Last month author discussed CO its ef fect stability second three-part series talks about Mean Aerodynamic chord find various configurations Brad Powers IN LAST months issue discussed CG its effect stability determined must always lie forward Neutral Pointat about 25% chord conventional designs question arose What exactly meant chord rectangular planform having no taper chord constant what about tapered wing Mustang elliptical wing Spitfire delta shape Mirage What about flying saucers what about biplanes assume wing uniformly loaded Lift evenly distributed over its surface lift may regarded acting along chord lying center area wing panel resultant total lift both panels lies center line airplane shown Fig 1 wings high taper sweepback tips square rather rounded assumption uniform loading may quite true disparity small usually neglected usual criterion just mentioned lift acts along chord center area centroid wing panel Such chord called Mean Aerodynamic Chord MAC along MAC must balance airplane often shown plans being chord line wing CG rarely disposed vertically highwing models CG below wing low-wing models CG above wing little consequence far longitudinal stability goes important thing have fore aft position CG properly located straight wing rectangular planform placing CG quarter-chord point problem wing swept tapered both essential accurately determine length position MAC airplane correctly balanced MAC sometimes confused average chord average chord wing area divided span always lies halfway out along semi-span wing MAC varies length taper ratio mid point semi-span rectangular wing moves inboard increasing taper until delta wing has infinite taper lies -span shown Fig 4 Now lets find MACs wing shapes mentioned beginning rectangular planform MAC average chord lies halfway out along semi-span shown Fig 2 tapered planform MAC can found graphically adding root chord tip chord tip chord root chord drawing diagonal intersection 50% chord line de termines centroid panel graphic method should accurate enough model however precision desired MAC its lateral longitudinal positions may calculated relationships shown Fig ULiLL L3LULTET 4 3 As long span held constant effect sweepback increase m whiled unchanged Getting back delta wing shown Fig 4 convenient know MAC always th rootchordC andmis always rther 25% point MAC coincides 50% point root chord Note tailless designs CG 20% MAC Before going further should emphasized general unless fuselage extremely large very dirty aerodynamically case lower wing some biplanes effect fuselage lift distribution over span wing negligible lift developed wing therefore position MAC may considered same whether wing has fuselage attached Ellipses circles members same family Thus Spitfires flying saucers same parentage hold up coin view square circle turned sideways itis ellipse Sothe spanwise position MAC same both shown Fig 5 planform consists fuller ellipse aft quarter-chord line forward spanwise location same both odd shapes such butterfly-wing planforms etc simplest procedure finding MAC simply draw panel piece cardboard cut out balance triangular scale table edge Balance least three times marking time marks will inter sect centroid figure MAC may usually regarded length chord through point Sometimes wings have acenterpanel outer panels shown Fig 6 MAC such arrangement found taking moments areas both panels solving d moment center section center line airplane its area times d dSc moment outer panel its area times d dSp total wing area S equals Sc o dSc dSdScdSpandd ls MAC length simply chord between dashed lines Fig 6 Again greater precision desired length MAC MAC Cp CpXd-d 2 1 MACaverage - CENTROID 25%MACFig IIEOUIVALENT AREAS h -h ________________________2 MAC 7---25%MAcII Fig.2I 1980 23 AF _-- 6 MAC11- Lir_- rITt hR2T mi—-- -II c7_ 7 - -- I 7 IqKi F V - __ C 5G9C-2- _____ 2OMAC -OSS~ ---1 \lII NV* Cp outer panel see Fig 3 Cc center section see Fig 2 models graphical methods should adequate since can probably draw relationships accurately can build anyway configuration found AT6 Texan PBY flying boat gliders upper wing some biplanes am sure have overlooked other arrangements cant think what might lets go take look biplanes wonderful airplanes became extinct fore time anything have say about probably presumptuous wealth detail character realism make ideal subjects models lets have critical look always case upper wing often mounted forward lower wing some times greater incidence make stall first thus contributing recovering mentioned Part upper wing flies somewhat less disturbed air contributes greater effi ciency often carries greater share load lower wing affected disturbances generated fuselage its protuberances landing gear interplane struts also disruptive flow over lower wing Aside fact biplane dirty 424h- Fig5 MAC MAC saucer spitfire d E3 C ci dSp scsp cCcCD{dd MAC Fig,7 25%. MAC aerodynamically has additional disadvan tage inherently less efficient monoplane having equivalent area due so-called mutual interference highpressure region under upper wing rendered less effective proximity low pressureregion above lower wing vice versathe low pressure region above lower wing higher pressure would otherwise early designers realized men such Blenot stuck monoplanes albeit pretty dirty ones draped lots wire bracing biplane configuration selected early designers enable build light strong structure available materials biplane just truss Nieuport biplane has large upper wing lower wing relatively small particu larly chord open conjecture suspect designer aware inherent shortcomings lower wing decided minimize nevertheless keep could use bottom truss Before can go further must learn some biplane tenninology Decalage case biplanes decalage relative incidence between upper lower wings Since biplanes no longer built term has used recently describe relative incidence between wing tail discussed Part Gap vertical distance between leading edges wings Gap/Chord Ratio gap expressed percent chord wings tapered have unequal chords chord 24 Model Aviation MAC pair Stagger positioning wing forward other upper wing forward lower wing stagger positive lower wing forward Beechcraft Staggerwing stagger negative Fig 7 shows simplest case no stagger no decalage wings equal area MAC therefore equal chord either wings lies vertically halfway between loading wing same However mentioned earlier upper wing will carry larger share load vertical position MAC will somewhat closer upper wing Since no stagger fore aft position will same asthatofthewingsthemselVesandtheCG location will affected vertical position MAC 25 Cv Fig 8 wings again identical no decalage However time have some positive stagger will tend load up upper wing sure amount depending degree stagger also inverse propor tion Gap/Chord Ratio Because stagger horizontal position MAC will now influenced vertical position wings differ area upper wing larger MAC position will move upward forward further still decalage upper wing will further influence MAC position Thus determination MAC length position biplane complex because factors involved Fig 9 shows method determining MAC biplane no decalage involved should adequate modelers use purloined old aerodynamics text Elements Practical Aerodynamics Bradley Jones Published John Wiley Sons copy third edition printed 19421 dont suppose still print run across copy buy want clearly written understandable yet thorough treat ment subject fundamentals aerodynamics covering sub-sonic propeller-driven aircraft Looking sub Fig 94 Fig 9 showing relative loading versus stagger see condition shown Fig 7 gap/chord ratio unity stagger zero upper wing loaded 110% lower wing due mutual interference alone solving MAC position g will determine vertical position just speculating about condition shown Fig 8 have 10 degrees stagger same gap/chord ratio unity runs relative loading e up 118% will drive MAC higher further forward considerably further approximation own account decalage would follows Before solving expression Fig 9 MAC multiply upper wing area Su l08n exponent n decalage degrees Thus upper wing has say 1000 square inches area angular difference decalage between incidence two wings 2 degrees multiply Su upper wing area 1000 sq 1082 117 Su will become 1170 use value solve MAC because wings lift increases rate about 8% per degree increase angle attack Which case amounts decalage should enable determine MACs various configurations have dis cussed thus pinpoint precisely 25% MAC positionthe CG locationwill Now know exactly CG belongs can sure will wind up big quarter-scale model still drawing board next months exciting climax threepart series will discuss figure balance airplane still drawing board gleam eye thus saving us expense lead ballast Comments questions may addressed author care editor continued May 1980 25
Edition: Model Aviation - 1980/05
Page Numbers: 23, 24, 25
Last month author discussed CO its ef fect stability second three-part series talks about Mean Aerodynamic chord find various configurations Brad Powers IN LAST months issue discussed CG its effect stability determined must always lie forward Neutral Pointat about 25% chord conventional designs question arose What exactly meant chord rectangular planform having no taper chord constant what about tapered wing Mustang elliptical wing Spitfire delta shape Mirage What about flying saucers what about biplanes assume wing uniformly loaded Lift evenly distributed over its surface lift may regarded acting along chord lying center area wing panel resultant total lift both panels lies center line airplane shown Fig 1 wings high taper sweepback tips square rather rounded assumption uniform loading may quite true disparity small usually neglected usual criterion just mentioned lift acts along chord center area centroid wing panel Such chord called Mean Aerodynamic Chord MAC along MAC must balance airplane often shown plans being chord line wing CG rarely disposed vertically highwing models CG below wing low-wing models CG above wing little consequence far longitudinal stability goes important thing have fore aft position CG properly located straight wing rectangular planform placing CG quarter-chord point problem wing swept tapered both essential accurately determine length position MAC airplane correctly balanced MAC sometimes confused average chord average chord wing area divided span always lies halfway out along semi-span wing MAC varies length taper ratio mid point semi-span rectangular wing moves inboard increasing taper until delta wing has infinite taper lies -span shown Fig 4 Now lets find MACs wing shapes mentioned beginning rectangular planform MAC average chord lies halfway out along semi-span shown Fig 2 tapered planform MAC can found graphically adding root chord tip chord tip chord root chord drawing diagonal intersection 50% chord line de termines centroid panel graphic method should accurate enough model however precision desired MAC its lateral longitudinal positions may calculated relationships shown Fig ULiLL L3LULTET 4 3 As long span held constant effect sweepback increase m whiled unchanged Getting back delta wing shown Fig 4 convenient know MAC always th rootchordC andmis always rther 25% point MAC coincides 50% point root chord Note tailless designs CG 20% MAC Before going further should emphasized general unless fuselage extremely large very dirty aerodynamically case lower wing some biplanes effect fuselage lift distribution over span wing negligible lift developed wing therefore position MAC may considered same whether wing has fuselage attached Ellipses circles members same family Thus Spitfires flying saucers same parentage hold up coin view square circle turned sideways itis ellipse Sothe spanwise position MAC same both shown Fig 5 planform consists fuller ellipse aft quarter-chord line forward spanwise location same both odd shapes such butterfly-wing planforms etc simplest procedure finding MAC simply draw panel piece cardboard cut out balance triangular scale table edge Balance least three times marking time marks will inter sect centroid figure MAC may usually regarded length chord through point Sometimes wings have acenterpanel outer panels shown Fig 6 MAC such arrangement found taking moments areas both panels solving d moment center section center line airplane its area times d dSc moment outer panel its area times d dSp total wing area S equals Sc o dSc dSdScdSpandd ls MAC length simply chord between dashed lines Fig 6 Again greater precision desired length MAC MAC Cp CpXd-d 2 1 MACaverage - CENTROID 25%MACFig IIEOUIVALENT AREAS h -h ________________________2 MAC 7---25%MAcII Fig.2I 1980 23 AF _-- 6 MAC11- Lir_- rITt hR2T mi—-- -II c7_ 7 - -- I 7 IqKi F V - __ C 5G9C-2- _____ 2OMAC -OSS~ ---1 \lII NV* Cp outer panel see Fig 3 Cc center section see Fig 2 models graphical methods should adequate since can probably draw relationships accurately can build anyway configuration found AT6 Texan PBY flying boat gliders upper wing some biplanes am sure have overlooked other arrangements cant think what might lets go take look biplanes wonderful airplanes became extinct fore time anything have say about probably presumptuous wealth detail character realism make ideal subjects models lets have critical look always case upper wing often mounted forward lower wing some times greater incidence make stall first thus contributing recovering mentioned Part upper wing flies somewhat less disturbed air contributes greater effi ciency often carries greater share load lower wing affected disturbances generated fuselage its protuberances landing gear interplane struts also disruptive flow over lower wing Aside fact biplane dirty 424h- Fig5 MAC MAC saucer spitfire d E3 C ci dSp scsp cCcCD{dd MAC Fig,7 25%. MAC aerodynamically has additional disadvan tage inherently less efficient monoplane having equivalent area due so-called mutual interference highpressure region under upper wing rendered less effective proximity low pressureregion above lower wing vice versathe low pressure region above lower wing higher pressure would otherwise early designers realized men such Blenot stuck monoplanes albeit pretty dirty ones draped lots wire bracing biplane configuration selected early designers enable build light strong structure available materials biplane just truss Nieuport biplane has large upper wing lower wing relatively small particu larly chord open conjecture suspect designer aware inherent shortcomings lower wing decided minimize nevertheless keep could use bottom truss Before can go further must learn some biplane tenninology Decalage case biplanes decalage relative incidence between upper lower wings Since biplanes no longer built term has used recently describe relative incidence between wing tail discussed Part Gap vertical distance between leading edges wings Gap/Chord Ratio gap expressed percent chord wings tapered have unequal chords chord 24 Model Aviation MAC pair Stagger positioning wing forward other upper wing forward lower wing stagger positive lower wing forward Beechcraft Staggerwing stagger negative Fig 7 shows simplest case no stagger no decalage wings equal area MAC therefore equal chord either wings lies vertically halfway between loading wing same However mentioned earlier upper wing will carry larger share load vertical position MAC will somewhat closer upper wing Since no stagger fore aft position will same asthatofthewingsthemselVesandtheCG location will affected vertical position MAC 25 Cv Fig 8 wings again identical no decalage However time have some positive stagger will tend load up upper wing sure amount depending degree stagger also inverse propor tion Gap/Chord Ratio Because stagger horizontal position MAC will now influenced vertical position wings differ area upper wing larger MAC position will move upward forward further still decalage upper wing will further influence MAC position Thus determination MAC length position biplane complex because factors involved Fig 9 shows method determining MAC biplane no decalage involved should adequate modelers use purloined old aerodynamics text Elements Practical Aerodynamics Bradley Jones Published John Wiley Sons copy third edition printed 19421 dont suppose still print run across copy buy want clearly written understandable yet thorough treat ment subject fundamentals aerodynamics covering sub-sonic propeller-driven aircraft Looking sub Fig 94 Fig 9 showing relative loading versus stagger see condition shown Fig 7 gap/chord ratio unity stagger zero upper wing loaded 110% lower wing due mutual interference alone solving MAC position g will determine vertical position just speculating about condition shown Fig 8 have 10 degrees stagger same gap/chord ratio unity runs relative loading e up 118% will drive MAC higher further forward considerably further approximation own account decalage would follows Before solving expression Fig 9 MAC multiply upper wing area Su l08n exponent n decalage degrees Thus upper wing has say 1000 square inches area angular difference decalage between incidence two wings 2 degrees multiply Su upper wing area 1000 sq 1082 117 Su will become 1170 use value solve MAC because wings lift increases rate about 8% per degree increase angle attack Which case amounts decalage should enable determine MACs various configurations have dis cussed thus pinpoint precisely 25% MAC positionthe CG locationwill Now know exactly CG belongs can sure will wind up big quarter-scale model still drawing board next months exciting climax threepart series will discuss figure balance airplane still drawing board gleam eye thus saving us expense lead ballast Comments questions may addressed author care editor continued May 1980 25
Edition: Model Aviation - 1980/05
Page Numbers: 23, 24, 25
Last month author discussed CO its ef fect stability second three-part series talks about Mean Aerodynamic chord find various configurations Brad Powers IN LAST months issue discussed CG its effect stability determined must always lie forward Neutral Pointat about 25% chord conventional designs question arose What exactly meant chord rectangular planform having no taper chord constant what about tapered wing Mustang elliptical wing Spitfire delta shape Mirage What about flying saucers what about biplanes assume wing uniformly loaded Lift evenly distributed over its surface lift may regarded acting along chord lying center area wing panel resultant total lift both panels lies center line airplane shown Fig 1 wings high taper sweepback tips square rather rounded assumption uniform loading may quite true disparity small usually neglected usual criterion just mentioned lift acts along chord center area centroid wing panel Such chord called Mean Aerodynamic Chord MAC along MAC must balance airplane often shown plans being chord line wing CG rarely disposed vertically highwing models CG below wing low-wing models CG above wing little consequence far longitudinal stability goes important thing have fore aft position CG properly located straight wing rectangular planform placing CG quarter-chord point problem wing swept tapered both essential accurately determine length position MAC airplane correctly balanced MAC sometimes confused average chord average chord wing area divided span always lies halfway out along semi-span wing MAC varies length taper ratio mid point semi-span rectangular wing moves inboard increasing taper until delta wing has infinite taper lies -span shown Fig 4 Now lets find MACs wing shapes mentioned beginning rectangular planform MAC average chord lies halfway out along semi-span shown Fig 2 tapered planform MAC can found graphically adding root chord tip chord tip chord root chord drawing diagonal intersection 50% chord line de termines centroid panel graphic method should accurate enough model however precision desired MAC its lateral longitudinal positions may calculated relationships shown Fig ULiLL L3LULTET 4 3 As long span held constant effect sweepback increase m whiled unchanged Getting back delta wing shown Fig 4 convenient know MAC always th rootchordC andmis always rther 25% point MAC coincides 50% point root chord Note tailless designs CG 20% MAC Before going further should emphasized general unless fuselage extremely large very dirty aerodynamically case lower wing some biplanes effect fuselage lift distribution over span wing negligible lift developed wing therefore position MAC may considered same whether wing has fuselage attached Ellipses circles members same family Thus Spitfires flying saucers same parentage hold up coin view square circle turned sideways itis ellipse Sothe spanwise position MAC same both shown Fig 5 planform consists fuller ellipse aft quarter-chord line forward spanwise location same both odd shapes such butterfly-wing planforms etc simplest procedure finding MAC simply draw panel piece cardboard cut out balance triangular scale table edge Balance least three times marking time marks will inter sect centroid figure MAC may usually regarded length chord through point Sometimes wings have acenterpanel outer panels shown Fig 6 MAC such arrangement found taking moments areas both panels solving d moment center section center line airplane its area times d dSc moment outer panel its area times d dSp total wing area S equals Sc o dSc dSdScdSpandd ls MAC length simply chord between dashed lines Fig 6 Again greater precision desired length MAC MAC Cp CpXd-d 2 1 MACaverage - CENTROID 25%MACFig IIEOUIVALENT AREAS h -h ________________________2 MAC 7---25%MAcII Fig.2I 1980 23 AF _-- 6 MAC11- Lir_- rITt hR2T mi—-- -II c7_ 7 - -- I 7 IqKi F V - __ C 5G9C-2- _____ 2OMAC -OSS~ ---1 \lII NV* Cp outer panel see Fig 3 Cc center section see Fig 2 models graphical methods should adequate since can probably draw relationships accurately can build anyway configuration found AT6 Texan PBY flying boat gliders upper wing some biplanes am sure have overlooked other arrangements cant think what might lets go take look biplanes wonderful airplanes became extinct fore time anything have say about probably presumptuous wealth detail character realism make ideal subjects models lets have critical look always case upper wing often mounted forward lower wing some times greater incidence make stall first thus contributing recovering mentioned Part upper wing flies somewhat less disturbed air contributes greater effi ciency often carries greater share load lower wing affected disturbances generated fuselage its protuberances landing gear interplane struts also disruptive flow over lower wing Aside fact biplane dirty 424h- Fig5 MAC MAC saucer spitfire d E3 C ci dSp scsp cCcCD{dd MAC Fig,7 25%. MAC aerodynamically has additional disadvan tage inherently less efficient monoplane having equivalent area due so-called mutual interference highpressure region under upper wing rendered less effective proximity low pressureregion above lower wing vice versathe low pressure region above lower wing higher pressure would otherwise early designers realized men such Blenot stuck monoplanes albeit pretty dirty ones draped lots wire bracing biplane configuration selected early designers enable build light strong structure available materials biplane just truss Nieuport biplane has large upper wing lower wing relatively small particu larly chord open conjecture suspect designer aware inherent shortcomings lower wing decided minimize nevertheless keep could use bottom truss Before can go further must learn some biplane tenninology Decalage case biplanes decalage relative incidence between upper lower wings Since biplanes no longer built term has used recently describe relative incidence between wing tail discussed Part Gap vertical distance between leading edges wings Gap/Chord Ratio gap expressed percent chord wings tapered have unequal chords chord 24 Model Aviation MAC pair Stagger positioning wing forward other upper wing forward lower wing stagger positive lower wing forward Beechcraft Staggerwing stagger negative Fig 7 shows simplest case no stagger no decalage wings equal area MAC therefore equal chord either wings lies vertically halfway between loading wing same However mentioned earlier upper wing will carry larger share load vertical position MAC will somewhat closer upper wing Since no stagger fore aft position will same asthatofthewingsthemselVesandtheCG location will affected vertical position MAC 25 Cv Fig 8 wings again identical no decalage However time have some positive stagger will tend load up upper wing sure amount depending degree stagger also inverse propor tion Gap/Chord Ratio Because stagger horizontal position MAC will now influenced vertical position wings differ area upper wing larger MAC position will move upward forward further still decalage upper wing will further influence MAC position Thus determination MAC length position biplane complex because factors involved Fig 9 shows method determining MAC biplane no decalage involved should adequate modelers use purloined old aerodynamics text Elements Practical Aerodynamics Bradley Jones Published John Wiley Sons copy third edition printed 19421 dont suppose still print run across copy buy want clearly written understandable yet thorough treat ment subject fundamentals aerodynamics covering sub-sonic propeller-driven aircraft Looking sub Fig 94 Fig 9 showing relative loading versus stagger see condition shown Fig 7 gap/chord ratio unity stagger zero upper wing loaded 110% lower wing due mutual interference alone solving MAC position g will determine vertical position just speculating about condition shown Fig 8 have 10 degrees stagger same gap/chord ratio unity runs relative loading e up 118% will drive MAC higher further forward considerably further approximation own account decalage would follows Before solving expression Fig 9 MAC multiply upper wing area Su l08n exponent n decalage degrees Thus upper wing has say 1000 square inches area angular difference decalage between incidence two wings 2 degrees multiply Su upper wing area 1000 sq 1082 117 Su will become 1170 use value solve MAC because wings lift increases rate about 8% per degree increase angle attack Which case amounts decalage should enable determine MACs various configurations have dis cussed thus pinpoint precisely 25% MAC positionthe CG locationwill Now know exactly CG belongs can sure will wind up big quarter-scale model still drawing board next months exciting climax threepart series will discuss figure balance airplane still drawing board gleam eye thus saving us expense lead ballast Comments questions may addressed author care editor continued May 1980 25