Today, the
uses of rockets cover two main categories. To carry objects into space
and in the atmosphere, while serving as a national defense system. The
basic form of a rocket was invented in the 11th century by the
Chinese, when they found that an object could be propelled through the
use of gunpowder as a fuel. The initial use for this discover was to defend
the Great Wall. The Chinese would strap the rockets onto their arrows to
greatly extend the range of the bow and arrow. Toy rockets began the space
age in the early 20th century. Konstantin Tsiolkovsky was one
of the first men to theorize rockets as a way for space travel (Maurer).
Tsiolkovsky was the first scientist to understand the use of rockets in
space travel. His first rocket ship in 1903 was to be powered by liquid
hydrogen and liquid oxygen (Von Braun). Tsiolkovsky was the inventor of
the train effect, two single powered rockets; one goes off after the other
burns out. This idea is used today in every space launch. But, the idea
might have never made it, if it weren’t for that little toy rocket. Today,
Rockets are also used for space travel, national defense, and worldwide
communication via satellite. For my investigation I will be analyzing the
flight of solid-fueled model rocket. First, rocket engines are reaction
engines. The basic principle of the driving motion of the rocket derives
from
From the know elements that I measured, I will be able to graph the aspects like velocity, acceleration, and elevation of a rocket.
My approach to measuring the data consisted of finding the force the rocket exerted when in flight. This was the only way to achieve accurate data, since I couldn’t measure the rockets velocity or max height while it was in flight. First, I measured the mass of the rocket. Second, I built a structure using clamps, a stand, and ppc pipe to hold the engine. The clamps held onto the pipe to enable the engine to be able to slide through the pipe without friction. The force probe was set below the engine to measure the thrust it exerted. The engine was placed upside down, to make it push into the force probe. I didn’t want to get the floor dirty. Before I ignited the rocket, I calibrated the force probe to zero. I used 500g (4.9 Newtons of Force) weights to give the force probe a range. I set the range at 19.6 N, even though the peak 10.6 N. I approximated the max force from my resources as 13.3 N, but I didn’t want to take any chances. The connection wires were about 7ft in length. This allowed me to set off the rocket from inside the building with the door closed. This helped me stay safe in the experiment. Here’s what my setup looked liked
I went through many trials because the machine would not calibrate to 0. I predicted that max force would less than 19.6 N because 4.9 N = 500g of weight. In addition I found that the average force of the rocket type I was using was 13.3 N. I measured the thrust of the rocket engine through the force probe. I took the data and created a thrust vs. time graph. Third I measured the mass the rocket after I had used it. Basically, I could calculate the weight of the fuel in the engine at any moment by having the weight of the engine with the fuel and without it. Next, I derived formulas to find the velocity, acceleration, burn rate and elevation. With theses elements I could graph the aspects of the flight of the rocket.
Useful
Numbers:
|
Mass
of rocket whole
|
18.74
|
Drag
Coeff
|
0.0111089
|
|
Time
interval
|
0.05
|
|
|
|
Rocket
engine mass
|
13.32
|
|
|
|
Initial
fuel
|
12.48
|
|
|
|
Burn
rate
|
6.24
|
|
|
|
time
to burn
|
2
|
|
|
Burn rate = Fuel/t
In my research, it proved very difficult to calculate the drag and coasting portion of the rocket’s flight. According the dynamics of a rocket flight, my data proves logical and very similar. After testing the force of the rocket I came up with what I expected. There is no formula for the force because this is what I measured. In the graph below, the straight line is known as the delay period in the rocket.It admitted a constant thrust, which I expected. The dramatic fall of the line at the end of the graph indicates that the second stage was completed. At this time, the rocket coasts for a moment until the ejection charge activates.
(Click on the picture to get the excel spreadsheet)
The acceleration proved difficult to find because of the loss of mass and the thrust. I predicted that the acceleration would follow the same pattern as the thrust until 1.8 s. I made this theory because the acceleration goes to 14.55 seconds not 1.8s. Formula a = F – mg – Dcoeff * V
Dcoeff = .0111089
Unlike the
acceleration and thrust, the velocity followed a distinct pattern that
was not similar to any other elment . I hypothesized that the velocity
would increase until the rockets thrust would equal 0. At this point the
rockets velocity would begin decreasing and eventually hit the max altitude.
From there it would descend into negative numbers until it arrived at a
constant terminal velocity. In this graph the terminal velocity point is
at 28.7 (s). It is hard to see because my time intervals are so close.
The graph is endeavored with about 700 data points. Formula v = u +
a (delta)t
(delta)t = .05 s
According to my data the elevation looked like this: I calculated the change in elevation with the formula delta(h) = ((u+v)/2)*(delta)t
Then I used the formula h
= delta h + h0
to find the elevation and each point (this formula is what I graphed).
This is just the elevation; the distance would not be very far because
I shot the rocket straight up with no wind change.
The mass
deterioration like the fuel was consistent until about 2 seconds. This
is when the rocket ran out of fuel. Also the fuel changes as the rocket
goes. The formula m = m(whole rocket) + Fuel(decreasing)
In my data, it was very hard to calculate the elevation due to drag and coasting of the rocket. While the rocket was powered the mass would change according to the fuel burn rate of .00624 kg/s. When the rocket starting coasting the mass would stay constant and the rocket would coast to its maximum altitude. The problem was calculating the drag and velocity of the rocket as it coasted. I went through many formulas until I found data points that looked appropriate. Beginning, the acceleration follows the lines of the change in velocity. First the accelerations copies the graph of thrust, except that is only for the first two seconds. After the two second mark the rocket loses its thrust or push. Due to the lose of power, and by factoring the effects of gravitational forces and drag I can predict that acceleration will quickly become negative. As shown in the graph the acceleration drops to an astonishing -122.29 (m/s^2) then increases to 0 over time. For the acceleration, I derived the formula a = F – mg – Dcoeff * VDcoeff = .0111089. The weight and drag were difficult in finding, but I used the formula W=mg for the weight and calculated the drag by plugging in number’s until the velocity equaled 0 at 6 seconds. Once I got the drag coefficient, the calculation of the rocket coasting became very simple. Before I put in the drag coefficient, the velocity of the rocket was at about 400 m/s (it would not slow down). I realized that the drag played a major role in the rocket’s flight. The drag coefficient is the air friction correlated with gravity. At first, the rockets thrust created the drag coefficient; it had to resist gravity and air friction. The drag had little effect on the velocity of the rocket because it was powered. However, once the rocket began its coasting the drag began to have a major effect on the rocket’s velocity and acceleration. The drag dramatically helped the rocket decrease its acceleration and velocity. If the drag was taking away, I would be simulating the rocket in a weightless environment. It would never slow down. The velocity is the speed of the rocket. For the velocity, I used the formula v = u + a (delta)t because I had to factor in the gravitational push on the rocket and the drag created by the air and the rockets velocity. I did not have to factor the drag in to the velocity formula because it already existed in the acceleration formula. The velocity graph is very similar to the thrust graph because thrust is a form of propulsion as is velocity. As the propulsion increases or decreases the velocity will also. After 2 seconds the velocity of the rocket started to decrease at a rapid rate. Eventually the velocity and the acceleration hit 0 at 6 seconds. Using the formula a = F – mg – Dcoeff * V I was able to calculate a drag without having to the take the surface area of my rocket. Even though the drag is very little, it makes a significant difference in the rockets flight. From watching model rockets in flight and taking a few estimations from my resources, I was able to conclude that the rocket with a model C rocket engine would reach its max altitude at 6 seconds. At the max altitude the acceleration is 0. From my data a conducted a trial and error experiment until the drag made the acceleration equal 0 at 6 seconds. I factored the drag coefficient into the flight of the rocket and saw that it dramatically affected its flight. This new data signified the max altitude of the rocket (476.91 ft). Alot farther then a trebuchet. From that point the rocket began to fall, which lasted 30.1 seconds. Mass of .01874 (kg) played a major factor in the rocket’s descent. As shown in the graph the velocity hit its terminal velocity of 28.7 (s). At this velocity, the rocket was going as fast as it could go. The velocity would stay the same until the rocket hit the ground at 36.31 (s). Also, in my quest to know the elements of a rocket flight, I found many of my formulas based on drag and weight, which I got from http://www.grc.nasa.gov/WWW/K-12/airplane/shortr.html. It was very helpful.
There could be some errors in my experiment. For one, I only measured the force once because I wasted numerous rockets trying to get the force probe to work. Second, the force probe was only within a .05 interval and a .1 accuracy. Even though .05s is a extraordinarily small interval, there were still ascents of the force that had significant gaps in them. For example from .1s to .15s the thrust jumped from 2.8N to 7.1N(that’s fast). Also, I measured the force in .1’s, which created unseen change in the thrust. From .9s to 1.5s the thrust stayed constant at 4.5N. I know that the thrust changed during this period; however, the reading measuring made the computer round the nearest decimal. This prevented me from knowing the exact change in that period. The lack of exact data could prove to create a small amount of error in my calculations. Also, in calculating the drag of the rocket, I estimated that the velocity would equal 0 at 6 seconds. Realistically, this isn’t the time the velocity would equal 0. Since I didn’t have the proper equipment to measure the drag, I calculated a drag that would make the rocket’s velocity become 0 at 6 seconds. I estimated from the various resources I collected and my personal experience, that a rocket with that type of engine would begin its descent at 6 seconds. Normally the drag coefficient would vary according to weather condition and the size and mass of the rocket. In a real launch, the drag would equal my simulated drag if the conditions were right. The formulas for acceleration and velocity were a challenge to get right. There were various factors that related to outcome of the velocity and acceleration. My calculations have some error because of the time interval and the accuracy of the force probe, but the data points seem logical. In addition, according to my resources the simulated data points would match the flight of real rocket (with no wind change and ignited at 90 degree angle). In addition, the model engines play a difference since they are not always performing the same as the manufacture says. If I had done numerous test of the same type of engine, the data would be extremely similar, but would vary in spots. Each engine reacts differently. To improve on this experiment, I would make my time interval .005s and set the accuracy of the force probe to .01N. This would help me measure the data more accurately, even though there would be about 100 pages. In addition, if I had the correct equipment, I would measure the actual drag of the rocket. This would allow me to calculate the time when the rocket’s velocity did equal 0.
From the beginning of this experiment, I hoped that it would run smoothly and the results would be astonishing. Even though I ran into a few calculations problems on the way, I still managed to pull through. From the force (N) I was able to calculate the many aspects of a rockets flight. I decided not to calculate the distance horizontally traveled by the rocket because I shot the rocket straight up with no wind change. Therefore the rocket would land in the same spot it took off. Since there are not really any averages in my raw data because the numbers are changing the whole time, I am not going to give it to you. And of course it is about 20 pages long. Save the trees! In search for knowledge of rocket engines I found useful information. Rockets are simple in their whole, but when taken apart they are very complicated. I learned detailed information and the purpose of the three stages of rocket. I also found that the velocity of the rocket did not follow the same pattern as the thrust. I also learned that my rocket only went 476 ft into the air. I thought the elevation would be lot higher. The Chinese used rocketry over 900 years ago, that’s a lot of advancement since then. Every type of propulsion system that used commonly in today’s society are all derived from the Chinese model rockets. I also learned that the elements and aspects of the rocket engine all depend on each other. The drag, velocity, acceleration, correlates to the mass and thrust of the rocket. Over all the experiment was a success; I now know the mechanics of a rocket flight. I have learned much from this experience.
