So. How high did it go ?

video

These images have been edited from a short 16 second video called Greenstreak887.mpg.To help illustrate the problems encountered whilst filming a fast moving object like a rocket.

The image of the nice blue sky is in fact an image selected from the video 

Skillfully filmed by my eldest son Alex. His eyesight is good enough to keep the object in view.

The tiny black speck in the middle of this photograph actually shows the rocket at apogee. 

Remember this is how you would see the image in real life.

Get your inclinometer focused on that. Well yes... It could be difficult even if you have 20:20 vision.

Now add to this the time factor. It took less than 4 seconds to climb to apogee with a total flight time of Tvol = 8secs.

A combination of both high  velocity and the small image size render most manual measuring systems inadequate. 

Or at best open to a large degree of  error and  limited repeatability.

The higher the rocket apogee. The greater the possible error.

So how can we improve the experimental technique?

• Optical image size. Using more powerful lenses.

• Electronic on board flight data logging.

• Line spooling

 On board electronic flight data logging.

The main objectives for any on board instrumentation are low weight, accuracy and survival !

Low mass is essential. To keep initial mass M1 to a minimum and reduce any potential affects on flight stability and overall rocket performance.

Our current system has an all inclusive mass of 22gms.

Accuracy. It is important to obtain accurate recordings of flight trajectory with  time histories.

Rocket  height,  velocity and acceleration could be recorded.

The recording  sample frequency is important in order to be able to record sufficient data points to produce a good curve or graph.

System response time delay or lag can effect the accuracy of the initial 0.2 secs of the flight data recorded.

Survival. There is nothing more frustrating than loosing your instrumentation due to a failure in the recovery system.

It can also be very expensive.

So it is best to spend sometime developing a good  reliable recovery system first so that you can record lots of useful data..

Our electronic system records data to an eprom which is then transferred to a computer using an adapter cable and analysed using some  mathematical graph  generating software.

Estimating potential reading accuracy .

This can be helped by using the same system to record other moving objects whose velocity and position are known or by cross calibration with other aircraft/aerospace. instrumentation of known accuracy.

Types of sensor/ capteur

How high can you go ?

Our atmosphere.

Satellite orbits and escape velocity.

 Graphic courtesy Cambridge University.

The height that any projectile can achieve requires the mass to be accelerated to overcome Earth's gravitational attraction force for long enough to achieve the required escape velocity.

If the projectile fails to obtain either the required height or the minimum escape velocity, it will be pulled back towards  the Earth's   surface. Captured by the gravity of the Earth pulling the object towards the center.

As happens when you throw a ball upwards.

This is also what happens to a water rocket.

To go vertically upwards becomes difficult when the projectile attains higher altitudes due to the fact that the Earth rotates.

So the higher you go and the longer the flight lasts the more the rocket will have displaced relative to the original launching point.

One way of reducing the energy required to put a satellite into orbit is to use the centrifugal force of the spinning earth.

The centrifugal force is at a maximum when the radius reaches a maximum value about the spinning axis. Fcent = mrw²

Which is why it helps if your launch site is at or near the equator. Like the Arianespace launch site at 'Kourou' in Guyana.

Another additional aid is due to the Earth being slightly elliptic. Its equatorial radius 6.378.10⁶m is larger than that at the poles

polar radius 6.357.10⁶m making the acceleration due to gravity lower at the equator because it is further from the center of the Earth.

The value for g at the equator  ge = 9.780m/s²

^{Whilst g at the poles}                gp = 9.832m/s²

Giving a difference in the acceleration due to gravity at launch of 0.052m/s^2.

 ^{Now allowing for the centrifugal force} g' =  ge - rw²

                                                  rw² =  ge - g' 

Assuming values of  r = 6.375.10⁶m

and the rotational angular velocity of the Earth

               w = ( 2p/ 24*3600)    radians/sec

Then the reduction in g due to the centrifugal force acting on any mass at the equator.

 ge - g' = rw² =  6.375.10⁶* ( 2p/ 24*3600)²

                  =  0.034 m/s²

^{So the effective value of geff} = 9.746 m/s²

This effectively means that for the same launch energy you can achieve a higher escape velocity or you can increase the mass of the satellite to be put in orbit. 

Or if you want to get a water rocket apogee record them do it at the equator !

Another way of expressing this advantage of using the energy of the spinning Earth is to express this in terms of delta V.

So if you launch at the equator  v = rw

Then substituting the values for r at the equator 6.378 10³ Km

and w  = 7.273 10^{-5 c}/sec

 Dv = -0.464 Km/s

The same applies if you want to say you have lost weight  Go to the equator.

For a satellite to stay in a base circular orbit of 200kms. The velocity required is 7.82 Kms /sec and is referred to as the 'First Cosmic Velocity'.

At 1000kms altitude the satellite needs to be traveling at a velocity of 7.3Kms/sec

To maintain a TV satellite in a geo-stationary orbit of 36000Kms from the Earth it needs to have a velocity of 3 Km/sec.

Note: Geo-stationary means that the satellite will stay above the same point of the Earth's surface as it rotates.

Say you were planning a voyage to the moon.

To escape the attraction of the Earth's gravitational force the space module needs to be traveling at at least 11.2 Km/sec.

This is known as the Second Cosmic velocity

To explore outer space beyond our solar system you need to be traveling at a velocity of  16.6 Km /sec.

This is the Third Cosmic velocity.

Rocket Escape velocities

First cosmic velocity     =    7.82Km/sec

Second cosmic velocity = 11.2  Km/sec

Third cosmic velocity    =  16.6  Km/sec

Calculating escape velocity:

Kinetic energy of the rocket needs to be at least equal to the potential energy of the planet at a radius r from its center

 0.5m.v² = G.M.m /r

Rearranging for the value of the escape velocity v_esc

 v  = ( 2G.M /r )^0.5

Where  m   is the mass of the projectile or rocket.

             v   is the escape velocity m/s

             M is the mass of the planetary body we are trying to escape. In our case Earth.

             G  is the gravitational constant.6.67.10^-11 Nm²/Kg²

              r   is the radius or distance between the center of mass of the rocket from the center of mass of planet mass M.

Note:  (  )^{0. 5} Is equivalent to square root

Table for calculating escape velocities form Earth and other planets

Now how much pressure do we need to reach the 3rd cosmic velocity....

Where's my calculator..

The maximum velocity currently known is the reference velocity of light in a vacuum at 300000 Km/sec.

This velocity decreases when light passes through higher density materials:

Speed of light through water 225000kms/sec

                      through glass  200000kms/sec

                through diamond  125000kms/sec

This means that we would need to improve our current rocket performance by18.10^3..to approach the speed of light.

A pretty humbling thought.

There is another slight problem in that Einstein's E=mc² means that as the space craft approaches the speed of light its mass would increase. Since  for this formula to be true the speed of light cannot be exceeded no matter how much energy you put into the system.

Second problem is that the majority of images we see of stars in the night sky have taken light years to arrive. A sought of cosmic archive if you like.

So some of the stars we see might not exist any longer!

The further  we can look into the depths of space the further we actually travel back in light time towards the origin of the universe. The so called 'Big Bang'.

esa Global gravity variation research satellite

http://www.esa.int/SPECIALS/GSP/SEMCO8NQS7E_0.html

 To be honest we are currently unable to explain what makes gravity ?

Pretty basic really. But inspite of all the formula it is still a scientific blind spot.

Gravity or the existence of graviton particles that could create a gravito-magnetic field around an accelerating mass is an interesting possibility.

If gravito-magnetic fields exist then there signal would be be transmitted at the speed of light.If they conform to Einstein's relativity theory.

Understanding gravitational attraction

http://www.fourmilab.ch/gravitation/

 Real Rocket Page

Find out more about our Earth

http://jvsc.jst.go.jp/earth/guide/english/

http://www.krysstal.com/solarsys_earth.html