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Calculating and applying pitch moment using JSBsim

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Calculating and applying pitch moment using JSBsim

Postby Bomber » Mon Aug 22, 2016 12:26 pm

Anyone up for a discussion ?

SO if I understand this correctly ALL these functions are added together to create a single pitch moment ?
Some of these functions are +ve whilst the others are -ve and visa versa.... the application of a pitch moment and it's damping
At a non pitching flight path the pitch moment is zero... by that I mean whilst flying at a constant attitude.

Code: Select all
        <axis name="PITCH">
            <function name="aero/coefficient/Cmo">
                <description>Pitching_moment_at_zero_alpha</description>
                <product>
                    <property>aero/qbar-psf</property>
                    <property>metrics/Sw-sqft</property>
                    <property>metrics/cbarw-ft</property>
                    <value>0.1000</value>
                </product>
            </function>
            <function name="aero/coefficient/Cmalpha">
                <description>Pitch_moment_due_to_alpha</description>
                <product>
                    <property>aero/qbar-psf</property>
                    <property>metrics/Sw-sqft</property>
                    <property>metrics/cbarw-ft</property>
                    <sin>
                        <property>aero/alpha-rad</property>
                    </sin>
                    <value>-1.8000</value>
                </product>
            </function>
            <function name="aero/coefficient/Cmq">
                <description>Pitch_moment_due_to_pitch_rate</description>
                <product>
                    <property>aero/qbar-psf</property>
                    <property>metrics/Sw-sqft</property>
                    <property>metrics/cbarw-ft</property>
                    <property>aero/ci2vel</property>
                    <property>velocities/q-aero-rad_sec</property>
                    <value>-12.4000</value>
                </product>
            </function>
            <function name="aero/coefficient/Cmadot">
                <description>Pitch_moment_due_to_alpha_rate</description>
                <product>
                    <property>aero/qbar-psf</property>
                    <property>metrics/Sw-sqft</property>
                    <property>metrics/cbarw-ft</property>
                    <property>aero/ci2vel</property>
                    <property>aero/alphadot-rad_sec</property>
                    <value>-7.2700</value>
                </product>
            </function>
            <function name="aero/coefficient/Cmde">
                <description>Pitch_moment_due_to_elevator_deflection</description>
                <product>
                    <property>aero/function/qbar-induced-psf</property>
                    <property>metrics/Sw-sqft</property>
                    <property>metrics/cbarw-ft</property>
                    <property>fcs/elevator-pos-rad</property>
                    <value>-1.1220</value>
                </product>
            </function>
            <function name="aero/coefficient/Cmdf">
                <description>Delta_pitching_moment_due_to_flap_deflection</description>
                <product>
                    <property>aero/qbar-psf</property>
                    <property>metrics/Sw-sqft</property>
                    <property>metrics/cbarw-ft</property>
                      <table>
                          <independentVar>fcs/flap-pos-deg</independentVar>
                          <tableData>
                              0.0000   0.0000
                              10.0000   -0.0654
                              20.0000   -0.0981
                              30.0000   -0.1140
                          </tableData>
                      </table>
                </product>
            </function>
        </axis>
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Re: Calculating and applying pitch moment using JSBsim

Postby Alant » Mon Aug 22, 2016 1:59 pm

These moments are all about the aerodynamic centre.

In the case of trimmed level flight this sum of pitching moments will equal mass x (distance of cg from aerodynamic reference point).

Note that the cg position moves with load and fuel etc, but the aerodynamic reference point is a fixed reference point.
Last edited by Alant on Mon Aug 22, 2016 2:21 pm, edited 1 time in total.
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Re: Calculating and applying pitch moment using JSBsim

Postby Necolatis » Mon Aug 22, 2016 2:05 pm

Isn't moments about the CoG and forces around AeroRP?
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Re: Calculating and applying pitch moment using JSBsim

Postby Alant » Mon Aug 22, 2016 2:21 pm

Let me put the same argument a different way.

Forces do act at a point. To get a moment due to force about a different point, multiply the force by the distance between the two points.

The aircraft mass acts at the c.g.
The aerodynamic forces are measured about the aerodynamic reference point.

If you are taking moments about the aerodynamic centre (as in Bomber´s example), then the pitching moment due to aerodynamic forces is that shown in the example, and the pitching moment due to mass equals (mass x 1g x distance between cg and aerodynamic centre). -- in trimmed level flight.

(please note that I have edited my initial reply, changing "aerodynamic centre" to" aerodynamic reference point")
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Re: Calculating and applying pitch moment using JSBsim

Postby Bomber » Mon Aug 22, 2016 2:50 pm

I think if I'm not mistaken there's two things going off so far...

1) there's the calculating of how much pitching moment is taking place
2) there's the applying of this moment to the jsbsim model

So 1) is calculated using armatures (distances) from the aerodynamic reference point... both to the applied forces and the mass of the vehicle who's position is at the CoG... all of these calcs both as the above code and internally to jsbsim which calculate the CoG to aerodynamic reference point distance are then added together.... at which point if the force moment and the mass moment are equal and opposite we have no moment force and the plane doesn't pitch.

I think then this pitching moment is applied around the CoG.... the plane has to spin around this point surely ?

Simon
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Re: Calculating and applying pitch moment using JSBsim

Postby Alant » Mon Aug 22, 2016 3:46 pm

You can take the moments about any point. It is not necessarily the cg or the AeroRP. This point could equally well be the nose or the tip of the tail.
As long as you use the same point for the whole of your sum of moments calculation, when it comes to balancing them you will get the same result - which is that the sum of the moments is zero. At balance, this fundamental law of mechanics holds no matter which point you choose.

JSBSim takes all of your forces, moments, masses, cg position, AeroRP etc and resolves them the into its own set of axes. Hopefully it does this correctly and we need not bother ourselves with the axes it uses internally.
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Re: Calculating and applying pitch moment using JSBsim

Postby Thorsten » Mon Aug 22, 2016 6:29 pm

SO if I understand this correctly ALL these functions are added together to create a single pitch moment ?


I think what's a potential point of confusion is that we formulate this in terms of moments (or sometimes even just talk about the coefficients), but JSBSim internally deals with the force vectors.

You could equally well specify all the force vectors acting where they happen to act, then do a (vector) sum of them. You'd find that a large part effectively goes through the CoG and (in stationary flight) cancels, but there are sometimes residual components left which cause rotational accelerations - i.e. change pitching, yawing and rolling moments.

If you would use force vectors, it would be fairly obvious that it doesn't matter what coordinate system you use to express them. It's less obvious if you talk about the moments directly, but since the physics doesn't change, it's still true that the coordinate system you use doesn't matter.
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Re: Calculating and applying pitch moment using JSBsim

Postby bugman » Mon Aug 22, 2016 6:46 pm

Why does it have to be centred around the centre of gravity? It is related to the airfoil rather than the total inertia tensor.

Regards,
Edward
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Re: Calculating and applying pitch moment using JSBsim

Postby Thorsten » Mon Aug 22, 2016 6:52 pm

By definition of the center of gravity, whatever force component goes through the center of gravity does not exert a torque and hence doesn't cause rotational acceleration.

That doesn't seem a priori the same property mentioned above (that the center of gravity is where gravity attaches), but since gravitational mass is equal to inertial mass, they're really fundamentally the same property.

If that was the question (not sure what 'it' refers to).
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Re: Calculating and applying pitch moment using JSBsim

Postby Bomber » Mon Aug 22, 2016 7:02 pm

bugman wrote in Mon Aug 22, 2016 6:46 pm:Why does it have to be centred around the centre of gravity? It is related to the airfoil rather than the total inertia tensor.

Regards,
Edward


Not quite... as what we're actually after calculating is the planes total centre of lift and it's position relative to the CoG....

So you can have a main wings airfoils center of lift forward of the planes CoG yet because of the h-stab's higher moment the planes centre of lift being behind the CoG...

With regards to what Thorsten was saying... you could calculate the main and h-stab moments from the CoG using their lift forces, sum these values together and then divide the total LIFT force by it to determine where the planes centre of lift point is relative to the CoG..... during non-pitching flight it's gonna be smack on the CoG... it simply has to be.

You could then position this external lift force at this centre of lift position.... and do away with all the complicated equations.

or not....

Simon
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Re: Calculating and applying pitch moment using JSBsim

Postby Alant » Mon Aug 22, 2016 8:43 pm

I am not sure what you are proposing. Could you post the xml code which you would use to replace your initial example.

Alan
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Re: Calculating and applying pitch moment using JSBsim

Postby Bomber » Mon Aug 22, 2016 9:18 pm

If it's me you're asking Alan..... I'd rather not as it'd only be a distraction from getting a greater understanding of just how the present moment calcs and values used are determined....

Maybe later we could return and investigate the possibility of doing things differently.
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Re: Calculating and applying pitch moment using JSBsim

Postby Alant » Mon Aug 22, 2016 9:58 pm

If that is the question, then the answer is really straightforward. The equations specified by your xml mirror the equations of motion used in just about every aircraft stability textbook that I have read. e.g. equation 2 on page 21 of the JSBSim manual. The nomenclature, subscripts etc vary from country to country and from book to book.

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Re: Calculating and applying pitch moment using JSBsim

Postby Richard » Mon Aug 22, 2016 10:15 pm

Pitch Moment is one of the more straightforwards ones as it is mostly from alpha and elevator angle with damping on Q. Flaps and gear will have quite an impact, AlphaDot not so much, and possibly need to consider the effect of sideslip / rudder.

This is from windtunnel data for the F-15

Image

This is what I've calculated using VSPAero for the BAe Hawk; it's not quite perfect but it is getting there. I've overlaid the F-15 windtunnel data as a comparitive

Image

There are lots of different ways to achieve this, I've seen separate tailplane equations that are quite complex, but can be rolled up into a basic table as above with little difference. I don't think there's a need for a different approach - just solving using the tried and tested approach using whatever data is available.
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Re: Calculating and applying pitch moment using JSBsim

Postby Bomber » Mon Aug 22, 2016 10:21 pm

I see the equation you mean... (I'd type it in but it's got some crazy lettering that I can't at present reproduce)


but lets look at this part of the above moment calcs

<function name="aero/coefficient/Cmo">
<description>Pitching_moment_at_zero_alpha</description>
<product>
<property>aero/qbar-psf</property> = dynamic presssure
<property>metrics/Sw-sqft</property> = wing area
<property>metrics/cbarw-ft</property> = wing cord
<value>0.1000</value> = ?
</product>
</function>


so how is this equation derived ?
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