R/C Soaring DigestPage 12

TECH TOPICSDave Register

Bartlesville, Oklahomaregdave@aol.com

Planform Optimization for HandLaunch and Discus LaunchGliders, Continued

Picking up from last month, we’llcontinue our review of planform

optimization for Hand Launch andDiscus Launch Gliders (HLG, DLG).The driver for this study is to get abetter feel for the appropriate aspectratio (AR: wing span/average chord)for a good DLG design.

Previous work in this column reporteda value of ~ 10 as pretty good for a 2channel HLG (javelin launch). In thatcase we dealt with a total glider weightof ~ 8 oz. using the SD7080 airfoil.

DLG designs require a bit more beef inthe wings and fuselage to survive thelaunch stresses which can reachupwards of 80Gs. They also requiresomewhat larger vertical stabilizers foryaw correction of the spin and yaw-roll coupling at the moment of release.Additionally, we’re seeing morecontrol surface functionality (flaps,ailerons).

All of these factors add to the totalweight of the sailplane. Coupling thiswith another trend - the move towardsthinner, lower lift airfoils usinglaminar flow and we’ve got severalinteresting twists to the earlier prob-lem.

Last month we developed the basicinput data for the project. Using Prof.Mark Drela’s X-Foil code, we calcu-lated Cl and Cd data for the SA7035and AG12 airfoils as a function ofReynolds number (Re - Eppler’snotation). The SA7035 represents thegeneral class of airfoils used a fewyears ago for HLG while the AG12represents the newer class of airfoilsused for DLG.

The Cd vs Cl curves are repeated hereas Figures 1 and 2. As noted, the dragbucket is wider and the Cl is higher forthe SA7035. But the AG12 is definitelybetter behaved in the lower Re range

which is important for the cruise andthermal stage of flight. At high Re andlow Cl (launch conditions) the Cdvalues for both sections are compa-rable.

Since we’re going to perform a polaranalysis (sink rate vs horizontalvelocity over the flight profile of thesailplane), we need to make someconsistent assumptions about weights,moment arms, fuselage area andempennage. That data is summarizedin Table 1 for the HLG case and Table 2for the DLG case. Three differencesshould be noted:

Page 13December 2002

1) The wing area density is higherfor the DLG. This represents thestronger construction needed forthis case,

2) The vertical (rudder) volumecoefficient (VVC) is larger for theDLG. This represents the sub-rudder contribution needed tomaintain good initial launchtrajectory, and

3) The fuselage weight is higher forthe DLG. This is the addedstructure needed to withstand

high G launches as well as thepiezoelectric gyroscopic stabilizercircuit (lingua franca: piezo orgyro) used for launch control.

Please note that my definition of VVCis:

VVC = (Av * Dm) / (Aw * S/2)

where Av is the vertical stabilizer area,Dm is the moment arm (º chord wingto º chord stabilizer), Aw is the wingarea and S/2 is Ω the total span (30inches in this case). Some definitions

for this volume coefficient may use Srather than S/2 so be sure you knowwhich is being used by the particularauthor.

The numbers are taken from a series ofHLG designs I’ve built over the pastseveral years. That basic design wasconverted to DLG. Some trial and error(Umm, that really means wreckage!)resulted in the extra structures that Ineeded to add to keep things in onepiece. You may be able to build lighterand stronger so we’ll guesstimate fromthis work what the likely trends couldbe as a function of weight.

In Table 2 we’ve done the SA7035 DLGonly for a 2 channel ship. Since theAG12 works well in this example,we’ve added estimated weights for 4servo and 6 servo cases to see howwing loading affects things with thisairfoil.

Comparing polars for the simple HLGcase, we’ve plotted the results (Figures3 and 4) for AR of 6, 8, 10 and 12.Although this may seem an extremerange, some craft have been made atthe 7 end while a few have been flownat 11 or slightly higher. So we’rebracketing the wing planform valuesactually used at the field.

For HLG, good minimum sink is veryimportant. But it’s also important toachieve that at a relatively low speedso you can linger longer in a lightthermal. Additionally, you’d like to beas efficient as possible when you’recruising around so a good Lift to Drag(L/D) ratio is also desired.

In the earlier work with the SD7080,the UIUC database was used for Redependence. Since this data ended at60k, and the higher aspect ratiosrequire values down to ~ 35k, a linearextrapolation of that data was made tothe lower range. As can be seen inFigure 1, below 50k a linear extrapola-tion of Cd with Re is not appropriate.Consequently, the poorer performanceof the SA7035 at AR = 10 and 12 islikely due to the high drag at low Reexhibited by this section.

For the AG12, an aspect ratio ofaround 10 appears to be a reasonablygood optimum. However, anywhere inthe 8 to 10 range is probably indistin-guishable in practice. So I wouldconclude that using the older large

R/C Soaring DigestPage 14

plane airfoils should tend towards thelow end of this range to avoid poor Reperformance. The more recentlydesigned laminar flow sections can stillperform well at the upper end of thisaspect ratio range.

What’s interesting to note is that thepolars all become broader as aninverse function of Re at higherspeeds. Although not shown here, thisis the opposite of the tendencies forthis same type of calculation for openclass ships. For the HLG/DLG wing-span, a high aspect ratio apparentlyproduces poor performance in theintermediate speed range due to Rescaling. For open class ships it appearsyou are above a critical Re value forthese problems and higher aspectratios are generally favored over theentire speed range.

If we look at an expanded speed rangefor the AG12, we find that the curvesindeed cross over to the expectedtendency at speeds in excess of 65 ft/sec. This is shown in Figure 5 only forAR 6 and 12 to keep the graph frombeing too cluttered. I hope this empha-sizes the need for careful considerationof Re effects at the scales encounteredwith HLG and DLG designs. Thisfactor is not nearly as critical for openclass ships.

Turning our attention to the DLGweight class, for the two channelconfiguration, the polar is shown inFigures 6 for the AG12. Although theincrease in weight is only a fewounces, it tends to shift the optimumperformance to a slightly lower aspectratio. This trend favors both Re andwing loading and suggests that a valueof ~ 9 may be a good choice.

For the DLG case we can now add twomore parameters for evaluation - theestimated launch height and theestimated flight time at minimum sink.These numbers are derived from alaunch height calculation which iscoupled to the polar program and usesthe calculated drag coefficients derivedfrom the polar evaluation. To arrive atthese numbers, an estimated releasevelocity and launch angle is assumedto calculate the launch height. Theflight time is then the sum of thelaunch time and the value for theheight divided by the minimum sinkrate.

For this study, the launch angle is 70degrees and the release velocity is 65ft/sec. The results will roughly scalewith initial launch velocity. The launchheight for a given velocity is not muchchanged for angles > 60 degrees. Sothese are conservative, but practicalnumbers for sport flying.

It is notable that the launch heights areall comparable for most cases but theflight time varies somewhat more

widely. This is mostly in response tothe change in minimum sink. Compar-ing these values with the minimumsink and max L/D terms we also findan optimization somewhere between8-10 for the aspect ratio.

In Figures 7 and 8, the polars for theAG12 for a 4 servo and 6 servo esti-mated ship are also shown. There aresubtle differences as the weight isincreased. The minimum sink, max L/

Page 15December 2002

D and flight time values optimizearound an aspect ratio of 8 at thehigher weight. So we can conclude thata heavier plane probably favors asomewhat lower aspect ratio. Howevergoing much below 8 does not seem tooffer any significant advantage - unlessyou build somewhat heavier than I do.

Although the changes appear subtle, afinal comparison of a subset of thisdata is shown in Figure 9. This plot

compares the polar and associated keyflight parameters, for the 2 channeland 6 channel DLG. Here we see thatthe 2 channel DLG in straight flightwill generally outperform the 6channel estimation for minimum sink,total flight time and efficiency as seenin the max L/D value.

In the heat of battle (contests) theadded functionality of the multi-function ship very likely has the

advantage by increasing effectivecamber for light air conditions andusing reflex for launch and movingaround in the wind. But for the simplepleasures of sport flying, there is nodisadvantage (and maybe even anadvantage!) to keeping it real simple.The case of flaperons may be a verynice compromise for contest conditions(4 servos).

As a reality check on the overallresults, an AR of 8 converts to about450 sq.in. wing area while an AR of 10gives 360 sq.in. In prowling the webfor present day designs, I find thatmost ships bracket the 350 sq.in. to 420sq.in. range. One could claim Q.E.D.and leave it at that. But why shouldone celebrate about predicting theobvious?

Well, if these calculations had said thatan AR of 16 is great for a 4 channelDLG, they wouldn’t have muchcredibility. Since the results do seem tomatch with reality, we can continue touse this as a tool to simulate perfor-mance for conditions we haven’t yettried (different airfoils, details of winglayout, etc.). Ultimately, the proof is atthe flying field, but studies like thiscan provide some confidence in theexpected performance of untestedconfigurations.

I also like knowing that for just mess-ing around, a properly designed twochannel ship with a real light sporttype radio (Hitec III, for instance) isprobably going to give me just aboutas much performance as a top endmulti-function sailplane. Now Iwonder what would happen if Ichange the base airfoil to increasecamber for the higher wing loading?Do I get back to a somewhat higheraspect ratio? Sounds like another studyis developing here. Let’s look at thatnext time.

Until then, hope you’ve had a happyholiday. Remember that flying some-thing is a whole lot better than flyingnothing so have fun and don’t sweatthe details too much!

(Figures 7-9 are on the next page! Ed.)

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R/C Soaring DigestPage 16

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Page 17December 2002

THE NATURAL SIDE OFTHERMAL SOARING

by Lee MurrayAppleton, Wisconsinlmurray@athenet.net

Time Deg F Dew Point %RH Event8:45 59.0 57.2 0.94 Scattered Clouds9:45 60.8 51.8 0.72 Scattered Clouds10:45 64.4 46.4 0.52 Scattered Clouds11:45 64.4 44.6 0.49 Scattered Clouds12:45 66.2 42.8 0.43 Scattered Clouds13:45 66.2 39.2 0.37 Mostly Cloudy14:45 66.2 39.2 0.37 Mostly Cloudy15:45 64.4 35.6 0.34 Mostly Cloudy16:45 62.6 39.2 0.42 Overcast18:45 59.0 42.8 0.55 Overcast

Temperature history for September 21st, 2002 in Appleton, WI.

In a recent column, I wrote about afrontal system coming through

during a local thermal duration contestand how it affected the flight times.The lift was neutral to certain pointthen became good as the ground levelair temperatures reached a triggerlevel allowing the height of the mixedboundary layer to go much higher1 .

During a recent fun flying experience,a point was reached when the liftchanged from neutral to wide-areasand long in duration2 . The Soarcast*indicated that it should have been agood day. However, flight times hadbeen about 3-5 minutes until about 3PM when they were 20+ minutes forseveral of us. Was it just some fluke inthe stability of the atmosphere not

The degree of stability ofthe lifted air determineswhether cloudiness will bepredominately stratiform(stretched horizontally) orcumuliform (stackedvertically).

In chapter 5 of hisbook4 , Dennis Pagentalks about the weatherfronts, wind directionand lift. A comparison ismade to cooler seabreezes that displace andrun under warmer air.On a larger scale, thesituation of cold frontsconverging with warm,moist air often involves

predicted by lapse rate and groundlevel air temperature or did it havesomething to do with the approachingcold front? This is the topic of thisarticle.

The book Aviation Weather describeswhat can happen with frontal weatherwhen masses of air with differenttemperatures mix3 .

Weather occurring with a front depends on(1) the amount of moisture available, (2)the degree of stability of the air that isforced upward, (3) the slope of the front,(4) the speed of frontal movement, and (5)the upper wind flow.

Sufficient moisture must be available forclouds to form, or there will be no clouds.

thunderstorms, a condition not recom-mended for full size soaring.

On the day I mentioned, a cold frontarrived from the northwest, and withit, a distinct line of dark clouds withincreasing elevation into the distance.The cold air was coming in fromCanada with a North West direction.The ground level warm breeze was outof the West. You can see the winddirections on the left side of theSoarcast Plot in Figure 2. The angledlines show wind direction (goingstraight up indicating wind out of thenorth). A line extending from the leftedge of the plot to the right is a graphof the wind velocity.

The confluence, or the frontal line,where the air was mixing was advanc-ing slowly to the east as the afternoonwent on. According to one theory, thecolder air was slipping underneath thewarmer air as shown in Figure 1.Models in the air were gaining altitudeas the air they were in was generallybeing forced up. As we flew the skybecame darker, we packed up and left.A few hours later it was raining.

Weather front theory has to get a littlemore complex to explain some limitedareas where the air was not going up. Ifound two possible explanations for

R/C Soaring DigestPage 18

this, either one or both of which mayhave existed.

Explanation 1: The ground was nowwarmer than the air filling in under therising warmer air. This gave thepossibility of convective cooling andsinking air mixed in with the generalrising air.

Explanation 2: There was turbulencealong the interface of the two airmasses that would cause areas wherethe model would be sinking.

Weather information was downloadedfrom the Internet: The temperature,dew point, wind, RH and conditionshistory was recovered from:

http://www.wunderground.com/history/airport/KATW/2002/9/21/

DailyHistory.html

KATW is the abbreviation forAppletons Outagamie County Airportjust a few miles from the flying field.

Wind Speed, mph/Temperature, F

The conventional theory for why wehad good conditions so late in the daywould rely on the temperature historyfor the day and the lapse rate. Thelapse rate data from Green Bay (about25 miles away) suggests that thetemperature exceeded the triggertemperature by noon. The goodthermals didn’t happen when ex-pected, perhaps because of somespecial condition imposed by theweather font. Or perhaps the very localconditions had too much evaporativecooling to participate in the convectivecooling (thermal processes) until moreinstability took place. The scatteredclouds in the weather history earlier inthe day suggest this may have been thecase.

The exercise of looking at weatherinformation should be useful to you inbeing able to analyze your localweather conditions. I believe the more‘in-tune’ an RC or full size sailplanepilot is to his local atmospheric condi-tions, the better thermal flyer he canbe.

I’m closing with a photo of a line ofcumulus clouds seen in late October inSW Florida shown on page 17. This isthe result of converging coastal front ofcooler coastal breezes running under

warmer interior air with enoughmoisture to form clouds. Why thereisn’t more full size thermal soaring inSouthern Florida? Perhaps the air istoo unstable. I bet some readers havesome answers.

1 RCSD: Jan 99 pg10, May 99 pg 24,Sep 99 pg 22, Apr 00 pg 22 and Jul00 pg 14.

2 A method developed by Pearsonpredicts when thermals will liftsailplanes to specific altitudeswhen a temperature is reached.

3 Soarcast Version 1.0.4 was pro-vided as a free download from theweb page of the Soaring Society ofAmerica. Newer versions arecurrently available.

4 US Depts. of Transportation andCommerce, Aviation Weather forPilots and Flight OperationsPersonnel Reprinted by ASAPublications, 1975 ed.

5 Pagen, Dennis, Understanding theSky, p. 185, Dennis Pagen Pub-lisher.

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