Malibuflyer wrote:
To summarize that:
- The straight&level stall speed is not only depending on the weight but also on CG and other things.
- The increase factor of stall speed due to dynamic wing loading is proportional to the square root of loading if (and only if) CG (and some other factors) remain unchanged.
OK got it !
If you drop 50% of the aircraft mass in a turn, the resulting stall speed is depending on the new CG of the plane and not automatically the “straight and level” stall speed of the plane with the weight.
To summarize that:
- The straight&level stall speed is not only depending on the weight but also on CG and other things.
- The increase factor of stall speed due to dynamic wing loading is proportional to the square root of loading if (and only if) CG (and some other factors) remain unchanged.
But G-load and weight is the same thing as long as aircraft shape is the same? if one drop 50% of aircraft charge on a 2G turn while keeping same shape aircraft it will stall at same “TAS” speed as straight & level with initial weight for same air density
Or you think the way how initial weight impacts straight and level stall speeed differs to how load factor will impact stall speed in a turn? (ignoring IAS, CAS EAS corrections and considerations and any change in aircraft geometry)
Ibra wrote:
But why these don’t manifest on dynamic stalls in the turns which tend to accurately track those “square-root” law formulas?
You mean the effect that in a turn the stall speed increase (e.g. the factor you have to apply to the straight and level stall speed) is the square root of the load factor?
That already implies the answer to your question: The described aerodynamic effects are already reflected in the straight and level stall speed and therefore the increase is independent from them.
lionel wrote:
But in these POHs, it is not.
Perhaps there are other effects. Vref does not have to be 1.3 Vs, it just has to be above 1.3 in most cases. There might even be some aircraft where even this doesn’t apply. i.e. It just have to a safe speed. You have to check of actual certification rules applicable at the time the TC was issued.
Also some aircraft are not capable of full stall at forward CG at low weights power off. e.g. some model of the bonanza don’t have enough elevator authority. Some aircraft have some stability issues at very low speed this increases the minimum speed. i..e this becomes the limit used to calculate Vref not Vs.
Malibuflyer wrote:
there are mainly two effects that make things more complex than your “square root law”:
But why these don’t manifest on dynamic stalls in the turns which tend to accurately track those “square-root” law formulas?
My feeling they are mostly IAS, EAS, KCAS related aberrations and instrument errors near the stall than “deep physics issues” with the “square-root” model or zero-lift drag characteristic, for approach speed one will be far away for these and flying same AoA will give a square-root forumula between approach speed and weight
But there maybe more to it to deviate from an ideal square-root law, drag curve shape, forward visibility, approach stability in gusts vs weight, gear max/min touchdown speeds, changes of flaps config with weight
I flew a D31 turbulent, stall speed is 35kts but everybody decided the approach speed to be 60kts for any weight & conditions unless you want troubles 
In the idealized case of a wing only airplane your model is close to reality. For real existing planes – especially small ones like ours – there are mainly two effects that make things more complex than your “square root law”:
“lift=weight” is only true if you take “lift” as equivalent of “total vertical component of aircraft lift”. The main difference of that from the lift which is generated by the wing is a) the pitch angle of the plane (as the wing lift is perpendicular to the body axis while the weight is perpendicular to the horizontal) and b) the (negative) lift of the stabilizer
Both are relevant at higher AoAs/lower speeds and b) is even depending on the CG.
Therefore The POH stall speed is depending on the CG diagram as the stall speed is always given at the allowed most forward CG (as the required negative lift of the stabilizer increases with forward CG).
I guess that is also the reason why some microlight planes that need to demonstrate low stall speeds in some regulations have a very narrow CG envelope and are very limited in terms of front CG at higher weights.
Xlr8tr wrote:
Vref is a factor of the stall speed, usually 1.3 x Vs for the configuration. As the stall speed increases with weight therefore the Vref increases accordingly.
I was not speaking qualitatively (I understand that), but quantitatively.
But in these POHs, it is not.
lionel wrote:
I expected the square of the speed to be proportional to the weight (mass), but it is not. Not in the Diamond POH and not in the Mooney POH. Interestingly, the ratio increases with weight on the Diamond, but decreases on the Mooney.
If linking speed to weight via lift at specific approach AoA, that should be the formula for Va(W) which is along Vref(W)= 1.3*VS(W) at max AoA, yes POH numbers for Mooney & Diamond do go out of fashion vs that exact formula but we are talking 3kts here
Maybe Diamonds can’t land slow at max MTOW (limited to 1210kg landing vs takeoff at 1280kg) due to weak gear design while on the Mooney can’t just land 5kts faster due to flat drag curve on higher speeds above 1.3*VS 
I actually don’t understand the approach speed variation with weight
Vref is a factor of the stall speed, usually 1.3 x Vs for the configuration. As the stall speed increases with weight therefore the Vref increases accordingly.
