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Saturday, January 3, 2015

Rocketry Basics and Parts of rockets

Before proceeding to the subject, a fact:    Did you know that one of the most efficient Nozzle design is  known as Rao Nozzle, named after its designer GVR Rao who derived the theory in 1950s?

There is a basic difference in a projectile launched with a Gun and the one launched by using a Rocket.

Gun has a cylinder shaped barrel for providing the direction. When ignited, the fuel ( mixed with oxidizer ) explodes instantly, and the expanded gases create a pressure behind the projectile. In the whole system all sides of chamber are made up of solid material which contains the pressure within.

 It forces the projectile out of the barrel because that is the only part which can move to release the generated pressure. After it comes out of barrel there is no force to increase the velocity and so it continues to move due the kinetic energy that it has achieved at the time of escape from barrel and if it does not hit the target then it falls as the energy gets spent fully.

 The Rocket uses the same principle..  that of releasing the pressure to impart the speed to the projectile ...   but in a different way. The Rocket is continuously accelerated  using an exhaust of hot gases till its velocity matches with that of the escaping gases.

Most of us have handled the basic rocket ..  The  Rocket firecracker. shown in next left image. Middle figure is a cutaway view and the operating principle is shown in the figure on right.

It works a straight out of Newton’s law :   action = reaction!


When ignited, a mixture of Sulfur and Charcoal burns in a closed chamber and the oxygen required for this burning is provided by Potassium Nitrate.  This fast burning mixture produces large volumes of hot N2 and CO2 gases which try to escape out to a lower ( atmospheric ) pressure through the opening at bottom.

The  burning mixture continuously produces hot gases and these escaping gases cause the rocket to force upwards into air. The long stick stabilizes the rocket in vertical position so that it climbs up ( does not deviate sideways ) continuously.
Obviously,  the speed of the outcoming gases has  to be more than the rocket speed.

Let's explore the process in detail:

a. The rocket moves forward because of the exhaust and more the exhaust speed more the thrust.
b. This speed of the hot gas  coming out of the rocket is a resultant of the difference in 
  ( Pressure of gases  inside chamber, Cp  )  and ( Pressure outside the chamber, Ep,  near nozzle  ) i.e.
Cp - Ep.
and the forward force is generated by this pressure difference.

Obviously the speed can be increased by increasing this pressure difference.  BUT HOW????

 Let’s look at the process in detail to answer this question.

1. The burning chamber of this toy rocket is a cylinder with fully opened bottom
2. As the burning progresses the ‘fuel’ gets burnt and the position of the plane in which the burning is taking place, travels inwards creating more empty volume so the pressure of gases falls. 
3.Hot gases come out through the big circular opening of the bottom of cylinder so the output is haphazardly directed.
4. This blast also throws out energy in the form of Gas pressure and heat which goes waste.

If we somehow control these parameters then  we can improve efficiency.  

This was recognized by Robert Goddard who pioneered the research and he was able to increase he efficiency from contemporary 2% to  ( hold your breath .. ) above  60%  !!!!

And How did he do it? By a minor change in exhaust geometry!!

He made two changes:
               One - he reduced the bottom opening to a smaller diameter hole;
                                 This trapped the heat generated within the confines of the chamber, 
                                 which in earlier designs was being thrown out. 
       Two -  he added a nozzle at  the  bottom portion of chamber as shown in the next figure.

This small change improved efficiency In 3 ways!!!

1.      The hot gases generated by the burning try to escape through the back opening and encounter the narrowing path near the nozzle ( the ‘throat’ ). This prevents excessive escape of Heat and pressure which recycles to generate more pressure and their exit velocity increases creating thereby more Thrust to push the rocket forward with a higher speed.

 2.      As the exhaust comes out of the orifice, it faces wide flaring opening in the form of a nozzle. This sudden expansion cools the gases coming out.

The cooling is so intense that in some cases the temperature of exhaust ( although coming out of burning chamber ) is as low as atmospheric temperature.

     3.      The sudden expansion also makes the dispersion freely and so the outcoming  gases  which are facing a cooler region accelerate more and exert more thrust. 

The adjecent figure shows the photo of  a nozzle from the 2nd stage of PSLV rocket of ISRO.

Essential parameters of the nozzle geometry are marked in yellow.

Two factors which are  critical for maximizing Thrust are

                            ( Nozzle Exit Area )
  The ratio      - - - - - - - - - - - - - - - - - - 
                               ( Throat area )  

  and   The length of the Nozzle.   

A few more tricks of the trade.  

1.      Shape of the stream of hot gases

Basic Physics tells us that for best efficiency the blast of gases has to be along the axis of the cylindrical body of rocket that is exactly pointing perpendicularly to the rocket body. Streams not parallel to the axis do not exert maximum push. 

Next figure shows 3 cases of chamber pressures :  
Cp is the pressure inside the chamber  and Ep is the external pressure surrounding the vehicle.

If Cp  >  Ep  then the exhaust expands after coming out of the chamber and the ( Green and Yellow arrows ) produce less reaction to push the vehicle forward than the middle ( Red ) component.

Same logic applies for the 3rd case when
 Cp < Ep.

A very well defined non-spreading
exhaust of Falcon 9 rocket
So  the thrust is most efficient when the flame is not spread out or constricted.  This happens if the pressure of gases coming out of the chamber is equal to that of with atmosphere. 

Of course you can’t have a nozzle which will be equally efficient throughout its flight because as the rocket climbs higher the outside pressure drops rapidly. One has to have a compromise design because the flare will initially be narrow and will expand as the rocket rises.
But what do you do in the very low pressures and in vacuum? The nozzles are so shaped that the gas gust is parallel to motion direction. 

To achieve this objective the nozzles used at higher heights and in vacuum are lengthy in nature as compared to the ones used near earth.
Right side figure shows the Nozzle of 1st stage of PSLV core.   Compare the length of this nozzle with the one of 2nd stage shown earlier.

2. Reduction in weight over time

 As the burning continues over a period of time another factor starts making an impact.   
 For a time being we assume that the thrust developed by the rocket is constant. Initially this thrust has to LIFT the rocket from stationary condition. After the liftoff and after it has acquired momentum the thrust  is used only in accelerating the rocket.  
There is another important effect that is taking place.  As the  burning process continues, the weight of the rocket reduces continuously due to the burning of fuel. However the thrust does not change because chamber geometry is unchanged. Therefore same thrust is pushing a lighter rocket now. This increases the speed of the rocket further.
 In this way even though the thrust of a particular engine is constant, the rocket continuously accelerates till the rocket velocity comes near to the exhaust gas speed. Burning the engine further has no use because the rocket has already achieved the velocity of exhaust gas and can't accelerate further.  Operating the engine beyond this limit does not help in accelerating further. 

At this stage this rocket becomes useless and This fact is used in a clever way:  this stage is discarded.

Such a process is called as Staging. The discarded engine  is a Heavy,big chunk of metal and so after its separation the remaining system is now a lighter one with another engine at bottom. This new engine is now ignited and it has to push a  remaining weight now. In this way 3 or 4 stages are used during a rocket launch to place the satellite in its desired orbit.

= = =
Let us deviate a little to understand what is Coasting.

When the earlier heavy stage is discarded, the remaining portion of Rocket consisting of upper stage(s) continues to move with the attained kinetic energy. This movement - without the active rocket power - is called as coasting. Mission designers  make extensive use of this technique. 
We will study coasting used during the launch of Magalyaan using a PSLV rocket.

In this launch 3rd stage of rocket ignited, ( marked as PS3I in the adjecent figure )  at 266 seconds after launch ( T+266 ) and it shut off and separated from 4th stage at T+584 seconds when it was at 195 kms height. ( PS3S marker in figure ). Due to the kinetic energy it continued to rise even in the absence of any active engine power rising to about 340 kms and then descending under gravity.
What did the flight designers achieve with this?

To answer this question we have to see the ground trace plotted in this figure.
See the PS3S marker indicating that the 3rd stage separated near the southern tip of Vietnam. The remaining portion ( 4th stage and satellite ) travelled about 10000 kms ( to South Pacific ..  midway between Fiji and Cook islands ) when the 4th stage ignited ( PS4I ),
This 10000 kms free ride ... thanks to Coasting.
That is Coasting.

= = =
We return to our original thread now.

3.  Propellants :  
There are 3 basic types  of Propellents  in use ..  Solid, Liquid and Hybrid .

A Propellant has two components; Fuel and Oxidizer
A Fuel which burns  when combined with oxygen  producing gas for propulsion. This oxygen is provided by Oxidizer.
( Oxidizer / fuel ) ratio is called the mixture ratio.
The efficiency of propellants is stated as units of thrust produced when a unit mass of propellent burnt in one second. It is called as Specific impulse.
Propellents,  is a vast subject and we will not go into it ( right now..  may be in future )

We have seen that more the exhaust velocity, more the rocket velocity. How to increase the velocity? For answer we go to basic kinetic theory of gases and the answer lies in one of the first equations

Vrms  =  sqrt( 3RT/M )  where M is the Molar mass of particle and R is Gas constant. We can re-write this  = sqrt( 3kT/m ) where m is the physical  mass of particle and k is Boltzman const. So what do we derive from this?
The  high temperature burning and  low particle mass yields higher velocity of particles. 

Solid fuels burn at high temp but produce larger particles ( that is why large smoke plumes are seen when the rocket starts from launchpad ). They have a disadvantage that they can't be controlled once ignited.

Liquid fuels give a higher impulse per unit weight compared to solid fuels ( nearly double ) but the engine is more complex due to pumps,pipes and large storage tanks making the rocket heavy. They have an advantage in the fact that they can be switched off and on at will so give a flexibility in controlling thrust.

4. Internal Fuel Geometry of Solid rockets:

We had seen that in toy rocket the burn starts at one end of cylinder and it continues to other end of cylinder over time. Such type of design is rarely used in precision, high power rockets.

These rockets are generally hollow in center and are ignited along full length in the central cavity.
The central cavity shape plays important role in the distribution of Thrust over time.

 The thrust varies as the internal surface area varies. e.g. with a circular cross section the diameter of internal cavity increases at the square of radius and so the thrust also increases as a square law function.

Star shape  ( adjacent figure )is a popular choice because the thrust quickly reaches to a constant value and remains there till the burn is almost over.

Cross shaped cavity results in a thrust which falls as the time progresses.

In an ingenious arrangement, the Space X corp has used nine small motors arranged as an octagon  surrounding a central motor, Each of this motor is a Merlin engine and SpaceX claims that with this arrangement even a simultaneous failure of 2 engines will not affect the launch as remaining 7 engines will be able to support the torque requirements of  mission. This has made it a highly reliable class of rocket.

In our next post we will continue with this subject by seeing how these principles are used in a practical case by studying in detail  a PSLV lauch.

1 comment:

  1. hi...
    liked your approach to the "rocket science..." in fact, i live in Hyd... work at UoH... mail id is: ... would be glad to interact...