Coke bottle rocket

[davidsuffolkParticipant @davidsuffolk]

When I saw the title I thought at first of a different coke bottle rocket. I had seen the water pressure type but I had also seen the combustion type and made one for my grandson. These involve using a spark generator such as a BBQ lighter and a fuel.

The video I saw recommended rubbing alcohol but I found lighter fuel more reliable (a VERY small amount).

The resulting flash and bang is quite something and the plastic bottle goes maybe 60yards.

Link for anyone interested to make https://www.youtube.com/watch?v=wuz0curb_hg

[martin perman 1Participant @martinperman1]

Gentlemen,

A couple a links to multistage water rockets https://www.youtube.com/watch?v=mTUGKhrt7fM         https://www.youtube.com/watch?v=4r9gmLfpFTg

The heights are impressive.

 

Martin P

Edited By martin perman on 09/10/2016 11:12:21

[SillyOldDufferModerator @sillyoldduffer]

Posted by Mike on 08/10/2016 20:40:15:

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

V² x w

64×7000

​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!

Picking up on the challenge, with no apologies for working in MKS. (Dividing by 64 x 7000 indeed!)

With thanks to Wikipedia for the approximate weights of the Lee Enfield and 303 bullet.

From this I conclude that firing a Lee Enfield whilst holding the butt against the tip of one's nose would be a very bad idea! Has anyone who has done any shooting tried this?

When the gun is held correctly, the mass of the soldier must become part of the system, helping to further reduce the effect of recoil, but it must still be quite a kick. This reminds me: for a few years I went to an Army Primary School in Malta that was part of a large Barracks. It had a firing range. Somehow we knew that many soldiers don't like firing practice and that some of them would bury live rounds rather than shoot them. We used to dig them up and try and set them off with small bonfires and rocks, never with any success. Ignorance is bliss!

The same equations can be applied to the bottle rocket. The mass of the water is equivalent to the mass of the gun, and the mass of the bottle is equivalent to the mass of the bullet.

As usual hoping I got the sums right!

Dave

 

Edited By SillyOldDuffer on 09/10/2016 12:08:22

[Neil WyattModerator @neilwyatt]

Sorry, no. The same amount of momentum goes into bullet and gun. It's the average force generated by the charge over the time the charge is acting on projectile and gun in newton-seconds.

p = mv

so momentum of bullet = 0.01 x 750 = 7.5 newton-seconds

momentum of gun = 7.5 newton-seconds

velocity of gun = 7.5/5 = 1.5 m/s

Which is rather less likely to rip your shoulder off your body…

I remember doing this in school physics and it explains why most of the energy goes into the bullet. If you think about it the explosive force on bullet and gun is effectively the same, but the bullet moves much further and as energy = force x distance moved…

Neil

[SillyOldDufferModerator @sillyoldduffer]

Posted by Neil Wyatt on 09/10/2016 12:59:23:

Sorry, no. The same amount of momentum goes into bullet and gun. It's the average force generated by the charge over the time the charge is acting on projectile and gun in newton-seconds.

p = mv

so momentum of bullet = 0.01 x 750 = 7.5 newton-seconds

momentum of gun = 7.5 newton-seconds

velocity of gun = 7.5/5 = 1.5 m/s

Which is rather less likely to rip your shoulder off your body…

I remember doing this in school physics and it explains why most of the energy goes into the bullet. If you think about it the explosive force on bullet and gun is effectively the same, but the bullet moves much further and as energy = force x distance moved…

Neil

Sackcloth and ashes again – I think you have a point about momentum. Not too sure about "most of the energy goes into the bullet" though, because every force has an equal and opposite reaction?

Back to the drawing board for me. Where's that Physics Textbook gone, and why didn't I pay attention at school…

Dave

[MikeParticipant @mike89748]

Dave, If any of those live rounds you lit fires underneath had gone off, you would have been in more danger from the cases than the bullets, as much of the preceding mathematics shows. Well-documented experiments I read of years ago show that it's very difficult to seriously hurt yourself if a rifle or shotgun cartridge goes off outside a barrel.

I know I'm old-fashioned, but I still prefer to do my ballistic maths using grains and feet per second. I'm not even sure what a newton-second is. In the interests of research for the job I do, writing for a shooting magazine, I have just bought the latest edition of Frank C. Barnes's "Cartridges of the World", in which, being an American publication, grains and feet per second are still used. Sorry, Neil, but most shooting men prefer things this way.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Mike on 09/10/2016 13:26:53:

Dave, If any of those live rounds you lit fires underneath had gone off, you would have been in more danger from the cases than the bullets, as much of the preceding mathematics shows. Well-documented experiments I read of years ago show that it's very difficult to seriously hurt yourself if a rifle or shotgun cartridge goes off outside a barrel.

I know I'm old-fashioned, but I still prefer to do my ballistic maths using grains and feet per second. I'm not even sure what a newton-second is. In the interests of research for the job I do, writing for a shooting magazine, I have just bought the latest edition of Frank C. Barnes's "Cartridges of the World", in which, being an American publication, grains and feet per second are still used. Sorry, Neil, but most shooting men prefer things this way.

Now I'm old I'm much more cowardly than when I was aged 10 but I'm still glad to know that setting fire to ammunition isn't quite as dangerous as it sounds!

As to ballistics measurements, I'm now finding that most of the web speaks in grains and feet per second. I think you mentioned in another post that you write professionally on shooting, in which case you're very wise not to try to metricate your readers.

Personally I'm more comfortable with metric because it avoids most of the 'magic numbers' that pop up in imperial calculations. Having a system were you have to know that there are 7000 grains to the pound seems an unnecessary complication, especially when your maths is as accident prone as mine! On the other hand, if I'd spent a lifetime working in fps I'm sure I'd see metric as an unnecessary complication, even though it is easier.

Regards,

Dave

[SillyOldDufferModerator @sillyoldduffer]

Posted by Neil Wyatt on 09/10/2016 12:59:23:

Sorry, no

…

Neil

I was ready to put that young whippersnapper Neil back in his box by quoting "Actioni contrarium semper & aequalum esse reactionem, sive corporum duorum actiones in se mutuo semper esse aequales & in partes contrarias dirigi.". This was to be rounded off with a sharp reference to the proof given by Cremona, Le figure reciproche nella statica grafica, 2nd ed., Milan 1872

Regrettably, the evidence doesn't support my attempt at the recoil calculation. He's right and I'm wrong.

Much chastened the wretched duffer retreats to his workshop…

Cheers,

Dave

[not done it yetParticipant @notdoneityet]

Time of acceleration is the key to the calculations, for Newton's second law to apply. Time of flight being for the projectile exiting the muzzle.

Applying f=ma for this time results in the energy transfer. Using the average acceleration and time one can calculate the average force applied.

Whatever that value (it matters not) because applying that same force, whatever it might be, to a large inertial body (mass of gun) will provide the average acceleration for the given time. Because the gun is so much more massive, the final velocity will be so much smaller than that of the bullet. Because the energy in Joules is proportional to both the mass and velocity squared, the energy of the bullet will be far higher due to the velocity squared part of the calculation.

Firing shotgun cartridges outside the gun normally results in the case splitting. So the burn energy is dissipated sideways through the split. Furthermore, the burn rate is far diminished because there is little pressure build-up. In the case of a steel cased bullet, things are not quite so benign. Pressure build-up rate can result in far higher pressure before the bullet is discharged from the case.

Not anywhere near as high velocities, of course (time of acceleration is short), but there is the possibility of lethality, all the same, at close range. Depends if the bullet and case fly apart in opposite directions or if the case bursts. Not something to try. Years ago, many .303 bullets were fired by the village lads by sticking the bullet in a crevice and firing them off with an airgun touching the primer. They certainly carried a punch! I've fired cartriges stood on the end of an airgun, but never tried to fire a .303 that way.

At junior school in the 1950s we used to make long cordite or gunpowder trails around the playground and light them off at the end of the playtime. There were plenty of live ammo around in those days. It was not until about 1973, when the army disposal teams were enlightened to our local ammo dump (after a WWII practice mortar bomb killed a lad who found it, took it home and was told to take it away), that the area was cordoned off and cleaned up. I also know that a Stirling sub machine gun was thrown in a pond where I lived. The 'easier' days of the black home guard cartriges. Certainly lethal when used to blow carrion crow's nests out of high trees from a good distance. Dad only used his best gun, and the open choke, for those cartridges!

[HacksawParticipant @hacksaw]

I was born on the same day as Issac Newton (but not the same year ) 

Edited By Hacksaw on 09/10/2016 18:14:28

[DodParticipant @dod]

Back to Coke bottles, we did quite a few days of shooting off various sized mineral water bottles in the skool in what I work and the best, most memorable shot is always the last one, just like the RPG, ask for a volunteer to do a shoulder launch and the cockiest show off steps up not having worked out why the launch area is sodden, shove cork in extra well.

Pump up bottle and watch class fall about laughing

[Robin GrahamParticipant @robingraham42208]

But how does one get TeX to produce a jpeg – that's the real problem. Dave's analysis of the rocket problem may have been flawed, but the presentation was impeccable. My (possibly antediluvian) software only does postscript.

Robin

[SillyOldDufferModerator @sillyoldduffer]

Posted by Robin Graham on 10/10/2016 00:49:41:

But how does one get TeX to produce a jpeg – that's the real problem. Dave's analysis of the rocket problem may have been flawed, but the presentation was impeccable. My (possibly antediluvian) software only does postscript.

Robin

For the interested latex is a publication quality mathematical typesetter. It's available free for Linux, OS/X and Windows. It converts a character script entered with an ordinary editor into presentable maths. For example $$e=mc^2$$ is turned into a proper rendition of Einstein's e=mc²

I used latex (pdfTex) 3.14159265-2.6-1.40.16 on Ubuntu 16.04. (Yes, the version number is based on pi)

The tex family are command line programs. By default my latex outputs DVI files. I also have pdflatex, where the default output is a pdf file, and – although I haven't installed it – there is pslatex, which outputs postscript.

There are many ways to convert DVI, pdf and postscript to jpg (see the DVI files link for an incomplete list). I wouldn't normally convert any typesetting format to jpg, except that this forum uses it. The main limitations of jpg in this context are that it's a single page format, and the compression algorithm isn't good at typescript or line drawings.

I normally use the ImageMagick convert utility for this kind of job – it would be as simple as typing 'convert recoil.dvi recoil.jpg' except that fine control is needed to get an un-pixilated rendition. It can be quite a fiddle with the parameters to get a good looking DVI conversion.

In this case I generated the DVI file and displayed it on screen. Then I used gnome-screenshot (SHIFT-PrintScreen to get the cursor select option), and saved the screen-shot as a jpg. (Normally screen shots are saved as png, but changing the suffix to jpg produces a decent jpg directly.)

Regards,

Dave

Edited By SillyOldDuffer on 10/10/2016 12:48:15

Edited By SillyOldDuffer on 10/10/2016 12:48:51

[SillyOldDufferModerator @sillyoldduffer]

Posted by SillyOldDuffer on 10/10/2016 12:46:57:

Posted by Robin Graham on 10/10/2016 00:49:41:

But how does one get TeX to produce a jpeg – that's the real problem. Dave's analysis of the rocket problem may have been flawed, but the presentation was impeccable. My (possibly antediluvian) software only does postscript.

Robin

…

I normally use the ImageMagick convert utility for this kind of job – it would be as simple as typing 'convert recoil.dvi recoil.jpg' except that fine control is needed to get an un-pixilated rendition. It can be quite a fiddle with the parameters to get a good looking DVI conversion.

…

Edited By SillyOldDuffer on 10/10/2016 12:48:51

Just found that the simple answer to getting a good conversion from convert seems to be to specify a density on the input file, thus 'convert -density 400 recoil.dvi recoil.jpg' The default input density is only 72 dots per inch. For printing 400 dpi or higher will be much better.

[Jon GibbsParticipant @jongibbs59756]

Posted by not done it yet on 09/10/2016 17:45:30:

Years ago, many .303 bullets were fired by the village lads by sticking the bullet in a crevice and firing them off with an airgun touching the primer. They certainly carried a punch!

Sorry it's off topic but your post really made me smile. My old Dad is no longer with us but sported a small light coloured scar up the side of his right eye.

As a kid he'd been "lucky" to receive just the glancing blow when a 303 cartridge stuffed into a wall returned almost on the same path as the air rifle pellet.

He was always a good shot becoming a firearms office in the Police after a spell in the Guards.

Jon

Edited By Jon Gibbs on 10/10/2016 14:52:09

[Jon GibbsParticipant @jongibbs59756]

Posted by Neil Wyatt on 09/10/2016 12:59:23:

Sorry, no. The same amount of momentum goes into bullet and gun. It's the average force generated by the charge over the time the charge is acting on projectile and gun in newton-seconds.

p = mv

so momentum of bullet = 0.01 x 750 = 7.5 newton-seconds

momentum of gun = 7.5 newton-seconds

velocity of gun = 7.5/5 = 1.5 m/s

Which is rather less likely to rip your shoulder off your body…

… That is the primary recoil but there is the stronger secondary recoil to consider due to the gasses leaving the barrel.

This is what muzzle brakes are designed to mitigate against and I guess what powers the coke bottle rocket after the stopper has blown out of the bottom.

Jon

[duncan webster 1Participant @duncanwebster1]

Posted by SillyOldDuffer on 10/10/2016 13:35:09:

Posted by SillyOldDuffer on 10/10/2016 12:46:57:

Posted by Robin Graham on 10/10/2016 00:49:41:

But how does one get TeX to produce a jpeg – that's the real problem. Dave's analysis of the rocket problem may have been flawed, but the presentation was impeccable. My (possibly antediluvian) software only does postscript.

Robin

…

I normally use the ImageMagick convert utility for this kind of job – it would be as simple as typing 'convert recoil.dvi recoil.jpg' except that fine control is needed to get an un-pixilated rendition. It can be quite a fiddle with the parameters to get a good looking DVI conversion.

…

Edited By SillyOldDuffer on 10/10/2016 12:48:51

Just found that the simple answer to getting a good conversion from convert seems to be to specify a density on the input file, thus 'convert -density 400 recoil.dvi recoil.jpg' The default input density is only 72 dots per inch. For printing 400 dpi or higher will be much better.

I'm going to have a look at LaTex, but for simpler solutuion, which actually does the arithmetic for you as well see SmathStudio. Alternative (and might be better) is MathCad 14, which seems now to be a free download

[Robin GrahamParticipant @robingraham42208]

Posted by SillyOldDuffer on 10/10/2016 12:46:57:

Posted by Robin Graham on 10/10/2016 00:49:41:

But how does one get TeX to produce a jpeg – that's the real problem. Dave's analysis of the rocket problem may have been flawed, but the presentation was impeccable. My (possibly antediluvian) software only does postscript.

Robin

For the interested latex is a publication quality mathematical typesetter. It's available free for Linux, OS/X and Windows. It converts a character script entered with an ordinary editor into presentable maths. For example $$e=mc^2$$ is turned into a proper rendition of Einstein's e=mc²

I used latex (pdfTex) 3.14159265-2.6-1.40.16 on Ubuntu 16.04. (Yes, the version number is based on pi)

The tex family are command line programs. By default my latex outputs DVI files. I also have pdflatex, where the default output is a pdf file, and – although I haven't installed it – there is pslatex, which outputs postscript.

There are many ways to convert DVI, pdf and postscript to jpg (see the DVI files link for an incomplete list). I wouldn't normally convert any typesetting format to jpg, except that this forum uses it. The main limitations of jpg in this context are that it's a single page format, and the compression algorithm isn't good at typescript or line drawings.

I normally use the ImageMagick convert utility for this kind of job – it would be as simple as typing 'convert recoil.dvi recoil.jpg' except that fine control is needed to get an un-pixilated rendition. It can be quite a fiddle with the parameters to get a good looking DVI conversion.

In this case I generated the DVI file and displayed it on screen. Then I used gnome-screenshot (SHIFT-PrintScreen to get the cursor select option), and saved the screen-shot as a jpg. (Normally screen shots are saved as png, but changing the suffix to jpg produces a decent jpg directly.)

Regards,

Dave

Edited By SillyOldDuffer on 10/10/2016 12:48:15

Edited By SillyOldDuffer on 10/10/2016 12:48:51

Thanks Dave, all explained. I had just wondered if there a version of LaTeX which converted from DVI to jpg directly . The developers of this excellent code will get a well deserved rest at the 762nd point of Pi – 999999 and so on….

Rob

[Mike StaceyParticipant @mikestacey71444]

In the bottle rocket,the way I see it is the mass of the expelled fluid relative to the mass of the projectile tells the tale;water shoves it along quite nicely,but when just air is released,the bottle hardly notices it,couldn't care less,really.Enter Murphy's third law"If one Can get wet,one Will get wet"Someone might try Coca Cola as a working fluid,as things go better with Coke.

[Neil WyattModerator @neilwyatt]

Posted by Jon Gibbs on 10/10/2016 15:52:23:

Posted by Neil Wyatt on 09/10/2016 12:59:23:

Sorry, no. The same amount of momentum goes into bullet and gun. It's the average force generated by the charge over the time the charge is acting on projectile and gun in newton-seconds.

p = mv

so momentum of bullet = 0.01 x 750 = 7.5 newton-seconds

momentum of gun = 7.5 newton-seconds

velocity of gun = 7.5/5 = 1.5 m/s

Which is rather less likely to rip your shoulder off your body…

… That is the primary recoil but there is the stronger secondary recoil to consider due to the gasses leaving the barrel.

This is what muzzle brakes are designed to mitigate against and I guess what powers the coke bottle rocket after the stopper has blown out of the bottom.

Jon

I've looked at this. While the speed of the gases is 1.25 to 1.75 times the speed of the projectile, the weight of the gases is the weight of the propellant . 35-70 grains compared to ~200 for the bullet (to keep mike happy) so the kick from the gases will be smaller (say 1/2 to 1/4) than the kick from the bullet.

Sorry to be a nerd!

[Jon GibbsParticipant @jongibbs59756]

Posted by Neil Wyatt on 11/10/2016 07:29:20:

I've looked at this. While the speed of the gases is 1.25 to 1.75 times the speed of the projectile, the weight of the gases is the weight of the propellant . 35-70 grains compared to ~200 for the bullet (to keep mike happy) so the kick from the gases will be smaller (say 1/2 to 1/4) than the kick from the bullet.

Sorry to be a nerd!

It's ok but I think it depends upon the specifics of the charge and bullet combination how efficiently all of the energy is transferred to the projectile. I think it probably depends on the comparative length of the barrel to the calibre – relatively long barrels with small light projectiles will tend to have less secondary recoil.

I agree with your gas weight but I think that your gas speed may be a bit low in some cases but the major missing effect is that there will also be a time factor in operation. I think it's quite likely that the gasses will continue to escape for some time after the bullet has left the barrel and the charge gets completely burnt. In effect the charge may be acting like a rocket motor for some time for relatively short barrel lengths or high calibre/mass projectiles.

Muzzle brakes were designed specifically to reduce the magnitude of the secondary recoil and have no impact on the primary. I think they were first used on the 25 pounder FG but could be wrong.

My gut feeling is that if the secondary recoil was always only relatively small compared to the primary they would have negligible effect and wouldn't get used much but that's clearly not the case. They even get used on handguns to limit muzzle lift, AK47's and and .50 calibre sniper rifles.

This may be interesting… **LINK**

Jon

[SillyOldDufferModerator @sillyoldduffer]

Posted by duncan webster on 10/10/2016 15:55:19:

Posted by SillyOldDuffer on 10/10/2016 13:35:09:

Posted by SillyOldDuffer on 10/10/2016 12:46:57:

Posted by Robin Graham on 10/10/2016 00:49:41:

…

I'm going to have a look at LaTex, but for simpler solutuion, which actually does the arithmetic for you as well see SmathStudio. Alternative (and might be better) is MathCad 14, which seems now to be a free download

Thanks for the pointers Duncan, I'll have a look at those. A easy to use package that does the sums as well as display the formula would be rather useful.

latex is aimed at a rather different target. It's for producing publication quality maths papers, theses, books, and articles etc. As such it does various standard maths publication formats extraordinarily well, but it can't crunch numbers itself. I use it the old-fashioned way with a text-editor: but there's TexMaker and TexStudio if you want a GUI with advanced features.

Open Office and Word both have maths extensions that can produce many of the symbols, but the typist has to arrange the formatting himself. Fine for small examples but a real pain writing a big document.

My own usage is far more likely to be on a small scale than big, so thanks again for the suggestions.

Dave

[SillyOldDufferModerator @sillyoldduffer]

Wikipedia looks to have a good overview of recoil. I haven't had time to read it properly or to try and redeem my shattered reputation. Somehow I've lost momentum on this one…

Dave

[Neil WyattModerator @neilwyatt]

All my shooting experience is with airguns, I don't really have the practical experience to go further, but it's an interesting diversion!

Neil

[SillyOldDufferModerator @sillyoldduffer]

As the thread is about Coke Bottle Rockets, I wonder if the group could put their minds to optimising CBR performance? For starters:

• What's the burst pressure of a 2L coke bottle?
• What's the optimum ratio between water and compressed air?
• What's the maximum height and time of flight that could be achieved on earth?
• What's the most efficient way of releasing the rocket once operating pressure is reached?

Could be the new IMLEC!

Cheers,

Dave (who should be cleaning aluminium out of clogged files)

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