User:AKAF/Equations From Wikipedia, the free encyclopedia in the form of the Breguet range formula Π f = 1 − e x p [ − g 0 R η 0 h P R ( 1 − ϕ e ) C L C D ] {\displaystyle \Pi _{f}=1-exp\left[-{\frac {g_{0}R}{\eta _{0}h_{PR}\left(1-\phi _{e}\right){\frac {C_{L}}{C_{D}}}}}\right]} d m m = − ( d ( V 2 2 ) + g d r g 0 I s p V ( 1 − D + D e F ) ) {\displaystyle {\frac {dm}{m}}=-\left({\frac {d\left({\frac {V^{2}}{2}}\right)+gdr}{g_{0}I_{sp}V\left(1-{\frac {D+D_{e}}{F}}\right)}}\right)} d m m = − ( d ( V 2 2 ) + g d r η 0 h P R ( 1 − D + D e F ) ) {\displaystyle {\frac {dm}{m}}=-\left({\frac {d\left({\frac {V^{2}}{2}}\right)+gdr}{\eta _{0}h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)}}\right)} η 0 = g 0 r 0 ( 1 − 1 2 r 0 r ) h P R ( 1 − D + D e F ) ln ( 1 Π e + 1 Γ ) {\displaystyle \eta _{0}={\frac {g_{0}r_{0}\left(1-{\frac {1}{2}}{\frac {r_{0}}{r}}\right)}{h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)\ln \left({\frac {1}{\Pi _{e}+{\frac {1}{\Gamma }}}}\right)}}} η 0 = g 0 r 0 ( 1 − 1 2 r 0 r ) h P R ( 1 − D + D e F ) ln ( 1 1 − Π f ) {\displaystyle \eta _{0}={\frac {g_{0}r_{0}\left(1-{\frac {1}{2}}{\frac {r_{0}}{r}}\right)}{h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)\ln \left({\frac {1}{1-\Pi _{f}}}\right)}}} I s p = g 0 r 0 g 0 ( 1 − D + D e F ) ln ( 1 1 − Π f ) {\displaystyle I_{sp}={\frac {\sqrt {g_{0}r_{0}}}{g_{0}\left(1-{\frac {D+D_{e}}{F}}\right)\ln \left({\frac {1}{1-\Pi _{f}}}\right)}}} η 0 = g 0 V 0 h P R ⋅ I s p = Thrust Power Chemical energy rate {\displaystyle \eta _{0}={\frac {g_{0}V_{0}}{h_{PR}}}\cdot I_{sp}={\frac {\mbox{Thrust Power}}{\mbox{Chemical energy rate}}}} Π f = 1 − e x p [ − ( V i n i t i a l 2 2 − V i 2 2 ) + ∫ g d r η 0 h P R ( 1 − D + D e F ) ] {\displaystyle \Pi _{f}=1-exp\left[-{\frac {\left({\frac {V_{initial}^{2}}{2}}-{\frac {V_{i}^{2}}{2}}\right)+\int {g}\,dr}{\eta _{0}h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)}}\right]} Π f = 1 − e x p [ − g 0 r 0 ( 1 − 1 2 r 0 r ) η 0 h P R ( 1 − D + D e F ) ] {\displaystyle \Pi _{f}=1-exp\left[-{\frac {g_{0}r_{0}\left(1-{\frac {1}{2}}{\frac {r_{0}}{r}}\right)}{\eta _{0}h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)}}\right]} Π f = 1 − e − B R {\displaystyle \Pi _{f}=1-e^{-BR}} B = g 0 η 0 h P R ( 1 − ϕ e ) C L C D {\displaystyle B={\frac {g_{0}}{\eta _{0}h_{PR}\left(1-\phi _{e}\right){\frac {C_{L}}{C_{D}}}}}} Related Articles
![{\displaystyle \Pi _{f}=1-exp\left[-{\frac {g_{0}R}{\eta _{0}h_{PR}\left(1-\phi _{e}\right){\frac {C_{L}}{C_{D}}}}}\right]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/3a3bf38d85b8d4a4c4c2f6eaa6795455806da3bf)
![{\displaystyle \Pi _{f}=1-exp\left[-{\frac {\left({\frac {V_{initial}^{2}}{2}}-{\frac {V_{i}^{2}}{2}}\right)+\int {g}\,dr}{\eta _{0}h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)}}\right]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/4cb2cc5885bf77250e71e8fdf0bcec3ef2dc7751)
![{\displaystyle \Pi _{f}=1-exp\left[-{\frac {g_{0}r_{0}\left(1-{\frac {1}{2}}{\frac {r_{0}}{r}}\right)}{\eta _{0}h_{PR}\left(1-{\frac {D+D_{e}}{F}}\right)}}\right]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/d5ebeb0c81f4ff10d577ea326585360c9bc9246f)
