Best Glide physics?

Guest Discussion
#1

Just when you start to think you understand some aerodynamics…

I was working on a spreadsheet to provide V speeds at different weights, etc. (things you do when your airplane is grounded!) when I became confused by the Best Glide figures for the SR22.

Best Glide is also V L/D, which to my understanding is proportional to the square root of the weight of the ship. Since Best Glide is given as 88kias at max gross (3400 pounds for the SR22) then at some other weight W Best Glide would be 88*sqrt(W/3400). That would make Best Glide 82kias at 2900 pounds, but the POH states 87kias.

Why is there so little variation in the Best Glide speed at lower weights?

-Curt

#2

Best glide speed is the speed that gives the best glide ratio. It is a function of the power required curve (which is derived from drag curves). If you draw the curve, best glide is determined by drawing a tangent to the the curve with a line that goes through the 0,0 point. Weight does not come into play as a squared term when figuring power required although it will affect the power available curve. Probably the best way to think of best glide speed is using a constant angle of attack. Since most light aircraft do not have an angle of attack indicator, some smart fella with a pocket protector has determined what speeds you need to hold for various weights. If you reference Kershner (the king of using formulas) he does not even address a formula to find best glide speed based on weight (that I could find anyway). I hope this makes sense to you.

Jim

#3

Checkout this site.

http://142.26.194.131/aerodynamics1/Performance/Page3.html

#4

Well, that doesn’t help really. For example, on p.371 of “Aerodynamics for Naval Aviators” they present the formula V2/V1 = sqrt(W2/W1) for relating best glide speeds at different weights. This is also discussed in Prof. David Rogers’ classic papers (see the first one on weight effects).

It reminds me of the mysterious decrease in Vo on the SR20 that went with the Gross Weight increase. There seem to be factors other than classical aerodynamics involved in some of these Cirrus speed limitations.

-Curt

#5

Have heard a reasonably plausible explanation for the odd behavior of Vo with gross weight.

As you obviously know (and I think I understand), Vo is normally set so that a stall occurs with max control deflection prior to the aircraft hitting max rated g’s (3.8 in the SR2x). Thus, when gross weight increases, stall speed increases (thus limiting the impact of max control deflection), so Vo increases as well.

However, for the SR22 at least, I’ve been told that Vo was set at the minimum of conventionally calculated Vo and the max parachute deployment speed. Max parachute deployment speed was governing at max gross weight (though not at lower gross weights). I believe the same was true for the SR20. At least the numbers match. If so, max deployment speed would probably drop with an increase in gross weight. Now why Vo is set by parachute deployment speed is somewhat problematical, but I suppose you can make an argument for it.

Make sense?

Bob

#6

I’m not a physics guru (although I did minor in physics in college). Did anyone who is working on this debate take into account that the wing of an SRX has to be modeled as 2 wings, each with differing lift and drag coefficients? Add in the complex airfoil issues of the rest of the curved composite structure and the wing cuff, and I’m willing to bet the problem is that best glide characteristics for the inboard wing section and best glide characteristics for the outboard section interact in some mathematically interesting ways. Has anyone asked Cirrus’ engineers for an answer?

Also, I had a talk with a flight test engineer from the FAA’s Atlanta Aircraft Certification Office last week. Seems he worked for NASA and the Air Force during the original development of stall-resistant wing shapes. His simplified answer to my question about wierd #s when dealing with Cirrus airspeeds (simple because I wasn’t following the math and this was a social setting) was that almost none of the “classic” formulae for aircraft performance can be appled directly to modern computer-designed complex “discontinuous” airfoils. (the old ways will get you into the ballpark, but won’t be better than 90-95% accurate.) There is math that will work, but since the engineering is complex, so is the math. He promised to send me the working papers that came out of the program, and left our conversation at …“trust the #s Cirrus provides. Feel free to interpolate, we allowed for that in the certification process, but whatever you do, don’t extrapolate…” One thing he did specifically mention was that the cuff changes the math significantly all by itself.

Again, I’m not the sharpest knife in the drawer when dealing with aerodynamics, but this is something those of you fretting about this concept perhaps should account for…

BTW, for those who think the CAPS is a far-out invention for airplanes, this guy had some interesting stories to tell about testing wing-tip parachutes and wing-tip rockets for spin recovery devices!

#7

I hadn’t heard that but had thought of it. I assume Vpd changed as well. By the way that change was only for the SR20, not the SR22.

One way to test that theory is to see what Vo does with less weight. On the SR22 when weight goes from 3400 to 2900 Vo goes from 133 to 123, which is just in line with the change in stall speed and proportional to the square root of the weight. So Vo on the SR22 seems to be set by the stall speed, and Vpd was presumably set by testing up to Vo.

What happens to Vo as weight is reduced on the SR20 with the new gross weight increase and reduced max gross Vo?

-Curt

#8

The only real way to get the best glide numbers was figured out a long time ago by the glider crowd. You have to take the airplane up to a high altitude in smooth air with a drag probe attached and take precise measurements with an extremely well calibrated airspeed indicator and a variometer, which is a highly sensitive vertical speed indicator. The measurements are plotted on a graph yielding a curve that depicts the L/D for various airspeeds. My last glider had three airfoils merged into one wing and the L/D curve had a couple of ‘bumps’ in it as a result. One of the benefits of the three airfoils was a 10-12 knot range that yielded almost all of the 43:1 max glide ratio. However, there was a pretty steep drop in glide ratio when you flew past the highest speed in that range. On days when there is a lot of lift available and you do not expect to be climbing in thermals more than about 25-30% of the time, you load up with water ballast to increase the gross weight (wing loading) and move the entire L/D curve to higher airspeeds. This degrades your climb performance a bit, but allows for faster cruising between thermals.
FWIW