Thrust

on . Posted in Classical Mechanics

Thrust or thrust force, abbreviated as T, is a term used in physics and engineering to describe the force that propels an object forward.  It is commonly associated with propulsion systems, such as those used in rockets, jet engines, and other vehicles.

Thrust Index

Thrust is generated by expelling or accelerating a mass of fluid or gas in the opposite direction to the desired motion.  According to Newton's third law of motion, for every action, there is an equal and opposite reaction.  In the case of thrust, the action is the expulsion or acceleration of the fluid or gas, and the reaction is the force that propels the object forward.  The magnitude of thrust depends on various factors, including the mass flow rate of the expelled fluid or gas and its velocity relative to the vehicle.  The design and efficiency of the propulsion system also play a significant role in determining the amount of thrust generated.

In rockets, thrust is generated by expelling high speed exhaust gases produced by the combustion of rocket propellant.  Jet engines, on the other hand, generate thrust by drawing in air, compressing it, and then expelling it at high speed through a nozzle.  In both cases, the expelled mass creates a reaction force that propels the vehicle forward.

These formulas provide the basic framework for calculating thrust, but in practice, various factors such as air density, temperature, pressure, and engine efficiency need to be considered for accurate calculations.  Additionally, different types of engines may have variations in their specific thrust formulas.

Thrust formula

$$T \;=\; v \; ( dm \;/\; dt )$$     (Thrust)

$$v \;=\; T \; dt \;/\; dm$$

$$dm \;=\; T \; dt \;/\; v$$

$$dt \;=\; v \; dm \;/\; T$$

Symbol English Metric
$$T$$ = thrust $$lbf$$  $$N$$
$$v_e$$ = exhaust velocity relative to the rocket of jet $$ft / sec$$ $$m / s$$
$$dm$$ = change in mass $$lbm$$ $$kg$$
$$dt$$ = change in time $$sec$$ $$s$$

Rocket Engine Thrust formula

$$T \;=\; \dot m_f \; v_e +[\; \left( p_e - p_a \right) \; A_c \;]$$     (Rocket Engine Thrust)

$$\dot m_f \;=\; [\; T - \left( p_e - p_a \right) \; A_c\;] \;/\; v_e$$

$$v_e \;=\; [\; T - \left( p_e - p_a \right) \; A_c\;] \;/\; \dot m_f$$

$$p_e \;=\; [\;T - \dot m_f \; v_e + p_a \; A_c\;] \;/\; A_c$$

$$p_a \;=\; p_e - ( T - \dot m_f \; v_e \;/\; A_c )$$

$$A_c \;=\; (T - \dot m_f \; v_e) \;/\; (p_e - p_a )$$

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

$$T \;=\; \dot m_f \; ( v_e - v_a )$$     (Jet/vehicle Engine Thrust)

$$\dot m_f \;=\; T \;/\; (v_e - v_a )$$

$$v_e \;=\; ( T \;/\; \dot m_f ) + v_a$$

$$v_a \;=\; v_e - ( T \;/\; \dot m_f )$$

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 $$ft / sec$$ $$m / s$$

Tags: Acceleration Force