I-rocket equation ne-delta-v

Ngo-1903 umfundi wesikole esiphuthumayo e Kaluga, Konstantin Tsiolkovsky, wabhala phansi i-equation ethi ingabe isize yonke i-rocket. Kuchaza ukuthi kungani i-Falcon 9 iqukethe amaphesenti angama-89 wezinto ezihamba phambili, kungani ubunzima obuyingxenye encane kuphela yobunzima uma kuqashwa, nokuthi kungani izimoto zishiya izingxenye zazo ngendlela.

Yonke i-rocket iyimpi phakathi kwejubane ofuna ukuyithola nenani lobunzima odinga ukulithwa ukuze uyithole.

Bona

I-rocket ihamba ngokushaya umthwalo emuva. Thola ngokushesha, noma thola kaningi, bese uhamba ngokushesha. Kukhona iphutha: uphethiloli ongawushisayo kufanele futhi uthunyelwe futhi ukhawulelwe. Lokhu kwenza ukuthi ufinyelele ku logarithmic: ukungeza inani elifanayo lejubane futhi, kufanele uphinde uphinda igesi, hhayi ukuyingeza.

Delta-v (Δv, “ushintsho kwijubane”) yimali yendiza yangaphandle. Umsebenzi ngamunye unentengo ekm/s:

• Isimo sezulu somhlaba ku-orbit ephansi: cishe amakhilomitha angu-9.4/s, kufaka phakathi ukulahleka.
• I-orbit ephansi ukuya ku-geostationary orbit: cishe amakhilomitha angama-3.9/s.
• I-orbit ephansi yokushiya iplanethi ye-Mars: cishe amakhilomitha angama-3.6/s.

Imali yohlelo lwe-rocket yilokho okuningi Δv ama-engine ayo, igesi nesisindo singanikeza.

Ukuqonda

Δv = I_sp · g₀ · ln(m₀ / m_f)

• I_sp: i-impulse ekhethekile, ukuhlolwa kwempumelelo yenjini ngemizuzu (ukushesha kokuphuma okuhlukaniswe yi-g₀).
• g₀ = 9.80665 m/s², ukunyakaza okujwayelekile.
• m₀: isisindo ekuqaleni kokuqhuma; m_f: isisindo esiphethweni.

Umzekelo ngesigaba sesithathu se-rocket efana ne-simulated (Isp 348 s): igcwele, isisindo sayo siyi-112 tons kuhlanganise nobunzima obungu-15 tons; akukho lutho lwe-propellant, cishe ama-19 tons. Δv = 348 × 9.81 × ln(112 / 19) ≈ 6.0 km/s. Isikhashana sokuqala sihlanganisa isikhala.

Isigaba esisodwa nenani lesisindo se-10 kanye ne-Isp 350 s inikeza kuphela ama-7.9 km / s, akwanele ukujikeleza lapho ukulimala kubhekwa khona, futhi isakhiwo esingu-10% kuphela kokubili sikhanya kakhulu. Lokhu kusho ukuthi cishe wonke i-orbital rocket isebenzisa amasigaba amabili noma ngaphezulu.

Umphathi

Ukuhlela kwenza kube ngama-ratio aphezulu. Imoto esezingeni elimibili,

Δv_total = I₁ g₀ ln(m₁₁/m_f₁) + I₂ g₀ ln(m₁₂/m_f₂)

lapho isiqephu sesibili sokuqala ubunzima bengxenye engaphandle konke okuthunyelwe yisigaba sokuqala. Ukuthuthukisa ukuhlukaniswa phakathi kwesigaba (nge-Isp elinganayo, cishe ilingana Δv ngesigaba) kuyinkinga ejwayelekile: ungxenye yokufaka impahla iphansi ngokuqhubekayo ne-Δv edingekayo, ngakho-ke ukwehlisa i-Δv ku-orbit ngamaphesenti ambalwa m / s (ukuqashwa emaphakathi, eduze kwe-equator) kubaluleke kakhulu.

I-equation ichaza futhi umbono wesigaba sokuqala esisebenzisekayo: babuyela emuva besebenzisa isithako esingesabi ukuthuthwa, bethengisa amaphesenti ambalwa esisindo sokuthuthwa ukuze bangathuthi ingxenye ebiza kakhulu ye-rocket.