Optimal chordwise spar placement
rer...@mmm.com
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I have been studying NACA airfoils as described in
_Theory_of_Wing_Sections_ by Abbot and Doenhoff, as well as in other
texts. I have a clear understanding of the airfoil geometry, coefficient
of lift (and drag) as a function of angle of attack, effect of camber on
zero-lift angle of incidence, stall angle, etc.
What I seem to be missing, however, is an understanding of how to
determine (either through computation, existing data, or experimentally)
the optimal chordwise position at which to place a spar when only one
spar is used. Is this station, in practice, equivalent to the chordwise
position of the "mean aerodynamic center"? I am assuming that this
becomes the focal point of the lifting force when pressure is integrated
over the surface of the wing.
Is the mean aerodynamic center, by nature, also the point about which
there is no torque if the wing is permitted to pitch freely about a
horizontal axis through this point?
How does this concept relate to "pitching moment" and the so-called
"quarter chord point"?
Explanations or references appreciated,
Richard E. Raby
EAA #508848
USPA C-28836
--
rer...@mmm.com S.E.M.S./Digital Imaging Systems Lab
(612) 575-1979 Phone 3M Center Building 235-2AWS-63
(612) 737-0410 FAX St. Paul, MN 55144-1000
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I have been studying NACA airfoils as described in _Theory_of_Wing_Sections_
by Abbot and Doenhoff, as well as in other texts. I have a clear understanding
of the airfoil geometry, coefficient of lift (and drag) as a function of
angle of attack, effect of camber on zero-lift angle of incidence, stall
angle, etc.
<P>What I seem to be missing, however, is an understanding of how to determine
(either through computation, existing data, or experimentally) the optimal
chordwise position at which to place a spar when only one spar is used.
Is this station, in practice, equivalent to the chordwise position of the
"mean aerodynamic center"? I am assuming that this becomes the focal point
of the lifting force when pressure is integrated over the surface of the
wing.
<P>Is the mean aerodynamic center, by nature, also the point about which
there is no torque if the wing is permitted to pitch freely about a horizontal
axis through this point?
<P>How does this concept relate to "pitching moment" and the so-called
"quarter chord point"?
<P>Explanations or references appreciated,
<P>Richard E. Raby
<BR>EAA #508848
<BR>USPA C-28836
<PRE>--
rer...@mmm.com S.E.M.S./Digital Imaging Systems Lab
(612) 575-1979 Phone 3M Center Building 235-2AWS-63
(612) 737-0410 FAX St. Paul, MN 55144-1000</PRE>
</HTML>
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Mark Drela
> What I seem to be missing, however, is an understanding of how to determine
> (either through computation, existing data, or experimentally) the optimal
> chordwise position at which to place a spar when only one spar is used.
> Is this station, in practice, equivalent to the chordwise position of the
> "mean aerodynamic center"? I am assuming that this becomes the focal point
> of the lifting force when pressure is integrated over the surface of the
> wing.
The position of an I-beam type of spar is dictated
by numerous considerations. It naturally wants to
be at the max-thickness location for minimum spar weight.
But if this is too far from the center of lift, then
there will larger torsion shear loads on the skin,
which will need to be heavier. Having the spar too
far back makes the wing more prone to flutter, if
that is at all any consideration. It's all a tradeoff.
> Is the mean aerodynamic center, by nature, also the point about which
> there is no torque if the wing is permitted to pitch freely about a horizontal
> axis through this point?
You are describing the "center of lift", which is the
location where the pitching moment is zero. For cambered
airfoils, the center of lift moves forward with increasing
angle of attack.
The aerodynamic center is the location where the pitching
moment does not change with angle of attack. For subsonic
airfoils this is always very close to the quarter-chord
location.
Mark Drela First Law of Aviation:
MIT Aero & Astro "Takeoff is optional, landing is compulsory"
lui...@spainmail.com
> What I seem to be missing, however, is an understanding of how to
> determine (either through computation, existing data, or experimentally)
> the optimal chordwise position at which to place a spar when only one
> spar is used. Is this station, in practice, equivalent to the chordwise
> position of the "mean aerodynamic center"? I am assuming that this
> becomes the focal point of the lifting force when pressure is integrated
> over the surface of the wing.
> Is the mean aerodynamic center, by nature, also the point about which
> there is no torque if the wing is permitted to pitch freely about a
> horizontal axis through this point?
No. The point you are claiming is the CENTER of PRESSURE, and it moves as the
angle of attack changes. The aerodynamic center is the point whose aerodynamic
moment is constant when changing AOA.
As far as I understand, the unique spar should be near to the center of
pressure. The cruise AoA should be assumed to estimate its placement.
> How does this concept relate to "pitching moment" and the so-called
> "quarter chord point"?
The pitching moment is what you call "torque moment". The "quaerter chord
point" is a roughly approximated position for the aerodynamic center (the
approximation is exact in inviscid flow).
Regards.
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DavidP5543
general, at the maximum thickness of the airfoil (somewhere between 30% - 50%
of the chord, depending on the airfoil). This is to maximize the moment of
inertia of the spar. This spar resists the lifting loads on the wing. To resist
the drag loads on the wing a cap must be used at the leading edge (l.e.) of the
wing. This cap plus the spar form the upper and lower flanges of an I-beam that
resists the chordwise bending due to drag on the wing. The l.e. skin forms the
shear web between the l.e. cap and spar. The D-section formed by the l.e. cap,
l.e. skin and main spar form a torque box to resist the torsion in the wing.
The wing must be attachedto the fuselage at the l.e. cap and upper and lower
flanges of the main spar.
The exact placement and sizing of the spar, l.e. cap and l.e. skin depends on
the magnitude of the loads on the wing for the various flight conditions
expected to be encountered.
A good reference for wing structural design can be found in Bruhn's "Analysis
and Design of Flight Vehicle Structures".
Some definitions:
Center of pressure: That point on the airfoil where the resultant of the
pressure distribution on the airfoil creates no pitching moment. This point
will shift fore and aft with changes in angle of attack. The resultant force is
normally resolved into lift and drag forces normat to the chord.
Aerodynamic center: The point on the airfoil (about the quarter chord point, it
varies slightly with each airfoil) where the variation in pitching moment
coefficient with respect to lift coefficient is constant. This has more to do
with aircraft stability than wing structure considerations.
There are many basic aero texts and NACA/NASA reports that discuss and present
data on these subjects. If there is a university nearby with a good aero
library, they would probably have the above references.
Dave Palmer
Eric J. Whitney
You can actually put the spar *anywhere* in the wing that is convenient for you, but don't. Mostly people
place a single spar at the maximum thickness point of the wing, so as to maximise bending strength of the
wing (strength of the spar goes up as the cube of the depth, ignoring edge cripling/buckling of the caps
etc). You then have the option of putting your torsion structure (reacting pitching moment) ahead (in a D
nose) or behind (boxed in with a false spar) or both ahead and behind to some extent.
In either case, these structures have to be carefully analysed for tension fields etc. A good book is Bruhn.
Regard the aerodynamic centre, sure it is desirable to place the spar near this point somewhere. However
what is much more important is that the elastic axis (not nec. the spar) be quite close to this point to
avoid flutter problems.
rer...@mmm.com wrote:
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>
> I have been studying NACA airfoils as described in
> _Theory_of_Wing_Sections_ by Abbot and Doenhoff, as well as in other
> texts. I have a clear understanding of the airfoil geometry, coefficient
> of lift (and drag) as a function of angle of attack, effect of camber on
> zero-lift angle of incidence, stall angle, etc.
>
> What I seem to be missing, however, is an understanding of how to
> determine (either through computation, existing data, or experimentally)
> the optimal chordwise position at which to place a spar when only one
> spar is used. Is this station, in practice, equivalent to the chordwise
> position of the "mean aerodynamic center"? I am assuming that this
> becomes the focal point of the lifting force when pressure is integrated
> over the surface of the wing.
>
> Is the mean aerodynamic center, by nature, also the point about which
> there is no torque if the wing is permitted to pitch freely about a
> horizontal axis through this point?
>
> How does this concept relate to "pitching moment" and the so-called
> "quarter chord point"?
>
> Explanations or references appreciated,
>
> Richard E. Raby
> EAA #508848
> USPA C-28836
>
> --
> rer...@mmm.com S.E.M.S./Digital Imaging Systems Lab
> (612) 575-1979 Phone 3M Center Building 235-2AWS-63
> (612) 737-0410 FAX St. Paul, MN 55144-1000
--
---------------------------------
Eric "The Wingnut" Whitney
<whi...@hydra12.aero.usyd.edu.au>
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