Results and Discussion:
Mass of rocket: 0.095kg
Mass of Spent Motor: 0.01045kg
Mass of Full Motor: 0.0186kg
Area of Rocket body base (circle): 4.91×10¯⁴m²
Weight of rocket: 0.931N
To ensure that the rocket was relatively efficient a few factors had to be considered such as centre of gravity, centre of pressure, and drag. Centre of Gravity C.G was the point along the rocket body where it was balanced and centre of pressure C.P, the point at which all the aerodynamic forces were equal. When constructing the rocket it was important to ensure that the C.P. was behind the C.G. so that the rocket, in flight would be stable. To determine this, the centre of gravity of the rocket was found, and hung at this point in a wind tunnel, and observing the rocket’s motion. To also ensure stability, fins were necessary, however it was important to not make them too big, or drag would be increased. To decrease drag, the nose cone was made streamline so that the air molecules would flow smoothly down the rocket body.
Drag is a force which acts upon an object which is travelling through a medium such as air at any velocity. In the situation of falling or travelling through air, the objected will have less velocity than in ideal situations, due to the force of drag, caused by the air molecules colliding and being pushed away by the object. Thus, as the object’s velocity is increased, so is the drag force upon the object, until the object reaches terminal velocity; the point at which the weight force is equal to the drag force, and therefore travels at a constant velocity with no acceleration. The wind tunnel was utilised to determine the drag constants which could be later used for further calculations to predict the flight characteristics. The rocket was hung on a string length of 16cm in the wind tunnel at the centre of gravity. Next, the wind tunnel was turned on and the length the rocket swung backwards was recorded to be 2cm.
The diagram below shows how the drag force was calculated:
From above:
and
∴
=0.116375N
When the drag force is calculated, the drag constants can then be determined if the velocity is known.
Where
C is the drag coefficient, A is the area and ρ is the density of the medium (air) of which the object is falling through.
ρ=1.2kgm¯³
A= 4.91×10¯⁴m²
is always constant(k) so:
The velocity in the wind tunnel was 7.5ms¯¹
=0.0020689
Some of these calculations may be incorrect or have some amount of error as they were based on assumptions such as that the wind tunnel had a velocity of 7.5ms¯¹. Measuring the amount the rocket was pushed backwards by the wind in the tunnel was also difficult, as personal judgement of sight was used. This was difficult as the rocket did not always swing back by the same amount of distance and was not always stable. Therefore, an estimate was taken. These results would have been more accurate if the wind speed had been first measured prior to using the wind tunnel, and two or more people judging how far the rocket was being pushed back.
Without Drag
Ideal calculations were calculated to predict the flight of the rocket without allowance for drag. This allows for comparison between calculations for when flight is predicted with drag considered and the actual flight of the rocket. This will demonstrate the impact that drag has upon an object travelling through air.
The rocket was predicted to fly a certain distance for the amount of time that the thrust was detonated and providing the force for the rocket to launch. From this, the point at which the rocket was at its maximum height was then able to be calculated. The distance total or the maximum height is thus:
This is more clearly explained in the diagram below:
To find
To find acceleration- the resultant force was needed. The force from the thrust, the force provided by the mass flow rate from the rocket motor to launch the rocket, was on average 6N for a period of 0.8s. However, at 0.8s not all the fuel may have been used up, so an average mass of the rocket when the motor was full and empty was calculated.
=
= 0.10953kg
= 0.10953x -9.8
=-1.073N
∴
= 6 + -1.073
= 4.927N
=
= 44.98ms¯²
Velocity:
v=?
u=0
a=44.98ms¯²
t=0.8s
∴v=35.987ms¯¹
Displacement:
s=?
u=0
a=44.98ms¯²
t=0.8s
=14.39m
To find
The thrust had already provided the force for the rocket to fly- and now the rocket was travelling due to inertia, but was slowing down due to the weight force down of the rocket now with an empty motor. In this situation drag is not included so . At the maximum height the velocity was 0.
m=kg
g=-9.8ms¯²
F=-1.033N
Time:
v=0
u=35.987ms¯¹
a=-9.8ms¯²
t=?
=3.67s
Displacement:
s=?
u=35.987ms¯¹
a=-9.8ms¯²
t=3.67s
=66.08m
∴maximum height= 14.39+66.08
=80.47m
What was the total flight time if the recovery device did not open?
Time:
s=-80.47m
u=0ms¯¹
a=-9.8ms¯²
t=?
=4.05s
Total flight time= 0.8 + 3.67 + 4.05
= 8.52s
Ejection charge for the recovery device is delayed 6s maximum after thrust phase.
So at 6.8s during the flight the ejection should have occurred. This is at 2.33s when the rocket is falling.
Displacement:
s=?
u=0ms¯¹
a=-9.8ms¯²
t=2.33
= -26.6m
∴ has another 53.87m with the parachute open
Terminal velocity is when and is when an object reaches its highest possible velocity- acceleration is 0 and the velocity is constant.
Terminal Velocity:
k=0.0020689
0.0020689
v=22.35ms¯¹
∴ the equations calculated previously will be inaccurate in real life situations as the rocket will not be able to have velocities greater than 22.35ms¯¹, so that means lower velocities, less height, less acceleration and less flight time.
With Drag
Flight predictions were made with the inclusion of drag as a factor. This was done by calculating the average ideal velocity and then finding the average drag, using the k value calculated from the wind tunnel.
Average Velocity:
u=0
v=35.987¯¹
=17.99ms¯¹
Average Drag:
k=0.0020689
=17. 99ms¯¹
= 0.66958N
To find
Drag is now considered in these calculations, and therefore flight predictions in comparison to the ideal situations should display lesser velocities, accelerations, displacements and time, because drag is affecting the overall resultant force.
=4.2574N
=
=38.87ms¯²
Velocity:
v=?
u=0
a=38.87ms¯²
t=0.8s
∴v=31.096ms¯¹
Displacement:
s=?
u=0
a=38.87ms¯²
t=0.8s
=12.44m
To find
The thrust force is now no longer involved and the rocket is still travelling through the air due to inertia, however, should be becoming slower and have less acceleration than in ideal situations due to the greater resultant force in the downwards direction.
-1.033N
= -1.7026N
=
= -16.93ms¯²
Time:
v=0
u=31.096ms¯¹
a=-16.93ms¯²
t=?
=1.93s
Displacement:
s=?
u=31.096ms¯¹
a=-16.93ms¯²
t=1.93s
=28.48m
∴maximum height= 12.44+28.48
=40.92m
What was the total flight time if the recovery device did not open?
-1.033N
= -0.3634N
=
= -3.45ms¯²
Time:
s= -40.92m
u=0ms¯¹
a= -3.45ms¯²
t=?
=4.87s
Velocity:
v=?
u=0
a= -3.45ms¯²
t=4.87s
∴v= -16.8ms¯¹
Total flight time= 0.8 + 1.93+ 4.87
= 7.6s
Ejection charge for the recovery device is delayed 6s maximum after thrust phase.
So at 6.8s during the flight the ejection should have occurred. This is at 4.07s when the rocket is falling.
Displacement:
s=?
u=0ms¯¹
a=-3.45ms¯²
t=4.07s
= -28.57m
∴ has another 12.35m with the parachute open
-However, terminal velocity was calculated to be 22.34ms‾¹ and according to flight predictions calculated when considering drag, the velocity reached 31.096ms¯¹. Therefore, in real situations the rocket will have less velocity, acceleration, time and displacement.
In comparison to the ideal predictions of the flight, it is evident that drag has a significant effect on the flight of the rocket as with drag predictions, the rocket flew half as high and flew for 0.92s less.
Actual Flight:
During the actual flights, the actual flight characteristics were varied from the predicted ones as there are additional factors besides drag which contributed to the results such as the wind and angle the rocket was launched. Two observers stood 100m from the rocket launch pad with inclinometers to measure the angle, and four people timed how long the rocket took to reach the maximum height. The angles and times were recorded and an average calculated.
Average angle: 25˚
Average time: 3.34s
∴h=46.6m
However, this was inaccurate as the rocket did not fly straight, but on an angle as it was a windy day and the rocket was on a slight angle when launched. Also the time may have been affected as each person’s recording, motor reaction skills are varied. Assuming these calculations are correct, this would mean that the rocket flew higher in real life than during predictions with drag, despite the numerous factors affecting the rocket. This could be because the motor thrust of 6N used to predict the flight characteristics was only an average over a period of 0.8s and therefore may have provided a higher amount of thrust, the drag constant k may actually be less due to inaccuracies with the calculations from the wind tunnel; therefore, providing less drag, and the predictions calculated were using averages for drag and velocities. The wind may have provided leverage if blowing from below the rocket to push it upwards, however, this is unlikely.
Complications during the flight was that the recovery device did not open and that the thrust chamber was not thoroughly fixated within the rocket and moved upwards within the rocket, changing the centre of balance. It was not known how long the actual flight took as it was not recorded, but perhaps the recovery device did not open in the air due to the fact that the flight may have taken less than 6.8 s and the ejection charge may not have had time to open the device. However, this would have meant that the nose cone was ejected on the ground; but this did not happen. When examining the rocket later it was found that the wadding in the rocket had not been burnt and was blocking the passageway for the ejection charge. The wadding was possibly placed too far away from the thrust for it to be burnt and was too thick within the rocket, or this could also mean that no ejection charge occurred. If the ejection charge did occur, it may have occurred during the flight but was ineffective, or like previously thought, the rocket did not have enough time.
In order to improve results, several adjustments could be made. Such adjustments are that the rocket could be lighter to increase the maximum height and flight time. To decrease drag, a different, smoother material could be utilised instead, such as plastic, and the nose cone made to have a rounder tip, as this would break and disperse the colliding air molecules more smoothly. The wadding should have been less thick, and placed closer to the motor so that the ejection charge would be effective.
Video footage of the flight was obtained, and using windows media movie maker, the time, displacement, velocity and acceleration was calculated.
According to video footage the whole flight takes place in 5.6s, taking 2.16s to reach the maximum height and 3.44s to fall. This would mean that the rocket would have not been able to eject the recovery device whilst the rocket was in flight.
Rocket Flight from 0-0.24s
These results were derived from the video:
Average acceleration is the gradient of the line that plots the average velocity versus time graph.
Average Acceleration= 42.85714ms‾²
Idealistically, the graph of the velocity in the first few seconds of flight should be linear, displacement-time a curve, and the acceleration constant until the rocket becomes closer to the point of terminal velocity. These graphs are a visual representation of the unpredictability of real life situations, showing the affect of external factors on the experiment.
Conclusion:
This experiment was effective as it demonstrated the physics involved in rocketry such as Newton’s laws, velocity, acceleration and the affect of drag upon objects. Calculations of flight predictions and the actual flight characteristics exhibit that real life situations are different from predictions and ideal situations, showing that there are many inconsistencies, errors and factors which affect the flight. Improvements maybe made to improve results and calculations.
Appendix:
How to make the rocket:
BIBLIOGRAPHY
