David Edwards BE(Hons) FIEAust CPEng

David Edwards BE(Hons) FIEAust CPEng

1. Introduction 2. What is a billycart? 3. Theory 4. Practice

Introduction I started building billycarts when I was about 8 years old, but stopped when I was about 14, in 1974. While I never achieved as much destruction as Clive James* did in Sunbeam Avenue, Kogarah when he demolished Mrs Braithwaite s poppy garden, I certainly had some thrills and spills. This cart was my first attempt at a steering wheel in a billycart it worked perfectly except that turning the steering wheel to the right made the cart go to the left!!! When concentrating, I could actually make it go where I wanted it to go, but in an emergency my instincts took over with disastrous consequences. In my case, this meant that when some one stepped out in front of me at speed, I ended up upside down in the ditch rather than in the driveway escape route!!!! *See pages 53 57 in his hilarious Unreliable Memoirs

Introduction I started building billycarts again in about 1996 when my elder daughter finally took the hint and said Dad, can you build me a billycart?.

What is a billycart? The Macquarie Dictionary defines a billycart as: billycart // (say 'bileekaht) noun a small four-wheeled cart, usually homemade, consisting essentially of a box on a bellyboard and steered by ropes attached to its movable front axle. Also, go-cart; Especially WA, hill trolley; Especially WA and SA, soapbox. [billy(goat) male goat + cart] Bibliography: The Macquarie Dictionary Online Macquarie Dictionary Publishers Pty Ltd.

A Traditional Billycart

How are billycarts used? In Australia, the tradition is to find a convenient hill, and simply race down it, usually in pairs. Current practice is to have a standing start if the hill is steep enough, or a ramp start. For a standing start, the only energy available is the gravitational potential energy E p = m G h where E p is the potential energy in Joules m is the mass of the billycart and rider in kg G is the gravitational constant (9.8 m/s 2 ) h is the height of the hill in meters.

How fast can you go? Assuming there are no frictional losses, and that there is no rotational kinetic energy stored in the wheels, then at the bottom of the hill there is only translational kinetic energy E t = ½ m V 2 where E t is the translational kinetic energy in Joules m is the mass of the billycart and rider in kg V is the speed in m/s

How fast can you go? We can equate these two energies, and then calculate the speed (at the bottom of the hill) as V = sqrt(2 G h) V is the speed in m/s G is the gravitational constant (9.8 m/s 2 ) h is the height of the hill in meters. Notice that the mass m cancels out, so that the final speed does not depend on the mass The shape of the hill doesn t matter only the height.

BillycartEngineering Height of hill (m) Theoretical speed (m/s) 0 0.0 0.0 2 6.3 22.5 4 8.9 31.9 6 10.8 39.0 8 12.5 45.1 10 14.0 50.4 12 15.3 55.2 14 16.6 59.6 16 17.7 63.8 18 18.8 67.6 20 19.8 71.3 22 20.8 74.8 24 21.7 78.1 26 22.6 81.3 Theoretical speed (kph)

What about the real world? In the real world, wheels have inertia, hills are not vertical cliffs, and there is friction which generates retarding forces. As speeds get higher, we need to ensure stability, so steering is important. Stopping is also important. I will deal with each of these topics in turn.

Wheel Inertia Real wheels have rotational inertia, so some of our potential energy will become rotational energy, and this will reduce the translational energy, so our speed will be reduced. If we ignore the hub and the spokes, we can model a wheel as a mass m w concentrated in the tyre and rim. A wheel of radius r meters on a billycart at speed v meters/sec will have an angular speed ω = V / r radians/sec. The rotational energy E r will be ½ I ω 2 where I is the moment of inertia, calculated as I = m w r 2. Combining these formulae shows us that E r = ½ m w V 2

Wheel Size Note that the wheel size is not a direct component of this formula. However, the wheel mass m w will increase as the wheel size is increased, so smaller wheels are better. Smaller wheels have a smaller frontal area, and this is also a benefit. Smaller wheels also make it easier to reduce the centre of gravity, which enhances stability. Finally, smaller spokedwheels are stronger than larger spoked wheels.

Practical Wheels A thinner tyre and rim profile would be advantageous, but these are hard to find for 12 inch wheels. For my four 12 inch wheels, I have calculated that the rotational kinetic energy E r is less than 1.5% of the total kinetic energy E = E t + E r, so there is not a significant benefit in reducing the wheel size and mass.

Wheel Rolling Resistance This is minimised by having smooth pneumatic tyres. Rolling resistance decreases with increasing air pressure but beware of hot sun and the dreaded blowout!!! If the road is rough, larger diameter wheels will roll better. Three wheels are better than four, but stability is not as good and some competitions require four wheels. Bearings also add a retardation force, but with careful adjustment and the remove of oil seals and heavy greases, this is easily minimised.

Wheel Alignment This is critical. At the front, a solid front swing axle helps here, but does compromise stability. Parallelogram or Ackermann steering, as used in cars, is easy to achieve but does require careful adjustment. Stability is better with Ackermann steering. It is also important to ensure that the rear wheels are correctly aligned a solid one piece axle helps here. Billycarts don t usually have suspension, but chassis flex can cause miss-alignment of the wheels.

Hill Profile I showed earlier that we can calculate a maximum theoretical speed which is independent of the billycart mass and the hill profile. If we consider the hill in two parts, a vertical drop followed by a horizontal run out, then we can start to look at the effects of billycart mass and hill profile. Consider two identical carts, but with one more massive than the other. The frictional losses for both carts are the same. At the bottom of the vertical drop, both carts will have the same speed.

Hill Profile However, the more massive cart will have more translational energy, so as the two carts continue along the horizontal run out, the lighter cart will fall behind, because the frictional losses (assumed identical) will reduce the translational energy (and hence speed) at a proportionally faster rate. On real hills, this is not very significant, as the frictional losses, particularly air resistance, have a more significant effect on maximum speed. Telescope is instrumented, and there is little difference between the speeds I achieve compared with those of my wife Kerry, who is significantly lighter than my 100 kg.

BillycartEngineering GPS Data for Telescope at Yass 5 Nov 2011 45 40 35 Speed (kp ph) 30 25 20 15 10 5 0 0 500 1000 1500 2000 2500 3000 3500 Distance (m) Runs by David & Kerry alternate in this graph. There is no significant difference in maximum speed.

Wind Resistance where F = ½ rho V 2 CdA F is the drag force (Newtons) rho is the density of air (kg/m 3 ) V is the speed relative to the air (m/sec) Cd is the drag coefficient (a dimensionless parameter, 0.25 to 0.45 for a car (dimensionless) A is the frontal area (m 2 )

Wind Resistance Wind resistance increases with the square of the speed, so it becomes very important at high speeds. We can: reduce the frontal area by lying down instead of sitting up reduce the frontal area by having a narrower cart use a streamlined body to reduce the drag coefficient But there is not much else we can do. My Telescope billycart has a frontal area of about 0.5 m 2 and is not very streamlined. My friend Jim s cart has a much smaller frontal area and is much better streamlined so I haven t beaten him yet!!!

BillycartEngineering

BillycartEngineering

Chassis My Sydney cart is named Telescope, because it was designed to telescope in length so as to fit in my Renault Kangoo panel van. Built primarily of wood (recycled IKEA beds!!!), it can be adjusted in length from 1.6 to 2.0 meters. The body is detachable, and is only used in the long version.

Brakes Telescope has 4 wheel disk brakes operated from a dual foot pedal. The dual pedal allows both feet to be used. The brakes are mechanically balanced using 3 levers, so that an equal braking force is applied to each wheel. Modern cars use a hydraulic system to do this, but my system uses strings in practice bicycle Bowden cables. The brakes must be applied carefully, as it is easy to lock up all four wheels and generate flat spots on the tyres.

Steering Telescope uses a string based version of rack and pinion steering. The steering wheel is from an old pram, the steering column is an adjustable walking stick. The rack is a square aluminium tube reinforced with a threaded rod, and slides in steel brackets. The rack is moved sideways by a string wrapped around the steering column. Small ball joints are used to connect the rack to the wheel control arms. The king pins are custom made hinges and about 30 mm of trail is used to make the steering self centering.

Safety A steel roll bar makes a convenient push handle and provides rollover protection. A six point safety harness (recycled from Falcon rear seatbelts) makes sure the driver stays inside the cart. The driver, as required by most billycart rules, wears long trousers, a long sleeved shirt, a bicycle helmet and closed shoes, as well as gloves.

Instrumentation Bicycle computers can be used, but sometimes have difficulty with the high rotational speeds of small wheels. Nowadays, it seems easy just to use a GPS, or even a mobile phone with GPS. The speed profiles I showed earlier were recorded with a GPS my bicycle speedo. However, the data is only recorded at approximately 5 second intervals, so you don t get much data in a 40 second run down the hill.

BillycartEngineering GPS Data for Telescope at Yass 5 Nov 2011 45 40 35 Speed (kp ph) 30 25 20 15 10 5 0 0 500 1000 1500 2000 2500 3000 3500 Distance (m) Individual data points are at the intersection of the straight line segments

Instrumentation I built a custom instrumentation system, based on a commercially available USB Experimenters card and an old laptop. Speed is sensed using an infra red optical interrupter on one of the rear brake disks. There is an analog pitch sensor, and an analog output to drive a speedo. Software is written in Visual Basic. Data is stored in text format on the laptop Hard Disk Drive, and processed using a spreadsheet program.

BillycartEngineering This photo shows the remains of a photo-interrupter on the rear disk brake after the axle bent

Data Recording When the cart is moving, a date/time stamp, clock ticks, wheel counts and pitch data are recorded at half second intervals. The speedo displays actual speed (in kph). The instrumentation senses when the cart is not moving, and does not record data during this time. The speedo displays maximum speed. The clock ticks occur at approximately 1 ms intervals, and are generated using the microprocessors crystal controlled oscillator. The wheel counts are generated from the holes in the brake disk.

Raw Data 6/05/2012 11:13:22 Program started 6/05/2012 11:13:30 K8055 connected Wheel Circumference (mm), 990 Disk Slots, 32 Sample Period (msec), 500 Pitch Offset (counts), 127 Pitch Gain (x 100), 10 Roll Offset (counts), 127 Roll Gain (x 100), 100 TimeStamp, Ticks, Counts, Pitch, Roll 6/05/2012 11:14:25, 64559, 23, 153, 132 6/05/2012 11:14:26, 65149, 32, 152, 132 6/05/2012 11:14:26, 65731, 42, 151, 133 6/05/2012 11:14:27, 66321, 53, 151, 133 6/05/2012 11:14:27, 66903, 62, 149, 132

Data Processing The wheel counts are differentiated to get speed. Speed is differentiated to get acceleration. A hill profile can also be generated by integrating the acceleration data. This means that the hill profile is the same shape (but upside down) as the speed profile. A hill profile can also be generated from the pitch data. This works best when the hill is flat are at the end, and when the start does not involve a ramp.

BillycartEngineering 1400 Distance 1200 1000 Distance (m m) 800 600 400 200 0 0 1 1 2 2 3 Elapsed Time (hours) The 1 st and 3 rd steep vertical sections of this graph represent down hill runs. The 2 nd and 4 th steep vertical sections are when Telescope was towed back up the hill!!

BillycartEngineering Speed 45 40 35 30 Speed (kph) 25 20 15 10 5 0 0 1 1 2 2 3 Elapsed Time (hours) This graph is the differential of the previous graph, and shows speed for the two down hill runs

BillycartEngineering Speed David 45 40 35 30 Speed (kph) 25 20 15 10 5 0 100 150 200 250 300 350 400 Distance (m) The graph shows a single run down hill

BillycartEngineering Speed (kph) 30 25 20 15 10 5 0 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0 50 100 150 200 Distance (m) Heigh ht (m) This graph shows a speed profile and a hill profile, both calculated from wheel count data

BillycartEngineering Hill Profile Run 3 David (no push) 4.0 3.5 3.0 2.5 Height from Pitch (m) Height from Acceleration (m) 2.0 1.5 1.0 0.5 0.0 0 10 20 30 40 50 60 70 80 90 100 Distance (m) This graph shows hill profiles generated from the pitch sensor (blue) and from wheel count data (red)

Test System In order to facilitate development of the instrumentation, I have also built a test system, which is much more convenient than Telescope. The test system uses a small motor to rotate a disk brake hub and disk, and a complete spare set of electronics. A DC power supply and laptop computer are also part of the test system. The pitch sensor is replaced with a hand adjustable potentiometer, and a small panel meter takes the place of Telescope s speedo.

BillycartEngineering Telescope Test System

This is a screenshot of my Billycart Monitor

Conclusion I have a web page devoted to billycarts. If you do a Google search for billycarts, you will help me keep it at the top of the search results.