Coke bottle rocket

I was posed this question recently and could not really answer it. I was wondering if any of the scientific brains here assembled could help me?

I make a coke bottle rocket by half filling an empty, inverted, coke bottle with water and then pressurise the air in the bottle to, say, 100psi. Then remove the stopper and watch the bottle launch into the air as the air pressure forces the water out and Newton's third law of motion comes into play.

I then repeat the exercise, but do not use any water. I have twice the volume of air and pressurise it to the same 100psi, but when I release the stopper, I just get a pop and the bottle hardly lifts at all.

In the second case, I have twice as much compressed air, so there must be twice as much stored energy in it, but why so little impulse thrust?

Thanks

In the first version ... the 'jet' is mostly water, which has much greater density than the air., so the reaction is proportionally higher.

MichaelG.

This is really going back to collage (and it is late in the night, for me) but I would Goggle "Rocket specific impulse". Forty five years ago I would have explained what was happening without a seconds thought. The flu jab tomorrow is more important now.

JA

I'd approach this as a conservation of momentum rather than a 3rd law problem. At the start the momentum is zero and as the Coke bottle flies off it must carry as much upward momentum as the stuff left behind does downwards. But the bottle is light, air is light, water is heavy and momentum is mass times velocity. So the bottle has to go fast to make it balance. Bit simplified, I can see other factors, but maybe that helps.

Robin

That's fascinating . If you blow a balloon up and let it go it 'll fly off ..If you half fill it with water and blow it up, invert it and let it go ...I reckon it 'll just hit the floor and make a mess .. Must be something to do with the vessel or that bloke Gifford ! Does a gun still recoil with a blank cartridge ?

Water is incompressible and does not expand as it is expelled. Until the water is expelled, the air can't expand much, so retains most of its energy (pressure) to expel all the water. If it is just air, the air expands very rapidly immediately, with very rapid pressure loss. It might also be that a water jet is more directional, having more momentum, than air which will expand in all directions.

You know i wouldn't recommend this but it probably is the case that coke/water and air are not explosive enough for rapid expansion that would enable flight for something like the bottle.

The answer to the second question is, yes, if the bullet or shell, still retains the firing cap but wouldn't do much without it. There are some designs of weapons than enable a small amount of gas to expell from the rear of the weapon at the moment of ignition, hence the name "recoiless"

Michael W

Edited By Michael Walters on 08/10/2016 05:40:32

If a BFA (Blank Firing Attachment) is fitted it provides a restriction to the gas so that a semi-automatic weapon has enough pressure to re-cock the action. (Typically by a piston acting on the bolt)

So to answer your question, a slight amount of recoil may be felt but nothing like when the real cartridge is fired.

* Danny M *

I think the right answer is that most of the air expelled is still considerably compressed, so it expends most of its energy expanding outside the bottle.

Some of the Physics.

Newton's Second Law of:

Force = Mass x acceleration

a

pplies as soon a 'firing' commences.

For a propulsion system the thrust must be caused by the force of the propellant against the rocket. This will, indeed, invoke Newton's Third Law, so the rocket will move in the opposite direction.

The coke bottle ejects water according to F=ma, but the problem is one of inertia as well as thrust. That bottle is heavy at maximum force (Force = Pressure x Area) and acceleration will be reduced, but as the bottle gets lighter (reduced water content) the force will reduce because the pressure is dropping (not like a space rocket with diminishing mass, but constant force).

It is a balance of pressure and volume of water expelled for our coke bottle and there will be an optimum fill volume for any given pressure. Too little water and the thust will disappear before the rocket has achieved maximum velocity and too much will mean the pressure will be much reduced, thereby expelling water more slowly while still with a high inertia. Added to that, the water being expelled at low pressure will have little increase in velocity in the opposite direction of rocket direction. Of course, the aperture area through which the water is being expelled will have an effect also (ignoring the ever present air friction as the rocket moves faster).

Nothing simple, but while momentum must be conserved, the momentum of the water contained in the bottle and ejected from it will be a very complicated system, with forces of gravity dragging the whole lot towards the centre of the Earth whether inside or outside the bottle! Momentum is easier to sort out when a couple of bodies strike or become a single item.

Back in my Airforce days, and school cadets before that we used .303 rifles, #3 and #4*, and firing blanks from these there was no recoil that I remember.

Ian S C

lol this is so funny we did this in primary school many years ago, so funny to see so many answers lol

The water is about 15,000 times less compressible than air so is inherently more uncompressible.

The water does shoot out, but not explosively as a gas would.

The pressure is almost instantaneously reduced to atmospheric. The air therefor just expells under pressure

This said Water is less compressible as so it can't store energy the way air does. The water is heavier than the air so sinks to the bottom of the vessel it is dense and is ejected by the air pressure under force. Newtons laws come in: To every action there is a reaction, up the bottle goes.

Edited By Martin Newbold on 08/10/2016 19:26:14

There is some recoil from firing a blank cartridge but it's much less than usual because the gun is expelling only the weight of the propellant, which is very much less than the weight of a projectile.

What might not be obvious is that firing blanks makes a gun much hotter than firing live ammunition would. This is because the hot gas is cooled when it does work accelerating the heavy bullet in a live round . Much of the heat is converted into motion, whereas firing a blank produces a lot of hot gas that does nothing but cook the barrel and make a bang.

Dave

The energy of a bullet in ft/lb can be calculated by using the formula

V² x w

64x7000

​when V= projectile velocity in feet per second and w = projectile weight in grains. 64 is the coefficient for gravity and there are 7000 grains to 1lb. To determine recoil, it's a matter then of comparing bullet energy to gun weight - and this is where I forget the rest of the mathematics. I am sure one of you guys out there will soon put me right!

To add to the above, clearly the mass and velocity of what's expelled from a rocket determines thrust. Air alone does not have a lot of mass: water does.

Edited By Mike on 08/10/2016 21:33:31

See **LINK**

This brings back memories of a present I got for my birthday when I was perhaps 7 or 8. A pair of water rockets! They worked just like your Coke bottle but looked MUCH more like proper rockets. They were launched from a hand-held pump/launch pad. My brother and I ran outside to test them before even dressing and returned with saturated PJs and smiles a mile wide. I presume that they were well researched and if I remember correctly, the water level was slightly less than half full.

On a more serious note. Shoulder launched RPGs (Rocket Propelled Grenades) use this principle. If they were to rely solely on their rocket motors (I think) they would probably fall to the ground before getting up much speed. But when fired, there is an explosion which shoots a bunch of stuff that looks like pieces of hard (heavy) rubber bands out of the back of the launcher in a huge blast that levels everything behind the shooter. All that mass rushing backwards launches the RPG forward and the rocket motor takes over. I like to believe that when the loader taps the shooter on the helmet (or is it the shoulder?) to indicate that all is ready to fire, he has also checked behind to ensure that no friendly forces are in the blast area!

In connection with recoil-less weapons. The recoil-less (anti-tank) rifles I have seen also emit a huge blast out of the back of the barrel. They were either jeep mounted or fired from a tripod on the ground. I seem to remember that the caliber was 105mm. If I am mistaken, please forgive me this was all many decades ago.

Recoil of a gun is most easily calculated from the momentum law, as it basically an impulse, where one part of the original body (the projectile) exits the muzzle with a known velocity and mass. Momentum will be mass x velocity and as momentum must be conserved, the recoil of the rest of the original (the gun) will have the same momentum, but in the opposite direction (so if the first value was positive, this will be negative).

Energy can easily be calculated by use of the Kinetic Energy equation E = 1/2mv^2, where, in SI units energy (E) is in Joules, mass(m) is in kg and velocity (v) is in metres/second.

This ignores things like the mass of propellant (that is converted from solid to gas) and any wadding, etc., but is a good approximation for all but the real scientific boffins.

Edited By not done it yet on 09/10/2016 01:32:03

This also explains why a lightweight hunting rifle recoils a bit more fiercely than a heavy barreled rifle of the same calibre and using the same ammunition.

All bets are off though when using something largish such as a .338 Lapua or a .50 cal Barrett as then some of the propellant gas is used to compensate for the recoil by redirecting it to the rear with a muzzle brake. **LINK**

The projectile is up to speed by the time that it exits the barrel but for anybody nearby there is a massive increase in noise and blast because it now coming sideways and backwards..

For that very reason, muzzle brakes are banned under the roofed area at my local rifle range

For sniper use in sandy/dusty areas this blast signature is a giveaway so moving to a new position immediately is advised.

* Danny M *

Thanks for the replies. I think the best answer Is that for the air only case, the very small mass of compressed air is expelled from the bottle and does virtually all of its expanding outside the bottle.