SIMPLE BUT NOT ALWAYS EASY TO EXPLAIN
Raffiniert ist der Herrgott, aber boshaft ist er nicht.
[Subtle is the Lord God, but malicious He is not.]
Albert Einstein speaking at Princeton University, 1921
1. BLUNDERSPUDS AND CARROT CANNONSâARTILLERY AND BOYLEâS LAW
Encyclopedia Britannica, 1911
The spud gun was a staple weapon of junior soldiers from at least the 1960s onwards. It comprised a tiny piston mounted on the handle of a toy handgun, the trigger of which pulled back a cylinder over the piston. The cylinder had a nozzle that could be jabbed into a potato, removing a pellet. When you squeezed the pistol hard, you compressed air in the cylinder and the pellet of spud was ejected like a small bullet. Later a three-in-one design came out that could do more. It could not only fire pieces of potato, but also squirt water and ignite tiny explosive caps.
I have to admit, however, that I have recently tried out these weapons of my youth, and they are much less impressive than I recall. Perhaps instead of a potato pistol, we should aim for something a little bigger, a potato musket maybe?
In the olden days there was a very large-bore musket rather wonderfully named a âblunderbuss.â With the assistance of the kids at our Saturday Science Club in Guildford and a little science, I decided to come up with a vegetable equivalent worthy of the name âBlunderspud.â (Though as it turns out, we discovered that carrots actually made the best bullets . . . so I guess weâll have to call it a Carrot Cannon from now on.)
What You Need
A metal tube about 600 mm (24") long, preferably steel, thin-walled, with an internal diameter of 10â20 mm (3/8"to 3/4"), or a plastic tube of the same length, thin-walled (about 1.5 mm), with an internal diameter of about 20 mm (3/4")
A plunger: a strong round wooden rod or bamboo stick that fits inside the tubing
Sponge rubber or plastic, duct tapeâto make a hand protector for the plunger
Carrotsâlarge onesâlarger in diameter than the outside of the tubing
A rod or tube (of steel or some other strong metal) that fits loosely inside the tube (for widening the tube at the ends)
A hacksaw
A round file, a deburring tool, or a knife
What You Do
You can use plastic, copper, or other metal tubing for the carrot cannon. First cut your barrel to, say, 600 mm (2') long. The longer the barrel, the more compressed air there will be to store energy, so long is good. However, there is an ergonomic limit to how long you can make the barrel, because the plunger needs to be longer than the barrel, and you need to be able to push the plunger with a high degree of force into the barrel. So, unless you have arms like a gorilla, the plunger shouldnât be much longer than 900 mm (3'), including 150 mm (6") for a handgrip.
Next you need to bevel the edge of the ends of the tube on the inside of the tube to sharpen it. You will then be able to cut into the vegetable with a reasonably low force. More subtly, that bevel should be on the inside so that the piece of vegetable cut off will be slightly larger than the inner diameter of the tube; that way it will form a gas-tight seal. I find that a simple craft knife will do a reasonable job of this on plastic, but you may find it easier to use a file, and a file is certainly indicated for metal. I also have a slightly unusual workshop tool called a âdeburring tool.â A deburring tool consists of a tiny curved blade made of hardened steel that is mounted so that it rotates freely in its handle. It is easy to use and does a neater job. The edge of the tube doesnât need to be razor sharpâcutting the edge down from its normal 1.5 mm to, say, 0.7 mm or 0.5 mm will be fine.
Now, if you are using copper tubing, it may help to widen both ends of the tube further by bellying the tubing out slightly as follows: insert the steel rod 1/2"to 1" into the tube and roll it around, so that it bellies out the ends of the tubing slightly. Copper tends to be surprisingly malleable and can be worked in this way quite easily. Repeat this process until you have a tube end 1 mm (1/32") or more wider than the body of the tube.
Then you must tape a hand protector securely to the plunger, leaving a large enough portion of the plunger-rod projecting out to ensure that your hand can get a firm grip. The protector prevents you from cutting your hand on the sharp end of the tube when you shoot. You could also incorporate a handgrip near the breech end of the tube to allow you to put more force on the carrot cannon when firing. Now place a large carrot on a flat surface, use one hand to guide the tube into the side of the carrot, and the other to push it downwards, thus cutting a piece of carrot and pushing it up the tube. Do the same again at the other end, so that you have carrot in both ends. Now place the plunger on the ground or on a tabletop and, guiding it with one hand, force the tube down onto the plunger, pushing in one piece of carrot (the bullet carrot) 25 mm (1"). Do the same at the other end with the piston carrot, pushing it in perhaps 50 mm (2") or more. You are now ready to fire.
Push the plunger hard and reasonably fast, while aiming the muzzle of the tube at the target. With luck, the piston carrot should slide down smoothly toward the bullet carrot until the bullet carrot suddenly shoots out at high speed.
Trouble can arise if the piston or projectile leaks. If this happens, just eject them and try again, or simply put another carrot plug in the piston end and try again; you then will probably fire two plugs of vegetable instead of one.
The cannon we have constructed here works by compressing air, with the breech carrot plug acting as a piston inside the cylindrical tube. As the air is compressed, force builds up on the other piece of carrot until the static friction between the latter and the tube wall is insufficient to keep it in place, and it shoots out of the tube at very high speed. The piston carrot should just fall to the ground in front of the weapon.
You will find that carrots work well. They are best loaded transversely, but obviously you need good large carrots, large enough so that when the tube cuts into them the tube is entirely filled. Vegetables that are hard and fresh are best, although aged carrots can be restored somewhat by soaking them in cold water for a while.
Try other vegetables: carrots are very good, but is there something better?
- Potatoes work pretty wellâbut theyâre not as good as carrots.
- Try a larger-bore cannon, a veritable blunderspud (âblundercarrotâ just doesnât have the same ring to it . . . )âbut beware!âit may need a lot of force from your arms to make it work well.
You can now try out various ways to improve your weapon. One neat feature might be the ability to use the piston of one shot as the projectile for the next shot, but youâll have to get the length of the plunger just right. (Thanks to Geoff Thomson for this excellent refinement.) How well does this work? Does a pellet of potato that has been used as a piston actually work properly as a projectile after it has been pushed down the barrel and perhaps lost some of its frictional properties? Could you deal with this by actually narrowing the muzzle end of a carrot cannon? And what about extending a widened barrel to act as a low-friction expansion chamber, to ensure that as much of the energy in the compressed air as possible becomes available when the pellet starts to move. A related question: Is it worth packing the projectile further down inside the barrel? Does this give it longer to accelerate under the compressed air pressure?
What is the best angle at which to aim the tube for maximum range? And what happens when you use bigger or smaller tubes?
Hazard Warning
Donât fire a carrot cannon directly at anyone unless they are wearing high-quality protective goggles, such as those sold for use in paintball games, and do not fire at anyone who is close at hand. Although carrot bullets are pretty harmless, they can cause a big bruise at close range, and a direct hit on someoneâs eye could cause blindness, which would be appalling.
Less dramatically, watch out that you donât cut your hand while loading the carrot cannon. Leather gloves may be helpful at first. And donât forget to include the hand protector and to position your hand behind it so that it protects you.
How much does the rate at which the potato musket is driven affect the final muzzle velocity?
And what about the accuracy of the device? Does the short ride up the barrel mean that the weaponâs aim is necessarily inaccurate?
The amount by which the barrel and breech ends are bellied out is important. The first affects the frictional grip of the muzzle end, and the second the gas seal of the piston. How tight does its fit have to be to give a good seal?
How It Works: The Science behind the Carrot Cannon
Boyleâs Law tells you how much pressure increases when you compress a gas. It says that the pressure increases in proportion to the reciprocal of the volume. So when the volume goes down, the pressure goes up. In math, we might put this as:
P = k / V,
where P is the pressure, k is a constant, and V is the volume of the gas. The pressure we talk about here is the absolute pressure, not the pressure relative to atmospheric pressure or gauge pressure. The air in the cannon starts off at 0 barg (0 psig), which is 1 bara (15 psia).
So if we start with a volume of, say, 60 cm3, and finish with 6 cm3, then the pressure will have gone from 1 bar absolute (15 psia) to 10 bara, which is 9 bar gauge (130 psi).
Another way to consider the carrot cannon is to estimate the energy (E) stored in the compressed gas as being proportional to the logarithm of the pressure reached and to the volume of the tube. Using this formula, we can estimate the energy as roughly 10 Joules.
If all of this energy were delivered to the projectile, then the projectile would have a speed proportional to the square root of the energy divided by its mass. In fact, 10 Joules would be enough, theoretically, to take a 5 g (1...