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  1. #1
    Dave the RcFlyer's Avatar
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    CP Versus CG Where are the Topics?

    Ok I'm new to rc but not to model rocketry where I've dabbled a bit in the mathmatics of CP (Center of Pressure) and CG calculation. In model rocketry the placement of CG and CP are quintessential to the stability of your model. Is this not the case with model airplanes? I understand that there may be different areas of CP versus CG (E.g. Wing, fusalage, total airplane) yet I see no topics about placement of these. Maybe they're termed differently than in model rocketry so don't flame me if it is. Here is a link to a good explanation to how CP and CG are in relationship to each other along with Barrowman's Stability equation.

    Ps. If I can get a hold of the .net software runtimes that are supposed to be comming I'm going to code a program to take the guesswork out of cp calculation. much more acurate that that pesky cardboard method. PM me if your interested.
    \"As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.\"--Albert Einstein

  2. #2
    Moderator BMatthews's Avatar
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    RE: CP Versus CG Where are the Topics?

    Your theory is alive and well under a different set of names. The point of balance of all the aerodynamic forces is called the neutral point and the CG cannot be behind that point but it can get pretty close if you're good on the sticks. Most folks keep it about 10 to 15% in front of it for general flying. The location of the neutral point is related to the horizontal tail volume coefficient and a little equation that is around here someplace but that I can't find just now. There is also a vertical tail volume coefficient that related to the vertical tail size. If you try a search within the Aerodynamics forum only you'll probably hit about 15 good threads on the matter.
    Witty saying to be plagarized shortly.....

  3. #3
    rmh's Avatar
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    RE: CP Versus CG Where are the Topics?

    Also -for you guys who really want to see if the calculations and rules on this actually play out - now you can.
    buy a cheap electric motor and little servos etc. and make some little foam board or cardboard or what-ever-board models
    fly em -if they crash - so what -it is usually just a flop into the grass.
    If you want a reall treat - build a pusher canard -and see what happens when one of these gets into a spin.
    the neutral point and CG will sometimes appear to swap ends-
    Libby is still watching you

  4. #4

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    RE: CP Versus CG Where are the Topics?

    ORIGINAL: Ima RcFlyer

    Ok I'm new to rc but not to model rocketry where I've dabbled a bit in the mathmatics of CP (Center of Pressure) and CG calculation. In model rocketry the placement of CG and CP are quintessential to the stability of your model. Is this not the case with model airplanes? I understand that there may be different areas of CP versus CG (E.g. Wing, fusalage, total airplane) yet I see no topics about placement of these. Maybe they're termed differently than in model rocketry so don't flame me if it is. Here is a link to a good explanation to how CP and CG are in relationship to each other along with Barrowman's Stability equation.

    Ps. If I can get a hold of the .net software runtimes that are supposed to be comming I'm going to code a program to take the guesswork out of cp calculation. much more acurate that that pesky cardboard method. PM me if your interested.
    For conventional designs (with a main wing and a horizontal stab) the CG location
    range is usually between 28% and 33% from the leading edge of the main
    wing's MAC, which means between about 5% and 15% ahead of the aircraft's
    Neutral Point NP.
    This is called the static margin, which is expressed as a percentage of the MAC.
    When the static margin is zero (CG coincident with NP) the aircraft is considered
    "neutrally stable".
    However, for conventional designs the static margin should be between 5% and
    15% of the MAC ahead of the NP.

    The CG location as described above gets close to the main wing's Aerodynamic
    Center AC because the lift due to the horizontal stab has only a slightly effect on
    the conventional R/C models.

    However, those figures may vary with other designs, as the NP location depends
    on the size of the main wing vs. the stab size and the distance between the main
    wing's AC and the stab's AC.
    The simplest way of locating the aircraft's NP is by using the areas of the two
    horizontal lifting surfaces (main wing and stab) and locate the NP proportionately
    along the distance between the main wing's AC point and the stab's AC point.
    For example, the NP distance to the main wing's AC point is:
    D = L Β· (stab area) / (wing area + stab area) as shown on the picture below:
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

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    http://adamone.rchomepage.com

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    RE: CP Versus CG Where are the Topics?

    There are other factors, however, that make the simple formula above inaccurate.
    In case the two wings have different aspect ratios (different dCL/d-alpha) the NP
    will be closer to the one that has higher aspect ratio.
    Also, since the stab operates in disturbed air, the NP will be more forward than
    the simple formula predicts.

    For further equations on how to find the proper CG location with different wing
    shapes and design configurations including Canards, you may check the following link:
    http://www.palosrc.com/instructors/putte.pdf
    http://adamone.rchomepage.com

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    alasdair's Avatar
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    RE: CP Versus CG Where are the Topics?

    "Also, since the stab operates in disturbed air, the NP will be more forward than
    the simple formula predicts."


    Also, since you have not taken account of the downwash from the wing (or loss of dynamic pressure) your formula for D is on the dangerous side of useless.
    The NP will be further forward than that formula suggests. I too suggest a Static Margin (Stability Margin) of 10% to 15% of MAC. That is, the CG must be 10 - 15% of MAC ahead of the REAL position of the NP.

    The NP position can be roughly calculated from NP = 25 + 40*Vbar (as a % of MAC)
    where Vbar is the tail Volume ratio
    Alasdair

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    RE: CP Versus CG Where are the Topics?

    The NP position can be roughly calculated from NP = 25 + 40*Vbar (as a % of MAC)
    where Vbar is the tail Volume ratio
    Well, that's another roughly calculation… Nice.
    But it would be even nicer if you could tell us how to calculate the tail Volume ratio.
    Also, from which reference point you measure to determine NP location according to your formula?
    Thanx
    http://adamone.rchomepage.com

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    Dave the RcFlyer's Avatar
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    RE: CP Versus CG Where are the Topics?

    whoa this seems a bit more complicated than with rockets but anyway once I get my software would anyone like to see these formulas put into a program? thanks for all of the great information.
    \"As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.\"--Albert Einstein

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    RE: CP Versus CG Where are the Topics?

    ORIGINAL: Ima RcFlyer

    whoa this seems a bit more complicated than with rockets but anyway once I get my software would anyone like to see these formulas put into a program? thanks for all of the great information.
    Hi,

    Could you create a java script that one may add to an html web page?
    If so, I would greatly appreciate if you could use the formulas shown on the following file:
    http://www.chrisgood.com/rcplanes/fw...of_gravity.xls
    Thanx
    http://adamone.rchomepage.com

  10. #10
    alasdair's Avatar
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    RE: CP Versus CG Where are the Topics?

    adam-one,
    sorry, I assumed anyone reading the aerodynamic Forum would know, but I should have explained.
    <<"The NP position can be roughly calculated from NP = 25 + 40*Vbar (as a % of MAC)
    where Vbar is the tail Volume ratio ">>

    Tail Volume Ratio = (tail net area/wing gross area) x (tail arm/wing MAC)
    tail arm being the distance from the wing MAC quarter chord point to the tail quarter chord point (L in your drawing).
    MAC is Mean Aerodynamic Chord.

    The formula gives the NP position as a percentage (%) of the wing MAC aft of its leading edge. It is an empirical formula, but from comparisons with the full-blown formula I think it is pretty accurate for conventional monoplanes with wing AR between 4 and 9

    For example, if the tail has an area 20% of the wing, on a tail arm of 2.5 wing chords, then the Tail Volume Ratio (V-bar) is 0.5
    Put that in the formula and you get a NP at 25 + 20 = 45% of MAC
    If you allow a Stability Margin of 15% MAC you put the CG at 30% MAC.

    That formula you gave: <<<"D = L Β· (stab area) / (main wing area + stab area) as shown on the picture">>>
    would put the NP at 67% MAC. Much too far aft. If you aim for the usual Static Margin of 15% MAC and a CG at 52% MAC you are likely to have an unstable aeroplane. That's why I said it was the dangerous side of useless.

    Alasdair

  11. #11

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    RE: CP Versus CG Where are the Topics?

    Alasdair,
    Yes, as I've previously mentioned, my formula doesn't take into account the fact that the disturbed air from the main wing may affect the stab, so the actual NP should be located further forward.
    However, if the stab is located so that it lies outside the influence of the main wing's downwash (they're often placed at different height to improve stabilising effectiveness), then this factor may be reduced.

    Your empirical formula seems to give a sort of compensation for that, but why do you mention tail "net" area / wing "gross" area, is there a difference between "net area" and "gross area" in this context?
    Thanx
    http://adamone.rchomepage.com

  12. #12
    alasdair's Avatar
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    RE: CP Versus CG Where are the Topics?

    Yes,
    the gross wing area includes the bit inside the fuselage. That's standard practice, because it is assumed that for purposes of lift curve slope the fuselage will supply enough lift change to make up for the missing bit of wing.
    The net tail area is the wetted area out in the breeze, i.e. excluding any area inside the fuselage or cut away to clear the rudder swing.
    Alasdair

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    rmh's Avatar
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    RE: CP Versus CG Where are the Topics?

    What is the "main wing" referrence I see currently?
    Is it to clearify it is not the "little wing" on the rear of the craft?
    Or is it a carry over from "main gear and tail gear?"
    Libby is still watching you

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    RE: CP Versus CG Where are the Topics?

    ORIGINAL: dick Hanson
    What is the "main wing" referrence I see currently?
    Is it to clearify it is not the "little wing" on the rear of the craft?
    Or is it a carry over from "main gear and tail gear?"
    Yes you've got it, the term "main wing" is just to clarify that's not the "little wing" on the rear, which may be also called horizontal stabiliser or stab.
    http://adamone.rchomepage.com

  15. #15
    Dave the RcFlyer's Avatar
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    RE: CP Versus CG Where are the Topics?

    sorry anytime I touch javascript I FUBAR it really bad. I'm not half bad with html though or visual basic .net I'm supposed to be getting software for .net sometime this summer. could someone please post just the formula and what the variables stand for. this pseodocode stuff I'm seeing is confusing. just the formula the variables is all I need. lol
    \"As far as the laws of mathematics refer to reality, they are not certain; as far as they are certain, they do not refer to reality.\"--Albert Einstein

  16. #16

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    RE: CP Versus CG Where are the Topics?

    Neutral Point NP: is the Aerodynamic Center of the whole aircraft.
    NP is the position through which all the net lift increments act for a change in
    angle of attack.
    The major contributors are the main wing, stabiliser surfaces and fuselage.

    AC: is the Aerodynamic Center of each lifting surface (main wing and stab).
    For a rectangular wing the AC is located at 25% of its chord (at subsonic speed).
    For wings with other than rectangular form (such as triangular, trapezoidal,
    compound, etc.) one has to find the Mean Aerodynamic Chord MAC, which
    is the average for the whole wing.

    Below is a drawing based on alasdair's formula, despite it's still a roughly calculation, I think it's somewhat safer than the one I've shown previously:
    Hope this helps.
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

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    http://adamone.rchomepage.com

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    RE: CP Versus CG Where are the Topics?

    ORIGINAL: Ima RcFlyer
    sorry anytime I touch javascript I FUBAR it really bad. I'm not half bad with html though or visual basic .net I'm supposed to be getting software for .net sometime this summer. could someone please post just the formula and what the variables stand for. this pseodocode stuff I'm seeing is confusing. just the formula the variables is all I need. lol
    Hi,
    For those who are not so keen on formulas and calculations I've modified an existing javascript code, which calculates the NP and CG position based on the impirical formula suggested above by Alasdair .
    You may check it at the following link:
    http://sky.prohosting.com/air2/cg_calc.htm

    Suggestions are welcome.
    http://adamone.rchomepage.com


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