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From: (Mark Drela)
Subject: Re: Swept Wings Questions
Date: Fri, 29 Mar 1996 02:03:54 GMT

In article <>, Dirk Lorek
<> writes:

|> 1) It is my understanding that a backward swept wing is inferior to a
|> straigt one on subsonic aircraft because it produces lesser lift.
|> OTOH, a bkwd swept wing delays compessibility in supersonic flight. My
|> question (provided that I'm right of course) is at what point
|> (speed/altitude ?, very rough) a bkwd swept wings advantage can be
|> regarded as superior in comparision with its disadvantage.

Sweeping a wing makes sense only if you are up against the Mach number
limit, and want to fly faster, as with a jetliner.  It doesn't make
sense if you want to fly higher, as with the U-2, or if Mach is of no
concern, such as with a General Aviation aircraft.

The airfoils on a swept wing behave as though they were flying at a
reduced speed, reduced Mach number, and reduced dynamic pressure.

  effective speed = V cos(L)
  effective Mach  = M cos(L)
  effective q     = 0.5 rho V^2 [cos(L)]^2

where L is the sweep angle, and V and M are the airplane's speed and

Imagine a straight-wing airplane flying at its maximum Mach number.
As you sweep the wing in flight from 0 to L degrees, the available
lift drops by a factor of [cos(L)]^2, and the Mach compressibility
effects on the wing's airfoils decrease (weaker shocks, etc.).  You
then increase the speed by a factor of 1/cos(L), so that the effective
dynamic pressure and lift are increased back to their original levels.
The effective Mach is also increased back to its original level.  In
effect, you haven't done anything to the wing's lift or
compressibility effects, but the airplane is now flying faster!

In reality, this isn't a complete freebie, since the skin friction
drag has increased by a factor of [1/cos(L)]^2 -- the wing skin
friction isn't affected by sweep very much, and feels the full brunt
of the real dynamic pressure increase, just like the rest of the
airplane.  So the overall L/D will typically decrease from the sweep.
An airliner depends on the higher speed to more than compensate for
the lower L/D and give better overall range (the product V x L/D is
what appears in the range equation).  And of course flying faster
gives faster revenue stream for the airlines.

If you repeat the above sweep exercise for a U-2, you find that you
haven't gained any additional altitude capability, although you may
have gained some range.  Since ceiling is paramount for the U-2, it
doesn't have sweep.

Sweep also doesn't make sense on slower piston and turboprop
airplanes.  In general, if Mach number is not a speed-limiting factor,
it makes more sense to get more speed by reducing the wing area.

|> 2) What is the advantage/disadvantage of a forward swept wing ?

To first order, sweeping the wing forward is aerodynamically the same
as sweeping if back:

  cos(-L) = cos(L)

There are also secondary compressibility effects having to do with
taper which tend to favor forward sweep.

However, the forward swept wing has much more severe structural
problems which tend to overwhelm any minor aero advantages.

  Mark Drela                          First Law of Aviation:
  MIT Aero & Astro          "Takeoff is optional, landing is compulsory"

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