JIRGI MARA MATUƘI MAI ƊAUKE DA KAYA YA KAMATA YA ƘARA GUDU

Jirage marasa matuƙi masu fanka masu juyawa da yawa (multirotor drones) suna ɗaukar hoto, suna duba abubuwa (inspection), suna yin safiyo (survey) kuma, ƙara-ƙara, suna isar da kunshi. Raunin su shi ne juriya (endurance): lokacin tashinsu yawanci kusan minti 30 ne. Don haka kowane ɗan makamashi da aka adana a lokacin tafiya a sama (cruise flight) yana ƙara nisan da za su iya kaiwa.

Ma’aunin da ya dace shi ne makamashin da ake kashewa a kowace mita da aka yi tafiya. Idan aka tashi a hankali sosai, rotors suna kashe ƙarfin aikinsu (power) kawai wajen riƙe jirgin a sama na dogon lokaci; idan aka tashi da sauri sosai, ja da baya (drag) na jikin jirgin ne ke rinjaye. A tsakani akwai saurin da ya fi tattalin makamashi (energy-optimal speed). Binciken baya sun lura cewa wannan mafi kyawun sauri yana ƙaruwa idan jirgi ya ɗauki ƙarin kaya — amma babu wanda ya fitar da ƙa’idar.

Dokoki uku daga daidaito (symmetry) ɗaya

Ayush Patnaik, Nicolas Michel da Xinfan Lin, a University of California, Davis, tare da Leonard Bauersfeld da Davide Scaramuzza na University of Zurich, sun yi samfurin jirgi mara matuƙi a tsayayyiyar tafiya ta kwance: ƙarfin (forces) da ke kan jikinsa, kwararar iska ta cikin kowane fanka (propeller), ƙarfin aiki (power) da rotors ke ja. Sannan suka sauya nauyi (mass) kawai — firam ɗaya, siffa ɗaya, rotors iri ɗaya, kamar lokacin da aka ƙara kaya — kuma suka gano dokoki uku:

1. saurin da ya fi tattalin makamashi yana girma da tushen murabba’i na nauyi;
2. kusurwar sunkuyawa (pitch angle) da jirgin ke karkata gaba don tashi da wannan sauri ba ta sauyawa da nauyi;
3. mafi ƙarancin makamashi a kowace mita yana daidai gwargwado da nauyi (proportional).

Dukkansu uku sun fito daga wata siffa ɗaya. Idan aka ninka nauyi da wani adadi k, dole a ninka kowane ƙarfi (force) da k. Amma kowane ƙarfin iska (aerodynamic force) — ja da baya na jiki, turawar rotor (thrust) da murɗewa (torque) — yana girma da murabba’in sauri. Don haka ninka kowane sauri da √k yana yin aikin, yayin da kowace kusurwa ke zama iri ɗaya. A kalaman marubutan, ababen hawa masu nauyi suna tashi ta cikin kwararar iska mai kama da juna a siffa (geometrically similar), kawai da sauri. Ƙarfin aiki (power), wato ƙarfi sau sauri, sai ya girma kamar nauyi da aka ɗaga zuwa exponent 1.5; raba shi da sauri, kuma makamashi a kowace mita yana girma daidai da nauyi.

A cikin kwaikwayon kwamfuta (simulations) na marubutan, jirgi mai nauyin kilogram 8 yana da mafi kyawun saurinsa a mita 14.0 a kowace daƙiƙa; a kilogram 12, 17.2; a kilogram 16, 19.8. Raba kowanne da tushen murabba’i na nauyin, kuma lamba ɗaya, 4.95, tana fitowa kowane lokaci. Mafi kyawun karkacewa yana tsayawa a digiri 15.4, makamashi a kowace mita da kowane kilogram kuma a joule 6.2.

An gwada a fili

Ƙungiyar ta tashi jirage biyu na gaske a wani filin jiragen sama na samfuri (model-aircraft field) kusa da Davis: jirgi mai rotors takwas a kilogram 7, 8 da 9 (ƙarin nauyi 29%), da jirgi mai rotors huɗu a nauyi biyar daga kilogram 3.58 zuwa 5.17 (ƙarin 44%). An ɗora ƙarin kayan a dunƙule don kada ya sauya siffar jirgin. Kowane sauri an tashi da shi gaba da baya a kan madaidaiciyar hanya don daidaita tasirin iska (wind).

Jirgin gwaji mai rotors takwas, a ƙasa da kuma a tsayayyiyar tafiya ta kwance. — Hoto na 1a, Patnaik da abokan aiki (2026), arXiv:2611.04748.

Da zarar an raba sauri da tushen murabba’i na nauyi, ƙarfin aiki kuma da nauyi da aka ɗaga zuwa exponent 1.5, ma’aunan dukkan nauyin suna faɗawa a kan lanƙwasa na bai ɗaya, cikin ’yan kashi kaɗan. Ga jirgi mai rotors takwas, mafi kyawun karkacewa ya bambanta da digiri 0.84 kawai a cikin sauyin nauyi na 29%, kuma mafi kyawun sauri da aka raba da tushen murabba’i na nauyi, kamar mafi ƙarancin makamashi a kowace mita da kowane kilogram, ya bambanta ƙasa da 2% daga wani nauyi zuwa wani. Ga kaya uku mafi nauyi na jirgi mai rotors huɗu, saurin da ya fi tattalin makamashi ya wuce abin da jirgin zai iya tashi da shi, don haka an tantance mafi kyawun wurin (optimum) a cikin tsare-tsare biyar daga cikin takwas.

Daga dokoki zuwa tsare-tsaren isar da kaya

Ribar aiki nan take take. A auna ko a lissafa mafi kyawun sauri sau ɗaya, a nauyi ɗaya; ga kowane nauyi, kawai a ninka da tushen murabba’i na rabon nauyin (mass ratio). Kuma a wannan mafi kyawun sauri, makamashin wani ɓangare na tafiya adadi tsayayye ne sau jimillar nauyi sau nisa — abin da ke mayar da tsara zagayen isar da kaya, wa ke ɗaukar me kuma ta wace hanya, zuwa matsala mai sauƙi ta layi (linear problem). Mafi girman nisan tafiya (range) yana biyo baya kai tsaye daga makamashin batirin.

Marubutan sun ƙara gargaɗi: samfuran makamashi da dama da ake amfani da su suna ɗauka cewa makamashi a kowace mita yana girma da nauyi a kowane sauri. Ba haka ba ne. Daidaiton gwargwado mai sauƙi yana aiki a mafi kyawun sauri kawai.

Dokokin suna ɗauka tsayayyiyar tafiya, kayan da ke sauya nauyi amma ba siffa ko daidaiton (balance) jirgin ba, da injuna da batura waɗanda ingancinsu (efficiency) ke zama kusan tsayayye. A cikin waɗannan iyakoki, jirgi mara matuƙi mai nauyi bai kamata ya rage gudu don adana makamashi ba, sai dai ya karkata gaba iri ɗaya ya ƙara gudu.