Billycart Theory
Introduction
This page is an attempt to explain some of the basic theory of
billycarts. A billycart can be considered as a machine for converting
gravitational energy into kinetic energy, using a hill.
Starting at the top of the hill, a billycart and rider will have
maximum gravitational energy, and no kinetic energy at all. If
all goes according to plan, at the bottom of the hill there will be no
gravitational energy and maximum kinetic energy. Hopefully,at the
bottom of the hill the gravitational energy will all have been
converted into kinetic energy, and the billycart will be going quite
fast and its driver will be having fun.
Let's consider a stationary billycart and driver of mass m kg on top of a hill of height h metres. The gravitational energy of the billycart can be calculated using elementary theory as Eg = mgh Joule, where g is the acceleration of a mass towards the centre of the earth, and equals 9.81 m/sec^2. The kinetic energy can be calculated as Ek = 1/2mv^2, where v is the speed of the billycart in metres/second, and again m is the mass in kg. Since the billy cart is stationary, we will have v = 0 metres/second and hence Ek = 0 Joule.
At the bottom of the hill (we'll worry later how we get there) , our height h will be 0 metres, and we will have a speed of v metres/second. We will have gravitational energy Eg = 0 Joule and kinetic energy Ek = 1/2mv^2 Joule.
Assuming no energy losses, we can equate the gravitational energy at
the top of the hill with the kinetic energy at the bottom of the hill,
getting
mgh = 1/2mv^2 Joule
Some elementary algebra allows us to solve this equation for v, so that
v = sqrt(2gh) metres/second
The first thing to notice about this equation is that the speed v at the bottom of the hill does not depend on the mass m.
This is in accordance with Galileo's famous theory where he found that
the time it takes a body to fall does not depend on the mass of the
body. This link allows you to download a zipped movie showing the Apollo 15 astronauts demonstrating this on the moon.
The table below shows the speed calculated in accordance with this equation for a range of hill heights
| Height
(m) |
Speed (m/s) |
Speed (kph) |
| 0 |
0.0 |
0.0 |
| 2 |
6.3 |
22.6 |
| 4 |
8.9 |
31.9 |
| 6 |
10.8 |
39.1 |
| 8 |
12.5 |
45.1 |
| 10 |
14.0 |
50.4 |
| 12 |
15.3 |
55.2 |
| 14 |
16.6 |
59.7 |
| 16 |
17.7 |
63.8 |
| 18 |
18.8 |
67.7 |
| 20 |
19.8 |
71.3 |
| 22 |
20.8 |
74.8 |
| 24 |
21.7 |
78.1 |
| 26 |
22.6 |
81.3 |
| 28 |
23.4 |
84.4 |
| 30 |
24.3 |
87.3 |
The Technopark Hill at Dowsings Point in Tasmania is 18 metres high,
and our calculated speed is 67.7 kph. The maximum speed reached by
members of the Southern Tasmanian Billycart Group down this hill is
about 62 kph.
