Rocket Engine Thrust Formula |
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\( T \;=\; \dot m_f \cdot v_e +[\; \left( p_e - p_a \right) \cdot A_c \;] \) (Rocket Engine Thrust) \( \dot m_f \;=\; \dfrac{ T - \left( p_e - p_a \right) \cdot A_c }{ v_e } \) \( v_e \;=\; \dfrac{ T - \left( p_e - p_a \right) \cdot A_c }{ \dot m_f } \) \( p_e \;=\; \dfrac{ T - \dot m_f \cdot v_e + p_a \cdot A_c }{ A_c } \) \( p_a \;=\; p_e - \dfrac{ T - \dot m_f \cdot v_e }{ A_c } \) \( A_c \;=\; \dfrac{ T - \dot m_f \cdot v_e }{ p_e - p_a } \) |
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| Symbol | English | Metric |
| \( T \) = Thrust (Force) | \( lbf \) | \(N\) |
| \( \dot m_f \) = Mass Flow Rate of Exaust Gases | \(lbm / sec\) | \(kg / s\) |
| \( v_e \) = Exhaust Velocity of the Gases Related to the Rocket | \(ft / sec\) | \(m / s\) |
| \( p_e \) = Pressure of Exhaust Gases at Exit of Rocket Nozzle | \(lbf / in^2\) | \(Pa\) |
| \( p_a \) = Ambient Pressure Outside of Rocket Nozzle | \(lbf / in^2\) | \(Pa\) |
| \( A_c \) = Exit Area Cross-section of the Rocket Nozzle | \(ft^2\) | \(m^2\) |
Thrust is the force that propels an object forward by pushing against a medium, such as air or water, or by expelling mass in the opposite direction. It is most commonly associated with the motion of vehicles like airplanes, rockets, and boats. In essence, thrust is the reaction force described by Newton's Third Law of Motion: for every action, there is an equal and opposite reaction. The magnitude of thrust depends on factors like the mass of the expelled material and the speed at which it is ejected, making it a critical factor in designing efficient propulsion systems. In everyday terms, thrust is what gets things moving, whether it’s a plane slicing through the sky or a swimmer kicking through water.- Mechanical Thrust - Generated by physically pushing against a medium, e.g., oars in water or wings flapping in air.
- Jet Thrust - Produced by jet engines (turbojets, turbofans) expelling high-speed exhaust gases, common in aircraft.
- Rocket Thrust - Created by expelling combustion gases from onboard fuel and oxidizer, used in rockets and spacecraft, independent of external mediums.
- Propulsive Thrust (Propeller) - Generated by rotating blades pushing air or water backward, as in propeller-driven planes or boats.
- Electromagnetic Thrust - Found in ion thrusters for spacecraft, where charged particles are accelerated to produce a small, efficient force.
- Biological Thrust - Seen in nature like squid using jet propulsion by ejecting water to move.
- Each type is suited to specific environments and purposes, varying in efficiency and power.
Rocket Engine Thrust Formula |
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\( T \;=\; \dot m_f \cdot v_e +[\; \left( p_e - p_a \right) \cdot A_c \;] \) (Rocket Engine Thrust) \( \dot m_f \;=\; \dfrac{ T - \left( p_e - p_a \right) \cdot A_c }{ v_e } \) \( v_e \;=\; \dfrac{ T - \left( p_e - p_a \right) \cdot A_c }{ \dot m_f } \) \( p_e \;=\; \dfrac{ T - \dot m_f \cdot v_e + p_a \cdot A_c }{ A_c } \) \( p_a \;=\; p_e - \dfrac{ T - \dot m_f \cdot v_e }{ A_c } \) \( A_c \;=\; \dfrac{ T - \dot m_f \cdot v_e }{ p_e - p_a } \) |
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| Symbol | English | Metric |
| \( T \) = Thrust (Force) | \( lbf \) | \(N\) |
| \( \dot m_f \) = Mass Flow Rate of Exaust Gases | \(lbm / sec\) | \(kg / s\) |
| \( v_e \) = Exhaust Velocity of the Gases Related to the Rocket | \(ft / sec\) | \(m / s\) |
| \( p_e \) = Pressure of Exhaust Gases at Exit of Rocket Nozzle | \(lbf / in^2\) | \(Pa\) |
| \( p_a \) = Ambient Pressure Outside of Rocket Nozzle | \(lbf / in^2\) | \(Pa\) |
| \( A_c \) = Exit Area Cross-section of the Rocket Nozzle | \(ft^2\) | \(m^2\) |
Jet/Vehicle Engine Thrust Formula |
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\( T \;=\; \dot m_f \cdot ( v_e - v_a ) \) (Jet/vehicle Engine Thrust) \( \dot m_f \;=\; \dfrac{ T }{ v_e - v_a }\) \( v_e \;=\; \dfrac{ T }{ \dot m_f } + v_a \) \( v_a \;=\; v_e - \dfrac{ T }{ \dot m_f } \) |
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| Symbol | English | Metric |
| \( T \) = Thrust (Force) | \( lbf \) | \(N\) |
| \( \dot m_f \) = Mass Flow Rate of Air Through the Engine | \(lbm / sec\) | \(kg / s\) |
| \( v_e \) = Exhaust Velocity of the Gases Related to the Engine | \(ft / sec\) | \(m / s\) |
| \( v_a \) = Velocity of Aircraft (or Vehicle) Related to the Surrounding Air | \(ft / sec\) | \(m / s\) |