Rocket propulsion

Introduction to rocket propulsion:
Rockets range in size from fireworks so small that ordinary people use them to immense Saturn Vs that once propelled massive payloads toward the Moon. The propulsion of all rockets, jet engines, deflating balloons, and even squids and octopuses is explained by the same physical principle—Newton’s third law of motion. Matter is forcefully ejected from a system, producing an equal and opposite reaction on what remains. Another common example is the recoil of a gun. The gun exerts a force on a bullet to accelerate it and consequently experiences an equal and opposite force, causing the gun’s recoil or kick.

Figure shows a rocket accelerating straight up. In part (a), the rocket has a mass m and a velocity v relative to Earth, and

hence a momentum mv . In part (b), a time Δt has elapsed in which the rocket has ejected a mass Δm of hot gas at a

velocity Ve relative to the rocket. The remainder of the mass (m − Δm) now has a greater velocity (v + Δv) . The momentum

of the entire system (rocket plus expelled gas) has actually decreased because the force of gravity has acted for a time Δt ,

producing a negative impulse Δp = −mgΔt . (Remember that impulse is the net external force on a system multiplied by the

time it acts, and it equals the change in momentum of the system.) So, the center of mass of the system is in free fall but, by

rapidly expelling mass, part of the system can accelerate upward. It is a commonly held misconception that the rocket exhaust

pushes on the ground. If we consider thrust; that is, the force exerted on the rocket by the exhaust gases, then a rocket’s thrust isg in outer space than in the atmosphere or on the launch pad. In fact, gases are easier to expel into a vacuum.

By calculating the change in momentum for the entire system over Δt , and equating this change to the impulse, the following

expression can be shown to be a good approximation for the acceleration of the rocket.

a =(VeΔm)/(mΔt)− g

“The rocket” is that part of the system remaining after the gas is ejected, and g is the acceleration due to gravity.

ACCELERATION OF A ROCKET

Acceleration of a rocket is

a=vemΔmΔt−g,$$$$

where a
is the acceleration of the rocket, Ve

 is the exhaust velocity, m
 is the mass of the rocket, Δm is the mass of the ejected gas, and Δt is the time in which the gas is ejected.

A rocket’s acceleration depends on three major factors, consistent with the equation for acceleration of a rocket . First, the greater the exhaust velocity of the gases relative to the rocket, ve the greater the acceleration is. The practical limit for ve is about 2.5×103m/s for conventional (non-nuclear) hot-gas propulsion systems. The second factor is the rate at which mass is ejected from the rocket. This is the factor Δm/Δt in the equation. The quantity (Δm/Δt)ve, with units of newtons, is called "thrust.” The faster the rocket burns its fuel, the greater its thrust, and the greater its acceleration. The third factor is the mass m of the rocket. The smaller the mass is (all other factors being the same), the greater the acceleration. The rocket mass m decreases dramatically during flight because most of the rocket is fuel to begin with, so that acceleration increases continuously, reaching a maximum just before the fuel is exhausted.

FACTORS AFFECTING A ROCKET’S ACCELERATION

• The greater the exhaust velocity veof the gases relative to the rocket, the greater the acceleration.
• The faster the rocket burns its fuel, the greater its acceleration.
• The smaller the rocket’s mass (all other factors being the same), the greater the acceleration.

References:

College physics by Ian Blokland, Google,etc.