U Bradford W Powers HERE ARE few questions kind arise scale mentioned gether answers Lets see can discover bow answers ob tained 1 Bud Nosen builds A-scale kit Citabria airplane real airplane has 130-hp engine much power should model have Answer 117 hp 2 If real Citabria has high speed 150 mph fast should scale mod el fly look natural Answer 38 mph fast will actually fly Answer 75 mph 3 I want take real-looking movies model flight suspect slow motion involved much 24 frames per second normal film trans port speed what speed should shoot Answer 48 frames per second 4 If real pilot chute weigh 200 lbs what weight would represent pilot chute Y4-scale mod el Answer 3 lbs 2 oz 5 My grandson got Dumas 1 / 12scale Trojan Cruiser Xmas real boat weighs 12000 lbs what should model weigh float proper scale water line Answer 69 lbs 6 A Ryan ST experiences 5 gs acceler ation performing maneuver put Sig 1/5-scale model through same maneuver what acceleration should present Answer 5 gs Taking off water San Diego 1945 dynamic model Consolidated R3Y four-en gined flying boat controlled pilot baby grand transmitter used airplane-type controls triple-redundant photographers Intuitively felt widely understood relationship between mod els full-scale counterparts changes size scale power weight speed almost everything else vary different precise ways model embodying proper relative values items said dynamically similar full-scale prototype shall see very much same own pet scale job 7 If above maneuver puts stress 5000 lbs/sq spar flanges real Ryan what will stress spar flanges model Answer 1000 lbs/sq 8 If Trojan Cruiser problem No 5 cruises 20 knots 23 mph what should speed model pro duce dynamically similar wake spray pattern Answer 58 knots 66 mph 9 Joe building 1/10th-scale model Lockheed P-80 airplane 4000 lbs thrust will Joes Scozzi fan rated 5 lbs thrust adequate power model Answer yes 10 If real Chattanooga Choo Choo can go 65 mph 96 ft/sec fast should run HO gauge 1/96th scale model train achieve 65 mph scale speed Answer 1 ft/sec Except questions 7 10 answers foregoing problems appear bear no relation scale go further shall see indeed Since about time development steamboat engineers have employed laws dynamic similitude find answers vexing questions reliably inexpensively through use dynamic ally similar models dynamic model would result some magic full-scale article could liter ally shrunk convenient size testing Strictly speaking such model should identical way pro totypejust smaller However such mod8 Model Aviation TABLE NO 1 VALUES FOR ITEMS AT LEFT AT INCREASING SCALE FACTORS 1/10 SCALE OBJECT SCALE WT THUS PILOT WEIGHING 200 LBS 1000 OR 2 LBS IN 1/10 SCALE MODEL FULL SCALE WOULD WEIGH 200 LBS 1000 els rarely ever built such com plexity weight CG location general configuration held small ad justments weight distribution can make model dynamically similar prac tical purposes photos shows test being run Convair hydrodynamics engineers cinematographers way back about 1945 subject dynamic model Convair R3Y being tested spray clear ances landing takeoff accelera tions examining frames taken cameras uniform known speed values desired can found high ac curacy Note compact transmitter complete honest gosh pilots seat Another photo shows Skate high performance turbojet seaplane design cre ated author back 40s water-based airplanes still popular model being towed aside launch proper speeds evaluate landing takeoff characteristics spary patterns Notice blended hull required no tip floats As can see test shows flaperons almost green water must slightly reduced span such test carried out prop erly worth thousand expert opin ions Note also leading edge slats compensate Reynolds Number ef fectswhich will discuss later Now lets see closely typical scale kit comes meeting require ments dynamic model Sig makes excellent kit famous Ryan ST classic airplane designed have gross weight 1600 lbs wing span RYAN FULL SCALE Gross Weight Horsepower V Max V Stall Takeoff Run 1600 lbs 125 hp 150 mph 60 mph 525 ft 30 ft 125-hp engine top speed 150 mph stalling speed flaps 60 mph Lets make comparison fullscale Ryan proposed dynamic model Sig kit Sig kit has 6-ft span therefore 1/5-scale model will make dynamic model same scale Thus see typical scale kit different after dynamic model anything Sig kit will have snappier performance since has con siderably power less weight No tice distancethe takeoff runvaries same way scale 1/5 SCALE DYNAMIC MODEL 128 lbs 45 hp 67 mph 27 mph 105 ft 1/5 SCALE SIG KIT lOto 11 lbs Bto 1Ohp 70 80 mph 25 mph 90 95 ft January 1978 9 HOW SCALE FACTOR K MUST VARY THE ABOVE TABLE SHOWS THE POWER TO WHICH THE SCALE FACTOR MUST BE RAISED FOR GIVEN ITEM TO BE DYNAMICALLY SIMILAR TO THE PROTOTYPE IE THE ITEM WEIGHT MUST ALWAYS VARY AS K3 SCALE CUBED IN THE BODY OF THE TABLE ARE THE VALUES THAT ARE OBTAINED FOR COMMONLY USED SCALE FACTORS RANGING FROM K 2 TO K 20 WHEN RAISED TO THE APPROPRIATE POWER IE. THE WEIGHT OF other items again seem have little nothing scale Notice ever weight far below 1/5 real airplane yet speed 67 mph double 1/5 X 150 30 mph would have speed scale characteristic makes models fly outrageously fast spoils effectfor some least problem 10 able slow model train down scale speed zero danger falling out sky model airplane must sustain itself air shall see wing loading speed must vary di rectly scale Thus can see really two kinds speed far scale concerned visual speed dynamic speed Visual speed pleases ob servers dynamic speed pleases Mother Nature Now its about time got down nitty-gritty see can discover principles involved First lets look scale itself Scale simply ra tio dimensions object similar object differing size like large tuna small tuna large tuna small halibut Before going further lets put some commonly used scales proper form pur pose COMMONACTUALSCALE USAGE SCALE FACTORK 3D fl 1 l/~t 4 1 -0 1/4 1/8 1/4 1/6 1/8 1/12 1/16 1/24 1/48 1/96 4 6 8 12 16 24 48 96 Sig Ryan has dimensions 1/5 full-scale airplane may said have scale factor 5 scale factor placed numerator compar ing big things little ones placed denominator little things compared big ones Thus full-scale Ryan 5/1 5 times size mod el model 1/5 size full-scale Ryan order facilitate com putation will engineers indicate scale factor Greek letter Kappa K gives certain mys tique process makes other peo ple think smarter sort like doctor writing prescriptions Latin Now physical properties can expressed terms Length Mass purpose Force propor tional Mass Time follows L linear measurementLength Width Height Distance Circumfer ence F Any Force Weight Thrust tAny interval Time Using three basic parameters can describe following ITEMSYMBOLSDESCRIPTIONUNITS Accelerationa 12 Distance Feet2 tTime SquaredSecond Velocity Distance Feet t meSecond Workw rce x DistancePound-Feet MomentM rce x DistancePound-Feet Moment ofI Force x Distance2Pound-Feet 2 Inertia FLForce x DistancePound-Feet HorsepowerHP e Second AreaS ngth SquaredSquare Feet 3 Volumev gth CubedCubic Feet WeightW ForcePounds ForceF ForcePounds ThrustT F cePounds Now lets take few items foregoing see might af fected Scale take Length Area Volume start Fig 1 see doubling Length line amounts doubling Scale reason can say dimensions vary di rectly Scale L L2 Fig 2 square measuring 1 inch side see blow up scale 2 making side 2 inches long have increased area four foldfrom square inch four square inches Thus see Area varies square Scale S III Fig2 Fig 3 shaded area one-inch cube see double dimensions cube increase its vol ume cube 2 2 X 2 X 2 mes So Volumes vary cube Scale L 1 L2 Fig 3I Now assume cube made wood lets say weighing ounce per cubic inch small cube weighs ounce large cube weighs eight ounces Thus Weight varies same way Volumeas cube Scale Weight measured pounds ounces grams etc Force Thrust So now can say Weight Fig 1Force Thrust also vary cube Scale W F T oint say Well OK suspected sort like what about Speed Power Well good way proceed might find something Scale doesnt affect Lets try Aspect Ratio ratio span chord Everybody knows doesnt change Scale 4 its simplest termsfor simple rec tangular planform ct Ratio equals Since both Span b Chord c c same units namely feet feet cancel out expression said dimensionless remains constant dependent Scale can go step further say b L equals y equals F turn equals L equals 1 say both b c di mensions L precisely L L first power Now high school know divide ex ponents subtract denomi nator numerator Thus wind up L0 Now number exponent zero equal 1 1 has way retaining its identity pres ence exponents example 12 1 etc Thus can say terms dimensionlessthat have exponents zerodo change 10 Model Aviation Scale Lets try another Density Density Weight K3 equals K again VolumeK know true cup sea wa ter has same density ocean came say Yeah great now about Speed Power Well lets see can find another constant has Time since Time involved Speed Power surface planet up altitudes model airplanes fly bombers butterflies ants ele phants respond exactly same way start accelerating toward cen ter earth whenever what holding up pulled out under Disregarding air resistance will ac celerate rate 32 ft per second second acceleration constant re gardless Scale Other accelerations such 5-g maneuver simply mul tiples basic gravitational accelera tion too remain constant inso far Scale concerned have seen describing pa rameters Acceleration expressed L L thetermNow since know txt expression represents constant also know will have expon ent zero just like Aspect Ratio Den sity did Thus may say LL xt e L has exponent 1 two Ts must have exponent 5 turn may expressed terms Scale K-K K5 K Thus have determined time has exponent 5 same square root So can say Time var ies asjhe square root Scale t an now proceed Speed Power Speed Velocity V _ K terms Scale K3 K5 Which says Speed like Time varies square root Scale V wer said Force X Distance ime terms Scale K3K — K35 K Power varies 35 power Scale HP Wing Loading Weight K3 K AreaK2 varies directly Scale Stress Force — K3 — K AreaK2 also varies Scale Power Loading WeighL K3 — Power K33 K varies reciprocal square root Scale Thrust Loading WeighL K3 — K Thrust K3 Velocity V varies square root Scale K3 Power HP varies three-and-onehalf power Scale K3 Wing Loading Y varies directly Sale K sses I vary directly Scale K S Loading recipro dimensionless does change Power varies ScaleHP summarize Acceleration constant does change Scale K Dimensions L vary directly Scale K Areas 5 vary Scale squared K2 Volumes v vary Scale cubed K3 Weights W vary Scale cubed K3 Forces F vary Scale cubed K3 Thrust T varies Scale cubed K3 Work w varies Scale fourth power K4 Moments M vary Scale fourth power K4 Moments Inertia vary Scale fifth power K Time t varies square root Scale K cal square root Scale K Aspect Ratio other geometrical ra tios Density Thrust Loading other dimensionless items change Scale K 35 power some other terms easy figure cal culator have handy well calculate values foregoing items several appropriate scale factors tabulate Table 1 Now understand mysteries scale lets go back check values gave dynamic model Ryan ST Table No 1 Now lets check answers ques tions posed beginning January 1978 11 late forties Consolidated testing all-metal model proposed jet-powered Skate flying boat shown skimming water test basin Full-span slats blended hull 1600 lbs 53 125 hp 35 5 150 mph 55 60mph 525 ft 1 5 1 From Table 1 scale factor 4 speed horsepower factor 128 Ignoring Reynolds No effects power required model thereforei9or 117 As 128 discussed further however would wise increase say 15 hp ac count relative disparity propeller efficiencies 2 Visual scale speed simply speed divided scale factor 150 equals4—-or 375 say 38 mph However dynamic scale speed 150150 h K52 3 Since visually model going fly twice fast full-scale air plane will necessary shoot twice pictures per unit time film projected normal speed Citabria model will appear flying slow easy just like real 4 Weight varies cube scale factor case 43 64 Therefore pilots weight is29. 3125 lbs 64 5 again weight model prototype divided cube scale factor case 12 Table 1 120001bs or69lbs 1728 6 If maneuvers same accelerations produced prototype duplicated model accelerations vary scale 7 Stress varies directly scale model stresses will 1000 5 pounds per sq size creases stronger stronger materials must used Howard Hughes Spruce Goose such sad waste taxpayers money No weight fi nally available payload 8 Dynamic speed varies square root scale 20 20 58 knots 12346 9 Thrust varies scale factor cubed 4000 bs 10 So Scozzi fan 5 lbs OK 10 96/96 /sec visual scale 1600 lbs 125 125hp 2795 150 mph 2236 -60mph 2236 525ft 5 understanding relationships very least recognize exist seems to essential has become addicted fasci nating hobby wishes pursue telligently particularly likes create adaptations interesting airplanes boats cars flood control projects anything else operates same means prototype origi nal designs own Obviously de termination such things engine size wing area weight etc should made rational basis know things vary scale have powerful tool indeed really needs scratch build anything wishes have data handy prototype data perhaps engine shelf workshop can select proper scale start reducing enlarging plans word caution however der mathematician can predict hairline accuracy trace moons shadow across earth during eclipse can approximate trajectory rifle bullet through unpredictable unruly air currents same token 128 lbsour rules dynamic similitude tell us pre cisely what things should account differences flow patterns 45 hp between full-scale wings propellers model wings propellers Big wings develop higher lift lower drag propor tionately small ones 67 mph differences studied eval uated long ago man named Osborne Reynolds actually interested flow fluid through pipes found 27 mph big pipes carried water better small pipes relationships discov ered expressed Reynolds Num 105 ft ber Because Reynolds Number match full-scale prototype very faithfully detail Ryan will probably land something higher 27 mph like 30 mph unless ways can found keep lift its proper value leading edge slats quite effective Skate model Such lead ing edge slats will help will turbula tionroughening leading edge stretching wire along front energize boundary layer thus de lay separation reduction lift Full-scale propellers develop 80 85% efficiencies doesnt seem much data available model propeller efficiencies fair guess might around 60% Thus rules say Ryan needs 45 hp might better part wis dom increase power factor something like 80/60 X 45 6 hp necessarily 60 cu engine time time reads modeler says landed fairly sizeable heavy radio model scale speed 10 mph can say just possible average model still air However air rarely still 10- 15-mph breeze could make seem possible visual scale speeds become mat ter real concern certainly could have merit answer think lies combination large size careful weight watching high-lift airfoils effective high-lift devices such full span flaps talking about speed reductions order 50% Finally important have talking about building dynam ic models full-scale aircraft deter mined weight power etc based full gross weight prototype models however particularly larger ones may able better appears Thirty-five 40% weight real airplane useful loadpilot baggage fuel cargo etc small models much gobbled up radio gear large quarter-size larger models radio weight becomes relatively insignificant carry ing three-pound pilot nor baggage etc may find ourselves lighter model truly dynamically similar turn will give us lighter wing load Continuedonpage86 12 Model Aviation Weight will Power will Vmaxwill V stall will Takeoff run will 1600 lbs K3 125 hp K 150 mph K 60 mph K 525 ft 1 K em em em em em em memo Bradford W Powers eme me me me SPECIAL PRO SERIES 2 FOR RC-FREE FLIGHT CONTROL LINE CIAPITCHPRICE 5%3489 63489 733%4119 53%456129 94566% 77%139 10467149 1066V 8W149 to6016159 114677% 7Y, 7%8159 it6E1W169 11%67169 126179 12555179 1356219 1496249 1566309 164%6389 W 55106 BLADE 855 EXTRA WIDE SERIES 400 B Poe SPEED & RACING ADVANCED DESIGN NO 1 IN PYLON RACING LEADING SPEED REGGRO HOLDER OF ALL TIMES RC PYLON RACING DIA PITCHPRICE 6%3%4129 755%6149 7SN 5/N 6N149 8%6% 6% 7 7%7%189 96%7 7A7%189 CONTROL LINE SPEED& RACING CIA PITCHPRICE 4/8A7129 4%55%129 6788%149 7 7%10%11169 889189 89N9%N189 8% 77%189 912 13219 51ARRflW Homebuilts Bill Youmans firstplace win Masters Class Greenville NRCHA Nationals last August seems increasing interest homebuilt helicopters won scratchbuilt own design composite components Bill came within 10 points aceing hover course local flier Norm Holland has developed scratchbuilt using Kavan mechanics tn-cycle landing gear Rev-o-lution canopy Futaba Sl5M ball-bearing servos EK single-stick radio Kraft engine Tach-Tron gover nor weight 12 1/2 pounds very smooth precise enough people inter ested could soon put kit form Look column further details Dual Counter Rotating Head ScratchBuilt Gilbert Laforest Montreal suc cessfully flew counter rotating-head heli copter own design Greenville NRCHA Nats Webra Speed 60 driving both heads unbelievably complicated pushrod system Self-designed transmitter two single sticks dual rudder knobs much Separate collective control head well separate cyclic control Tremendous under taking say nothing about getting mind synchronized hands Radio custom Can-Air Canadian ProLine some radio interference problems Next months column will cover unique finish helicopters first part building Aerospatiale SA-34 1 G Gazelle ducted fan-tail rotor youre flying youre trying hard enough Walt Schoonard 2080 Sharon Rd Winter Park FL 32789 Letters continued page 7 quality Model viation money best model aviation magazine field William R Barr AMA 31415 Claremont CA MA policy publish types models eventually shall get around Mr Barrs suggestions Mistaken Identity No doubt have received few letters already rare event havent would like point out photograph lower right hand corner page 25 Aug 1977 issue Model viation incorrectly captioned gentleman photo Rick Pear son winner last years Soar Nats well other contests sailplane holding Paragon Rick did outstanding job flying under less ideal conditions would shame did receive credit display flying skill Since generally true least 75% sailplanes performance direct function pilots skill would follow mention sailplane used would significant have no doubt uninten tional error know would want errors called attention proper caption can used Ed Slobod Pierce Aero Company Nonthridge CA Size It/Powers continued page 13 ing slower speed reduce somewhat power requirements because scaling down proto type its weight-empty condition rather its gross-weight condition thats ut Size Questions comments may ad dressed Bradford W Powers care magazine Seastrutz/Wi son continued page 18 full throttle some down-elevator Ed pulled up Seastrutz oil like scared duck full stall attitude 50 feet hit wind blowing toward hill blown end-over-end trees Damage minor Test flying continued next week Fall Brimfield meet time stabilizer shim under its leading edge rudder area doubled Seastrutz flew beautifully Among its test pilots Ted Straders son Eric testified flew very much like its predecessor Strutz Echo Seastrutz built mci dences shown will perform very well relatively docile its 46-in wing span compact biplane configuration felt might too quick average flier case diffi cult machine fly land water Have fun Radio Technique/Myers continued page 14 An ammeter measure charging discharging operating currents turntable drum-type chart feed measure servo transmit time shaker find intermittent prob lems heat lamp can Freezit similar chiller locate temperature-sensitive compon ents Special tools various types like desoldering irons Youve seen lot items listed under additional advertisements probability should leave will describe some simple non destructive tests should perform 86 Model Aviation NEWS FLASH Bob Smith Chatsworth CA set new World Speed Record June 19 Pylon mula 11125 RevUp 8%-6% new Pylon RaC ing prop OUT- PERFORMS ALL OTHERS AT THE 1976 NATIONALS 1st RC Masters Class 1st RC Advanced 1st RC Novice 1st RC Sport Scale 1st Formula Pylon 1st Quarter Midget Pylon 1st CL Stunt Open 1st CL Stunt Senior 1st CL Stunt Junior 1st CL Combat O & Sr 1st CL Slow Comb OP & Sr 1st CL Class 0 Speed Open 1st CL Class C Speed Jr & Sr 1st CLCIassB Speed Op & Sr 1st CL Cl Speed Op Sr Jr 1st FE Class B Open 1st FE Class C Open HIGH PERFORMANCE * COMPETITION PROVEN * THIN RIGID BLADES OP HARD MAPLE WOOD * SUPERBLY FINISHED COMPLETELY FUEL PIDOF 1st CL Carrier II Op Jr Sr 1st CL Carrier Jr & Sr 1st CL Formula 40 Opec 1st CL Class 6 Proto Jr
Edition: Model Aviation - 1978/01
Page Numbers: 8, 9, 10, 11, 12, 86
U Bradford W Powers HERE ARE few questions kind arise scale mentioned gether answers Lets see can discover bow answers ob tained 1 Bud Nosen builds A-scale kit Citabria airplane real airplane has 130-hp engine much power should model have Answer 117 hp 2 If real Citabria has high speed 150 mph fast should scale mod el fly look natural Answer 38 mph fast will actually fly Answer 75 mph 3 I want take real-looking movies model flight suspect slow motion involved much 24 frames per second normal film trans port speed what speed should shoot Answer 48 frames per second 4 If real pilot chute weigh 200 lbs what weight would represent pilot chute Y4-scale mod el Answer 3 lbs 2 oz 5 My grandson got Dumas 1 / 12scale Trojan Cruiser Xmas real boat weighs 12000 lbs what should model weigh float proper scale water line Answer 69 lbs 6 A Ryan ST experiences 5 gs acceler ation performing maneuver put Sig 1/5-scale model through same maneuver what acceleration should present Answer 5 gs Taking off water San Diego 1945 dynamic model Consolidated R3Y four-en gined flying boat controlled pilot baby grand transmitter used airplane-type controls triple-redundant photographers Intuitively felt widely understood relationship between mod els full-scale counterparts changes size scale power weight speed almost everything else vary different precise ways model embodying proper relative values items said dynamically similar full-scale prototype shall see very much same own pet scale job 7 If above maneuver puts stress 5000 lbs/sq spar flanges real Ryan what will stress spar flanges model Answer 1000 lbs/sq 8 If Trojan Cruiser problem No 5 cruises 20 knots 23 mph what should speed model pro duce dynamically similar wake spray pattern Answer 58 knots 66 mph 9 Joe building 1/10th-scale model Lockheed P-80 airplane 4000 lbs thrust will Joes Scozzi fan rated 5 lbs thrust adequate power model Answer yes 10 If real Chattanooga Choo Choo can go 65 mph 96 ft/sec fast should run HO gauge 1/96th scale model train achieve 65 mph scale speed Answer 1 ft/sec Except questions 7 10 answers foregoing problems appear bear no relation scale go further shall see indeed Since about time development steamboat engineers have employed laws dynamic similitude find answers vexing questions reliably inexpensively through use dynamic ally similar models dynamic model would result some magic full-scale article could liter ally shrunk convenient size testing Strictly speaking such model should identical way pro totypejust smaller However such mod8 Model Aviation TABLE NO 1 VALUES FOR ITEMS AT LEFT AT INCREASING SCALE FACTORS 1/10 SCALE OBJECT SCALE WT THUS PILOT WEIGHING 200 LBS 1000 OR 2 LBS IN 1/10 SCALE MODEL FULL SCALE WOULD WEIGH 200 LBS 1000 els rarely ever built such com plexity weight CG location general configuration held small ad justments weight distribution can make model dynamically similar prac tical purposes photos shows test being run Convair hydrodynamics engineers cinematographers way back about 1945 subject dynamic model Convair R3Y being tested spray clear ances landing takeoff accelera tions examining frames taken cameras uniform known speed values desired can found high ac curacy Note compact transmitter complete honest gosh pilots seat Another photo shows Skate high performance turbojet seaplane design cre ated author back 40s water-based airplanes still popular model being towed aside launch proper speeds evaluate landing takeoff characteristics spary patterns Notice blended hull required no tip floats As can see test shows flaperons almost green water must slightly reduced span such test carried out prop erly worth thousand expert opin ions Note also leading edge slats compensate Reynolds Number ef fectswhich will discuss later Now lets see closely typical scale kit comes meeting require ments dynamic model Sig makes excellent kit famous Ryan ST classic airplane designed have gross weight 1600 lbs wing span RYAN FULL SCALE Gross Weight Horsepower V Max V Stall Takeoff Run 1600 lbs 125 hp 150 mph 60 mph 525 ft 30 ft 125-hp engine top speed 150 mph stalling speed flaps 60 mph Lets make comparison fullscale Ryan proposed dynamic model Sig kit Sig kit has 6-ft span therefore 1/5-scale model will make dynamic model same scale Thus see typical scale kit different after dynamic model anything Sig kit will have snappier performance since has con siderably power less weight No tice distancethe takeoff runvaries same way scale 1/5 SCALE DYNAMIC MODEL 128 lbs 45 hp 67 mph 27 mph 105 ft 1/5 SCALE SIG KIT lOto 11 lbs Bto 1Ohp 70 80 mph 25 mph 90 95 ft January 1978 9 HOW SCALE FACTOR K MUST VARY THE ABOVE TABLE SHOWS THE POWER TO WHICH THE SCALE FACTOR MUST BE RAISED FOR GIVEN ITEM TO BE DYNAMICALLY SIMILAR TO THE PROTOTYPE IE THE ITEM WEIGHT MUST ALWAYS VARY AS K3 SCALE CUBED IN THE BODY OF THE TABLE ARE THE VALUES THAT ARE OBTAINED FOR COMMONLY USED SCALE FACTORS RANGING FROM K 2 TO K 20 WHEN RAISED TO THE APPROPRIATE POWER IE. THE WEIGHT OF other items again seem have little nothing scale Notice ever weight far below 1/5 real airplane yet speed 67 mph double 1/5 X 150 30 mph would have speed scale characteristic makes models fly outrageously fast spoils effectfor some least problem 10 able slow model train down scale speed zero danger falling out sky model airplane must sustain itself air shall see wing loading speed must vary di rectly scale Thus can see really two kinds speed far scale concerned visual speed dynamic speed Visual speed pleases ob servers dynamic speed pleases Mother Nature Now its about time got down nitty-gritty see can discover principles involved First lets look scale itself Scale simply ra tio dimensions object similar object differing size like large tuna small tuna large tuna small halibut Before going further lets put some commonly used scales proper form pur pose COMMONACTUALSCALE USAGE SCALE FACTORK 3D fl 1 l/~t 4 1 -0 1/4 1/8 1/4 1/6 1/8 1/12 1/16 1/24 1/48 1/96 4 6 8 12 16 24 48 96 Sig Ryan has dimensions 1/5 full-scale airplane may said have scale factor 5 scale factor placed numerator compar ing big things little ones placed denominator little things compared big ones Thus full-scale Ryan 5/1 5 times size mod el model 1/5 size full-scale Ryan order facilitate com putation will engineers indicate scale factor Greek letter Kappa K gives certain mys tique process makes other peo ple think smarter sort like doctor writing prescriptions Latin Now physical properties can expressed terms Length Mass purpose Force propor tional Mass Time follows L linear measurementLength Width Height Distance Circumfer ence F Any Force Weight Thrust tAny interval Time Using three basic parameters can describe following ITEMSYMBOLSDESCRIPTIONUNITS Accelerationa 12 Distance Feet2 tTime SquaredSecond Velocity Distance Feet t meSecond Workw rce x DistancePound-Feet MomentM rce x DistancePound-Feet Moment ofI Force x Distance2Pound-Feet 2 Inertia FLForce x DistancePound-Feet HorsepowerHP e Second AreaS ngth SquaredSquare Feet 3 Volumev gth CubedCubic Feet WeightW ForcePounds ForceF ForcePounds ThrustT F cePounds Now lets take few items foregoing see might af fected Scale take Length Area Volume start Fig 1 see doubling Length line amounts doubling Scale reason can say dimensions vary di rectly Scale L L2 Fig 2 square measuring 1 inch side see blow up scale 2 making side 2 inches long have increased area four foldfrom square inch four square inches Thus see Area varies square Scale S III Fig2 Fig 3 shaded area one-inch cube see double dimensions cube increase its vol ume cube 2 2 X 2 X 2 mes So Volumes vary cube Scale L 1 L2 Fig 3I Now assume cube made wood lets say weighing ounce per cubic inch small cube weighs ounce large cube weighs eight ounces Thus Weight varies same way Volumeas cube Scale Weight measured pounds ounces grams etc Force Thrust So now can say Weight Fig 1Force Thrust also vary cube Scale W F T oint say Well OK suspected sort like what about Speed Power Well good way proceed might find something Scale doesnt affect Lets try Aspect Ratio ratio span chord Everybody knows doesnt change Scale 4 its simplest termsfor simple rec tangular planform ct Ratio equals Since both Span b Chord c c same units namely feet feet cancel out expression said dimensionless remains constant dependent Scale can go step further say b L equals y equals F turn equals L equals 1 say both b c di mensions L precisely L L first power Now high school know divide ex ponents subtract denomi nator numerator Thus wind up L0 Now number exponent zero equal 1 1 has way retaining its identity pres ence exponents example 12 1 etc Thus can say terms dimensionlessthat have exponents zerodo change 10 Model Aviation Scale Lets try another Density Density Weight K3 equals K again VolumeK know true cup sea wa ter has same density ocean came say Yeah great now about Speed Power Well lets see can find another constant has Time since Time involved Speed Power surface planet up altitudes model airplanes fly bombers butterflies ants ele phants respond exactly same way start accelerating toward cen ter earth whenever what holding up pulled out under Disregarding air resistance will ac celerate rate 32 ft per second second acceleration constant re gardless Scale Other accelerations such 5-g maneuver simply mul tiples basic gravitational accelera tion too remain constant inso far Scale concerned have seen describing pa rameters Acceleration expressed L L thetermNow since know txt expression represents constant also know will have expon ent zero just like Aspect Ratio Den sity did Thus may say LL xt e L has exponent 1 two Ts must have exponent 5 turn may expressed terms Scale K-K K5 K Thus have determined time has exponent 5 same square root So can say Time var ies asjhe square root Scale t an now proceed Speed Power Speed Velocity V _ K terms Scale K3 K5 Which says Speed like Time varies square root Scale V wer said Force X Distance ime terms Scale K3K — K35 K Power varies 35 power Scale HP Wing Loading Weight K3 K AreaK2 varies directly Scale Stress Force — K3 — K AreaK2 also varies Scale Power Loading WeighL K3 — Power K33 K varies reciprocal square root Scale Thrust Loading WeighL K3 — K Thrust K3 Velocity V varies square root Scale K3 Power HP varies three-and-onehalf power Scale K3 Wing Loading Y varies directly Sale K sses I vary directly Scale K S Loading recipro dimensionless does change Power varies ScaleHP summarize Acceleration constant does change Scale K Dimensions L vary directly Scale K Areas 5 vary Scale squared K2 Volumes v vary Scale cubed K3 Weights W vary Scale cubed K3 Forces F vary Scale cubed K3 Thrust T varies Scale cubed K3 Work w varies Scale fourth power K4 Moments M vary Scale fourth power K4 Moments Inertia vary Scale fifth power K Time t varies square root Scale K cal square root Scale K Aspect Ratio other geometrical ra tios Density Thrust Loading other dimensionless items change Scale K 35 power some other terms easy figure cal culator have handy well calculate values foregoing items several appropriate scale factors tabulate Table 1 Now understand mysteries scale lets go back check values gave dynamic model Ryan ST Table No 1 Now lets check answers ques tions posed beginning January 1978 11 late forties Consolidated testing all-metal model proposed jet-powered Skate flying boat shown skimming water test basin Full-span slats blended hull 1600 lbs 53 125 hp 35 5 150 mph 55 60mph 525 ft 1 5 1 From Table 1 scale factor 4 speed horsepower factor 128 Ignoring Reynolds No effects power required model thereforei9or 117 As 128 discussed further however would wise increase say 15 hp ac count relative disparity propeller efficiencies 2 Visual scale speed simply speed divided scale factor 150 equals4—-or 375 say 38 mph However dynamic scale speed 150150 h K52 3 Since visually model going fly twice fast full-scale air plane will necessary shoot twice pictures per unit time film projected normal speed Citabria model will appear flying slow easy just like real 4 Weight varies cube scale factor case 43 64 Therefore pilots weight is29. 3125 lbs 64 5 again weight model prototype divided cube scale factor case 12 Table 1 120001bs or69lbs 1728 6 If maneuvers same accelerations produced prototype duplicated model accelerations vary scale 7 Stress varies directly scale model stresses will 1000 5 pounds per sq size creases stronger stronger materials must used Howard Hughes Spruce Goose such sad waste taxpayers money No weight fi nally available payload 8 Dynamic speed varies square root scale 20 20 58 knots 12346 9 Thrust varies scale factor cubed 4000 bs 10 So Scozzi fan 5 lbs OK 10 96/96 /sec visual scale 1600 lbs 125 125hp 2795 150 mph 2236 -60mph 2236 525ft 5 understanding relationships very least recognize exist seems to essential has become addicted fasci nating hobby wishes pursue telligently particularly likes create adaptations interesting airplanes boats cars flood control projects anything else operates same means prototype origi nal designs own Obviously de termination such things engine size wing area weight etc should made rational basis know things vary scale have powerful tool indeed really needs scratch build anything wishes have data handy prototype data perhaps engine shelf workshop can select proper scale start reducing enlarging plans word caution however der mathematician can predict hairline accuracy trace moons shadow across earth during eclipse can approximate trajectory rifle bullet through unpredictable unruly air currents same token 128 lbsour rules dynamic similitude tell us pre cisely what things should account differences flow patterns 45 hp between full-scale wings propellers model wings propellers Big wings develop higher lift lower drag propor tionately small ones 67 mph differences studied eval uated long ago man named Osborne Reynolds actually interested flow fluid through pipes found 27 mph big pipes carried water better small pipes relationships discov ered expressed Reynolds Num 105 ft ber Because Reynolds Number match full-scale prototype very faithfully detail Ryan will probably land something higher 27 mph like 30 mph unless ways can found keep lift its proper value leading edge slats quite effective Skate model Such lead ing edge slats will help will turbula tionroughening leading edge stretching wire along front energize boundary layer thus de lay separation reduction lift Full-scale propellers develop 80 85% efficiencies doesnt seem much data available model propeller efficiencies fair guess might around 60% Thus rules say Ryan needs 45 hp might better part wis dom increase power factor something like 80/60 X 45 6 hp necessarily 60 cu engine time time reads modeler says landed fairly sizeable heavy radio model scale speed 10 mph can say just possible average model still air However air rarely still 10- 15-mph breeze could make seem possible visual scale speeds become mat ter real concern certainly could have merit answer think lies combination large size careful weight watching high-lift airfoils effective high-lift devices such full span flaps talking about speed reductions order 50% Finally important have talking about building dynam ic models full-scale aircraft deter mined weight power etc based full gross weight prototype models however particularly larger ones may able better appears Thirty-five 40% weight real airplane useful loadpilot baggage fuel cargo etc small models much gobbled up radio gear large quarter-size larger models radio weight becomes relatively insignificant carry ing three-pound pilot nor baggage etc may find ourselves lighter model truly dynamically similar turn will give us lighter wing load Continuedonpage86 12 Model Aviation Weight will Power will Vmaxwill V stall will Takeoff run will 1600 lbs K3 125 hp K 150 mph K 60 mph K 525 ft 1 K em em em em em em memo Bradford W Powers eme me me me SPECIAL PRO SERIES 2 FOR RC-FREE FLIGHT CONTROL LINE CIAPITCHPRICE 5%3489 63489 733%4119 53%456129 94566% 77%139 10467149 1066V 8W149 to6016159 114677% 7Y, 7%8159 it6E1W169 11%67169 126179 12555179 1356219 1496249 1566309 164%6389 W 55106 BLADE 855 EXTRA WIDE SERIES 400 B Poe SPEED & RACING ADVANCED DESIGN NO 1 IN PYLON RACING LEADING SPEED REGGRO HOLDER OF ALL TIMES RC PYLON RACING DIA PITCHPRICE 6%3%4129 755%6149 7SN 5/N 6N149 8%6% 6% 7 7%7%189 96%7 7A7%189 CONTROL LINE SPEED& RACING CIA PITCHPRICE 4/8A7129 4%55%129 6788%149 7 7%10%11169 889189 89N9%N189 8% 77%189 912 13219 51ARRflW Homebuilts Bill Youmans firstplace win Masters Class Greenville NRCHA Nationals last August seems increasing interest homebuilt helicopters won scratchbuilt own design composite components Bill came within 10 points aceing hover course local flier Norm Holland has developed scratchbuilt using Kavan mechanics tn-cycle landing gear Rev-o-lution canopy Futaba Sl5M ball-bearing servos EK single-stick radio Kraft engine Tach-Tron gover nor weight 12 1/2 pounds very smooth precise enough people inter ested could soon put kit form Look column further details Dual Counter Rotating Head ScratchBuilt Gilbert Laforest Montreal suc cessfully flew counter rotating-head heli copter own design Greenville NRCHA Nats Webra Speed 60 driving both heads unbelievably complicated pushrod system Self-designed transmitter two single sticks dual rudder knobs much Separate collective control head well separate cyclic control Tremendous under taking say nothing about getting mind synchronized hands Radio custom Can-Air Canadian ProLine some radio interference problems Next months column will cover unique finish helicopters first part building Aerospatiale SA-34 1 G Gazelle ducted fan-tail rotor youre flying youre trying hard enough Walt Schoonard 2080 Sharon Rd Winter Park FL 32789 Letters continued page 7 quality Model viation money best model aviation magazine field William R Barr AMA 31415 Claremont CA MA policy publish types models eventually shall get around Mr Barrs suggestions Mistaken Identity No doubt have received few letters already rare event havent would like point out photograph lower right hand corner page 25 Aug 1977 issue Model viation incorrectly captioned gentleman photo Rick Pear son winner last years Soar Nats well other contests sailplane holding Paragon Rick did outstanding job flying under less ideal conditions would shame did receive credit display flying skill Since generally true least 75% sailplanes performance direct function pilots skill would follow mention sailplane used would significant have no doubt uninten tional error know would want errors called attention proper caption can used Ed Slobod Pierce Aero Company Nonthridge CA Size It/Powers continued page 13 ing slower speed reduce somewhat power requirements because scaling down proto type its weight-empty condition rather its gross-weight condition thats ut Size Questions comments may ad dressed Bradford W Powers care magazine Seastrutz/Wi son continued page 18 full throttle some down-elevator Ed pulled up Seastrutz oil like scared duck full stall attitude 50 feet hit wind blowing toward hill blown end-over-end trees Damage minor Test flying continued next week Fall Brimfield meet time stabilizer shim under its leading edge rudder area doubled Seastrutz flew beautifully Among its test pilots Ted Straders son Eric testified flew very much like its predecessor Strutz Echo Seastrutz built mci dences shown will perform very well relatively docile its 46-in wing span compact biplane configuration felt might too quick average flier case diffi cult machine fly land water Have fun Radio Technique/Myers continued page 14 An ammeter measure charging discharging operating currents turntable drum-type chart feed measure servo transmit time shaker find intermittent prob lems heat lamp can Freezit similar chiller locate temperature-sensitive compon ents Special tools various types like desoldering irons Youve seen lot items listed under additional advertisements probability should leave will describe some simple non destructive tests should perform 86 Model Aviation NEWS FLASH Bob Smith Chatsworth CA set new World Speed Record June 19 Pylon mula 11125 RevUp 8%-6% new Pylon RaC ing prop OUT- PERFORMS ALL OTHERS AT THE 1976 NATIONALS 1st RC Masters Class 1st RC Advanced 1st RC Novice 1st RC Sport Scale 1st Formula Pylon 1st Quarter Midget Pylon 1st CL Stunt Open 1st CL Stunt Senior 1st CL Stunt Junior 1st CL Combat O & Sr 1st CL Slow Comb OP & Sr 1st CL Class 0 Speed Open 1st CL Class C Speed Jr & Sr 1st CLCIassB Speed Op & Sr 1st CL Cl Speed Op Sr Jr 1st FE Class B Open 1st FE Class C Open HIGH PERFORMANCE * COMPETITION PROVEN * THIN RIGID BLADES OP HARD MAPLE WOOD * SUPERBLY FINISHED COMPLETELY FUEL PIDOF 1st CL Carrier II Op Jr Sr 1st CL Carrier Jr & Sr 1st CL Formula 40 Opec 1st CL Class 6 Proto Jr
Edition: Model Aviation - 1978/01
Page Numbers: 8, 9, 10, 11, 12, 86
U Bradford W Powers HERE ARE few questions kind arise scale mentioned gether answers Lets see can discover bow answers ob tained 1 Bud Nosen builds A-scale kit Citabria airplane real airplane has 130-hp engine much power should model have Answer 117 hp 2 If real Citabria has high speed 150 mph fast should scale mod el fly look natural Answer 38 mph fast will actually fly Answer 75 mph 3 I want take real-looking movies model flight suspect slow motion involved much 24 frames per second normal film trans port speed what speed should shoot Answer 48 frames per second 4 If real pilot chute weigh 200 lbs what weight would represent pilot chute Y4-scale mod el Answer 3 lbs 2 oz 5 My grandson got Dumas 1 / 12scale Trojan Cruiser Xmas real boat weighs 12000 lbs what should model weigh float proper scale water line Answer 69 lbs 6 A Ryan ST experiences 5 gs acceler ation performing maneuver put Sig 1/5-scale model through same maneuver what acceleration should present Answer 5 gs Taking off water San Diego 1945 dynamic model Consolidated R3Y four-en gined flying boat controlled pilot baby grand transmitter used airplane-type controls triple-redundant photographers Intuitively felt widely understood relationship between mod els full-scale counterparts changes size scale power weight speed almost everything else vary different precise ways model embodying proper relative values items said dynamically similar full-scale prototype shall see very much same own pet scale job 7 If above maneuver puts stress 5000 lbs/sq spar flanges real Ryan what will stress spar flanges model Answer 1000 lbs/sq 8 If Trojan Cruiser problem No 5 cruises 20 knots 23 mph what should speed model pro duce dynamically similar wake spray pattern Answer 58 knots 66 mph 9 Joe building 1/10th-scale model Lockheed P-80 airplane 4000 lbs thrust will Joes Scozzi fan rated 5 lbs thrust adequate power model Answer yes 10 If real Chattanooga Choo Choo can go 65 mph 96 ft/sec fast should run HO gauge 1/96th scale model train achieve 65 mph scale speed Answer 1 ft/sec Except questions 7 10 answers foregoing problems appear bear no relation scale go further shall see indeed Since about time development steamboat engineers have employed laws dynamic similitude find answers vexing questions reliably inexpensively through use dynamic ally similar models dynamic model would result some magic full-scale article could liter ally shrunk convenient size testing Strictly speaking such model should identical way pro totypejust smaller However such mod8 Model Aviation TABLE NO 1 VALUES FOR ITEMS AT LEFT AT INCREASING SCALE FACTORS 1/10 SCALE OBJECT SCALE WT THUS PILOT WEIGHING 200 LBS 1000 OR 2 LBS IN 1/10 SCALE MODEL FULL SCALE WOULD WEIGH 200 LBS 1000 els rarely ever built such com plexity weight CG location general configuration held small ad justments weight distribution can make model dynamically similar prac tical purposes photos shows test being run Convair hydrodynamics engineers cinematographers way back about 1945 subject dynamic model Convair R3Y being tested spray clear ances landing takeoff accelera tions examining frames taken cameras uniform known speed values desired can found high ac curacy Note compact transmitter complete honest gosh pilots seat Another photo shows Skate high performance turbojet seaplane design cre ated author back 40s water-based airplanes still popular model being towed aside launch proper speeds evaluate landing takeoff characteristics spary patterns Notice blended hull required no tip floats As can see test shows flaperons almost green water must slightly reduced span such test carried out prop erly worth thousand expert opin ions Note also leading edge slats compensate Reynolds Number ef fectswhich will discuss later Now lets see closely typical scale kit comes meeting require ments dynamic model Sig makes excellent kit famous Ryan ST classic airplane designed have gross weight 1600 lbs wing span RYAN FULL SCALE Gross Weight Horsepower V Max V Stall Takeoff Run 1600 lbs 125 hp 150 mph 60 mph 525 ft 30 ft 125-hp engine top speed 150 mph stalling speed flaps 60 mph Lets make comparison fullscale Ryan proposed dynamic model Sig kit Sig kit has 6-ft span therefore 1/5-scale model will make dynamic model same scale Thus see typical scale kit different after dynamic model anything Sig kit will have snappier performance since has con siderably power less weight No tice distancethe takeoff runvaries same way scale 1/5 SCALE DYNAMIC MODEL 128 lbs 45 hp 67 mph 27 mph 105 ft 1/5 SCALE SIG KIT lOto 11 lbs Bto 1Ohp 70 80 mph 25 mph 90 95 ft January 1978 9 HOW SCALE FACTOR K MUST VARY THE ABOVE TABLE SHOWS THE POWER TO WHICH THE SCALE FACTOR MUST BE RAISED FOR GIVEN ITEM TO BE DYNAMICALLY SIMILAR TO THE PROTOTYPE IE THE ITEM WEIGHT MUST ALWAYS VARY AS K3 SCALE CUBED IN THE BODY OF THE TABLE ARE THE VALUES THAT ARE OBTAINED FOR COMMONLY USED SCALE FACTORS RANGING FROM K 2 TO K 20 WHEN RAISED TO THE APPROPRIATE POWER IE. THE WEIGHT OF other items again seem have little nothing scale Notice ever weight far below 1/5 real airplane yet speed 67 mph double 1/5 X 150 30 mph would have speed scale characteristic makes models fly outrageously fast spoils effectfor some least problem 10 able slow model train down scale speed zero danger falling out sky model airplane must sustain itself air shall see wing loading speed must vary di rectly scale Thus can see really two kinds speed far scale concerned visual speed dynamic speed Visual speed pleases ob servers dynamic speed pleases Mother Nature Now its about time got down nitty-gritty see can discover principles involved First lets look scale itself Scale simply ra tio dimensions object similar object differing size like large tuna small tuna large tuna small halibut Before going further lets put some commonly used scales proper form pur pose COMMONACTUALSCALE USAGE SCALE FACTORK 3D fl 1 l/~t 4 1 -0 1/4 1/8 1/4 1/6 1/8 1/12 1/16 1/24 1/48 1/96 4 6 8 12 16 24 48 96 Sig Ryan has dimensions 1/5 full-scale airplane may said have scale factor 5 scale factor placed numerator compar ing big things little ones placed denominator little things compared big ones Thus full-scale Ryan 5/1 5 times size mod el model 1/5 size full-scale Ryan order facilitate com putation will engineers indicate scale factor Greek letter Kappa K gives certain mys tique process makes other peo ple think smarter sort like doctor writing prescriptions Latin Now physical properties can expressed terms Length Mass purpose Force propor tional Mass Time follows L linear measurementLength Width Height Distance Circumfer ence F Any Force Weight Thrust tAny interval Time Using three basic parameters can describe following ITEMSYMBOLSDESCRIPTIONUNITS Accelerationa 12 Distance Feet2 tTime SquaredSecond Velocity Distance Feet t meSecond Workw rce x DistancePound-Feet MomentM rce x DistancePound-Feet Moment ofI Force x Distance2Pound-Feet 2 Inertia FLForce x DistancePound-Feet HorsepowerHP e Second AreaS ngth SquaredSquare Feet 3 Volumev gth CubedCubic Feet WeightW ForcePounds ForceF ForcePounds ThrustT F cePounds Now lets take few items foregoing see might af fected Scale take Length Area Volume start Fig 1 see doubling Length line amounts doubling Scale reason can say dimensions vary di rectly Scale L L2 Fig 2 square measuring 1 inch side see blow up scale 2 making side 2 inches long have increased area four foldfrom square inch four square inches Thus see Area varies square Scale S III Fig2 Fig 3 shaded area one-inch cube see double dimensions cube increase its vol ume cube 2 2 X 2 X 2 mes So Volumes vary cube Scale L 1 L2 Fig 3I Now assume cube made wood lets say weighing ounce per cubic inch small cube weighs ounce large cube weighs eight ounces Thus Weight varies same way Volumeas cube Scale Weight measured pounds ounces grams etc Force Thrust So now can say Weight Fig 1Force Thrust also vary cube Scale W F T oint say Well OK suspected sort like what about Speed Power Well good way proceed might find something Scale doesnt affect Lets try Aspect Ratio ratio span chord Everybody knows doesnt change Scale 4 its simplest termsfor simple rec tangular planform ct Ratio equals Since both Span b Chord c c same units namely feet feet cancel out expression said dimensionless remains constant dependent Scale can go step further say b L equals y equals F turn equals L equals 1 say both b c di mensions L precisely L L first power Now high school know divide ex ponents subtract denomi nator numerator Thus wind up L0 Now number exponent zero equal 1 1 has way retaining its identity pres ence exponents example 12 1 etc Thus can say terms dimensionlessthat have exponents zerodo change 10 Model Aviation Scale Lets try another Density Density Weight K3 equals K again VolumeK know true cup sea wa ter has same density ocean came say Yeah great now about Speed Power Well lets see can find another constant has Time since Time involved Speed Power surface planet up altitudes model airplanes fly bombers butterflies ants ele phants respond exactly same way start accelerating toward cen ter earth whenever what holding up pulled out under Disregarding air resistance will ac celerate rate 32 ft per second second acceleration constant re gardless Scale Other accelerations such 5-g maneuver simply mul tiples basic gravitational accelera tion too remain constant inso far Scale concerned have seen describing pa rameters Acceleration expressed L L thetermNow since know txt expression represents constant also know will have expon ent zero just like Aspect Ratio Den sity did Thus may say LL xt e L has exponent 1 two Ts must have exponent 5 turn may expressed terms Scale K-K K5 K Thus have determined time has exponent 5 same square root So can say Time var ies asjhe square root Scale t an now proceed Speed Power Speed Velocity V _ K terms Scale K3 K5 Which says Speed like Time varies square root Scale V wer said Force X Distance ime terms Scale K3K — K35 K Power varies 35 power Scale HP Wing Loading Weight K3 K AreaK2 varies directly Scale Stress Force — K3 — K AreaK2 also varies Scale Power Loading WeighL K3 — Power K33 K varies reciprocal square root Scale Thrust Loading WeighL K3 — K Thrust K3 Velocity V varies square root Scale K3 Power HP varies three-and-onehalf power Scale K3 Wing Loading Y varies directly Sale K sses I vary directly Scale K S Loading recipro dimensionless does change Power varies ScaleHP summarize Acceleration constant does change Scale K Dimensions L vary directly Scale K Areas 5 vary Scale squared K2 Volumes v vary Scale cubed K3 Weights W vary Scale cubed K3 Forces F vary Scale cubed K3 Thrust T varies Scale cubed K3 Work w varies Scale fourth power K4 Moments M vary Scale fourth power K4 Moments Inertia vary Scale fifth power K Time t varies square root Scale K cal square root Scale K Aspect Ratio other geometrical ra tios Density Thrust Loading other dimensionless items change Scale K 35 power some other terms easy figure cal culator have handy well calculate values foregoing items several appropriate scale factors tabulate Table 1 Now understand mysteries scale lets go back check values gave dynamic model Ryan ST Table No 1 Now lets check answers ques tions posed beginning January 1978 11 late forties Consolidated testing all-metal model proposed jet-powered Skate flying boat shown skimming water test basin Full-span slats blended hull 1600 lbs 53 125 hp 35 5 150 mph 55 60mph 525 ft 1 5 1 From Table 1 scale factor 4 speed horsepower factor 128 Ignoring Reynolds No effects power required model thereforei9or 117 As 128 discussed further however would wise increase say 15 hp ac count relative disparity propeller efficiencies 2 Visual scale speed simply speed divided scale factor 150 equals4—-or 375 say 38 mph However dynamic scale speed 150150 h K52 3 Since visually model going fly twice fast full-scale air plane will necessary shoot twice pictures per unit time film projected normal speed Citabria model will appear flying slow easy just like real 4 Weight varies cube scale factor case 43 64 Therefore pilots weight is29. 3125 lbs 64 5 again weight model prototype divided cube scale factor case 12 Table 1 120001bs or69lbs 1728 6 If maneuvers same accelerations produced prototype duplicated model accelerations vary scale 7 Stress varies directly scale model stresses will 1000 5 pounds per sq size creases stronger stronger materials must used Howard Hughes Spruce Goose such sad waste taxpayers money No weight fi nally available payload 8 Dynamic speed varies square root scale 20 20 58 knots 12346 9 Thrust varies scale factor cubed 4000 bs 10 So Scozzi fan 5 lbs OK 10 96/96 /sec visual scale 1600 lbs 125 125hp 2795 150 mph 2236 -60mph 2236 525ft 5 understanding relationships very least recognize exist seems to essential has become addicted fasci nating hobby wishes pursue telligently particularly likes create adaptations interesting airplanes boats cars flood control projects anything else operates same means prototype origi nal designs own Obviously de termination such things engine size wing area weight etc should made rational basis know things vary scale have powerful tool indeed really needs scratch build anything wishes have data handy prototype data perhaps engine shelf workshop can select proper scale start reducing enlarging plans word caution however der mathematician can predict hairline accuracy trace moons shadow across earth during eclipse can approximate trajectory rifle bullet through unpredictable unruly air currents same token 128 lbsour rules dynamic similitude tell us pre cisely what things should account differences flow patterns 45 hp between full-scale wings propellers model wings propellers Big wings develop higher lift lower drag propor tionately small ones 67 mph differences studied eval uated long ago man named Osborne Reynolds actually interested flow fluid through pipes found 27 mph big pipes carried water better small pipes relationships discov ered expressed Reynolds Num 105 ft ber Because Reynolds Number match full-scale prototype very faithfully detail Ryan will probably land something higher 27 mph like 30 mph unless ways can found keep lift its proper value leading edge slats quite effective Skate model Such lead ing edge slats will help will turbula tionroughening leading edge stretching wire along front energize boundary layer thus de lay separation reduction lift Full-scale propellers develop 80 85% efficiencies doesnt seem much data available model propeller efficiencies fair guess might around 60% Thus rules say Ryan needs 45 hp might better part wis dom increase power factor something like 80/60 X 45 6 hp necessarily 60 cu engine time time reads modeler says landed fairly sizeable heavy radio model scale speed 10 mph can say just possible average model still air However air rarely still 10- 15-mph breeze could make seem possible visual scale speeds become mat ter real concern certainly could have merit answer think lies combination large size careful weight watching high-lift airfoils effective high-lift devices such full span flaps talking about speed reductions order 50% Finally important have talking about building dynam ic models full-scale aircraft deter mined weight power etc based full gross weight prototype models however particularly larger ones may able better appears Thirty-five 40% weight real airplane useful loadpilot baggage fuel cargo etc small models much gobbled up radio gear large quarter-size larger models radio weight becomes relatively insignificant carry ing three-pound pilot nor baggage etc may find ourselves lighter model truly dynamically similar turn will give us lighter wing load Continuedonpage86 12 Model Aviation Weight will Power will Vmaxwill V stall will Takeoff run will 1600 lbs K3 125 hp K 150 mph K 60 mph K 525 ft 1 K em em em em em em memo Bradford W Powers eme me me me SPECIAL PRO SERIES 2 FOR RC-FREE FLIGHT CONTROL LINE CIAPITCHPRICE 5%3489 63489 733%4119 53%456129 94566% 77%139 10467149 1066V 8W149 to6016159 114677% 7Y, 7%8159 it6E1W169 11%67169 126179 12555179 1356219 1496249 1566309 164%6389 W 55106 BLADE 855 EXTRA WIDE SERIES 400 B Poe SPEED & RACING ADVANCED DESIGN NO 1 IN PYLON RACING LEADING SPEED REGGRO HOLDER OF ALL TIMES RC PYLON RACING DIA PITCHPRICE 6%3%4129 755%6149 7SN 5/N 6N149 8%6% 6% 7 7%7%189 96%7 7A7%189 CONTROL LINE SPEED& RACING CIA PITCHPRICE 4/8A7129 4%55%129 6788%149 7 7%10%11169 889189 89N9%N189 8% 77%189 912 13219 51ARRflW Homebuilts Bill Youmans firstplace win Masters Class Greenville NRCHA Nationals last August seems increasing interest homebuilt helicopters won scratchbuilt own design composite components Bill came within 10 points aceing hover course local flier Norm Holland has developed scratchbuilt using Kavan mechanics tn-cycle landing gear Rev-o-lution canopy Futaba Sl5M ball-bearing servos EK single-stick radio Kraft engine Tach-Tron gover nor weight 12 1/2 pounds very smooth precise enough people inter ested could soon put kit form Look column further details Dual Counter Rotating Head ScratchBuilt Gilbert Laforest Montreal suc cessfully flew counter rotating-head heli copter own design Greenville NRCHA Nats Webra Speed 60 driving both heads unbelievably complicated pushrod system Self-designed transmitter two single sticks dual rudder knobs much Separate collective control head well separate cyclic control Tremendous under taking say nothing about getting mind synchronized hands Radio custom Can-Air Canadian ProLine some radio interference problems Next months column will cover unique finish helicopters first part building Aerospatiale SA-34 1 G Gazelle ducted fan-tail rotor youre flying youre trying hard enough Walt Schoonard 2080 Sharon Rd Winter Park FL 32789 Letters continued page 7 quality Model viation money best model aviation magazine field William R Barr AMA 31415 Claremont CA MA policy publish types models eventually shall get around Mr Barrs suggestions Mistaken Identity No doubt have received few letters already rare event havent would like point out photograph lower right hand corner page 25 Aug 1977 issue Model viation incorrectly captioned gentleman photo Rick Pear son winner last years Soar Nats well other contests sailplane holding Paragon Rick did outstanding job flying under less ideal conditions would shame did receive credit display flying skill Since generally true least 75% sailplanes performance direct function pilots skill would follow mention sailplane used would significant have no doubt uninten tional error know would want errors called attention proper caption can used Ed Slobod Pierce Aero Company Nonthridge CA Size It/Powers continued page 13 ing slower speed reduce somewhat power requirements because scaling down proto type its weight-empty condition rather its gross-weight condition thats ut Size Questions comments may ad dressed Bradford W Powers care magazine Seastrutz/Wi son continued page 18 full throttle some down-elevator Ed pulled up Seastrutz oil like scared duck full stall attitude 50 feet hit wind blowing toward hill blown end-over-end trees Damage minor Test flying continued next week Fall Brimfield meet time stabilizer shim under its leading edge rudder area doubled Seastrutz flew beautifully Among its test pilots Ted Straders son Eric testified flew very much like its predecessor Strutz Echo Seastrutz built mci dences shown will perform very well relatively docile its 46-in wing span compact biplane configuration felt might too quick average flier case diffi cult machine fly land water Have fun Radio Technique/Myers continued page 14 An ammeter measure charging discharging operating currents turntable drum-type chart feed measure servo transmit time shaker find intermittent prob lems heat lamp can Freezit similar chiller locate temperature-sensitive compon ents Special tools various types like desoldering irons Youve seen lot items listed under additional advertisements probability should leave will describe some simple non destructive tests should perform 86 Model Aviation NEWS FLASH Bob Smith Chatsworth CA set new World Speed Record June 19 Pylon mula 11125 RevUp 8%-6% new Pylon RaC ing prop OUT- PERFORMS ALL OTHERS AT THE 1976 NATIONALS 1st RC Masters Class 1st RC Advanced 1st RC Novice 1st RC Sport Scale 1st Formula Pylon 1st Quarter Midget Pylon 1st CL Stunt Open 1st CL Stunt Senior 1st CL Stunt Junior 1st CL Combat O & Sr 1st CL Slow Comb OP & Sr 1st CL Class 0 Speed Open 1st CL Class C Speed Jr & Sr 1st CLCIassB Speed Op & Sr 1st CL Cl Speed Op Sr Jr 1st FE Class B Open 1st FE Class C Open HIGH PERFORMANCE * COMPETITION PROVEN * THIN RIGID BLADES OP HARD MAPLE WOOD * SUPERBLY FINISHED COMPLETELY FUEL PIDOF 1st CL Carrier II Op Jr Sr 1st CL Carrier Jr & Sr 1st CL Formula 40 Opec 1st CL Class 6 Proto Jr
Edition: Model Aviation - 1978/01
Page Numbers: 8, 9, 10, 11, 12, 86
U Bradford W Powers HERE ARE few questions kind arise scale mentioned gether answers Lets see can discover bow answers ob tained 1 Bud Nosen builds A-scale kit Citabria airplane real airplane has 130-hp engine much power should model have Answer 117 hp 2 If real Citabria has high speed 150 mph fast should scale mod el fly look natural Answer 38 mph fast will actually fly Answer 75 mph 3 I want take real-looking movies model flight suspect slow motion involved much 24 frames per second normal film trans port speed what speed should shoot Answer 48 frames per second 4 If real pilot chute weigh 200 lbs what weight would represent pilot chute Y4-scale mod el Answer 3 lbs 2 oz 5 My grandson got Dumas 1 / 12scale Trojan Cruiser Xmas real boat weighs 12000 lbs what should model weigh float proper scale water line Answer 69 lbs 6 A Ryan ST experiences 5 gs acceler ation performing maneuver put Sig 1/5-scale model through same maneuver what acceleration should present Answer 5 gs Taking off water San Diego 1945 dynamic model Consolidated R3Y four-en gined flying boat controlled pilot baby grand transmitter used airplane-type controls triple-redundant photographers Intuitively felt widely understood relationship between mod els full-scale counterparts changes size scale power weight speed almost everything else vary different precise ways model embodying proper relative values items said dynamically similar full-scale prototype shall see very much same own pet scale job 7 If above maneuver puts stress 5000 lbs/sq spar flanges real Ryan what will stress spar flanges model Answer 1000 lbs/sq 8 If Trojan Cruiser problem No 5 cruises 20 knots 23 mph what should speed model pro duce dynamically similar wake spray pattern Answer 58 knots 66 mph 9 Joe building 1/10th-scale model Lockheed P-80 airplane 4000 lbs thrust will Joes Scozzi fan rated 5 lbs thrust adequate power model Answer yes 10 If real Chattanooga Choo Choo can go 65 mph 96 ft/sec fast should run HO gauge 1/96th scale model train achieve 65 mph scale speed Answer 1 ft/sec Except questions 7 10 answers foregoing problems appear bear no relation scale go further shall see indeed Since about time development steamboat engineers have employed laws dynamic similitude find answers vexing questions reliably inexpensively through use dynamic ally similar models dynamic model would result some magic full-scale article could liter ally shrunk convenient size testing Strictly speaking such model should identical way pro totypejust smaller However such mod8 Model Aviation TABLE NO 1 VALUES FOR ITEMS AT LEFT AT INCREASING SCALE FACTORS 1/10 SCALE OBJECT SCALE WT THUS PILOT WEIGHING 200 LBS 1000 OR 2 LBS IN 1/10 SCALE MODEL FULL SCALE WOULD WEIGH 200 LBS 1000 els rarely ever built such com plexity weight CG location general configuration held small ad justments weight distribution can make model dynamically similar prac tical purposes photos shows test being run Convair hydrodynamics engineers cinematographers way back about 1945 subject dynamic model Convair R3Y being tested spray clear ances landing takeoff accelera tions examining frames taken cameras uniform known speed values desired can found high ac curacy Note compact transmitter complete honest gosh pilots seat Another photo shows Skate high performance turbojet seaplane design cre ated author back 40s water-based airplanes still popular model being towed aside launch proper speeds evaluate landing takeoff characteristics spary patterns Notice blended hull required no tip floats As can see test shows flaperons almost green water must slightly reduced span such test carried out prop erly worth thousand expert opin ions Note also leading edge slats compensate Reynolds Number ef fectswhich will discuss later Now lets see closely typical scale kit comes meeting require ments dynamic model Sig makes excellent kit famous Ryan ST classic airplane designed have gross weight 1600 lbs wing span RYAN FULL SCALE Gross Weight Horsepower V Max V Stall Takeoff Run 1600 lbs 125 hp 150 mph 60 mph 525 ft 30 ft 125-hp engine top speed 150 mph stalling speed flaps 60 mph Lets make comparison fullscale Ryan proposed dynamic model Sig kit Sig kit has 6-ft span therefore 1/5-scale model will make dynamic model same scale Thus see typical scale kit different after dynamic model anything Sig kit will have snappier performance since has con siderably power less weight No tice distancethe takeoff runvaries same way scale 1/5 SCALE DYNAMIC MODEL 128 lbs 45 hp 67 mph 27 mph 105 ft 1/5 SCALE SIG KIT lOto 11 lbs Bto 1Ohp 70 80 mph 25 mph 90 95 ft January 1978 9 HOW SCALE FACTOR K MUST VARY THE ABOVE TABLE SHOWS THE POWER TO WHICH THE SCALE FACTOR MUST BE RAISED FOR GIVEN ITEM TO BE DYNAMICALLY SIMILAR TO THE PROTOTYPE IE THE ITEM WEIGHT MUST ALWAYS VARY AS K3 SCALE CUBED IN THE BODY OF THE TABLE ARE THE VALUES THAT ARE OBTAINED FOR COMMONLY USED SCALE FACTORS RANGING FROM K 2 TO K 20 WHEN RAISED TO THE APPROPRIATE POWER IE. THE WEIGHT OF other items again seem have little nothing scale Notice ever weight far below 1/5 real airplane yet speed 67 mph double 1/5 X 150 30 mph would have speed scale characteristic makes models fly outrageously fast spoils effectfor some least problem 10 able slow model train down scale speed zero danger falling out sky model airplane must sustain itself air shall see wing loading speed must vary di rectly scale Thus can see really two kinds speed far scale concerned visual speed dynamic speed Visual speed pleases ob servers dynamic speed pleases Mother Nature Now its about time got down nitty-gritty see can discover principles involved First lets look scale itself Scale simply ra tio dimensions object similar object differing size like large tuna small tuna large tuna small halibut Before going further lets put some commonly used scales proper form pur pose COMMONACTUALSCALE USAGE SCALE FACTORK 3D fl 1 l/~t 4 1 -0 1/4 1/8 1/4 1/6 1/8 1/12 1/16 1/24 1/48 1/96 4 6 8 12 16 24 48 96 Sig Ryan has dimensions 1/5 full-scale airplane may said have scale factor 5 scale factor placed numerator compar ing big things little ones placed denominator little things compared big ones Thus full-scale Ryan 5/1 5 times size mod el model 1/5 size full-scale Ryan order facilitate com putation will engineers indicate scale factor Greek letter Kappa K gives certain mys tique process makes other peo ple think smarter sort like doctor writing prescriptions Latin Now physical properties can expressed terms Length Mass purpose Force propor tional Mass Time follows L linear measurementLength Width Height Distance Circumfer ence F Any Force Weight Thrust tAny interval Time Using three basic parameters can describe following ITEMSYMBOLSDESCRIPTIONUNITS Accelerationa 12 Distance Feet2 tTime SquaredSecond Velocity Distance Feet t meSecond Workw rce x DistancePound-Feet MomentM rce x DistancePound-Feet Moment ofI Force x Distance2Pound-Feet 2 Inertia FLForce x DistancePound-Feet HorsepowerHP e Second AreaS ngth SquaredSquare Feet 3 Volumev gth CubedCubic Feet WeightW ForcePounds ForceF ForcePounds ThrustT F cePounds Now lets take few items foregoing see might af fected Scale take Length Area Volume start Fig 1 see doubling Length line amounts doubling Scale reason can say dimensions vary di rectly Scale L L2 Fig 2 square measuring 1 inch side see blow up scale 2 making side 2 inches long have increased area four foldfrom square inch four square inches Thus see Area varies square Scale S III Fig2 Fig 3 shaded area one-inch cube see double dimensions cube increase its vol ume cube 2 2 X 2 X 2 mes So Volumes vary cube Scale L 1 L2 Fig 3I Now assume cube made wood lets say weighing ounce per cubic inch small cube weighs ounce large cube weighs eight ounces Thus Weight varies same way Volumeas cube Scale Weight measured pounds ounces grams etc Force Thrust So now can say Weight Fig 1Force Thrust also vary cube Scale W F T oint say Well OK suspected sort like what about Speed Power Well good way proceed might find something Scale doesnt affect Lets try Aspect Ratio ratio span chord Everybody knows doesnt change Scale 4 its simplest termsfor simple rec tangular planform ct Ratio equals Since both Span b Chord c c same units namely feet feet cancel out expression said dimensionless remains constant dependent Scale can go step further say b L equals y equals F turn equals L equals 1 say both b c di mensions L precisely L L first power Now high school know divide ex ponents subtract denomi nator numerator Thus wind up L0 Now number exponent zero equal 1 1 has way retaining its identity pres ence exponents example 12 1 etc Thus can say terms dimensionlessthat have exponents zerodo change 10 Model Aviation Scale Lets try another Density Density Weight K3 equals K again VolumeK know true cup sea wa ter has same density ocean came say Yeah great now about Speed Power Well lets see can find another constant has Time since Time involved Speed Power surface planet up altitudes model airplanes fly bombers butterflies ants ele phants respond exactly same way start accelerating toward cen ter earth whenever what holding up pulled out under Disregarding air resistance will ac celerate rate 32 ft per second second acceleration constant re gardless Scale Other accelerations such 5-g maneuver simply mul tiples basic gravitational accelera tion too remain constant inso far Scale concerned have seen describing pa rameters Acceleration expressed L L thetermNow since know txt expression represents constant also know will have expon ent zero just like Aspect Ratio Den sity did Thus may say LL xt e L has exponent 1 two Ts must have exponent 5 turn may expressed terms Scale K-K K5 K Thus have determined time has exponent 5 same square root So can say Time var ies asjhe square root Scale t an now proceed Speed Power Speed Velocity V _ K terms Scale K3 K5 Which says Speed like Time varies square root Scale V wer said Force X Distance ime terms Scale K3K — K35 K Power varies 35 power Scale HP Wing Loading Weight K3 K AreaK2 varies directly Scale Stress Force — K3 — K AreaK2 also varies Scale Power Loading WeighL K3 — Power K33 K varies reciprocal square root Scale Thrust Loading WeighL K3 — K Thrust K3 Velocity V varies square root Scale K3 Power HP varies three-and-onehalf power Scale K3 Wing Loading Y varies directly Sale K sses I vary directly Scale K S Loading recipro dimensionless does change Power varies ScaleHP summarize Acceleration constant does change Scale K Dimensions L vary directly Scale K Areas 5 vary Scale squared K2 Volumes v vary Scale cubed K3 Weights W vary Scale cubed K3 Forces F vary Scale cubed K3 Thrust T varies Scale cubed K3 Work w varies Scale fourth power K4 Moments M vary Scale fourth power K4 Moments Inertia vary Scale fifth power K Time t varies square root Scale K cal square root Scale K Aspect Ratio other geometrical ra tios Density Thrust Loading other dimensionless items change Scale K 35 power some other terms easy figure cal culator have handy well calculate values foregoing items several appropriate scale factors tabulate Table 1 Now understand mysteries scale lets go back check values gave dynamic model Ryan ST Table No 1 Now lets check answers ques tions posed beginning January 1978 11 late forties Consolidated testing all-metal model proposed jet-powered Skate flying boat shown skimming water test basin Full-span slats blended hull 1600 lbs 53 125 hp 35 5 150 mph 55 60mph 525 ft 1 5 1 From Table 1 scale factor 4 speed horsepower factor 128 Ignoring Reynolds No effects power required model thereforei9or 117 As 128 discussed further however would wise increase say 15 hp ac count relative disparity propeller efficiencies 2 Visual scale speed simply speed divided scale factor 150 equals4—-or 375 say 38 mph However dynamic scale speed 150150 h K52 3 Since visually model going fly twice fast full-scale air plane will necessary shoot twice pictures per unit time film projected normal speed Citabria model will appear flying slow easy just like real 4 Weight varies cube scale factor case 43 64 Therefore pilots weight is29. 3125 lbs 64 5 again weight model prototype divided cube scale factor case 12 Table 1 120001bs or69lbs 1728 6 If maneuvers same accelerations produced prototype duplicated model accelerations vary scale 7 Stress varies directly scale model stresses will 1000 5 pounds per sq size creases stronger stronger materials must used Howard Hughes Spruce Goose such sad waste taxpayers money No weight fi nally available payload 8 Dynamic speed varies square root scale 20 20 58 knots 12346 9 Thrust varies scale factor cubed 4000 bs 10 So Scozzi fan 5 lbs OK 10 96/96 /sec visual scale 1600 lbs 125 125hp 2795 150 mph 2236 -60mph 2236 525ft 5 understanding relationships very least recognize exist seems to essential has become addicted fasci nating hobby wishes pursue telligently particularly likes create adaptations interesting airplanes boats cars flood control projects anything else operates same means prototype origi nal designs own Obviously de termination such things engine size wing area weight etc should made rational basis know things vary scale have powerful tool indeed really needs scratch build anything wishes have data handy prototype data perhaps engine shelf workshop can select proper scale start reducing enlarging plans word caution however der mathematician can predict hairline accuracy trace moons shadow across earth during eclipse can approximate trajectory rifle bullet through unpredictable unruly air currents same token 128 lbsour rules dynamic similitude tell us pre cisely what things should account differences flow patterns 45 hp between full-scale wings propellers model wings propellers Big wings develop higher lift lower drag propor tionately small ones 67 mph differences studied eval uated long ago man named Osborne Reynolds actually interested flow fluid through pipes found 27 mph big pipes carried water better small pipes relationships discov ered expressed Reynolds Num 105 ft ber Because Reynolds Number match full-scale prototype very faithfully detail Ryan will probably land something higher 27 mph like 30 mph unless ways can found keep lift its proper value leading edge slats quite effective Skate model Such lead ing edge slats will help will turbula tionroughening leading edge stretching wire along front energize boundary layer thus de lay separation reduction lift Full-scale propellers develop 80 85% efficiencies doesnt seem much data available model propeller efficiencies fair guess might around 60% Thus rules say Ryan needs 45 hp might better part wis dom increase power factor something like 80/60 X 45 6 hp necessarily 60 cu engine time time reads modeler says landed fairly sizeable heavy radio model scale speed 10 mph can say just possible average model still air However air rarely still 10- 15-mph breeze could make seem possible visual scale speeds become mat ter real concern certainly could have merit answer think lies combination large size careful weight watching high-lift airfoils effective high-lift devices such full span flaps talking about speed reductions order 50% Finally important have talking about building dynam ic models full-scale aircraft deter mined weight power etc based full gross weight prototype models however particularly larger ones may able better appears Thirty-five 40% weight real airplane useful loadpilot baggage fuel cargo etc small models much gobbled up radio gear large quarter-size larger models radio weight becomes relatively insignificant carry ing three-pound pilot nor baggage etc may find ourselves lighter model truly dynamically similar turn will give us lighter wing load Continuedonpage86 12 Model Aviation Weight will Power will Vmaxwill V stall will Takeoff run will 1600 lbs K3 125 hp K 150 mph K 60 mph K 525 ft 1 K em em em em em em memo Bradford W Powers eme me me me SPECIAL PRO SERIES 2 FOR RC-FREE FLIGHT CONTROL LINE CIAPITCHPRICE 5%3489 63489 733%4119 53%456129 94566% 77%139 10467149 1066V 8W149 to6016159 114677% 7Y, 7%8159 it6E1W169 11%67169 126179 12555179 1356219 1496249 1566309 164%6389 W 55106 BLADE 855 EXTRA WIDE SERIES 400 B Poe SPEED & RACING ADVANCED DESIGN NO 1 IN PYLON RACING LEADING SPEED REGGRO HOLDER OF ALL TIMES RC PYLON RACING DIA PITCHPRICE 6%3%4129 755%6149 7SN 5/N 6N149 8%6% 6% 7 7%7%189 96%7 7A7%189 CONTROL LINE SPEED& RACING CIA PITCHPRICE 4/8A7129 4%55%129 6788%149 7 7%10%11169 889189 89N9%N189 8% 77%189 912 13219 51ARRflW Homebuilts Bill Youmans firstplace win Masters Class Greenville NRCHA Nationals last August seems increasing interest homebuilt helicopters won scratchbuilt own design composite components Bill came within 10 points aceing hover course local flier Norm Holland has developed scratchbuilt using Kavan mechanics tn-cycle landing gear Rev-o-lution canopy Futaba Sl5M ball-bearing servos EK single-stick radio Kraft engine Tach-Tron gover nor weight 12 1/2 pounds very smooth precise enough people inter ested could soon put kit form Look column further details Dual Counter Rotating Head ScratchBuilt Gilbert Laforest Montreal suc cessfully flew counter rotating-head heli copter own design Greenville NRCHA Nats Webra Speed 60 driving both heads unbelievably complicated pushrod system Self-designed transmitter two single sticks dual rudder knobs much Separate collective control head well separate cyclic control Tremendous under taking say nothing about getting mind synchronized hands Radio custom Can-Air Canadian ProLine some radio interference problems Next months column will cover unique finish helicopters first part building Aerospatiale SA-34 1 G Gazelle ducted fan-tail rotor youre flying youre trying hard enough Walt Schoonard 2080 Sharon Rd Winter Park FL 32789 Letters continued page 7 quality Model viation money best model aviation magazine field William R Barr AMA 31415 Claremont CA MA policy publish types models eventually shall get around Mr Barrs suggestions Mistaken Identity No doubt have received few letters already rare event havent would like point out photograph lower right hand corner page 25 Aug 1977 issue Model viation incorrectly captioned gentleman photo Rick Pear son winner last years Soar Nats well other contests sailplane holding Paragon Rick did outstanding job flying under less ideal conditions would shame did receive credit display flying skill Since generally true least 75% sailplanes performance direct function pilots skill would follow mention sailplane used would significant have no doubt uninten tional error know would want errors called attention proper caption can used Ed Slobod Pierce Aero Company Nonthridge CA Size It/Powers continued page 13 ing slower speed reduce somewhat power requirements because scaling down proto type its weight-empty condition rather its gross-weight condition thats ut Size Questions comments may ad dressed Bradford W Powers care magazine Seastrutz/Wi son continued page 18 full throttle some down-elevator Ed pulled up Seastrutz oil like scared duck full stall attitude 50 feet hit wind blowing toward hill blown end-over-end trees Damage minor Test flying continued next week Fall Brimfield meet time stabilizer shim under its leading edge rudder area doubled Seastrutz flew beautifully Among its test pilots Ted Straders son Eric testified flew very much like its predecessor Strutz Echo Seastrutz built mci dences shown will perform very well relatively docile its 46-in wing span compact biplane configuration felt might too quick average flier case diffi cult machine fly land water Have fun Radio Technique/Myers continued page 14 An ammeter measure charging discharging operating currents turntable drum-type chart feed measure servo transmit time shaker find intermittent prob lems heat lamp can Freezit similar chiller locate temperature-sensitive compon ents Special tools various types like desoldering irons Youve seen lot items listed under additional advertisements probability should leave will describe some simple non destructive tests should perform 86 Model Aviation NEWS FLASH Bob Smith Chatsworth CA set new World Speed Record June 19 Pylon mula 11125 RevUp 8%-6% new Pylon RaC ing prop OUT- PERFORMS ALL OTHERS AT THE 1976 NATIONALS 1st RC Masters Class 1st RC Advanced 1st RC Novice 1st RC Sport Scale 1st Formula Pylon 1st Quarter Midget Pylon 1st CL Stunt Open 1st CL Stunt Senior 1st CL Stunt Junior 1st CL Combat O & Sr 1st CL Slow Comb OP & Sr 1st CL Class 0 Speed Open 1st CL Class C Speed Jr & Sr 1st CLCIassB Speed Op & Sr 1st CL Cl Speed Op Sr Jr 1st FE Class B Open 1st FE Class C Open HIGH PERFORMANCE * COMPETITION PROVEN * THIN RIGID BLADES OP HARD MAPLE WOOD * SUPERBLY FINISHED COMPLETELY FUEL PIDOF 1st CL Carrier II Op Jr Sr 1st CL Carrier Jr & Sr 1st CL Formula 40 Opec 1st CL Class 6 Proto Jr
Edition: Model Aviation - 1978/01
Page Numbers: 8, 9, 10, 11, 12, 86
U Bradford W Powers HERE ARE few questions kind arise scale mentioned gether answers Lets see can discover bow answers ob tained 1 Bud Nosen builds A-scale kit Citabria airplane real airplane has 130-hp engine much power should model have Answer 117 hp 2 If real Citabria has high speed 150 mph fast should scale mod el fly look natural Answer 38 mph fast will actually fly Answer 75 mph 3 I want take real-looking movies model flight suspect slow motion involved much 24 frames per second normal film trans port speed what speed should shoot Answer 48 frames per second 4 If real pilot chute weigh 200 lbs what weight would represent pilot chute Y4-scale mod el Answer 3 lbs 2 oz 5 My grandson got Dumas 1 / 12scale Trojan Cruiser Xmas real boat weighs 12000 lbs what should model weigh float proper scale water line Answer 69 lbs 6 A Ryan ST experiences 5 gs acceler ation performing maneuver put Sig 1/5-scale model through same maneuver what acceleration should present Answer 5 gs Taking off water San Diego 1945 dynamic model Consolidated R3Y four-en gined flying boat controlled pilot baby grand transmitter used airplane-type controls triple-redundant photographers Intuitively felt widely understood relationship between mod els full-scale counterparts changes size scale power weight speed almost everything else vary different precise ways model embodying proper relative values items said dynamically similar full-scale prototype shall see very much same own pet scale job 7 If above maneuver puts stress 5000 lbs/sq spar flanges real Ryan what will stress spar flanges model Answer 1000 lbs/sq 8 If Trojan Cruiser problem No 5 cruises 20 knots 23 mph what should speed model pro duce dynamically similar wake spray pattern Answer 58 knots 66 mph 9 Joe building 1/10th-scale model Lockheed P-80 airplane 4000 lbs thrust will Joes Scozzi fan rated 5 lbs thrust adequate power model Answer yes 10 If real Chattanooga Choo Choo can go 65 mph 96 ft/sec fast should run HO gauge 1/96th scale model train achieve 65 mph scale speed Answer 1 ft/sec Except questions 7 10 answers foregoing problems appear bear no relation scale go further shall see indeed Since about time development steamboat engineers have employed laws dynamic similitude find answers vexing questions reliably inexpensively through use dynamic ally similar models dynamic model would result some magic full-scale article could liter ally shrunk convenient size testing Strictly speaking such model should identical way pro totypejust smaller However such mod8 Model Aviation TABLE NO 1 VALUES FOR ITEMS AT LEFT AT INCREASING SCALE FACTORS 1/10 SCALE OBJECT SCALE WT THUS PILOT WEIGHING 200 LBS 1000 OR 2 LBS IN 1/10 SCALE MODEL FULL SCALE WOULD WEIGH 200 LBS 1000 els rarely ever built such com plexity weight CG location general configuration held small ad justments weight distribution can make model dynamically similar prac tical purposes photos shows test being run Convair hydrodynamics engineers cinematographers way back about 1945 subject dynamic model Convair R3Y being tested spray clear ances landing takeoff accelera tions examining frames taken cameras uniform known speed values desired can found high ac curacy Note compact transmitter complete honest gosh pilots seat Another photo shows Skate high performance turbojet seaplane design cre ated author back 40s water-based airplanes still popular model being towed aside launch proper speeds evaluate landing takeoff characteristics spary patterns Notice blended hull required no tip floats As can see test shows flaperons almost green water must slightly reduced span such test carried out prop erly worth thousand expert opin ions Note also leading edge slats compensate Reynolds Number ef fectswhich will discuss later Now lets see closely typical scale kit comes meeting require ments dynamic model Sig makes excellent kit famous Ryan ST classic airplane designed have gross weight 1600 lbs wing span RYAN FULL SCALE Gross Weight Horsepower V Max V Stall Takeoff Run 1600 lbs 125 hp 150 mph 60 mph 525 ft 30 ft 125-hp engine top speed 150 mph stalling speed flaps 60 mph Lets make comparison fullscale Ryan proposed dynamic model Sig kit Sig kit has 6-ft span therefore 1/5-scale model will make dynamic model same scale Thus see typical scale kit different after dynamic model anything Sig kit will have snappier performance since has con siderably power less weight No tice distancethe takeoff runvaries same way scale 1/5 SCALE DYNAMIC MODEL 128 lbs 45 hp 67 mph 27 mph 105 ft 1/5 SCALE SIG KIT lOto 11 lbs Bto 1Ohp 70 80 mph 25 mph 90 95 ft January 1978 9 HOW SCALE FACTOR K MUST VARY THE ABOVE TABLE SHOWS THE POWER TO WHICH THE SCALE FACTOR MUST BE RAISED FOR GIVEN ITEM TO BE DYNAMICALLY SIMILAR TO THE PROTOTYPE IE THE ITEM WEIGHT MUST ALWAYS VARY AS K3 SCALE CUBED IN THE BODY OF THE TABLE ARE THE VALUES THAT ARE OBTAINED FOR COMMONLY USED SCALE FACTORS RANGING FROM K 2 TO K 20 WHEN RAISED TO THE APPROPRIATE POWER IE. THE WEIGHT OF other items again seem have little nothing scale Notice ever weight far below 1/5 real airplane yet speed 67 mph double 1/5 X 150 30 mph would have speed scale characteristic makes models fly outrageously fast spoils effectfor some least problem 10 able slow model train down scale speed zero danger falling out sky model airplane must sustain itself air shall see wing loading speed must vary di rectly scale Thus can see really two kinds speed far scale concerned visual speed dynamic speed Visual speed pleases ob servers dynamic speed pleases Mother Nature Now its about time got down nitty-gritty see can discover principles involved First lets look scale itself Scale simply ra tio dimensions object similar object differing size like large tuna small tuna large tuna small halibut Before going further lets put some commonly used scales proper form pur pose COMMONACTUALSCALE USAGE SCALE FACTORK 3D fl 1 l/~t 4 1 -0 1/4 1/8 1/4 1/6 1/8 1/12 1/16 1/24 1/48 1/96 4 6 8 12 16 24 48 96 Sig Ryan has dimensions 1/5 full-scale airplane may said have scale factor 5 scale factor placed numerator compar ing big things little ones placed denominator little things compared big ones Thus full-scale Ryan 5/1 5 times size mod el model 1/5 size full-scale Ryan order facilitate com putation will engineers indicate scale factor Greek letter Kappa K gives certain mys tique process makes other peo ple think smarter sort like doctor writing prescriptions Latin Now physical properties can expressed terms Length Mass purpose Force propor tional Mass Time follows L linear measurementLength Width Height Distance Circumfer ence F Any Force Weight Thrust tAny interval Time Using three basic parameters can describe following ITEMSYMBOLSDESCRIPTIONUNITS Accelerationa 12 Distance Feet2 tTime SquaredSecond Velocity Distance Feet t meSecond Workw rce x DistancePound-Feet MomentM rce x DistancePound-Feet Moment ofI Force x Distance2Pound-Feet 2 Inertia FLForce x DistancePound-Feet HorsepowerHP e Second AreaS ngth SquaredSquare Feet 3 Volumev gth CubedCubic Feet WeightW ForcePounds ForceF ForcePounds ThrustT F cePounds Now lets take few items foregoing see might af fected Scale take Length Area Volume start Fig 1 see doubling Length line amounts doubling Scale reason can say dimensions vary di rectly Scale L L2 Fig 2 square measuring 1 inch side see blow up scale 2 making side 2 inches long have increased area four foldfrom square inch four square inches Thus see Area varies square Scale S III Fig2 Fig 3 shaded area one-inch cube see double dimensions cube increase its vol ume cube 2 2 X 2 X 2 mes So Volumes vary cube Scale L 1 L2 Fig 3I Now assume cube made wood lets say weighing ounce per cubic inch small cube weighs ounce large cube weighs eight ounces Thus Weight varies same way Volumeas cube Scale Weight measured pounds ounces grams etc Force Thrust So now can say Weight Fig 1Force Thrust also vary cube Scale W F T oint say Well OK suspected sort like what about Speed Power Well good way proceed might find something Scale doesnt affect Lets try Aspect Ratio ratio span chord Everybody knows doesnt change Scale 4 its simplest termsfor simple rec tangular planform ct Ratio equals Since both Span b Chord c c same units namely feet feet cancel out expression said dimensionless remains constant dependent Scale can go step further say b L equals y equals F turn equals L equals 1 say both b c di mensions L precisely L L first power Now high school know divide ex ponents subtract denomi nator numerator Thus wind up L0 Now number exponent zero equal 1 1 has way retaining its identity pres ence exponents example 12 1 etc Thus can say terms dimensionlessthat have exponents zerodo change 10 Model Aviation Scale Lets try another Density Density Weight K3 equals K again VolumeK know true cup sea wa ter has same density ocean came say Yeah great now about Speed Power Well lets see can find another constant has Time since Time involved Speed Power surface planet up altitudes model airplanes fly bombers butterflies ants ele phants respond exactly same way start accelerating toward cen ter earth whenever what holding up pulled out under Disregarding air resistance will ac celerate rate 32 ft per second second acceleration constant re gardless Scale Other accelerations such 5-g maneuver simply mul tiples basic gravitational accelera tion too remain constant inso far Scale concerned have seen describing pa rameters Acceleration expressed L L thetermNow since know txt expression represents constant also know will have expon ent zero just like Aspect Ratio Den sity did Thus may say LL xt e L has exponent 1 two Ts must have exponent 5 turn may expressed terms Scale K-K K5 K Thus have determined time has exponent 5 same square root So can say Time var ies asjhe square root Scale t an now proceed Speed Power Speed Velocity V _ K terms Scale K3 K5 Which says Speed like Time varies square root Scale V wer said Force X Distance ime terms Scale K3K — K35 K Power varies 35 power Scale HP Wing Loading Weight K3 K AreaK2 varies directly Scale Stress Force — K3 — K AreaK2 also varies Scale Power Loading WeighL K3 — Power K33 K varies reciprocal square root Scale Thrust Loading WeighL K3 — K Thrust K3 Velocity V varies square root Scale K3 Power HP varies three-and-onehalf power Scale K3 Wing Loading Y varies directly Sale K sses I vary directly Scale K S Loading recipro dimensionless does change Power varies ScaleHP summarize Acceleration constant does change Scale K Dimensions L vary directly Scale K Areas 5 vary Scale squared K2 Volumes v vary Scale cubed K3 Weights W vary Scale cubed K3 Forces F vary Scale cubed K3 Thrust T varies Scale cubed K3 Work w varies Scale fourth power K4 Moments M vary Scale fourth power K4 Moments Inertia vary Scale fifth power K Time t varies square root Scale K cal square root Scale K Aspect Ratio other geometrical ra tios Density Thrust Loading other dimensionless items change Scale K 35 power some other terms easy figure cal culator have handy well calculate values foregoing items several appropriate scale factors tabulate Table 1 Now understand mysteries scale lets go back check values gave dynamic model Ryan ST Table No 1 Now lets check answers ques tions posed beginning January 1978 11 late forties Consolidated testing all-metal model proposed jet-powered Skate flying boat shown skimming water test basin Full-span slats blended hull 1600 lbs 53 125 hp 35 5 150 mph 55 60mph 525 ft 1 5 1 From Table 1 scale factor 4 speed horsepower factor 128 Ignoring Reynolds No effects power required model thereforei9or 117 As 128 discussed further however would wise increase say 15 hp ac count relative disparity propeller efficiencies 2 Visual scale speed simply speed divided scale factor 150 equals4—-or 375 say 38 mph However dynamic scale speed 150150 h K52 3 Since visually model going fly twice fast full-scale air plane will necessary shoot twice pictures per unit time film projected normal speed Citabria model will appear flying slow easy just like real 4 Weight varies cube scale factor case 43 64 Therefore pilots weight is29. 3125 lbs 64 5 again weight model prototype divided cube scale factor case 12 Table 1 120001bs or69lbs 1728 6 If maneuvers same accelerations produced prototype duplicated model accelerations vary scale 7 Stress varies directly scale model stresses will 1000 5 pounds per sq size creases stronger stronger materials must used Howard Hughes Spruce Goose such sad waste taxpayers money No weight fi nally available payload 8 Dynamic speed varies square root scale 20 20 58 knots 12346 9 Thrust varies scale factor cubed 4000 bs 10 So Scozzi fan 5 lbs OK 10 96/96 /sec visual scale 1600 lbs 125 125hp 2795 150 mph 2236 -60mph 2236 525ft 5 understanding relationships very least recognize exist seems to essential has become addicted fasci nating hobby wishes pursue telligently particularly likes create adaptations interesting airplanes boats cars flood control projects anything else operates same means prototype origi nal designs own Obviously de termination such things engine size wing area weight etc should made rational basis know things vary scale have powerful tool indeed really needs scratch build anything wishes have data handy prototype data perhaps engine shelf workshop can select proper scale start reducing enlarging plans word caution however der mathematician can predict hairline accuracy trace moons shadow across earth during eclipse can approximate trajectory rifle bullet through unpredictable unruly air currents same token 128 lbsour rules dynamic similitude tell us pre cisely what things should account differences flow patterns 45 hp between full-scale wings propellers model wings propellers Big wings develop higher lift lower drag propor tionately small ones 67 mph differences studied eval uated long ago man named Osborne Reynolds actually interested flow fluid through pipes found 27 mph big pipes carried water better small pipes relationships discov ered expressed Reynolds Num 105 ft ber Because Reynolds Number match full-scale prototype very faithfully detail Ryan will probably land something higher 27 mph like 30 mph unless ways can found keep lift its proper value leading edge slats quite effective Skate model Such lead ing edge slats will help will turbula tionroughening leading edge stretching wire along front energize boundary layer thus de lay separation reduction lift Full-scale propellers develop 80 85% efficiencies doesnt seem much data available model propeller efficiencies fair guess might around 60% Thus rules say Ryan needs 45 hp might better part wis dom increase power factor something like 80/60 X 45 6 hp necessarily 60 cu engine time time reads modeler says landed fairly sizeable heavy radio model scale speed 10 mph can say just possible average model still air However air rarely still 10- 15-mph breeze could make seem possible visual scale speeds become mat ter real concern certainly could have merit answer think lies combination large size careful weight watching high-lift airfoils effective high-lift devices such full span flaps talking about speed reductions order 50% Finally important have talking about building dynam ic models full-scale aircraft deter mined weight power etc based full gross weight prototype models however particularly larger ones may able better appears Thirty-five 40% weight real airplane useful loadpilot baggage fuel cargo etc small models much gobbled up radio gear large quarter-size larger models radio weight becomes relatively insignificant carry ing three-pound pilot nor baggage etc may find ourselves lighter model truly dynamically similar turn will give us lighter wing load Continuedonpage86 12 Model Aviation Weight will Power will Vmaxwill V stall will Takeoff run will 1600 lbs K3 125 hp K 150 mph K 60 mph K 525 ft 1 K em em em em em em memo Bradford W Powers eme me me me SPECIAL PRO SERIES 2 FOR RC-FREE FLIGHT CONTROL LINE CIAPITCHPRICE 5%3489 63489 733%4119 53%456129 94566% 77%139 10467149 1066V 8W149 to6016159 114677% 7Y, 7%8159 it6E1W169 11%67169 126179 12555179 1356219 1496249 1566309 164%6389 W 55106 BLADE 855 EXTRA WIDE SERIES 400 B Poe SPEED & RACING ADVANCED DESIGN NO 1 IN PYLON RACING LEADING SPEED REGGRO HOLDER OF ALL TIMES RC PYLON RACING DIA PITCHPRICE 6%3%4129 755%6149 7SN 5/N 6N149 8%6% 6% 7 7%7%189 96%7 7A7%189 CONTROL LINE SPEED& RACING CIA PITCHPRICE 4/8A7129 4%55%129 6788%149 7 7%10%11169 889189 89N9%N189 8% 77%189 912 13219 51ARRflW Homebuilts Bill Youmans firstplace win Masters Class Greenville NRCHA Nationals last August seems increasing interest homebuilt helicopters won scratchbuilt own design composite components Bill came within 10 points aceing hover course local flier Norm Holland has developed scratchbuilt using Kavan mechanics tn-cycle landing gear Rev-o-lution canopy Futaba Sl5M ball-bearing servos EK single-stick radio Kraft engine Tach-Tron gover nor weight 12 1/2 pounds very smooth precise enough people inter ested could soon put kit form Look column further details Dual Counter Rotating Head ScratchBuilt Gilbert Laforest Montreal suc cessfully flew counter rotating-head heli copter own design Greenville NRCHA Nats Webra Speed 60 driving both heads unbelievably complicated pushrod system Self-designed transmitter two single sticks dual rudder knobs much Separate collective control head well separate cyclic control Tremendous under taking say nothing about getting mind synchronized hands Radio custom Can-Air Canadian ProLine some radio interference problems Next months column will cover unique finish helicopters first part building Aerospatiale SA-34 1 G Gazelle ducted fan-tail rotor youre flying youre trying hard enough Walt Schoonard 2080 Sharon Rd Winter Park FL 32789 Letters continued page 7 quality Model viation money best model aviation magazine field William R Barr AMA 31415 Claremont CA MA policy publish types models eventually shall get around Mr Barrs suggestions Mistaken Identity No doubt have received few letters already rare event havent would like point out photograph lower right hand corner page 25 Aug 1977 issue Model viation incorrectly captioned gentleman photo Rick Pear son winner last years Soar Nats well other contests sailplane holding Paragon Rick did outstanding job flying under less ideal conditions would shame did receive credit display flying skill Since generally true least 75% sailplanes performance direct function pilots skill would follow mention sailplane used would significant have no doubt uninten tional error know would want errors called attention proper caption can used Ed Slobod Pierce Aero Company Nonthridge CA Size It/Powers continued page 13 ing slower speed reduce somewhat power requirements because scaling down proto type its weight-empty condition rather its gross-weight condition thats ut Size Questions comments may ad dressed Bradford W Powers care magazine Seastrutz/Wi son continued page 18 full throttle some down-elevator Ed pulled up Seastrutz oil like scared duck full stall attitude 50 feet hit wind blowing toward hill blown end-over-end trees Damage minor Test flying continued next week Fall Brimfield meet time stabilizer shim under its leading edge rudder area doubled Seastrutz flew beautifully Among its test pilots Ted Straders son Eric testified flew very much like its predecessor Strutz Echo Seastrutz built mci dences shown will perform very well relatively docile its 46-in wing span compact biplane configuration felt might too quick average flier case diffi cult machine fly land water Have fun Radio Technique/Myers continued page 14 An ammeter measure charging discharging operating currents turntable drum-type chart feed measure servo transmit time shaker find intermittent prob lems heat lamp can Freezit similar chiller locate temperature-sensitive compon ents Special tools various types like desoldering irons Youve seen lot items listed under additional advertisements probability should leave will describe some simple non destructive tests should perform 86 Model Aviation NEWS FLASH Bob Smith Chatsworth CA set new World Speed Record June 19 Pylon mula 11125 RevUp 8%-6% new Pylon RaC ing prop OUT- PERFORMS ALL OTHERS AT THE 1976 NATIONALS 1st RC Masters Class 1st RC Advanced 1st RC Novice 1st RC Sport Scale 1st Formula Pylon 1st Quarter Midget Pylon 1st CL Stunt Open 1st CL Stunt Senior 1st CL Stunt Junior 1st CL Combat O & Sr 1st CL Slow Comb OP & Sr 1st CL Class 0 Speed Open 1st CL Class C Speed Jr & Sr 1st CLCIassB Speed Op & Sr 1st CL Cl Speed Op Sr Jr 1st FE Class B Open 1st FE Class C Open HIGH PERFORMANCE * COMPETITION PROVEN * THIN RIGID BLADES OP HARD MAPLE WOOD * SUPERBLY FINISHED COMPLETELY FUEL PIDOF 1st CL Carrier II Op Jr Sr 1st CL Carrier Jr & Sr 1st CL Formula 40 Opec 1st CL Class 6 Proto Jr
Edition: Model Aviation - 1978/01
Page Numbers: 8, 9, 10, 11, 12, 86
U Bradford W Powers HERE ARE few questions kind arise scale mentioned gether answers Lets see can discover bow answers ob tained 1 Bud Nosen builds A-scale kit Citabria airplane real airplane has 130-hp engine much power should model have Answer 117 hp 2 If real Citabria has high speed 150 mph fast should scale mod el fly look natural Answer 38 mph fast will actually fly Answer 75 mph 3 I want take real-looking movies model flight suspect slow motion involved much 24 frames per second normal film trans port speed what speed should shoot Answer 48 frames per second 4 If real pilot chute weigh 200 lbs what weight would represent pilot chute Y4-scale mod el Answer 3 lbs 2 oz 5 My grandson got Dumas 1 / 12scale Trojan Cruiser Xmas real boat weighs 12000 lbs what should model weigh float proper scale water line Answer 69 lbs 6 A Ryan ST experiences 5 gs acceler ation performing maneuver put Sig 1/5-scale model through same maneuver what acceleration should present Answer 5 gs Taking off water San Diego 1945 dynamic model Consolidated R3Y four-en gined flying boat controlled pilot baby grand transmitter used airplane-type controls triple-redundant photographers Intuitively felt widely understood relationship between mod els full-scale counterparts changes size scale power weight speed almost everything else vary different precise ways model embodying proper relative values items said dynamically similar full-scale prototype shall see very much same own pet scale job 7 If above maneuver puts stress 5000 lbs/sq spar flanges real Ryan what will stress spar flanges model Answer 1000 lbs/sq 8 If Trojan Cruiser problem No 5 cruises 20 knots 23 mph what should speed model pro duce dynamically similar wake spray pattern Answer 58 knots 66 mph 9 Joe building 1/10th-scale model Lockheed P-80 airplane 4000 lbs thrust will Joes Scozzi fan rated 5 lbs thrust adequate power model Answer yes 10 If real Chattanooga Choo Choo can go 65 mph 96 ft/sec fast should run HO gauge 1/96th scale model train achieve 65 mph scale speed Answer 1 ft/sec Except questions 7 10 answers foregoing problems appear bear no relation scale go further shall see indeed Since about time development steamboat engineers have employed laws dynamic similitude find answers vexing questions reliably inexpensively through use dynamic ally similar models dynamic model would result some magic full-scale article could liter ally shrunk convenient size testing Strictly speaking such model should identical way pro totypejust smaller However such mod8 Model Aviation TABLE NO 1 VALUES FOR ITEMS AT LEFT AT INCREASING SCALE FACTORS 1/10 SCALE OBJECT SCALE WT THUS PILOT WEIGHING 200 LBS 1000 OR 2 LBS IN 1/10 SCALE MODEL FULL SCALE WOULD WEIGH 200 LBS 1000 els rarely ever built such com plexity weight CG location general configuration held small ad justments weight distribution can make model dynamically similar prac tical purposes photos shows test being run Convair hydrodynamics engineers cinematographers way back about 1945 subject dynamic model Convair R3Y being tested spray clear ances landing takeoff accelera tions examining frames taken cameras uniform known speed values desired can found high ac curacy Note compact transmitter complete honest gosh pilots seat Another photo shows Skate high performance turbojet seaplane design cre ated author back 40s water-based airplanes still popular model being towed aside launch proper speeds evaluate landing takeoff characteristics spary patterns Notice blended hull required no tip floats As can see test shows flaperons almost green water must slightly reduced span such test carried out prop erly worth thousand expert opin ions Note also leading edge slats compensate Reynolds Number ef fectswhich will discuss later Now lets see closely typical scale kit comes meeting require ments dynamic model Sig makes excellent kit famous Ryan ST classic airplane designed have gross weight 1600 lbs wing span RYAN FULL SCALE Gross Weight Horsepower V Max V Stall Takeoff Run 1600 lbs 125 hp 150 mph 60 mph 525 ft 30 ft 125-hp engine top speed 150 mph stalling speed flaps 60 mph Lets make comparison fullscale Ryan proposed dynamic model Sig kit Sig kit has 6-ft span therefore 1/5-scale model will make dynamic model same scale Thus see typical scale kit different after dynamic model anything Sig kit will have snappier performance since has con siderably power less weight No tice distancethe takeoff runvaries same way scale 1/5 SCALE DYNAMIC MODEL 128 lbs 45 hp 67 mph 27 mph 105 ft 1/5 SCALE SIG KIT lOto 11 lbs Bto 1Ohp 70 80 mph 25 mph 90 95 ft January 1978 9 HOW SCALE FACTOR K MUST VARY THE ABOVE TABLE SHOWS THE POWER TO WHICH THE SCALE FACTOR MUST BE RAISED FOR GIVEN ITEM TO BE DYNAMICALLY SIMILAR TO THE PROTOTYPE IE THE ITEM WEIGHT MUST ALWAYS VARY AS K3 SCALE CUBED IN THE BODY OF THE TABLE ARE THE VALUES THAT ARE OBTAINED FOR COMMONLY USED SCALE FACTORS RANGING FROM K 2 TO K 20 WHEN RAISED TO THE APPROPRIATE POWER IE. THE WEIGHT OF other items again seem have little nothing scale Notice ever weight far below 1/5 real airplane yet speed 67 mph double 1/5 X 150 30 mph would have speed scale characteristic makes models fly outrageously fast spoils effectfor some least problem 10 able slow model train down scale speed zero danger falling out sky model airplane must sustain itself air shall see wing loading speed must vary di rectly scale Thus can see really two kinds speed far scale concerned visual speed dynamic speed Visual speed pleases ob servers dynamic speed pleases Mother Nature Now its about time got down nitty-gritty see can discover principles involved First lets look scale itself Scale simply ra tio dimensions object similar object differing size like large tuna small tuna large tuna small halibut Before going further lets put some commonly used scales proper form pur pose COMMONACTUALSCALE USAGE SCALE FACTORK 3D fl 1 l/~t 4 1 -0 1/4 1/8 1/4 1/6 1/8 1/12 1/16 1/24 1/48 1/96 4 6 8 12 16 24 48 96 Sig Ryan has dimensions 1/5 full-scale airplane may said have scale factor 5 scale factor placed numerator compar ing big things little ones placed denominator little things compared big ones Thus full-scale Ryan 5/1 5 times size mod el model 1/5 size full-scale Ryan order facilitate com putation will engineers indicate scale factor Greek letter Kappa K gives certain mys tique process makes other peo ple think smarter sort like doctor writing prescriptions Latin Now physical properties can expressed terms Length Mass purpose Force propor tional Mass Time follows L linear measurementLength Width Height Distance Circumfer ence F Any Force Weight Thrust tAny interval Time Using three basic parameters can describe following ITEMSYMBOLSDESCRIPTIONUNITS Accelerationa 12 Distance Feet2 tTime SquaredSecond Velocity Distance Feet t meSecond Workw rce x DistancePound-Feet MomentM rce x DistancePound-Feet Moment ofI Force x Distance2Pound-Feet 2 Inertia FLForce x DistancePound-Feet HorsepowerHP e Second AreaS ngth SquaredSquare Feet 3 Volumev gth CubedCubic Feet WeightW ForcePounds ForceF ForcePounds ThrustT F cePounds Now lets take few items foregoing see might af fected Scale take Length Area Volume start Fig 1 see doubling Length line amounts doubling Scale reason can say dimensions vary di rectly Scale L L2 Fig 2 square measuring 1 inch side see blow up scale 2 making side 2 inches long have increased area four foldfrom square inch four square inches Thus see Area varies square Scale S III Fig2 Fig 3 shaded area one-inch cube see double dimensions cube increase its vol ume cube 2 2 X 2 X 2 mes So Volumes vary cube Scale L 1 L2 Fig 3I Now assume cube made wood lets say weighing ounce per cubic inch small cube weighs ounce large cube weighs eight ounces Thus Weight varies same way Volumeas cube Scale Weight measured pounds ounces grams etc Force Thrust So now can say Weight Fig 1Force Thrust also vary cube Scale W F T oint say Well OK suspected sort like what about Speed Power Well good way proceed might find something Scale doesnt affect Lets try Aspect Ratio ratio span chord Everybody knows doesnt change Scale 4 its simplest termsfor simple rec tangular planform ct Ratio equals Since both Span b Chord c c same units namely feet feet cancel out expression said dimensionless remains constant dependent Scale can go step further say b L equals y equals F turn equals L equals 1 say both b c di mensions L precisely L L first power Now high school know divide ex ponents subtract denomi nator numerator Thus wind up L0 Now number exponent zero equal 1 1 has way retaining its identity pres ence exponents example 12 1 etc Thus can say terms dimensionlessthat have exponents zerodo change 10 Model Aviation Scale Lets try another Density Density Weight K3 equals K again VolumeK know true cup sea wa ter has same density ocean came say Yeah great now about Speed Power Well lets see can find another constant has Time since Time involved Speed Power surface planet up altitudes model airplanes fly bombers butterflies ants ele phants respond exactly same way start accelerating toward cen ter earth whenever what holding up pulled out under Disregarding air resistance will ac celerate rate 32 ft per second second acceleration constant re gardless Scale Other accelerations such 5-g maneuver simply mul tiples basic gravitational accelera tion too remain constant inso far Scale concerned have seen describing pa rameters Acceleration expressed L L thetermNow since know txt expression represents constant also know will have expon ent zero just like Aspect Ratio Den sity did Thus may say LL xt e L has exponent 1 two Ts must have exponent 5 turn may expressed terms Scale K-K K5 K Thus have determined time has exponent 5 same square root So can say Time var ies asjhe square root Scale t an now proceed Speed Power Speed Velocity V _ K terms Scale K3 K5 Which says Speed like Time varies square root Scale V wer said Force X Distance ime terms Scale K3K — K35 K Power varies 35 power Scale HP Wing Loading Weight K3 K AreaK2 varies directly Scale Stress Force — K3 — K AreaK2 also varies Scale Power Loading WeighL K3 — Power K33 K varies reciprocal square root Scale Thrust Loading WeighL K3 — K Thrust K3 Velocity V varies square root Scale K3 Power HP varies three-and-onehalf power Scale K3 Wing Loading Y varies directly Sale K sses I vary directly Scale K S Loading recipro dimensionless does change Power varies ScaleHP summarize Acceleration constant does change Scale K Dimensions L vary directly Scale K Areas 5 vary Scale squared K2 Volumes v vary Scale cubed K3 Weights W vary Scale cubed K3 Forces F vary Scale cubed K3 Thrust T varies Scale cubed K3 Work w varies Scale fourth power K4 Moments M vary Scale fourth power K4 Moments Inertia vary Scale fifth power K Time t varies square root Scale K cal square root Scale K Aspect Ratio other geometrical ra tios Density Thrust Loading other dimensionless items change Scale K 35 power some other terms easy figure cal culator have handy well calculate values foregoing items several appropriate scale factors tabulate Table 1 Now understand mysteries scale lets go back check values gave dynamic model Ryan ST Table No 1 Now lets check answers ques tions posed beginning January 1978 11 late forties Consolidated testing all-metal model proposed jet-powered Skate flying boat shown skimming water test basin Full-span slats blended hull 1600 lbs 53 125 hp 35 5 150 mph 55 60mph 525 ft 1 5 1 From Table 1 scale factor 4 speed horsepower factor 128 Ignoring Reynolds No effects power required model thereforei9or 117 As 128 discussed further however would wise increase say 15 hp ac count relative disparity propeller efficiencies 2 Visual scale speed simply speed divided scale factor 150 equals4—-or 375 say 38 mph However dynamic scale speed 150150 h K52 3 Since visually model going fly twice fast full-scale air plane will necessary shoot twice pictures per unit time film projected normal speed Citabria model will appear flying slow easy just like real 4 Weight varies cube scale factor case 43 64 Therefore pilots weight is29. 3125 lbs 64 5 again weight model prototype divided cube scale factor case 12 Table 1 120001bs or69lbs 1728 6 If maneuvers same accelerations produced prototype duplicated model accelerations vary scale 7 Stress varies directly scale model stresses will 1000 5 pounds per sq size creases stronger stronger materials must used Howard Hughes Spruce Goose such sad waste taxpayers money No weight fi nally available payload 8 Dynamic speed varies square root scale 20 20 58 knots 12346 9 Thrust varies scale factor cubed 4000 bs 10 So Scozzi fan 5 lbs OK 10 96/96 /sec visual scale 1600 lbs 125 125hp 2795 150 mph 2236 -60mph 2236 525ft 5 understanding relationships very least recognize exist seems to essential has become addicted fasci nating hobby wishes pursue telligently particularly likes create adaptations interesting airplanes boats cars flood control projects anything else operates same means prototype origi nal designs own Obviously de termination such things engine size wing area weight etc should made rational basis know things vary scale have powerful tool indeed really needs scratch build anything wishes have data handy prototype data perhaps engine shelf workshop can select proper scale start reducing enlarging plans word caution however der mathematician can predict hairline accuracy trace moons shadow across earth during eclipse can approximate trajectory rifle bullet through unpredictable unruly air currents same token 128 lbsour rules dynamic similitude tell us pre cisely what things should account differences flow patterns 45 hp between full-scale wings propellers model wings propellers Big wings develop higher lift lower drag propor tionately small ones 67 mph differences studied eval uated long ago man named Osborne Reynolds actually interested flow fluid through pipes found 27 mph big pipes carried water better small pipes relationships discov ered expressed Reynolds Num 105 ft ber Because Reynolds Number match full-scale prototype very faithfully detail Ryan will probably land something higher 27 mph like 30 mph unless ways can found keep lift its proper value leading edge slats quite effective Skate model Such lead ing edge slats will help will turbula tionroughening leading edge stretching wire along front energize boundary layer thus de lay separation reduction lift Full-scale propellers develop 80 85% efficiencies doesnt seem much data available model propeller efficiencies fair guess might around 60% Thus rules say Ryan needs 45 hp might better part wis dom increase power factor something like 80/60 X 45 6 hp necessarily 60 cu engine time time reads modeler says landed fairly sizeable heavy radio model scale speed 10 mph can say just possible average model still air However air rarely still 10- 15-mph breeze could make seem possible visual scale speeds become mat ter real concern certainly could have merit answer think lies combination large size careful weight watching high-lift airfoils effective high-lift devices such full span flaps talking about speed reductions order 50% Finally important have talking about building dynam ic models full-scale aircraft deter mined weight power etc based full gross weight prototype models however particularly larger ones may able better appears Thirty-five 40% weight real airplane useful loadpilot baggage fuel cargo etc small models much gobbled up radio gear large quarter-size larger models radio weight becomes relatively insignificant carry ing three-pound pilot nor baggage etc may find ourselves lighter model truly dynamically similar turn will give us lighter wing load Continuedonpage86 12 Model Aviation Weight will Power will Vmaxwill V stall will Takeoff run will 1600 lbs K3 125 hp K 150 mph K 60 mph K 525 ft 1 K em em em em em em memo Bradford W Powers eme me me me SPECIAL PRO SERIES 2 FOR RC-FREE FLIGHT CONTROL LINE CIAPITCHPRICE 5%3489 63489 733%4119 53%456129 94566% 77%139 10467149 1066V 8W149 to6016159 114677% 7Y, 7%8159 it6E1W169 11%67169 126179 12555179 1356219 1496249 1566309 164%6389 W 55106 BLADE 855 EXTRA WIDE SERIES 400 B Poe SPEED & RACING ADVANCED DESIGN NO 1 IN PYLON RACING LEADING SPEED REGGRO HOLDER OF ALL TIMES RC PYLON RACING DIA PITCHPRICE 6%3%4129 755%6149 7SN 5/N 6N149 8%6% 6% 7 7%7%189 96%7 7A7%189 CONTROL LINE SPEED& RACING CIA PITCHPRICE 4/8A7129 4%55%129 6788%149 7 7%10%11169 889189 89N9%N189 8% 77%189 912 13219 51ARRflW Homebuilts Bill Youmans firstplace win Masters Class Greenville NRCHA Nationals last August seems increasing interest homebuilt helicopters won scratchbuilt own design composite components Bill came within 10 points aceing hover course local flier Norm Holland has developed scratchbuilt using Kavan mechanics tn-cycle landing gear Rev-o-lution canopy Futaba Sl5M ball-bearing servos EK single-stick radio Kraft engine Tach-Tron gover nor weight 12 1/2 pounds very smooth precise enough people inter ested could soon put kit form Look column further details Dual Counter Rotating Head ScratchBuilt Gilbert Laforest Montreal suc cessfully flew counter rotating-head heli copter own design Greenville NRCHA Nats Webra Speed 60 driving both heads unbelievably complicated pushrod system Self-designed transmitter two single sticks dual rudder knobs much Separate collective control head well separate cyclic control Tremendous under taking say nothing about getting mind synchronized hands Radio custom Can-Air Canadian ProLine some radio interference problems Next months column will cover unique finish helicopters first part building Aerospatiale SA-34 1 G Gazelle ducted fan-tail rotor youre flying youre trying hard enough Walt Schoonard 2080 Sharon Rd Winter Park FL 32789 Letters continued page 7 quality Model viation money best model aviation magazine field William R Barr AMA 31415 Claremont CA MA policy publish types models eventually shall get around Mr Barrs suggestions Mistaken Identity No doubt have received few letters already rare event havent would like point out photograph lower right hand corner page 25 Aug 1977 issue Model viation incorrectly captioned gentleman photo Rick Pear son winner last years Soar Nats well other contests sailplane holding Paragon Rick did outstanding job flying under less ideal conditions would shame did receive credit display flying skill Since generally true least 75% sailplanes performance direct function pilots skill would follow mention sailplane used would significant have no doubt uninten tional error know would want errors called attention proper caption can used Ed Slobod Pierce Aero Company Nonthridge CA Size It/Powers continued page 13 ing slower speed reduce somewhat power requirements because scaling down proto type its weight-empty condition rather its gross-weight condition thats ut Size Questions comments may ad dressed Bradford W Powers care magazine Seastrutz/Wi son continued page 18 full throttle some down-elevator Ed pulled up Seastrutz oil like scared duck full stall attitude 50 feet hit wind blowing toward hill blown end-over-end trees Damage minor Test flying continued next week Fall Brimfield meet time stabilizer shim under its leading edge rudder area doubled Seastrutz flew beautifully Among its test pilots Ted Straders son Eric testified flew very much like its predecessor Strutz Echo Seastrutz built mci dences shown will perform very well relatively docile its 46-in wing span compact biplane configuration felt might too quick average flier case diffi cult machine fly land water Have fun Radio Technique/Myers continued page 14 An ammeter measure charging discharging operating currents turntable drum-type chart feed measure servo transmit time shaker find intermittent prob lems heat lamp can Freezit similar chiller locate temperature-sensitive compon ents Special tools various types like desoldering irons Youve seen lot items listed under additional advertisements probability should leave will describe some simple non destructive tests should perform 86 Model Aviation NEWS FLASH Bob Smith Chatsworth CA set new World Speed Record June 19 Pylon mula 11125 RevUp 8%-6% new Pylon RaC ing prop OUT- PERFORMS ALL OTHERS AT THE 1976 NATIONALS 1st RC Masters Class 1st RC Advanced 1st RC Novice 1st RC Sport Scale 1st Formula Pylon 1st Quarter Midget Pylon 1st CL Stunt Open 1st CL Stunt Senior 1st CL Stunt Junior 1st CL Combat O & Sr 1st CL Slow Comb OP & Sr 1st CL Class 0 Speed Open 1st CL Class C Speed Jr & Sr 1st CLCIassB Speed Op & Sr 1st CL Cl Speed Op Sr Jr 1st FE Class B Open 1st FE Class C Open HIGH PERFORMANCE * COMPETITION PROVEN * THIN RIGID BLADES OP HARD MAPLE WOOD * SUPERBLY FINISHED COMPLETELY FUEL PIDOF 1st CL Carrier II Op Jr Sr 1st CL Carrier Jr & Sr 1st CL Formula 40 Opec 1st CL Class 6 Proto Jr