I-rocket equation ne delta-v

Ngo1903 umfundi wesikolo esibi e Kaluga, uKonstantin Tsiolkovsky, wabhala phantsi i-equation eyaqhubeka isize yonke i-rocket. It explains why a Falcon 9 is about 89% propellant, why the payload is only a few per cent of the weight at liftoff, and why rockets drop parts of themselves on the way up.

Yonke i-rocket yimpi phakathi kwesantya ofunayo kunye nesisindo kufuneka uthwale ukusifumana.

Bona

I-rocket ihamba ngokutsala umthwalo ezantsi. Uyithule ngokukhawuleza, okanye uyithule ngaphezulu, kwaye uhambe ngokukhawuleza. Kukho i-catch: umbane owawungatshisiyo kufuneka uthunyelwe kwaye ukhawulezwe. Oku kwenza ukuba ifike i-logarithmic: ukudibanisa kwakhona inani elifanayo lesantya, kufuneka uphinde uphindaphindwe ifuthe, hayi ukudibanisa kuyo.

Delta-v (Δv, “utshintsho kwisantya”) yimali yexesha lokubhabha elwandle. Ukuhamba ngalinye linexabiso kwi km/s:

• Umhlaba wehlabathi ukuya kwi-orbit ephantsi: malunga ne9.4 km/s, kubandakanya ilahleko.
• I-orbit ephantsi ukuya kwi-orbit yendawo ehlala kuyo i-geostationary: malunga ne-3.9 km/s.
• Umjikelo ophantsi wokuphuma emhlabeni ukuya eMars: malunga ne-3.6 km/s.

Imali yorhwebo lweroketi yiyo yonke i-Δv yenjini yayo, umbane kunye nesisindo esikwazi ukunikela.

Ukuqonda

Δv = I_sp · g₀ · ln(m₀ / m_f)

• I_sp: i-impulse ekhethekileyo, uvavanyo lokusebenza kakuhle kwenjini ngemizuzwana (ukhawuleziso lwesithuthi esiphumayo sihlukaniswe yi g₀).
• g₀ = 9.80665 m/s², ubunzima bendalo obuqhelekileyo
• m₀: isisindo kwisiqalo sokutsha; m_f: isisindo esiphelweni.

Umzekelo ngenqanaba lesithathu le-rocket efana ne-Isp 348 s): igcwele, izitotywe malunga neetoni ezili-112 kubandakanya umthwalo ophezulu we-15 ton; engenanto yezinto eziqhubayo, malunga neetoni ezili-19. Δv = 348 × 9.81 × ln (112/19) ≈ 6.0 km/s. Inqanaba lokuqala lidibanisa elona xesha liseleyo.

Inqanaba elinye elinamacala amaninzi angama-10 kunye ne-Isp 350 s linika kuphela i7.9 km/s, akwanelanga ukuba kujikelezwe xa ulahleko lubalolwe, kwaye isakhiwo esingu-10% kuphela kobungakanani bonke sele sikhanya kakhulu. Le nto ibangela ukuba i-rocket ejikelezayo yonke isebenzise iziqendu ezimbini okanye ngaphezulu.

Umphathi

Ukubekwa phantsi kuphindaphindwa ubungakanani bezinto. Kwisithuthi senqanaba elinye,

Δv_total = I₁ g₀ ln(m₁/m_f₁) + I₂ g₀ ln(m₁₂/m_f₂)

apho inqanaba lesithathu eliqalayo lisusa konke inqanaba lokuqala lalibalisa. Ukunyusa uhlukaniso phakathi kweenkqubo (kwi-Isp elinganayo, malunga ne-Δv elinganayo ngenkqubo nganye) yingxaki eqhelekileyo: ubunzima bokuthuthwa buhla ngokuqhubekayo kunye ne-Δv efunekayo, leyo yintoni na ukunyusela iΔv kwimo yelanga ngamawaka amabini ambalwa m/s (ukuqalisa umntla, kufutshane ne-equator) kungenxa yokuba.

I-equation ichaza kwakhona umbono wokuphinda zisetyenziswe iziqendu zokuqala: ziya kuhamba zisebenzisa ifuthe elinokuthi lisebenze njengento enamandla, zirhweba ngeepesenti ezimbalwa zezinto ezinamandla ukuba zingathuthi indawo ebiza kakhulu yerocket.