Pitch Damping

[FSMuseum]

Working more on my 747, I have been using Roskam's very informative document on stability and control derivatives. When it comes to the pitching moments section in 1101, I've noticed some curious behavior.

Setting Cmq, pitch damping, Cma dot, dynamic stability, and Cm delta E, elevator control derivative, to the correct calculated values causes my 747 to be very 'bouncy', in that the elevator feels like it's giving the proper control authority, but the Cm graph and Cma dot cause the elevator to lose it's authority rather fast, and when I let it go, it will rapidly return to it's previous trimmed AOA. This quickly leads to some rather high oscillation, even with little control movement. I know an out of trim aircraft will not fly perfectly, but surely not like this?

This happens when I use a pitch damping value close to the real value, around -20 to -25 ish. If I set the pitch damping higher, to around -100 to -300, the oscillations feel much closer to reality, but the elevator lacks pitch authority.

While this behavior does seem somewhat correct in that the way it responds is right, but the response speed feels much too fast. I feel like the virtual passengers would be puking from even slight control inputs.

On a side note, I can't seem to properly figure out exactly how the slope of table 473 is supposed to work, and have borrowed the one from the Level-D 767, since it is another large jet transport and seems to fly properly.

And another side note, how do the horizontal stabilizer entries in section 1101 (Cm ih and CL h) actually work?

Thanks so much!
Chris

 

[Roy Holmes]

Chris,
Some of the pitch coefficients have their signs reversed in the sim compared to real life. Yves Guillame's document spells that out.
However, your value for pitch damping looks OK though I usually have mine around -90.
I suspect you have CG and static margin issues, both of which can lead to "bouncy" responses.
The CG should be somewhere near 25%MAC.
Static Margin for a large transport should be about 10%.
Static Margin =cm_slope/cl_slope.
cm_slope is table 473 and we'll get there in a minute.
cl_slope is table 404.
These slopes are usually per radian. However to calculate static margin they can be per degree which is easier to understand and as long as the units are the same the calculation is valid.
A 10% static margin is, for example, what you get if your 404 slope is 0.1 and your 473 slope is 0.01
So if 404 has 0.0 CL at 0.0 AOA and 1.0 CL at 10 degrees AOA the slope is 0.1
Your 473 should then be - 0.01 at -10 AOA and 0.01 at 10 AOA. and the slope is 0.01

Typically, fighters have static margins at 5% so the aircraft is more responsive than a transport at 10%.
Either way if you have not spent time reading Yves document, I really do think you will find it very helpful.
Roy

 

[FSMuseum]

Hi Roy,

Thanks for your input!

I have been reading Yves's document and attempting to wrap my head around all the stuff that is discussed. I believe I have ensured that the reference datum, empty weight CG (25% just for ease), and the positions of all other things relative to the datum are correct. Aside of the strange pitching behavior, she behaves exactly as I'd expect and the CG is exactly where I'd expect too, if the payload and fuel menu is accurate. AFSD also tells me in real time where the CG is in percent, and it stays precisely where I'd expect in all configurations.

I've moved on to the table 404, 473 and indirectly setting static margin.

A real 747 with a CG of 25% MAC has a static margin of 5.827 and a neutral point at about 46.35% MAC, which tells me it is rather responsive and maneuverable. The accounts of real world pilots seem to back this up.

Also at this CG, in level cruise, Roskam's document lists Cm alpha and CL alpha as around 1 - 1.4 and 4.0 to 6.0, respectively. This pretty closely matches my static margin I have determined. My issue is, how do I use these units for the 404 and 473 graphs? Cm alpha is the slope, but it seems that the values used for the table vs. real life are not exactly the same in so far as determining the slope of the curve.

Thanks!
Chris

 

[Roy Holmes]

Chris,
Roskam's CL alpha is in units of CL per radian. If it was 5.7 it would be the same as 0.1 per degree, which is typical and what you would expect in 404. This means CL= 1.0 at 10 AOA or 1.5 at 15 AOA which is about where the stall is.
Now, for a static margin of 5% you would expect the Cm slope to be 1/20 of the CL slope and is more like 1/5.
Bear in mind that the right hand column of data is for flaps down on an approach, if your data is the same as mine, and as such cannot be used for no-flap purposes. Still Cm is a bit puzzling.
The 747 handling qualities are well described in a section of D P Davies book Handling the big jets. Davies was the CAA test pilot who cleared the 747 for U.K. Flight ops.
Roy

 

[vololiberista]

Chris,

The 747 handling qualities are well described in a section of D P Davies book Handling the big jets. Davies was the CAA test pilot who cleared the 747 for U.K. Flight ops.
Roy

That and "The Aerodynamic Design of Aircraft" by Deitrich Kuchemann have pride of place on my bookshelves!

 

[FSMuseum]

Roy,

Thanks for the explanation. Knowing that my other numbers and graph are fairly accurate outside of the engines, I have come to a decent Cm curve. With my new Cm curve, the pitch response is almost right on the money. Now, just as real life, you do not need near full elevator to rotate, but the response is not exaggerated. The G-values are accurate to what I would expect for the maximum control inputs and the response just feels good. I have ordered a copy of the book you mentioned and will continue to develop based on that. Excellent find and thanks so much!

With some 'general ballpark' values for the engines, my 747 now finally behaves exactly as I would expect in any normal (and most abnormal) flight regimes.

vololiberista,

I will also take a look at that book too. Seems like an interesting read.

Thanks again!
Chris