Thanks for the reply on "Wing Sweep Back". It gets me to wonder then how E-flights new Sensor 4D is so successful. Last week one of the fellows flew one in the Dome and have never seen a bipe fly so slow and fly so slow and in any position. I could not believe the rolls at slow speed this bipe was capable of. I never flew a delta wing plane so I presume this also applies in this case also??

From : Don Stackhouse

The Tensor's wing is for all practical purposes not swept. It has a straight trailing edge, and only the leading edge at the tips for only about a chord length is swept. Aerodynamically that doesn't get into the sorts of issues I described, because the lift distribution, even on a constant chord wing, is nearly elliptical at higher lift coefficients. Because of this, the tips of that wing are not making much lift, and reducing their chord by that amount in that area approximates the amount of lift made by that part of the wing.

There are some theories, notably the work of Wil Schuemann in developing the Schuemann wing planform common in sailplanes (a progressively tapered and swept leading edge that approximates an elliptical planform, with a straight, unswept trailing edge), that argue that a straight, unswept trailing edge minimizes the amount of spanwise flow, which is the root cause of much of the swept wing's quirks. For very high aspect ratios that may be true, although for lower aspect ratios (such as delta wings) it almost certainly is not.

One of the other quirks of swept wings is the reduction of the "lift curve slope", or dCl/d-alpha (pronounced "dee-see-ell-dee-al-fah"). If you look at typical plots of airfoil data, one of them is typically the lift coefficient ("Cl") on the Y-axis, vs. the angle of attack ("alpha") on the X-axis. You will note that for most airfoils much of that curve is nearly a straight line in the middle portion, rounding off near the ends as the airfoil approaches the positive and negative stall angles. The slope of that straight line portion is the dCl/dalpha, which is nothing more than Calculus terminology for how sensitive the lift coefficient is to changes in angle of attack.

The raw airfoil data you find in the books is for what's called "2-dimensional" conditions, where the whole length of the wing sees the same operating conditions and lift generated. This pretty much only happens in an infinite span wing (which is rather difficult and time-consuming to build) or in a wind tunnel, after making corrections for the effects of the tunnel walls. In the real world, we have to make corrections for 3-D effects, such as a finite span, and for things like sweep. As a result, the overall lift coefficient developed by a real world finite span wing might only be about 80% of what the raw airfoil data suggests.

Since the real-world finite-span wing makes less lift at a given angle of attack than the raw wind tunnel data for that airfoil suggests, then obviously its lift curve slope is also somewhat less.

Swept wings, especially delta wings, take this effect to an extreme. The dCl/d-alpha of a swept wing is typically going to be about equal to the dCl/d-alpha of its straight equivalent times the cosine of the sweep angle. Thus, a 5 degree swept wing has a dCl/d-alpha of about 99.6% of the unswept wing, at ten degrees that drops to 98.5%, at 20 degrees it's 94% (still a relatively insignificant difference), at 30 degrees it's 87%, and at 40 degrees it's down to 77%. At 60 degrees it's dropped to only 50% of the lift curve slope of a straight wing.

Note, the airfoil involved will still stall at the same lift coefficient, but because the lift curve slope is flattened by the effects of sweep, it takes a lot more angle of attack to achieve that lift coefficient. Thus (assuming we ignore some of the other factors that become an issue on things like delta wings, such as vortex lift), if our baseline airfoil stalled with a lift coefficient of 1.3 at 12 degrees angle of attack in the wind tunnel, that same airfoil on a 60 degree swept wing would still stall at a a local lift coefficient of 1.3, but it would need an angle of attack of (theoretically) 24 degrees to reach that lift coefficient.

This is why the Concorde needed that droopable nose; the pitch attitude required for the landing flair was so high that the entire airport would disappear under a conventional fixed nose. The old Chance-Vought Cutlass had a similar problem. The original prototype had a normal-looking nose that made the entire aircraft carrier deck disappear from the pilot's view on final approach. The production version had a severely reshaped nose that was quite a bit uglier, but a whole lot easier to see over at final approach attitude.

Deltas do add some complications, although they still follow the basic theory to some extent. They can get to ridiculous pitch attitudes before stalling, and they can also get some very respectable lift coefficients when doing so, at least in some cases, through 3-D flow effects such as "vortex lift". This is a phenomenon involving some large vortices that form behind and above the leading edges at high angles of attack. The rotational airspeed from the vortices gets added to the plane's airspeed, resulting in a much higher than normal local airspeed over the top of the wing (even though that airspeed is not parallel to the plane's flight path). A higher local airspeed means a lower pressure on top of the wing, which means extra lift. The strakes on the noses of planes like the F/A 18 and SR-71 help create a similar effect.

Of course the downside of 3-D lift and very low aspect ratio wings (such as deltas) is massive amounts of induced drag. This might not be a problem when trying to bring in a heavy jet slowly and steeply, where they want to have lots of drag anyway, but it can become an issue for things like combat maneuvering. High drag means that these aircraft tend to scrub off energy very quickly in high-G maneuvers, and as any good fighter pilot can tell you, in a dogfight "energy is life".

I have a fair amount of experience with a Pibros, a little Depron foam delta-wing glider. It's capable of very high roll rates and extreme angles of attack with full control, but at high G loadings it bleeds off airspeed and energy extremely fast. As a result, it thermals poorly, and doing a loop requires a gentle hand on the elevator. Yank too hard and the induced drag will kill off the airspeed before it can make it over the top. OTOH, at 200 feet I can line it up in a 45 degree high speed dive straight at my face, at 5 to 6 feet away snap it to a 90 degree angle of attack (still with full control due to the airflow over the elevons induced by the leading edge vortices), and watch it come almost instantly to a full stop in mid air and plop to the ground right at my feet. Drag is not always a bad thing.

Don Stackhouse
DJ Aerotech