Scratching the bark of a rocket science

 

                                                          Scratching the bark of a rocket science

Rocket Science has become a synonym for something difficult to grasp/ understand. In some sense it is true but not completely infects explaining airplane is harder. However rocket science is difficult only from the prospective of how critical every components are but not from the prospective of understanding its physics. In rocket science even if you are 100% sure than still there could be a “/” unnoticed or that 1 pound = 4.44822 newton.

If you want to understand the rocket in bulk (assembled) and its trajectory than the first thing to begin with are Newton’s 3- laws of motion. Newton’s three laws of motion helps us to understand different aspects of one motion. You may heard that Rocket’s motion is due to newton’s 3^rd law of motion. This is 1/3 true. Newton’s laws of motions are not independent. They just explain different aspects of a motion.

A rocket in the launch pad is at rest. First we have to change that state of rocket (state of rest). So according to Newton:

            A body at rest or in uniform motion will continue to be in its state unless it is compelled to change that state by any external imbalance force.

This law only tell what to do – to move the rocket we have to apply an external imbalance force. However, it doesn’t say anything about ‘How much?’ and in ‘Which direction?’ Here comes Newton’s 2^nd law of motion. According to Newton’s 2^nd law of motion:

            The rate of change of momentum of a body is directly proportional to the applied (net) force and act in the direction of applied force.

That means the amount of push (force) required is proportional to how fast we want to change the state ( if the mass of the rocket is 1 kg and doesn’t changes than the amount of push is proportional to how quickly we want our velocity to change).

Mathematically we write is as:

So now we know “How much?” But still we haven’t asked “How?”

The answer to this question lies in Newton’s third law of motion which says:

            To every action there is an equal and opposite reaction.

Let us understand what “F” is.

‘F’ is the external forces acting on the rocket. Few of them are intentionally applied and few are by nature acts on the rocket. The external force which we intentionally apply is called ‘Thrust’. This force comes from the engine which in itself is a subject of few volumes. The engine pushes the hot gas particles (ideally) out of the nozzle (exit region of the engine) which is the action and so the rocket experience a push in opposite direction to the exit gas as reaction or we can say that hot gasses are bullets and rocket is the pistol, when bullet leaves the barrel it also pushes the pistol backward which we call "recoil motion". 

Let me put few (might be) easily misunderstood logic and this misunderstanding was such that early age few scientist have raise concern about working of rocket in space. The logic in the cause of reaction force. We might thing that when the hot gas come out of the exit nozzle it encounter atmospheric air (on earth) as a result the push received by rocket is due to the push of the hot gas against the air. Like when we push a static wall than we get push in return. Now because there is no air in space so rocket has nothing to push against hence we will not get thrust in space. This is not how Newton’s 3^rd law works. Yes it is true that a pushing medium have to be there for Newton’s 3^rd law to work but in case of rocket, air is not the pushing medium. Here the hot gas are infect represent the static wall. Because the hot gas are composed of tine byproduct from the violent chemical reaction (for combustion type engine) so when temperature raise inside the engine than it results in raise in pressure as well (which represents our hand) so this pressure makes those tiny particles to push against each and wall. Hence we get a net push. Presence of air doesn’t affect this part of ‘F’.

The statement which quantify our above explanations is as:

Another part of ‘F’ which acts on rocket (by nature) are: Gravity (under the influence of some celestial body) and air drag.  This is where the push against the air comes in play and it is something which we do not desire. Talking about gravity for rocket is not as simple as talking about gravity of a moving car of swinging pendulum. The reason why such a simple force (gravity) which we have commonly applied in the form of ‘mg’ becomes complicated while applying in rocket is that in case of rocket both ‘m’ and ‘g’ are constantly changing and because it is their instantaneous value which actually matters so the form ‘mg’ is not valid for rocket. Frankly speaking the term ‘mg’ is never constant in any case, whether it’s the moving car or German made weighting machine but in our most of the case their change is almost negligible. Obviously we can’t neglect this change in a vehicle whose almost 90-93% of mass gets reduce till it complete its mission. So, if we want to roughly make ‘mg’ valid for our use is than it is worth writing them in differentiable form as:  

 

Drag is that part of our discussion which is easy to visualize but equally difficult to theorize. As the rocket engine start to burn and start to ascent, hot gas will push against the air surrounding but that is not the only point of contact. The entire rocket is envelop by the air. As it starts to ascent, the air are being pushed in all direction as a result rocket get pushed back (as per Newton’s 3^rd law of motion) and the result is such that it always resist motion and this resist by air is named as drag. However it is very loyal and only comes in play when the rocket is in motion and within the atmosphere. Roughly above 100 km (from Earth’s Surface) this part of the force is almost negligible. Our effort is to minimize this part as much as possible and this is done only by aerodynamically designing the rocket. Let me defend my statement. The quantity of this part of the force is given by:

Contact surface area and coefficient of drag are only parameter which can be optimize to have maximum impact so the contact surfaces must be aerodynamically smooth and polished and Cd which is a measure of aerodynamic shape must be kept minimum.

Thus if we combine all the above pieces than we will get the following results:

Or

Roughly this equation governs the trajectory of a rocket. And actually it is from here our real rocket science (which is synonyms to something complicated) begins. The science of ‘chemistry and physics’ of hot gas, how to achieve and control exit velocity so that instead of orbiting the Earth, we may bypass our moon and crushed on Mars, how to design the most efficient nozzle so that in a fight between Pe & P(at) we have minimum loss, which fuel we should chose so that out of total mass of the rocket there is something more left to be used in space, which altitude ‘g(r)’ we should chose to serve our purpose and the shape of the vehicle etc.