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Need help with interpretation

J

johnor999

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sweden
Hello!

I have a question about the equation for CL_de found on page 23 in FS Flight Dynamics 1.0 by Yves Guillaume:

CL_de = (CL_e_basic + CL_e_M) * delta_e[elevator_up OR down_limit * R517_Elev_defl_limit_scalar_vs_q]

Does delta_e[elevator_up OR down_limit * R517_Elev_defl_limit_scalar_vs_q] mean:

delta_e * elevator_up OR down_limit * R517_Elev_defl_limit_scalar_vs_q

or does it mean the delta between delta_e and elevator_up OR down_limit * R517_Elev_defl_limit_scalar_vs_q?
 
I interpret it as:
Code: 
delta_e = [elevator up OR down limit] * R517
 
On page 7 it states that delta_e is the elevator deflection in radians. Therefore the formula is: CL_delta_e = delta_e * [elevator_up_limit OR elevator_down_limit * R517].
 
Let's throw some numbers into it then and see if I've got it right now (please don't focus on the numbers being realistic or not, they are made up):

delta_e = -1.2
elevator_down_limit = -2.0
R517 = 1.2
CL_e_basic + CL_e_M = 0.45

CL_de = 0.45 * -1.2 * -2.0 = 1.08

I just want to be 100% sure I've really got it, thus the silly-level maths.
 
(delta_e * [R517 * elevator_limit]) == (-1.2 * [1.2 * -2.0]) == (-1.2 * [-0.8]) == 0.96
CL_de = 0.45 / 0.96
CL_de = 0.46875
 
Hm.. okay, but where does the division between 0.45 and 0.96 come from? I thought the division seen in the equation on page 23 was just a way to express the sum of two steady state derivatives?
 
Erm....Isn't (-1.2 * [1.2 * -2.0]) == (-1.2 * [-2.4]) == 2.88?
 
Well, it certainly wasn't the first time through the calculator. LOL

Though to be honest... both elevator_up_limit and elevator_down_limit are positive values.

(delta_e * [R517 * elevator_limit]) == (-1.2 * [1.2 * 2.0]) == (-1.2 * [2.4]) == -2.88
CL_de = 0.45 / -2.88
CL_de = -0.15625

No, Johan that long line just means division.
 
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The more I review this... the worse it gets. He's stating that CL_delta_e is (derivative CL_delta_e_basic + derivative CL_delta_eM) / derivative delta_e * delta_e[elevator_limit * R517].

I think the use of the term derivative in the formula itself may be the misleading part as these do not appear to be partial derivative formulae.

It also assumes there is a R1539... and that's not an assured condition at all.... however..

It states derivative R1539_CLde_basic... well, it can't be a derivative as it's a static single value. Then it states derivative R410_CLde_M which is a linear slope calculation based on table entries and mach. I guess one could call that a derivative... but I don't think I would, no. I think the partial derivative symbol is being grossly misused and thus causing some confusion.
 
Ok

We will use delta_e as elevator deflection in radians. The value you had given of -1.2 I will treat as degrees as if it were indeed radians then it would result in a value of 68+ degrees!

1 - R1539_CLdelta_e_basic is a static value in the .air file. It's not a derivative.
2 - R410_CLdelta_e_M is a table of values referenced by Mach. I picked a value for low speed which resulted in a 0.
3 - The elevator limit values are pulled from the aircraft.cfg file and are not negative values.
4 - R517 is a scalar value that is applied to the elevator limit value based on dynamic pressure. For a jet it tends to remain at 1 until you approach the speed of sound.

Given the above the formula, as stated in the PDF, doesn't make much sense. It is essentially telling us that the coefficient of lift for the aircraft's elevator is based on ((derivative of R1539 + derivative of R410)/derivative of delta_e) * delta_e modified by elevator_limit and dynamic pressure scaling.

Wait... what? First, static values aren't derivatives. Second, the derivative symbol being used in the math is for a partial derivative... and a table lookup (R410) doesn't qualify as a partial derivative in my book, but maybe that's just me? I also think it's important to note that delta_e[elevator_limit * R517] is a nonsensical math statement as it implies a value that's indexed or otherwise related... but in reality [elevator_limit * R517] is a scaled value of the maxmimum possible elevator deflection during flight based on dynamic pressure. That would make it only useful as a ceiling for delta_e itself. And thus... the last part of the formula is technically just the value of delta_e under most conditions.

If I take the formula at face value and treat it as a partial derivative it makes even less sense. Going to plug some numbers into it...

I pulled values from a jet aircraft:

R1539_CLde_basic = -0.134961 // staic value
R410_CLde_M = 0 // varies by mach, this one was for 0.2M
R517 = 1.0 // varies by q... but typically is 1 unless nearing speed of sound.
delta_e = -0.02094

elevator_up_limit = 20
elevator_down_limit = 15

So we end up with:

(-0.13496 + 0/-0.02094) * -0.02094[0.261799388 * 1.0]

Now, like I said... that last part as defined makes no mathmatical sense so I would treat it more as a ceiling clamp on the actual delta_e value. Cleaning things up we end up with:

(-0.13496 + 0/-0.02094) * -0.02094

This result is -0.13496. That doesn't reflect any position of the elevator at all!

So... what am I missing?
 
What if delta_e[elevator_limit * R517] is an awkward way of expressing: [elevator_limit * R517] - delta_e?
In other words: "the delta between delta_e and [elevator_limit * R517]".

So:
CL_delta_e = (CL_delta_e_basic + CL_delta_e_M) * ([elevator_limit * R517]-delta_e)

This is just speculation on my part though and I haven't seen that nonsense in any mathematic notation to this date.
 
I think it is not difficult to understand.
If you want to calculate how much lift is produced by the elevator you need the usual things like TAS, air density etc plus the lift coefficient of the elevator. Just like a wing, the elevator lift coefficient varies with its angle relative to the airflow. For simplicity it is assumed that that angle is the amount of elevator deflection and the Cl is expressed as per radian of deflection, CL de.
However, like wing Cl, there is a Mach modifier, 410 for elevators.
The basic CL de is found in 1539 if present, if not it is in 1101 as explained on page 8 in Yve's document.
This gives us an equation where CL de is the basic value as modified by Mach effect applied to the amount of deflection controlled by the stick/yoke up to the maximum given in the .cfg, reduced by dynamic effects in 517.

So if I want to calculate the lift given by the elevator, I must include its CL which is a basic value, modified by Mach, times an elevator deflection in radians that could be less because of aeroelastic effects from dynamic pressure.

I'll let someone else do the calculations, but it should be pretty simple.
Roy
 
We still have the last part of the equation to figure out though Roy:

delta_e[elevator_limit * R517]

I'm totally with you regarding the "derivative" (CL_delta_e_basic + CL_delta_e_M) * delta_e. But what is the meaning of delta_e[]? Is it just a parenthesis or does it mean something else?
If it's just a parenthesis, "delta_e[elevator_limit * R517]" would be the same as "delta_e * elevator_limit * R517" which to me makes no sense. Why multiply delta_e by the elevator deflection limit?

Edit:
The only way I think makes sense is if this is just a way to express an upper/lower limit of delta_e as suggested by Ed.
 
Last edited:
I'm really unsure Table 517 has an effect on LIFT as a result of elevator deflection (CL_de). At least I couldn't see any (whatever the values I set in Table 517) during the tests I performed while CL was measured from standard aerodynamical equations
Moreover, Table 517 is described in SDK as "Elevator elasticity on effectiveness scaling due to dynamic pressure", aka in the compilator part as AIR_61S_ELEVATOR_ELASTICITY. Unfortunately, I didn't find any information in textbooks I have that helps understanding what is "elasticity" regarding elevator surface.
Another hypothesis could be Table 517 "scales" maximum elevator deflection (as defined in the aircraft.cfg) but I didn't investigate that.

Whatever it is, in some other documents I have this table is referred as Cm_de(q) so it could be that this scaling table acts on MOMENTs as a result of elevator deflection and not LIFT. If it is confirmed, may be Yves made a mistake here (he will let us know if he stills read this forum)

As far as I could investigate, lift due to elevator deflection is by now accurately estimated (with a 0.0001 precision) by
CL_de =(CL_e_basic+CL_e_M)*e, e being elevator deflection in radians
 
Herve has it right as usual.

hervesors said:
Another hypothesis could be Table 517 "scales" maximum elevator deflection (as defined in the aircraft.cfg) but I didn't investigate that.
Click to expand...
If your aircraft can do say 500 IAS and 517 reduces delta_e to zero by a zero scalar at a lower speed, you literally have frozen elevator control at 500 in the sim. You can pull the stick fully aft and it does nothing. Which obviously means there is no elevator lift under those circumstances.

One explanation is that in some old airplanes the control mechanism has some elasticity such that dynamic forces on the elevator could prevent elevator movement. You just run out of control authority because the mechanism bends. Any self-respecting test pilot military or civil would categorize that as unacceptable or decrease the maximum allowable speed to below that where such an event could occur. In which case the phenomenon would be mentioned in the Manual as something that could happen if you exceeded the maximum allowed indicated speed for a particular altitude.
This should not be confused with loss of elevator control at high Mach and relatively low IAS. This characteristic should, of course, be modeled by appropriate entries in 410.

hervesors said:
Whatever it is, in some other documents I have this table is referred as Cm_de(q) so it could be that this scaling table acts on MOMENTs as a result of elevator deflection and not LIFT. If it is confirmed, may be Yves made a mistake here (he will let us know if he stills read this forum)
Click to expand...

AirEd.ini has "517=*Cm_de(q) Elevator Deflection (Moment) Factor vs q,tbldb", but it is 10 years old. As you said it is now identified as AIR_61S_ELEVATOR_ELASTICITY.

Why are we interested in elevator lift? Just because it's CL is one of the many that are summed to give the total lift coefficient, which Yves spells out in his 5.3.2.
But the main function of the elevator is to produce a pitching moment and the same elasticity factors apply. They also apply to elevator trim, rudder and rudder trim, aileron and aileron trim effectiveness.

johnor999 said:
Why multiply delta_e by the elevator deflection limit?
Click to expand...
This just gives a maximum or minimum value for the expression. It does not apply for a specific amount of elevator deflection. To be clear, 517 can have an effect at any deflection.
Yves also uses that notation on page 24 though for spoiler limit. For consistency there should perhaps be a "*" before the square bracket.

I think Yves should have included 341 Elevator effectiveness aka AIR_61S_ELEVATOR_SCALING in this section because it is the grandpa of all things elevator.
Roy
 
The math is below, however that formula is wrong!

CL_de = (CL_e_basic + CL_e_M) * delta_e[elevator_up OR down_limit * R517_Elev_defl_limit_scalar_vs_q]

CL_de = (Elevator Lift table + Elevator lift due to Mach) * ( [Elevator limit] * [Elevator MOMENT scalar due to q] )


Formula errors are highlighted in red and notated below:

- As Roy pointed out, Elevator Effectiveness is missing (Scalar versus deflection angle)!
- Elevator moment coefficient should not be combined to find elevator lift.

Flight sim calculates these numbers correctly, separating moments from lift.


equation should be:

CL_de = (CL_e_basic + CL_e_M) * ( [Elevator limit] * [341 Elevator Effectiveness] )


it might look like

CL_de = (0.05 + 0.01) * ( 0.0833 * 0.9 )
 
341 is a scalar on Cm_de (moment) not CL_de and, from the tests I performed it has no effect on CL_de
If we are just interested by LIFT resulting from elevator deflection, I don't think there is any other parameter to take into account than true elevator deflection (e) applied to CL_e basic + CL_e_m
The only thing I didn't investigate yet is the possible effect of the "elevator_effectiveness" in the [flight_tuning] section of the aircraft.cfg but I guess it will also only apply to Cm
 
Hi everyone,

thanks for studying my documentation in such detail. Let me first try to clarify the formula on page 23, so we can discuss a way to mathematical depict it in a more correct way.

upload_2016-9-17_20-32-44.png


The result of the formula is a dynamic value which depends on the static values of R1539 + R410 and the dynamic values of the current elevator deflection and the current Mach no.
CL_de is just a linear function: CL_de = R1539_CL_de_basic (as a function of Mach no) * de. The first partial derivative of this formula is ∂R1539_CL_de_basic/∂de (the gradient/slope) and can directly be read from the air-file in R1539.
This partial derivative then changes with Mach number. The values in R410 are partial derivatives of de as well and must be added or subtracted to the derivative ∂R1539_CL_de_basic/∂de, not to the formula result CL_de!

The brackets in the second line are just additional information and not part of the results of CL_de. They say that the maximum elevator deflection is limited by other parameters (the brackets mean 'as a function of'). There are the elevator_up_limit (e.g. 20°) and elevator_down_limit (e.g. 15°) in aircraft.cfg. The 'OR' means that it depends on the current elevator deflection direction (up or down) which one applies. R517 is a scale on those two limits as a function of dynamic pressuere q (speed), e.g. the elevator_up_limit of 20° is scaled by 0.5 to 10° at q=100. Of course, all should be in radians not degrees.

Example:
Input
Dynamic values:
current elevator deflection de = 0.17 rad
dynamic pressure q = 100

From Air-file:
R1539_CL_de_basic from air-file = -3.0 per rad
R410_CL_de_M from air-file = 0.3 per rad
R517_Elev_defl at q of 100 = 0.5 --> not used for result​
From aircraft.cfg:
elevator_down_limit = 15.0° = 0.26 rad --> not used for result​

Result
CL_de = (-3.0 + 0.3) * 0.17 = -0.459

Why does the deflection limit matter if it does not influence the result of CL_de ? Because the user's concern is about joystick deflection and not elevator deflection. Full joystick pull-up coukd mean 25° elevator deflection at low speed and only 10° at high speed depending on R517. The user feels any change of the parameters in the brackets in his joystick although the result of CL_de is the same.

How would you represent this issue in a formal correct way?
 
hervesors said:
341 is a scalar on Cm_de (moment) not CL_de and, from the tests I performed it has no effect on CL_de
If we are just interested by LIFT resulting from elevator deflection, I don't think there is any other parameter to take into account than true elevator deflection (e) applied to CL_e basic + CL_e_m
The only thing I didn't investigate yet is the possible effect of the "elevator_effectiveness" in the [flight_tuning] section of the aircraft.cfg but I guess it will also only apply to Cm
Click to expand...


Yes I gave the wrong record number. 517 gives elevator angle limit at speed, not 341. It is 'Elevator DEFLECTION moment factor vs q'.

Yves_G said:
How would you represent this issue in a formal correct way?
Click to expand...

I'd say...

The sim needs true elevator angle in radians to calculate CL

One radian = 60 degrees deflection....

CL_elevator * (elevator deflection_radian * R517) gives elevator CL at current deflection

(CL_de + CL_de_M) * elevator angle in radians * R517 = CL_e


The significance of this for FS flight dynamics is the entry of CL_de should be for 1.00 radians in the airfile. If the real airplane produces a maximum of 0.5CL at max deflection of 25 degrees at the reference Mach 0.20, the airfile should have:

CL / (max angle/one radian) / 517 at Mach 0.20 = CL_de
0.5 / (25/60) / 517 at Mach 0.20 = CL_de.


The sim outputs CL_e = (CL_de + CL_de_M) * ( [Elevator angle] * [517 Elevator deflection vs q] )



*red denotes corrections to my previous post.
 
Thanks for the clarification Yves..that's perfectly clear now
Now on an aerodynamical point of view (CL_de calculation), the only important input variable is always true elevator deflection (radians).
Loss of effectiveness of joystick due to R517 acting on up and down limits is another fact that should be treated separately IMO (it is just a dynamic change of the default min/max values of the cfg file)

My 2 cents
 
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