl times dt
When you reach roll rate 0, you apply dl times dt again (or dl times dt twice as long) to get the airplane back with an opposing roll rate.
You get the wings level, and apply dl times dt again to erase the roll rate, at a zero roll angle.
- On an airbus, the airplane counters the gust, and the orders are added to yours.
The airplane counters the roll rate by applying dl times dt.
You just have to apply dl times dt (but only once, or for one single dt period, as opposed to two in the previous example). Then when the wings are level again you can fly your wings level as you know.
So, when counteracting a gust, telling myself I would only correct half as I would think I should worked very well to avoid overflying the plane.
You still have to counter the gust. Just counter it half as much as you would feel doing.
Final note : on the roll axis, it's not entirely true to say that an aileron input is strictly proportional to a roll rate rate. It is, at first, that is to say, this approximation works very well for the initial phase of controlling gust.
However, if you perform large bank variations, with an established roll rate, you need some ailerons to counter the difference in lift that occur on the wings due to rotation. The rising wing has a lower angle of attack. The lowering wing has a higher angle of attack. It results in a roll moment that is opposed to the roll (roll damping, or Clp coefficient ...). So you need some aileron applied in a steady state in order to get a roll motion.
However, it's also true that at first the aileron inputs are proportional to a roll rate rate.