How does control effectiveness change with density altitude?
 

Some of you test-flight bods may be able to help me here:

I'm playing about with high-altitude flight simulation in X-plane and an external autopilot controller to control the simulated aircraft, but I'm coming up with a problem when tuning the autopilot at high altitudes (>FL500), where the gains that work at lower altitudes are increasingly unstable.

Now, as far as I understand, C_L is a function of alpha with an added component to account for control deflection that is approximately linear with deflection. For level flight, the 1/2.rho.v^2 and wing area components of the lift equation are consistent, even though TAS is through the roof at the higher flight levels. I can't see then why X-plane, which uses some form of physical aerodynamic modelling, would be simulating a higher system gain at higher TAS/Mach/FL. Is there a compressibility effect coming into play here, or have I misread the lift equation?

What's going on here? Anyone wise to this?

Thanks in advance for your help.

A

Hello,

You are right on the lift. It depends only on the EAS. for a given incidence (and mach number if relevant)

Though, the vertical acceleration (load factor) is a mechanical effect, it depends on the TAS, not on EAS. Which explains why, for a given elevator input (for example), you don't have the same load factor at sea level, at 20,000ft, or higher

regards

If I'm understanding your general question correctly?

The major effect of TAS at high altitudes is reduced aerodynamic damping of flightpath perturbations as a result of a lesser effective restoring force component...:)

You will need more fin area to kill the dutch roll.

Thanks for the attempts. Further thoughts lead me to believe it's not the steady-state lift generated according to the lift equation, but how quickly that lift develops when the configuration is changed by the controller. It is obviously not instantaneous, but possibly some function of the sonic velocity and possibly also to do with the (true) speed of the air passing over the wing.

I think it's a sonic velocity issue, from gut feel, as the pressure field around the wing can only change at the speed of sound

More research needed, I think

Andy
 

I may be misunderstanding your problem. If so I apologise.

At 40000ft your TAS is roughly twice your IAS/EAS. At sea level they are both the same.

Momentum is dependant on TAS. So the tendency for the aircraft to carry on in whatever direction is hugely greater at 40 than at sea level when if at the same IAS/EAS.

Control power and lift however are both IAS/EAS dependant.

So at 40 Mr Newton wants you to carry on in a staight line in spades while Mr Bernoulli has even less to play with to generate a distubing force than at SL thanks to mach effects.

BTW I was nearly thrown off the course at ETPS for writing that the controls were less effective in certain circumstances. It was explained to me that a control was either effective (if it caused something to happen) or was ineffective (if it caused nothing to happen) and that what I should have been talking about was a reduced level of response. Happy days.

John, touche,been there,red ink everywhere...!

Thanks John, I see what you're saying there, but don't the control surfaces only control pitch. roll and yaw?

In level flight the average angular momentum is zero about any axis (not including the effects of the curvature of the earth) so if you're flying along up high S+L and you turn on your wing leveler which develops a limit cycle oscillation (in roll) that wouldn't have occured down at sea level, how is that related to the aircraft's momentum or kinetic energy in the translational sense?

Hmmm!!! Found my little problem and it was nothing to do with physics, but damn software!

The autopilot code was clipping the speed correction factor for the PID gains and so not allowing the gain to fall far enough at elevated TAS.

Nothing too complicated then! ;)

Andy
 

Glad you are sorted.

I was trying to explain why you can't change your flight path as quickly at 40 as you can at SL. Like I said sorry if I misunderstood your question.

sycamore
 

........and I thought it was only me who struggled. I owe you a beer.

Not at all, John. Thanks for helping me think through the problem!

PS: I also learned about the existence of EAS, which I didn't know before! :ok:

The tail of an aircraft that is rotating in pitch sees a change in apparent incidence relative to flying at a constant pitch angle. The resulting change in tail lift acts to oppose the rotation and is the main contribution to pitch damping. The magnitude of this rotation-induced incidence change is inversely proportional to TAS. So, using John's example, the same pitch rate at 40,000 ft will cause a change in airflow angle at the tail roughly half of that at the same IAS/EAS at sea level, halving the associated damping.

The same principles apply to the damping contributions of the fin due to yaw rate and the wing due to roll rate.

Density of air is defined as mass per unit volume .
Density reduces with height .
To get the lift ,we need certain density .
To get that density we fly a present speed (IAS.)
So , if you fly the constant IAS , irrespective of your density altitude , the lift will not change .
It is just because of density being less , drag component will reduce thus the TAS will increase .
Now let's talk about control effectivity ..
Suppose there is no air , control will have no effect .
Similarly when aircraft is stationary , control will move but will not produce enough forces to create couple to move the aircraft along its axises .
To get that we need to increase speed , so that density which it is encountering or mass per unit volume of air will increase , that will make the controls effective .
The first speed, which we comes into existence after rolling for take off is VMCG .
We can also say that we need more density to increase control effectivity .
So if can say that with the increase in density altitude , which we would say decrease in density per unit volume ..
The control effectivity will decrease .
Please note that VMCG is not to get enough lift to get airborne .

Utter rubbish my friend. :)

Agreed. By the time we reach the head it's mostly very low. :rolleyes:

I think it is meant to be 'For a given IAS/EAS as the density reduces the associated TAS would increase'. ;)