DragMath

I'm taking a bit of a break from experimenting this week as it's the bank holiday in the UK and everyone is away (apart from me - boo hoo). I've been thinking about the YourMathsTutor website and finding a neat way of integrating some sort of LaTeX maths editor into the forum to make it easier for people to include extracts of maths in their posts. I'm a Moodler, amongst other things (yes - it is legal. Click here for more information). And being a member of the Moodle Mathematical Tools forum I came across the new DragMath tool from Chris Sangwin and Alex Billingsley at The University of Birmingham here in the UK. I thought it would be marvellous to incorporate this tool into the YourMathsTutor forum. To view the results of an afternoon's sawing and hammering noises coming from the forum corner of the YourMathsTutor site click here.

The YourMathsTutor forum is actually an SMF (which stands for Simple Machines Forum) forum, a pretty powerful open source forum which has only been going a few years but even so is becoming extremely popular.

If you are interested in how I integrated DragMath into my forum then you can download a tar.gz archive with all the bits you need (and a readme) from here. Maybe there is a better way of doing it? If so then please do post a comment. I think DragMath is an excellent bit of work and would love to see it take off.

The Singing PC

I'm part way through attempting to knock together an experimental setup I saw many moons ago on a visit to the University Of Hull. The idea is pretty simple: convert sound to light, shine the light onto a detector, then finally convert the light back into sound again. This one is quite interesting from the - possibly boring, sorry :'( - physics point of view, because we are having to deal with different types of energy...

• Sound
  Sound is a pressure wave - a longitudinal wave - of moving air molecules. I have often read in text books and on the Net that sound is energy but that isn't right. Because sound is air moving about it is technically kinetic energy.
  
• Electricity
  This is a complicated one. The concept is quite simple:- all atoms contain electrons and in electrical conductors the electrons are free to move from one atom to another (in electrical insulators the electrons can't move so they don't conduct electricity). Actually how it works is a bit more complicated (involving magnetic fields and things). So although electricity is moving electrons this isn't simply kinetic energy - there is more to it than that.
  
• Light
  This is electromagnetic energy - a mixture of electrical and magnetic energy.
  

We are going to transform energy into these three different types of energy...

(COMING SOON)

Initially we will put together the light-to-sound converter. Here is the parts list (click on the part to jump to the relevant Maplin page)...

1. Photodiode SFH2030
2. Mono preamplifier
3. Norwich 3.5W audio amplifier
4. 49mm Mylar speaker

...and then there'll be wire, batteries, and all that, to power the thing. Note that the amp and preamp draw about 500mA (according to their spec.) so I powered this with 6xAA batteries (rechargeable, of course!).

At this stage I should admit that I was going to build my own preamp and amp but when I was wondering around Maplin looking for parts and found these I was overcome with a bad bout of idleness on my part. That said, I know that you can make a photo detector out of a piece of heated copper and a drop of brine - an idea for a later project there, I think.

Here is a schematic (click on the image to see an enlargement)...

And here is a picture of the prototype (on my particularly messy desk)...

Your eyes don't see continuous images - in other words what you actually see flickers, but you don't notice it (what you see is also, bizarrely, upside down. Your brain flips the image on the back of your eye the right way up). Your ears have much better resolution, is the term. So when I switched on the light over my desk it buzzed. That's because mains electricity is supplied at 50Hz (50 cycles per second). This means the bulb will be flickering 100 times a second - I can't see that but I can hear it with my new new detector.

I was having a play with the monitor refresh rate on the PC when my eldest lad came in and suggested that we have a look at a Linux project called Tempest For Eliza. This program uses your monitor to broadcast music on an AM radio signal. It does this by flickering the screen, causing your monitor to radiate radio waves that you can pick up on a radio (here is a YouTube video of this). Our idea was that our light detector should be able to pick up that flicker and turn it, in theory, into music.

Here are the results...

Lemon powered calculator!

In this project we are going to build a lemon battery, then use this to power a calculator. Many thanks to Jess for helping me with this one.


With a zinc and a copper electrode stuck into either side of a juicy lemon you can generate about 0.9 volts. Connect a couple of these lemon 'cells' together and you can make a battery that can generate enough power to supply a watch or a calculator.

What you will need

1. two galvanised screws (must be zinc coated - that's what galvanised means).
2. high current single core copper wire (not the stranded type). My wire was an offcut from Homebase.
3. stranded wire (from the Worcestershire Resource Exchange).
4. a cheap calculator (mine was £1.49 from Staples).
5. 2 lemons. Have a think about going organic. I know they are more expensive but by buying organic you are not promoting the use of nasty chemicals (they do less to them but they are more expensive. Erm...).
   
6. plastic cups (to hold the lemons).
7. piece of wood (to attach everything to).
8. wood screws and cup washers (to do the attaching).

You might also find a voltmeter useful to check the voltage your lemon battery is generating and the polarity (in other words which terminal is positive and which is negative). We also used a soldering iron to connect all the wires together but it isn't vital as long as you've got a good connection at each joint.

How to put it all together

Firstly cut the tops off the plastic cups so that they hold the lemons in place. Screw these onto the wood, nearer what will be the back.

Next cut yourself 2 bare lengths of copper wire about 6 or 7 cm long.

For each lemon, push a screw into one side and a length of copper into the other. The copper will be the positive terminal and the screw the negative terminal (if you have a voltmeter you can check this).

Now you need to connect the negative terminal of one cell to the positive terminal of the other (in other words connect the screw in one lemon to the copper wire in the other). We soldered a length of wire between them, but it really doesn't matter how you join them up as long as you have a good connection.

Now solder a longer wires to the two ends of the battery ready to connect to the calculator.

The calculator we have is solar powered (see the post Charge your batteries using the sun! for more info on solar cells) with a battery backup. We disconnected the solar cell and soldered the wires from our battery onto the calculator's battery terminals (if you see what I mean)...


Now try turning on your calculator! To prove to yourself that it is the lemon battery powering the calculator try pulling out one of the copper electrodes.

How does that work then?

All metals try to either give out or take in electrons. So to create a battery firstly we need two metals - one that gives out electrons and one that takes them in. We used zinc (the coating on the screw) and copper (the wire) because they are pretty easy to come by. If you put the wire and the screw into a liquid that will conduct electricity, technically called an electrolyte (in our case lemon juice), then electrons from the copper (which tries to give out electrons) will move over to the zinc (which tries to take in electrons). Electrons are negatively charged so the copper, which is now short of electrons, ends up being positively charged and the screw, which now has electrons from the copper, ends up being negatively charged.

Try putting a screw on one side of your tongue and a length of copper wire on the other. Does it tingle?

A Prisoner Of War Radio

Here is a clever experiment. It is a called a foxhole radio (US soldiers call dugouts 'foxholes') or a PoW radio (i.e. prisoner of war radio). If you were trapped in a prisoner of war camp, like R.G. Wells who was captured by the Japanese, then a vital skill was being able to knock up a radio out of anything you found around you. Prisoners of war often used a small piece of coke (the fuel, not the drink or the drug). Solders in the field used a Gillette Blue razor blade (see the picture, right). We are going to use a junior hacksaw blade from Homebase. It must be blued (when you hold the blade up to the light it has a blue'ish lustre to it). The blue comes from a heat treatment that is applied to the blade to make it stronger. We are also going to need...

1. 30 SWG enamelled copper wire
2. High impedance earpiece (or a piezoelectric speaker will do), but it must be high impedance - a crystal earpiece rather than a magnetic one.
3. A kitchen roll
4. A scrap piece of wood to attach everything to
5. Short-length self-tapping screws
6. Cup washers
7. Paper clip
8. Safety pin
   
9. A short length of pencil lead
10. Small piece of foil
11. Sand paper or emery cloth
    

The cup washers are quite a neat way of joining two bits of wire together, as you will see in the picture below (click on the picture to enlarge it). Here is the finished set up (thanks to Jess for helping me put this one together)...

Assembly Instructions

1. Wind 100-150 turns of our copper wire around the kitchen roll. Cut the spare, bare length of kitchen roll off as you don't need it and it will be in the way. Firmly attach this to the wood (Jess and I screwed it on).
2. Using some sandpaper or emery cloth remove the enamel off the ends of the wire and rub the enamel off the copper wound around the roll along the length of the tube, as you can hopefully see in the diagram (click on the diagram to enlarge it)
3. Rub some of the blue oxide off the end of the hacksaw blade ready for a wire to be attached to the bare metal (don't rub the oxide off all of it!)
   
4. Attach the pencil lead to the point of the safety pin by wrapping foil tightly around them both. The lead is then "sprung loaded" against a blued bit of blade (that's why we are using a safety pin).
5. Now join everything together using the schematic shown below (click on the image to see an enlargement)...

Wipe the paper clip against the exposed copper wrapped around the kitchen roll. If all is well you should be able to hear cracking from the earpiece. You should, in fact, be able to hear (probably) BBC Radio 5.

How does that work, then?
Our hacksaw blade is technically called a detector or diode. A diode allows electrons to flow one way but not the other. A coil and a capacitor together made an oscillator. Inside the oscillator electrons are actually doing the oscillating. If we adjust the position of the paper clip then we can make the electrons oscillate at different frequencies. That's how we can tune in this radio. The coil is obvious but where is the capacitor? Capacitors have two plates, and in our case the antenna is one plate and the ground beneath it is the other. The electrons are trying to oscillate back-and-forth, but the detector only allows the electrons to move one way. That means the electrons are shunted around the circuit, generating a current which is then converted to sound in the earpiece.

Now you are armed with this knowledge, if you are stuck in a dugout or a prisoner of war camp you should have a good idea of how to be able to put together a simple radio receiver for yourself!

Make Your Own Match Rocket

Here is a simple rocket you can make to while away an otherwise boring summer's afternoon. There are lots of plans for very complicated match rockets on the net (have a look at some of the videos on YouTube below - including one of our many attempts), but all you really need to get started is two matches and a small piece of kitchen foil.

Simply lay the matches head to head in the middle of a small rectangle of foil.Then wrap the foil around the matches but twist it tightly around one match and leave it loose around the other, so that the loose match can slip out easily (when a match head ignites it tends to expand slightly and can get stuck).

Prod the loose match into the ground at an angle of roughly 50^o. Hold a flame on the foil and wait for lift-off!

You can see from all the spent matches in the video below that we had a lot of fun with this one. I have to admit that the launch we recorded is a bit lame - one of our attempts managed to fly just over 3 metres but we didn't manage to catch it on film.