Gravitational Assist Slingshot Experiment
By Freddie H
Aim
My aim was to measure a simplified, one dimensional, version of the
slingshot affect used to increase the velocity of a spacecraft. I
measured the drop height of two balls, one substantially bigger than
the other, a then released them and after they were reflected of the
ground measure the height the smaller ball went to. The bigger ball
gave the smaller ball a “kick”, due to conservation of momentum,
accelerating the ball and increasing its final velocity meaning that the
ball was able to travel higher than its original drop height.
Method
In this experiment I dropped a yellow tennis ball, of radius 3.25, on
top of a size 5 football, of radius 10.95, with a rubber washer, of
thickness 3mm, inner radius of 1cm and an outer radius of 1.65cm,
separating them. I dropped the balls from varying heights between
37. 25cm and 116.35cm.
Factors that I think are going to affect the experiment:
1. The spin of the balls
2. Measuring accurately how high the ball is going
3. Temperature
In order to make sure that the balls did not spin I created a
mechanism that prevented the ball from spinning, but did not affect
the results. This worked by having a plank of wood with a small
plastic cup sitting of it attached to each other by string. I would hit
the plank with a hammer, making sure it pivoted around the end I
had not hit so as to increase the velocity of the plank at the with the
ball of it, the plank would the fly away from the ball and pull the cup
away. The cup would already be falling at this point so its removal
would not affect the spin of the ball. The balls would then hit the
ground and would be reflected back up with the tennis ball going
higher than its original height.
In order to measure the height I used a tape measure taped to a
length of wood. I then used a camera to video the flight of the ball.
Finally I put the videos on a computer and measure where the top of
the ball was at the top of the flight. To increase accuracy I used a
spirit level to ensure that the scale was vertical and I ensured that the
camera was at the height of the top of the ball’s flight to prevent
parallax error.
All the measurements were taken in the early evening to keep the
temperature roughly the same.
To ensure maximum safety I wore safety goggles and stood back
when I dropped the ball. I also made sure that people nearby new
what I was doing so as to stop unnecessary injury from falling balls
or in case of an accident new what had been happening.
Diagram
camera
scale
Tennis ball
washer
football
Pictures
Picture showing the balls set up to drop. The camera is on the left and
the scale is in the background. The balls are released by hitting the
wood sideways with the hammer.
Picture showing the scale with a spirit level to check that it is vertical.
Results
Mass (kg)
Radius (cm)
0.486
10.95
0.056
3.25
Table showing mass and radius of balls
Football
Tennis ball
Central drop
height
(cm)
37.3
48.8
69.9
92.3
116.4
Height 1
Height 2
Height 3
Average
(cm)
(cm)
(cm)
(cm)
64.3
64.6
61.0
63.3
111.1
106.8
111.1
109.6
183.8
168.3
174.8
175.6
224.3
226.3
238.3
229.6
277.3
276.1
284.1
279.1
Table showing measured heights of drop and top of flight
Central height is the height at which the centre of the tennis ball was at before it
was released.
Heights 1,2,3 are measurements of the height the centre of the tennis ball was
reflected up to
Average is the sum of heights 1,2,3 divided by three
To calculate Hf from the central drop height of the tennis ball
Hf = central drop height – tennis ball radius – football diameter
To calculate Vf from Hf
Vf = √2gHf
To calculate Ht
Ht = average height reached – football diameter – tennis ball radius
To calculate Vt from Ht
Vt = √2gHt
Hf
(cm)
12.1
23.6
44.7
67.1
91.2
Vf
Ht
Vt
(m/s)
(cm)
(m/s)
1.5
38.1
2.7
2.2
84.5
4.1
3.0
150.4
5.4
3.6
204.4
6.3
4.2
254.0
7.1
Table showing Hf and Vf for football and Hf and Vf for Tennis ball
Graph
The first graph shows the height reached for each drop height.
Tennis Ball Height reached versus drop
height
300.0
Ht - Height reached
(cm)
250.0
200.0
150.0
100.0
50.0
0.0
0.0
20.0
40.0
60.0
Hf - Drop Height
(cm)
80.0
100.0
The red line is the perfect velocity of the ball which is 3 times its original
velocity. The blue line is its calculated velocity from the measured height.
Tennis Ball Velocity after kick versus
before kick
Velocity "After Kick"
(m/s)
14.0
12.0
10.0
8.0
6.0
Vt
4.0
Expected
2.0
0.0
0.0
1.0
2.0
3.0
Velocity "Before Kick"
(m/s)
4.0
5.0
Errors
Possible errors are from measuring the height from the camera
image due to parallax and focus of around ± 0.5cm. Also if the ball did
not go vertically then it could affect the reading.
Conclusion
From this graph and results I am able to conclude that the calculated
velocity is less than the perfect velocity. This is due to factors such as
the balls not having perfect elasticity and air resistance. As the drop
height gets higher then these factors become more pronounced
meaning that the difference to the expected velocity increases and
the line is a curve.
As the tennis ball is about a tenth of the mass of the football it is not
an ideal slingshot and this is also why the expected velocity is not
reached.