Wing Sweep angle discrepancy

[vrmail...@gmail.com]

Hello,
The wing sweep angle refers to angle describing how airfoils are stacked in a wing with respect to the lateral axis. However, in VSP i notice that airfoil section alignment does not change on changing sweep angle and remains parallel to the longitudinal axis or fuselage reference line. I need some clarification on the same.

Thanks,
vrusty

[Rob McDonald]

Although you occasionally see wings defined with the airfoils
perpendicular to a swept line (say c/4), in my experience, the
definition used by OpenVSP is far more common. I.e. the airfoils
remain aligned with the 'flow' direction and the stack is sheared.

Even in cases where the wingtip is not parallel to the flow direction,
it usually seems to be a case of a chop and blend rather than airfoils
defined parallel to the wingtip (say F-15).

What is it that you are trying to achieve?

Rob

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[vrmail...@gmail.com]

If the airfoils remain aligned with the 'flow' direction then it should not be called as sweep. The effect of the sweep comes due to the angle between flow direction and airfoil chord. If there is no angle between flow direction and wing chord then sweep should not improve lateral-directional stability. Therefore, the aerodynamic coefficients obtained with this assumption would be incorrect. 

[Rob McDonald]

Have you made a wing in OpenVSP? Have you changed its sweep angle?
Do you have an accurate mental model of what OpenVSP does?

Once you make a wing and fly it -- I assure you, the flow does not
care which reference plane you used to define your airfoils.

Rob

[vrmail...@gmail.com]

For the first two questions, yes i have.  I am trying to understand what OpenVSP does. Are you saying that how one stacks the airfoils along the wing span is of no consequence? If so then there is no benefit of sweep besides increasing longitudinal static margin! And since that can't be the case, one of us is missing something. The flow should care how the airfoils are arranged.

[Rob McDonald]

A flow 'sees' a 3D shape. Perhaps we call that shape a wing.

The flow doesn't care how we define or perceive the shape. It only
cares about the final shape. The definition or perception of the
shape is an abstraction that is useful to humans -- the flow doesn't
care.

Lets start with OpenVSP's coordinate system. X generally runs nose to
tail. Y generally runs out the right wing. Z is up. You can rotate
your aircraft so this is not strictly true, but it is close enough.

Imagine a swept wing. Cut that wing with a cutting plane that is
parallel to the X-Z plane. The resulting shape is airfoil-like.

I speak in generalities here because these results are dependent on
the details of the wing -- taper, twist, spanwise airfoil variation,
etc.

Now, cut that wing with a cutting plane that is perpendicular to the
swept c/4 line. The resulting shape is airfoil-like.

These two airfoils are most likely not the same. One will have a
longer chord -- while the dimensional thickness will be very similar.
So, obviously the airfoils have different t/c. In simple cases, the
airfoils are related by stretching in one direction. If you have
strong taper or spanwise airfoil variation, then their relationship is
non-trivial.

Rob

[deenri...@gmail.com]

I want to revive this dead thread because I recently came across this quote in Raymer. This feels like it necessitates the capability to rotate the airfoil to perpendicular with the sweep line.

In Raymer’s Aircraft Design: A Conceptual Approach, the discussion of sweep makes it explicit:

“Shock formation on a swept wing at high subsonic speeds is determined not by the actual velocity of the air passing over the wing, but rather by the air velocity in a direction roughly perpendicular to the leading edge of the wing… This odd result… increases the speed at which shocks first form (the Critical Mach Number)”.

Any thoughts on this? 
- Daniel

[Neal Pfeiffer]

The flow over a swept wing has a component in the spanwise direction (along the local span lines) and another component perpendicular to those span lines. The spanwise flow is generally nearly constant while the flow perpendicular to it varies with the contour of the airfoils that form the wing shape.  For 3D analysis, both of these components are calculated.  However, when designing or analyzing 2D airfoils in transonic flow, an airfoil shape is generated that is perpendicular to the local span lines.  For a swept and tapered wing, this is a curved arc that is perpendicular to the leading and trailing edges of the wing and every span line in between.  The chord of a perpendicular airfoil is longer than the chord of the corresponding streamwise airfoil, yet the thickness is unchanged.  This means the thickness to chord ratio of the perpendicular airfoil is less than the streamwise one.  This is what helps a swept wing to achieve a higher critical Mach number.  For 2D analysis and design, the freestream Mach number is reduced by the cosine of the sweep angle and the local lift coefficient is increased by 1/(cos(sweep))^2.  For slower aircraft, the sweep may be defined at the quarter chord.  However, for transonic cruise, the sweep is often defined close to 50% chord to be closer to the anticipated location of a shock on the wing at high-speed cruise.  Once a family of 2D airfoils are defined, they are transformed back to streamwise coordinates to build the wing loft.  Then specialized 3D codes can be used to do final tweaks to the airfoils to generate the desired lift distribution while minimizing drag.  It is a fairly-complicated dance to design optimized transonic wings.

..... Neal

To view this discussion visit https://groups.google.com/d/msgid/openvsp/33d60d62-dd6b-4017-9c9e-b014d6956b26n%40googlegroups.com.

[Rob McDonald]

Well said Neal.

The only thing I'd add is that sweep theory originates from considering an infinite swept wing.

The infinite swept wing is un-twisted, is of constant chord, and has an identical airfoil for its entirety.  Lots of interesting things flow from this assumption.

Geometrically, there is only one sweep angle.  LE sweep, TE sweep, c/4, c/2, etc. are all the same -- because the LE and TE are parallel.

Next, when you decompose the flow into the components parallel and perpendicular to the sweep, it is easier to see how the decomposition works.

For a particle traveling parallel to sweep, nothing ever changes.  There are no gradients at all, velocity, pressure, temperature, etc. are all constant.

This puts all the variation perpendicular to the sweep -- which is what you describe and Raymer is talking about.

Of course, real wings are not infinite.  They have twist, the airfoil varies, and the chord changes with taper.  They have wingtips and junctions with the fuselage.  There are pylons and other imperfections.  So, things get a lot more complicated in a hurry.

However, the infinite swept wing theory is really quite beautiful -- and the scaling of properties by considering the perpendicular flow really does a great job of capturing the dominant terms despite all the imperfections of the real world.

Rob

[Neal Pfeiffer]

Thanks for the additional information Rob!

https://groups.google.com/d/msgid/openvsp/b346bc8c-02d9-4a30-bdfc-90f9e1727641n%40googlegroups.com

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