{"id":48624,"date":"2025-11-19T11:09:21","date_gmt":"2025-11-19T10:09:21","guid":{"rendered":"https:\/\/www.derivaty.sk\/?p=48624"},"modified":"2025-11-19T11:09:21","modified_gmt":"2025-11-19T10:09:21","slug":"aerodynamika-multirotorov-analyza-vztlaku-a-parazitickeho-odporu-pri-nizkych-reynoldsovych-cislach","status":"publish","type":"post","link":"https:\/\/www.vrtulniky.sk\/news\/aerodynamika-multirotorov-analyza-vztlaku-a-parazitickeho-odporu-pri-nizkych-reynoldsovych-cislach\/","title":{"rendered":"Aerodynamika multirotorov: Anal\u00fdza vztlaku a parazitick\u00e9ho odporu pri n\u00edzkych Reynoldsov\u00fdch \u010d\u00edslach"},"content":{"rendered":"<h2>Preh\u013ead: pre\u010do n\u00edzke Reynoldsovo \u010d\u00edslo men\u00ed aerodynamiku multirotorov<\/h2>\n<p>Multirotorov\u00e9 UAV (kvadrokopt\u00e9ry, hexakopt\u00e9ry) pou\u017e\u00edvaj\u00fa mal\u00e9 vrtule s n\u00edzkou obvodovou r\u00fdchlos\u0165ou a vysokou diskovou plochou. Pri mal\u00fdch priemeroch a stredn\u00fdch ot\u00e1\u010dkach sa listy vrt\u00fa\u013e pohybuj\u00fa v re\u017eime <strong>n\u00edzkych Reynoldsov\u00fdch \u010d\u00edsel<\/strong> (typicky <em>Re \u2248 2\u00b710<sup>4<\/sup> a\u017e 2\u00b710<sup>5<\/sup><\/em> na strednej polomere), kde sa men\u00ed spr\u00e1vanie pr\u00fadnic, profilov\u00fdch s\u00fa\u010dinite\u013eov vztlaku a odporu, vznikaj\u00fa lamina\u010dn\u00e9 separa\u010dn\u00e9 bubliny a v\u00fdrazne rastie visk\u00f3zny odpor. Tieto efekty priamo ovplyv\u0148uj\u00fa <strong>vyu\u017eite\u013en\u00fd \u0165ah, \u00fa\u010dinnos\u0165 vznosu (hover efficiency)<\/strong> a <strong>spotrebu energie<\/strong>.<\/p>\n<h2>Defin\u00edcie a z\u00e1kladn\u00e9 vz\u0165ahy<\/h2>\n<ul>\n<li><strong>Reynoldsovo \u010d\u00edslo<\/strong> listu na lok\u00e1lnej polomere <em>r<\/em>:\n<div><em>Re(r) = \\dfrac{\\rho \u00b7 V(r) \u00b7 c(r)}{\\mu}<\/em>, kde <em>V(r) \u2248 \\Omega \u00b7 r<\/em> v hoversk\u00fdch podmienkach, <em>c(r)<\/em> je lok\u00e1lna h\u013abka profilu, <em>\\rho<\/em> hustota a <em>\\mu<\/em> dynamick\u00e1 viskozita.<\/div>\n<\/li>\n<li><strong>Koeficient \u0165ahu a v\u00fdkonu vrtule<\/strong>:\n<div><em>C<sub>T<\/sub> = \\dfrac{T}{\\rho \u00b7 n^2 \u00b7 D^4}<\/em>, &nbsp; <em>C<sub>P<\/sub> = \\dfrac{P}{\\rho \u00b7 n^3 \u00b7 D^5}<\/em>, &nbsp; <em>\\eta = \\dfrac{C_T^{3\/2}}{C_P \u00b7 \\sqrt{2}}<\/em> (pre hover z odvodenia z te\u00f3rie hybnosti).<\/div>\n<\/li>\n<li><strong>Diskov\u00e1 z\u00e1\u0165a\u017e<\/strong>:\n<div><em>W\/A = \\dfrac{T}{\\pi (D\/2)^2}<\/em>, ni\u017e\u0161ia diskov\u00e1 z\u00e1\u0165a\u017e \u2192 men\u0161\u00ed indukovan\u00fd odpor, ni\u017e\u0161\u00ed po\u017eadovan\u00fd indukovan\u00fd r\u00fdchlostn\u00fd pr\u00edkon.<\/div>\n<\/li>\n<\/ul>\n<h2>N\u00edzke Re a profilov\u00e9 charakteristiky: lamina\u010dn\u00e1 separ\u00e1cia a \u201edrag bucket\u201c<\/h2>\n<p>Pri <em>Re &lt; 2\u00b710<sup>5<\/sup><\/em> sa hrani\u010dn\u00e1 vrstva \u0165a\u017e\u0161ie udr\u017eiava pri profile, vznik\u00e1 <strong>lamina\u010dn\u00e1 separa\u010dn\u00e1 bublina<\/strong>, ktor\u00e1 zvy\u0161uje <em>C<sub>D<\/sub><\/em> a zni\u017euje sklon krivky <em>C<sub>L<\/sub>(\u03b1)<\/em>. Mal\u00e9 zmeny hr\u00fabky, zakrivenia \u010di drsnosti povrchu (farba, prach) m\u00f4\u017eu prinies\u0165 ve\u013ek\u00e9 zmeny v <em>C<sub>L,max<\/sub><\/em> a v p\u00e1sme \u201edrag bucket\u201c. D\u00f4sledky pre vrtule multirotorov:<\/p>\n<ul>\n<li>Ni\u017e\u0161\u00ed <em>C<sub>L<\/sub>\/C<sub>D<\/sub><\/em> \u2192 vy\u0161\u0161\u00ed profilov\u00fd odpor pre dan\u00fd \u0165ah.<\/li>\n<li>Skor\u0161\u00ed n\u00e1stup lok\u00e1lnej straty pri \u0161pi\u010dke listu (vy\u0161\u0161ie <em>Re<\/em> + vy\u0161\u0161\u00ed uhol n\u00e1behu).<\/li>\n<li>V\u00fdrazn\u00fd vplyv povrchovej drsnosti (tla\u010d z FDM, mikroodreniny) na \u00fa\u010dinnos\u0165.<\/li>\n<\/ul>\n<h2>Rozklad odporu v hovore: indukovan\u00fd, profilov\u00fd a parazitn\u00fd<\/h2>\n<p>Celkov\u00fd v\u00fdkon <em>P<\/em> potrebn\u00fd na visenie je s\u00fa\u010dtom <strong>indukovan\u00e9ho<\/strong>, <strong>profilov\u00e9ho<\/strong> a <strong>parazitn\u00e9ho<\/strong> pr\u00edspevku:<\/p>\n<div> <em>P \u2248 P<sub>i<\/sub> + P<sub>0<\/sub> + P<sub>par<\/sub><\/em>, &nbsp; pri \u010dom<\/p>\n<ul>\n<li><em>P<sub>i<\/sub> \u2248 T \u00b7 v<sub>i<\/sub><\/em>, indukovan\u00fd v\u00fdkon (hybnos\u0165), <em>v<sub>i<\/sub> \u2248 \\sqrt{T\/(2\u03c1A)}<\/em>.<\/li>\n<li><em>P<sub>0<\/sub><\/em> je profilov\u00fd v\u00fdkon \u221d <em>C<sub>D,profile<\/sub><\/em>, dominuj\u00faci v n\u00edzkych <em>Re<\/em> pri mal\u00fdch vrtuliach.<\/li>\n<li><em>P<sub>par<\/sub><\/em> je parazitn\u00fd (r\u00e1m, ramen\u00e1, kabel\u00e1\u017e) \u2013 u mal\u00fdch UAV \u010dasto 5\u201315 % pri hovore, viac pri doprednom lete.<\/li>\n<\/ul>\n<\/div>\n<p>V\u00fdznam pre n\u00e1vrh: <strong>zv\u00e4\u010d\u0161enie priemeru a zn\u00ed\u017eenie ot\u00e1\u010dok<\/strong> zmen\u0161uje <em>P<sub>i<\/sub><\/em> aj <em>P<sub>0<\/sub><\/em> (vy\u0161\u0161\u00ed disk, vy\u0161\u0161ie <em>Re<\/em> na liste), pokia\u013e motory\/ESC dovol\u00ed kr\u00fatiaci moment a mechanika r\u00e1mu.<\/p>\n<h2>Te\u00f3ria hybnosti \u00d7 BEMT: kde sa l\u00ed\u0161ia v n\u00edzkych Re<\/h2>\n<ul>\n<li><strong>Te\u00f3ria hybnosti v hovore<\/strong> poskytuje r\u00fdchly odhad <em>v<sub>i<\/sub><\/em> a <em>P<sub>i<\/sub><\/em>, no nezachyt\u00ed profilov\u00e9 straty a \u0161pi\u010dkov\u00e9 efekty.<\/li>\n<li><strong>Blade-Element\u2013Momentum Theory (BEMT)<\/strong> rozklad\u00e1 list na elementy s lok\u00e1lnym <em>Re(r)<\/em> a pou\u017e\u00edva <em>C<sub>L<\/sub>(\u03b1,Re)<\/em>, <em>C<sub>D<\/sub>(\u03b1,Re)<\/em>. V n\u00edzkych <em>Re<\/em> je nutn\u00e9:\n<ul>\n<li>pou\u017ei\u0165 <em>Re-dependent<\/em> polarov\u00e9 d\u00e1ta (nie \u201eve\u013ek\u00e9\u201c aeroprofilov\u00e9 krivky),<\/li>\n<li>modelova\u0165 <strong>straty \u0161pi\u010dky<\/strong> (Prandtl tip loss) a <strong>n\u00faten\u00fa turbulenciu<\/strong> (tripy\/drsnos\u0165),<\/li>\n<li>zahrn\u00fa\u0165 <strong>neide\u00e1lny induk\u010dn\u00fd faktor<\/strong> pri mal\u00fdch po\u010dtoch listov a interakciu s ramenami r\u00e1mu.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Rozdelenie \u0165ahu a kr\u00fatiaceho momentu po polomere<\/h2>\n<p>Lok\u00e1lny \u0165ah a moment elementu <em>dr<\/em> s\u00fa:<\/p>\n<div> <em>dT = \u00bd \u00b7 \u03c1 \u00b7 V<sup>2<\/sup>(r) \u00b7 c(r) \u00b7 C<sub>L<\/sub>(\u03b1,Re) \u00b7 B \u00b7 dr<\/em><br \/> <em>dQ = \u00bd \u00b7 \u03c1 \u00b7 V<sup>2<\/sup>(r) \u00b7 c(r) \u00b7 C<sub>D<\/sub>(\u03b1,Re) \u00b7 B \u00b7 r \u00b7 dr<\/em> <\/div>\n<p>Kde <em>B<\/em> je po\u010det listov. Pri n\u00edzkych <em>Re<\/em> rastie <em>C<sub>D<\/sub><\/em> ne\u00famerne r\u00fdchlo s uhlom n\u00e1behu a rolu hr\u00e1 aj <strong>geometrick\u00e9 kr\u00fatenie<\/strong> (washout). Spr\u00e1vne kr\u00fatenie zni\u017euje lok\u00e1lne uhly n\u00e1behu pri \u0161pi\u010dke, kde je <em>V(r)<\/em> najvy\u0161\u0161ie, a t\u00fdm potl\u00e1\u010da skor\u00fa separ\u00e1ciu.<\/p>\n<h2>Po\u010det listov: 2 vs. 3 vs. 4 v n\u00edzkych Re<\/h2>\n<ul>\n<li><strong>2-list\u00e9<\/strong> vrtule: typicky vy\u0161\u0161\u00ed <em>\u03b7<\/em> pri malom za\u0165a\u017een\u00ed (ni\u017e\u0161\u00ed odpor), no hor\u0161ia \u201ehladkos\u0165\u201c kr\u00fatiaceho momentu a v\u00e4\u010d\u0161ie \u0161pi\u010dky hluku.<\/li>\n<li><strong>3-list\u00e9<\/strong>: lep\u0161ia regul\u00e1cia v poryvoch, vy\u0161\u0161\u00ed dostupn\u00fd \u0165ah pri obmedzenom priemere, no o 2\u20135 % ni\u017e\u0161ia \u00fa\u010dinnos\u0165 v hovore kv\u00f4li v\u00e4\u010d\u0161ej umelo zv\u00fd\u0161enej sol\u00eddnosti.<\/li>\n<li><strong>4+ listov<\/strong>: vhodn\u00e9 pri pr\u00edsnych rozmerov\u00fdch limitoch; v n\u00edzkych <em>Re<\/em> v\u0161ak zvy\u010dajne penalizuj\u00fa <em>C<sub>D<\/sub><\/em> a zahrievaj\u00fa motor\/ESC.<\/li>\n<\/ul>\n<h2>V\u00fdber profilu a geometrie listu pre n\u00edzke Re<\/h2>\n<ul>\n<li><strong>\u0160t\u00edhlej\u0161ie profily<\/strong> (ni\u017e\u0161ia relat\u00edvna hr\u00fabka 6\u20138 %) s jemn\u00fdm predn\u00fdm obl\u00fakom zni\u017euj\u00fa riziko lamina\u010dnej bubliny.<\/li>\n<li><strong>Mierne zakrivenie<\/strong> (camber) pom\u00e1ha z\u00edska\u0165 <em>C<sub>L<\/sub><\/em> pri ni\u017e\u0161om uhle n\u00e1behu, no zvy\u0161uje <em>C<sub>D<\/sub><\/em> \u2013 kompromis pod\u013ea za\u0165a\u017eenia disku.<\/li>\n<li><strong>Kr\u00fatenie<\/strong> (washout 8\u201315\u00b0 medzi kore\u0148om a \u0161pi\u010dkou) rozlo\u017e\u00ed uhol n\u00e1behu a posunie \u0165ah bli\u017e\u0161ie k stredu disku.<\/li>\n<li><strong>Drsnos\u0165\/\u201etrip\u201c<\/strong>: cie\u013eavedom\u00e9 zjemnenie alebo mikrodrsnos\u0165 v prednej tretine m\u00f4\u017ee premeni\u0165 nest\u00e1lu lamin\u00e1rnu vrstvu na stabilnej\u0161iu turbulentn\u00fa s ni\u017e\u0161\u00edm rizikom separ\u00e1cie.<\/li>\n<\/ul>\n<h2>R\u00e1m, ramen\u00e1 a interferencie: \u201efree-stream\u201c nie je zadarmo<\/h2>\n<p>Ramen\u00e1 r\u00e1mu vstupuj\u00fa do disku pr\u00fadenia a zvy\u0161uj\u00fa parazitn\u00fd odpor i nehomogenitu indukovan\u00e9ho po\u013ea. Efekty:<\/p>\n<ul>\n<li><strong>Tie\u0148ovanie prietoku<\/strong> pred listom \u2192 lok\u00e1lne zn\u00ed\u017eenie <em>Re<\/em>, kol\u00edsanie momentu, vibroakustick\u00e9 p\u00edky.<\/li>\n<li><strong>Interakcia v\u00edrov<\/strong> so \u0161pi\u010dkov\u00fdmi v\u00edrmi listov \u2192 zv\u00fd\u0161en\u00e9 \u0161pi\u010dky <em>C<sub>D<\/sub><\/em> a hluku.<\/li>\n<li><strong>Odpor\u00fa\u010dania<\/strong>: zaoblen\u00e9 profily ramien, orient\u00e1cia ramien pod uhlom k disku, ten\u0161ie ramen\u00e1 s pr\u00fadnicov\u00fdm obalom, v\u00e4\u010d\u0161\u00ed \u201earm offset\u201c od roviny listov.<\/li>\n<\/ul>\n<h2>\u0160k\u00e1lovanie: \u010do sa stane pri zmene priemeru a ot\u00e1\u010dok<\/h2>\n<ul>\n<li>Zv\u00e4\u010d\u0161enie <strong>D<\/strong> pri rovnakom \u0165ahu \u2192 men\u0161ie <em>W\/A<\/em>, ni\u017e\u0161\u00ed <em>v<sub>i<\/sub><\/em>, vy\u0161\u0161\u00ed <em>Re<\/em> (preto\u017ee <em>V \u221d r<\/em>), teda ni\u017e\u0161\u00ed <em>C<sub>D<\/sub><\/em> a lep\u0161\u00ed <em>\u03b7<\/em>.<\/li>\n<li>Zn\u00ed\u017eenie <strong>n<\/strong> pri zv\u00fd\u0161en\u00ed <strong>D<\/strong> (udr\u017eanie <em>T<\/em>) \u2192 men\u0161ia \u0161pi\u010dkov\u00e1 Machova hodnota, ni\u017e\u0161\u00ed hluk, men\u0161ie profilov\u00e9 straty.<\/li>\n<li>Limity: kr\u00fatiaci moment motora, pr\u00fad ESC, mechanick\u00e1 v\u00f4\u013ea a vibr\u00e1cie dlh\u0161\u00edch listov.<\/li>\n<\/ul>\n<h2>Typick\u00e9 rozsahy Re pre popul\u00e1rne priemery vrt\u00fa\u013e<\/h2>\n<table>\n<thead>\n<tr>\n<th>Priemer (palce)<\/th>\n<th>Re (stred polomeru) pri hoversk\u00fdch ot\u00e1\u010dkach<\/th>\n<th>Pozn\u00e1mka<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>2\u20133&#8243;<\/td>\n<td>1,0\u20132,5 \u00b7 10<sup>4<\/sup><\/td>\n<td>FPV mikr\u00e1; ve\u013emi citliv\u00e9 na drsnos\u0165 a presnos\u0165 tla\u010de<\/td>\n<\/tr>\n<tr>\n<td>5&#8243;<\/td>\n<td>2,0\u20136,0 \u00b7 10<sup>4<\/sup><\/td>\n<td>\u0160portov\u00e9\/FPV, vysok\u00e9 <em>C<sub>D<\/sub><\/em> pri agres\u00edvnych st\u00fapaniach<\/td>\n<\/tr>\n<tr>\n<td>7\u201310&#8243;<\/td>\n<td>6,0\u201312,0 \u00b7 10<sup>4<\/sup><\/td>\n<td>Filmov\u00e9\/long-range; zrete\u013en\u00e1 v\u00fdhoda 2-list\u00fdch vrt\u00fal pre \u00fa\u010dinnos\u0165<\/td>\n<\/tr>\n<tr>\n<td>12\u201313&#8243;<\/td>\n<td>1,2\u20132,0 \u00b7 10<sup>5<\/sup><\/td>\n<td>Mal\u00e9 \u201ecine-lift\u201c a mapovanie; bl\u00edzko hranice \u201estredn\u00fdch Re\u201c<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Dopredn\u00fd let: asymetria pr\u00fadenia a \u201eadvance ratio\u201c<\/h2>\n<p>V doprednom lete sa na list superponuje dopredn\u00e1 r\u00fdchlos\u0165 <em>V<sub>\u221e<\/sub><\/em>, \u010d\u00edm vznik\u00e1 asymetria n\u00e1be\u017enej r\u00fdchlosti medzi postupuj\u00facim a ustupuj\u00facim listom. Vhodn\u00e9 je definova\u0165 lok\u00e1lny bezrozmern\u00fd parameter <em>\u03bc = V<sub>\u221e<\/sub> \/ (\u03a9R)<\/em>. D\u00f4sledky v n\u00edzkom <em>Re<\/em>:<\/p>\n<ul>\n<li>Na ustupuj\u00facom liste kles\u00e1 lok\u00e1lne <em>Re<\/em> a sk\u00f4r nast\u00e1va separ\u00e1cia.<\/li>\n<li>Rast kr\u00fatiaceho momentu a v\u00fdkonu nad r\u00e1mec hovorov\u00e9ho <em>C<sub>P<\/sub><\/em> \u2013 profilov\u00e9 straty rast\u00fa prud\u0161ie ne\u017e indukovan\u00e9.<\/li>\n<li>Odpor\u00fa\u010danie: ni\u017e\u0161ie ot\u00e1\u010dky pri vy\u0161\u0161ej r\u00fdchlosti letu len do miery, k\u00fdm <em>\u03bc<\/em> nevyvol\u00e1 exces\u00edvnu asymetriu (<em>\u03bc \u2272 0,3<\/em> u multirotorov bez kolekt\u00edvu).<\/li>\n<\/ul>\n<h2>Stabilita, riadite\u013enos\u0165 a rezervy \u0165ahu v n\u00edzkom Re<\/h2>\n<ul>\n<li>Pre <strong>spo\u013eahliv\u00e9 riadenie<\/strong> potrebuje ka\u017ed\u00fd rotor rezervu \u0165ahu (Thrust-to-weight margin) aspo\u0148 30\u201340 % oproti hovorovej po\u017eiadavke \u2013 v n\u00edzkom <em>Re<\/em> inak r\u00fdchlo narast\u00fa uhly n\u00e1behu a\u017e k lok\u00e1lnej strate.<\/li>\n<li><strong>Diferenci\u00e1lny \u0165ah a moment<\/strong> pri yaw\/roll man\u00e9vroch \u010dasto pracuje v oblasti zhor\u0161en\u00e9ho <em>C<sub>L<\/sub>\/C<sub>D<\/sub><\/em>; prudk\u00e9 v\u00fdchylky zvy\u0161uj\u00fa <em>P<sub>0<\/sub><\/em> a zahrievaj\u00fa ESC.<\/li>\n<li><strong>Filtr\u00e1cia vstupov<\/strong> (slew rate limiter, \u201estabilized expo\u201c) zni\u017euje prepad \u00fa\u010dinnosti v prechodov\u00fdch javoch.<\/li>\n<\/ul>\n<h2>Meranie a valid\u00e1cia: \u010do sledova\u0165 na stolovom dynamometri<\/h2>\n<ul>\n<li><strong>Thrustometer<\/strong>: kontinu\u00e1lne meranie <em>T<\/em>, <em>P<\/em>, <em>n<\/em>, teploty motora a ESC.<\/li>\n<li><strong>Replik\u00e1cia Re<\/strong>: meranie pri rovnakom <em>n<\/em> a <em>D<\/em>, pr\u00edpadne korekcia na hustotu vzduchu (teplota, nadmorsk\u00e1 v\u00fd\u0161ka).<\/li>\n<li><strong>Polariz\u00e1cia listu<\/strong>: test s\u00e9rie uhlov n\u00e1behu (zmena st\u00fapania\/ot\u00e1\u010dok) pre z\u00edskanie <em>C<sub>L<\/sub>(\u03b1,Re)<\/em>, <em>C<sub>D<\/sub>(\u03b1,Re)<\/em> kriviek.<\/li>\n<li><strong>Drsnos\u0165<\/strong>: A\/B test s jemn\u00fdm prele\u0161ten\u00edm n\u00e1be\u017eky vs. zne\u010disten\u00fd list \u2013 rozdiel v <em>C<sub>P<\/sub><\/em> u mal\u00fdch vrt\u00fal m\u00f4\u017ee presiahnu\u0165 5\u201310 %.<\/li>\n<\/ul>\n<h2>Hluk a v\u00edrov\u00e1 \u0161trukt\u00fara pri n\u00edzkych Re<\/h2>\n<p>Akustick\u00fd v\u00fdkon s\u00favis\u00ed s tlakov\u00fdmi pulz\u00e1ciami a \u0161pi\u010dkov\u00fdmi v\u00edrmi. V n\u00edzkych <em>Re<\/em> sa pri vy\u0161\u0161\u00edch uhloch n\u00e1behu objavuj\u00fa nestabiln\u00e9 separa\u010dn\u00e9 kmity, ktor\u00e9 zvy\u0161uj\u00fa tonalitu. N\u00e1stroje zni\u017eovania hluku:<\/p>\n<ul>\n<li>Ni\u017e\u0161ie ot\u00e1\u010dky, v\u00e4\u010d\u0161\u00ed priemer, ni\u017e\u0161ia sol\u00eddnos\u0165.<\/li>\n<li>Skosen\u00e9 a \u201eanti-singing\u201c hrany, drobn\u00e9 z\u00fabkovanie odtokovky (kompromis s \u00fa\u010dinnos\u0165ou).<\/li>\n<li>Vyhladenie prietoku okolo ramien r\u00e1mu a vzdialenie roviny listu od prek\u00e1\u017eok.<\/li>\n<\/ul>\n<h2>Dopady na energetick\u00fa bilanciu a n\u00e1vrh pohonu<\/h2>\n<ul>\n<li><strong>Motor<\/strong>: vybera\u0165 s dostato\u010dn\u00fdm kr\u00fatiacim momentom pri ni\u017e\u0161\u00edch ot\u00e1\u010dkach (vy\u0161\u0161\u00ed <em>K<sub>t<\/sub><\/em>, ni\u017e\u0161\u00ed <em>K<sub>v<\/sub><\/em>), aby umo\u017enil v\u00e4\u010d\u0161\u00ed priemer bez satur\u00e1cie pr\u00fadu.<\/li>\n<li><strong>ESC<\/strong>: vy\u0161\u0161ia sp\u00ednacia frekvencia zjem\u0148uje momentov\u00e9 vlny (lep\u0161ie pre 2-list\u00e9), no zvy\u0161uje sp\u00ednacie straty \u2013 kompromis pod\u013ea teploty.<\/li>\n<li><strong>Bat\u00e9ria<\/strong>: men\u0161ie pr\u00fadov\u00e9 \u0161pi\u010dky pri v\u00e4\u010d\u0161\u00edch vrtuliach a ni\u017e\u0161\u00edch ot\u00e1\u010dkach zlep\u0161uj\u00fa nap\u00e4\u0165ov\u00fa stabilitu a zni\u017euj\u00fa \u201evoltage sag\u201c.<\/li>\n<\/ul>\n<h2>Praktick\u00e9 odpor\u00fa\u010dania pre multirotory v n\u00edzkych Re<\/h2>\n<ol>\n<li>Zv\u00e4\u010d\u0161ite disk a zn\u00ed\u017ete ot\u00e1\u010dky, pokia\u013e to dovo\u013euje platforma (r\u00e1m, motory, ESC).<\/li>\n<li>Preferujte 2-list\u00e9 vrtule pre maxim\u00e1lnu \u00fa\u010dinnos\u0165 v hovore; 3-list\u00e9 pou\u017e\u00edvajte tam, kde treba kontrolu v poryvoch alebo limitovan\u00fd priemer.<\/li>\n<li>Vo\u013ete profily a povrch s n\u00edzkou drsnos\u0165ou; kontrolujte a pravidelne me\u0148te opotrebovan\u00e9 vrtule.<\/li>\n<li>Optimalizujte kr\u00fatenie a rozlo\u017eenie h\u013abky <em>c(r)<\/em> pre rovnomern\u00fd <em>Re(r)<\/em> a oneskoren\u00fa separ\u00e1ciu.<\/li>\n<li>Minimalizujte interferencie r\u00e1mu s diskami \u2013 tvar ramien, offsety, pr\u00fadnicov\u00e9 kryty.<\/li>\n<li>Kalibrujte model (BEMT) na vlastn\u00e9 merania; univerz\u00e1lne polary z \u201eve\u013ek\u00fdch Re\u201c ved\u00fa k systematick\u00fdm chyb\u00e1m.<\/li>\n<\/ol>\n<h2>Uk\u00e1\u017ekov\u00fd v\u00fdpo\u010det: vplyv priemeru na po\u017eadovan\u00fd v\u00fdkon v hovore<\/h2>\n<p>Pre rovnak\u00fd \u0165ah <em>T<\/em> na rotor a hustotu <em>\u03c1<\/em> porovnajme dva disky D<sub>1<\/sub> a D<sub>2<\/sub> (&gt; D<sub>1<\/sub>):<\/p>\n<div> <em>P<sub>i<\/sub> = T \u00b7 \\sqrt{\\dfrac{T}{2 \u03c1 A}}<\/em> &nbsp;\u2192&nbsp; <em>P<sub>i,2<\/sub> \/ P<sub>i,1<\/sub> = \\sqrt{A<sub>1<\/sub> \/ A<sub>2<\/sub>} = D<sub>1<\/sub> \/ D<sub>2<\/sub><\/em> <\/div>\n<p>Ak sa z\u00e1rove\u0148 zv\u00fd\u0161i lok\u00e1lne <em>Re<\/em> a klesne <em>C<sub>D<\/sub><\/em>, zn\u00ed\u017ei sa aj <em>P<sub>0<\/sub><\/em>. Typicky mo\u017eno o\u010dak\u00e1va\u0165 <strong>\u00fasporu 10\u201325 % celkov\u00e9ho v\u00fdkonu<\/strong> pri prechode napr. z 5&#8243; na 7&#8243; vrtule pri spr\u00e1vnom preladen\u00ed ot\u00e1\u010dok a motora.<\/p>\n<h2>Tabu\u013eka: \u201er\u00fdchly n\u00e1vrhov\u00fd kompas\u201c pre n\u00edzke Re<\/h2>\n<table>\n<thead>\n<tr>\n<th>Cie\u013e<\/th>\n<th>Zmena<\/th>\n<th>Efekt na C<sub>L<\/sub>\/C<sub>D<\/sub><\/th>\n<th>Rizik\u00e1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Vy\u0161\u0161ia \u00fa\u010dinnos\u0165 v hovore<\/td>\n<td>V\u00e4\u010d\u0161\u00ed D, ni\u017e\u0161ie n, 2-list\u00e9<\/td>\n<td>\u2191 Re, \u2193 C<sub>D<\/sub>, \u2193 P<sub>i<\/sub><\/td>\n<td>V\u00e4\u010d\u0161\u00ed moment, vy\u0161\u0161ie n\u00e1roky na r\u00e1m<\/td>\n<\/tr>\n<tr>\n<td>Stabilita v poryvoch<\/td>\n<td>3-list\u00e9, mierne vy\u0161\u0161ia sol\u00eddnos\u0165<\/td>\n<td>Lep\u0161ie rozlo\u017eenie \u0165ahu<\/td>\n<td>\u2193 \u03b7 o 2\u20135 %, vy\u0161\u0161\u00ed hluk<\/td>\n<\/tr>\n<tr>\n<td>Ni\u017e\u0161\u00ed hluk<\/td>\n<td>Ni\u017e\u0161ie n, v\u00e4\u010d\u0161\u00ed D, tich\u0161ie hrany<\/td>\n<td>Menej ton\u00e1lnych p\u00edkov<\/td>\n<td>Mo\u017en\u00e1 rezonancia dlh\u00fdch listov<\/td>\n<\/tr>\n<tr>\n<td>Kontrola tepl\u00f4t<\/td>\n<td>Ni\u017e\u0161ie pr\u00fadov\u00e9 \u0161pi\u010dky<\/td>\n<td>Men\u0161\u00ed P<sub>0<\/sub> a straty v ESC<\/td>\n<td>Nutn\u00e9 doladi\u0165 PID\/filtr\u00e1ciu<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Zhrnutie: navrhujte pre re\u017eim, v ktorom skuto\u010dne lietate<\/h2>\n<p>Multirotory tr\u00e1via v\u00e4\u010d\u0161inu \u010dasu v hovorovo-doprednom prechode a operuj\u00fa v n\u00edzkych Reynoldsov\u00fdch \u010d\u00edslach. Preto sa oplat\u00ed optimalizova\u0165 <strong>geometriu vrtule, diskov\u00fa z\u00e1\u0165a\u017e, ot\u00e1\u010dky a r\u00e1m<\/strong> pr\u00e1ve pre tento re\u017eim, nie pre ide\u00e1lne \u201eve\u013ek\u00e9-Re\u201c krivky. V\u00e4\u010d\u0161\u00ed disk s ni\u017e\u0161\u00edmi ot\u00e1\u010dkami, kvalitn\u00fd povrch listov, spr\u00e1vne kr\u00fatenie a minimalizovan\u00e9 interferencie r\u00e1mu s\u00fa najistej\u0161ie cesty k vy\u0161\u0161iemu <em>C<sub>L<\/sub>\/C<sub>D<\/sub><\/em>, dlh\u0161iemu letu a ni\u017e\u0161iemu hluku.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>V n\u00edzkych Reynoldsov\u00fdch \u010d\u00edslach dominuje indukovan\u00fd odpor. Presn\u00e9 modely a valid\u00e1cia na stojane \u010di v tuneli zlep\u0161ia predikciu \u0165ahu a \u00fa\u010dinnosti.<\/p>\n","protected":false},"author":46,"featured_media":88624,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2629],"tags":[2114,2115,2116,2117,2118,2119,2120],"class_list":["post-48624","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-drony","tag-disko-zatazenie","tag-indukovany-odpor","tag-modely","tag-nizke-reynolds","tag-prudnice","tag-validacia","tag-vztlak-a-odpor-multirotorov"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Aerodynamika multirotorov: Anal\u00fdza vztlaku a parazitick\u00e9ho odporu pri n\u00edzkych Reynoldsov\u00fdch \u010d\u00edslach - Podnik\u00e1m, lietam a relaxujem<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.vrtulniky.sk\/news\/aerodynamika-multirotorov-analyza-vztlaku-a-parazitickeho-odporu-pri-nizkych-reynoldsovych-cislach\/\" \/>\n<meta property=\"og:locale\" content=\"sk_SK\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Aerodynamika multirotorov: Anal\u00fdza vztlaku a parazitick\u00e9ho odporu pri n\u00edzkych Reynoldsov\u00fdch \u010d\u00edslach - Podnik\u00e1m, lietam a relaxujem\" \/>\n<meta property=\"og:description\" content=\"V n\u00edzkych Reynoldsov\u00fdch \u010d\u00edslach dominuje indukovan\u00fd odpor. 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