Hello and a noobie question

[ARHOTEEHAROWER]

Hi everyone, thanks for having me in your forum. Looks like a powerhouse of mathematical know how.

I am a bit of an inventor but I quite often solve challenges along the way by iterative trail and error, hunches and instinct, testing then retesting. etc.
My math knowledge is pretty much non existent, seriously, so if I could get some help or ideas from this forum at least where to start looking to solve the problem I would appreciate it. I have a lot of respect for the utility of math but have no hope of understanding it at a deep level but thought for a change of approach I would poke my head into the math world via a forum such as this and see what would happen if i tried to apply some(one elses) math brain to a problem or if indeed it can even be of much use in this situation.

Having had my bike stolen recently I'm trying to create a new bike lock (not the lock itself, but the chain/cable part) that is less easily able to be cut by bolt cutters.

I have a principle for the idea in my head but there just seems to be so many ways I can approach/ refine the idea I was wondering if math could be used to somehow short cut the process and offer some kind of provable logical direction to head in or at least prove what is best should I come up with different solutions.

My math is truely abysmal so I dont even know what section to ask this in. So first question would be could someone please tell me what field of math (or maybe physics?) I need and where I should be posting this, or even if this question is appropriate for this forum. I have no idea. Im just trying it and if I get no response I will no pursue it any further, maybe just cut and paste it into a physics/engineering forum?

The way I see it is there has to be at least 3 stages.

I modelling the design(s),
Define the objectives and what is success,
testing the design.

I really should be uploading a picture and diagrams to help visualize it but Ill just do my best to describe the problem initially by words so I don't waste time if this is not the place for it.
By the way, I should say I am willing to reward anyone if I should be exceptionally happy about the outcome of what I learn.

Anyway.. sorry about all the waffle. Here's what Im thinking.

The nature of bolt cutters is that they need great leverage to allow a human to possess the power to use them to cut through the hardened steel of most bike locks. This leverage means that the handles range of movement has to be greatly geared compared to the cutting edges, hence the cutting edges cant open very far, usually not much more than an inch if that and they are reasonably thick and blunt.

They succeed on cables and d-locks /u-locks partly because they are able to get their jaws around the cable or metal of the lock and once pressure is applied the angle of the cutting edges in relation to the lock is reasonably close to parallel, or else it would just spit the cable out because the angle of the jaws is such that it pushes the cable away rather than applying pressure to both sides to give the cutting/crushing effect that is needed to break the lock.

Bike locks of nearly any strength steel can be cut by bolt cutters but only because they can get their jaws around them. I was Thinking that if you could have a weaker and lighter material that was of a larger circumference it could make bolt cutters useless because they could not get either the correct angle around the cable to maintain cutting pressure without sliding off or even not be able to get around it at all. This would mean that you could make a lock cheaper by not having to use such expensive materials because its not purely the strength of the material that is the determinant of success but the ability for the cutters to be on the right angle to "take a bite", or indeed use the expensive materials and make the lock even harder to break.

Another factor that aids bolt cutters effectiveness is the cables being tubular and consistent in their circumference. This means that when a cutting device does manage to get its jaws around them the consistant tubular profile aids the devices effectiveness because it tends to provide reasonably equal pressures either side of the point at where it is focusing its forces which aids in the concentration of the force and the stability when pressure is applied allowing the force of the bolter cutters to exceed the strength of the lock material, almost acting like a V shaped guide to aid the concentration of forces as more pressure is applied. To combat some of that factor and make it more difficult for forces to be concentrated I was thinking of making a pearl necklace kind of configuration of cable design, pretty much like a bunch of hollow ball bearings with holes drilled in them for a cable to run through, threding them onto the cable. Cutting a near spherical ball bearing (or maybe slightly elipse/pebble) shaped object would be a lot more difficult for the jaws to grasp and apply cutting pressure to. The obvious problem here is that gap between the ball bearings would act like a guide in itself to steady the jaws if you were to attempt to cut the cable at the point between the ball bearing shaped parts.

SO.. I thought about having the same pearl necklace arrangement but in between the ball bearings you have an equilateral triangle or maybe hexagonal shaped object, a bit like a thick washer threaded on the cable, that then naturally is of an angle that repels the jaws and the lock apart but in a different way to the ball shaped parts, Medially verses laterally. The idea being that when pressure is applied by the bolt cutters, the jaws slide probably sideways off the sperical shapes down into the v shaped gaps between the spheres then are repelled medially when they close up a bit more by the triangle (or whatever shape is best) parts that are in between. The jaws cant apply good pressure on the triangle part between the ball shapes because the jaws of the bolt cutters are necessarily too think to fit in enough to get a decent bite on them. This is the simplistic description of my idea. I have some refinements in my head but I think this is all that is needed to define the problem.

Friction coefficients at certain angles on the ball and triangle shapes, plus figuring pressures able to be applied from the angle of the bolt cutters jaw opening distance and handles against the hardness and crushing strength of the ball and triangle shapes that make up the layer that stops the bolt cutters being able to apply their pressure to the actual cable that threads through them all.

Now i think about it maybe i should have posted this to an engineering or physics forum, but hey like i said in my head the problem seems like it could all be boiled down to just a bunch of numbers.. I just happen to be a dunce with numbers lol.



anyway..

After all this waffle, I apologise if this is of not interest or inappropriate. Tell me to sod off out of your forum if you want, but if anyone has any useful suggestions about how or even if this could be modelled in math or another disipline and any mathmatical insights as to how I could find the ideal combinaton shapes/design to support the basic idea that I have described I would appreciate it.

The basic problem as i see it is to minimize the ability of the bolt cutters to gain a jaw opening size, which simultaneously allows a sustainable angle of attack, at friction and pressures great enough to overcome the sphere shape (and triangle shaped steel) of x hardness for long enough to break it.

The exact numbers dont matter at this point they are all variable at this point, its putting the whole thing into a sum of sorts where it can be modelled and understood then refined. How do i do it?

Thanks in advance for any advice.

cheers.

ARHO.

 

[lev888]

Yes, you can use math to model the shapes you have in mind. What are the requirements?
Don't forget about weight and cost aspects. And the possibility that bolt cutters are not the only tools used to steal bikes. If the cable that holds your design together is too thin a simple pry bar will break it. As you increase its diameter the weight increases. The cost for sure will be high compared to cable only designs. Not an easy task to balance everything.

 

[Deleted member 4993]

Another option could be electronic lock+alarm.

 

[ARHOTEEHAROWER]

The requirements are to have a model of the potential design and measure the designs theoretical ability in an exacting way with known variables to resist forces that would likely be employed to breach its integrity, so the components of its design can be optimised against the possible and most common forms of attack in a more scientific mathmatical way.

I mean if you have a set of jaws that have a surface area of x applying force to a spherical shape at a certain angle of jaw opening , with friction coefficient of metal against metal, the friction pressure will at some point be large enough that the spherical shape will likely force the jaws to slip down one or other side of the sphere because it is very unlikely to be perfectly lined up on the axis therefore it will take a path down the side that is slightly easier, where it will then encounter another possibly triangle or hex shape that it can not grip because it has been designed to be such the jaws have a negative probability of being able to have grip at angles that will allow friction to be maintained at the pressure required to break through the lock, rather that jaw pressure will translate to the medial plane and push the lock away as if a small hand was trying to pick up a baseball with to fingers .

A bit like how say a pair of household scissors could cut through a milkshake straw easily but if you made that same straw large enough in diameter , say 3 inches or so, the straw would likely naturally be propelled away and out from the blades rather than cut through because of of angles and friction in play. How could you model this same principle in regards to my lock idea?

I dont want to waste anyones time. It may not be worth the effort of actually going through the process but it interested me as a possible use of math that I would like to learn more about. Im a very curious person, and I was intrigued at the thought of how or indeed if the otherwise manual experimental process that I would normally use to arrive at a solution could be approached and resolved by using math.

The problem is I know so little about all this stuff despite it appealing as a challenge in my head.

And of course its completely impossible if I dont draw up the shapes exactly so there is something to go off.

OK.. well just asnwer me this then if you wou be so kind .. Given what I have told you so far, what field of mathmatics would likely be needed to address this kind of problem?

thank you

 

[ARHOTEEHAROWER]

Yes, you can use math to model the shapes you have in mind. What are the requirements?
Don't forget about weight and cost aspects. And the possibility that bolt cutters are not the only tools used to steal bikes. If the cable that holds your design together is too thin a simple pry bar will break it. As you increase its diameter the weight increases. The cost for sure will be high compared to cable only designs. Not an easy task to balance everything.

Thanks for you reply,
I just meant to add that yes I know there are several other ways to break a lock with grinders etc. There is not a lock made that can not be broken somehow. I was really just trying to build a better mousetrap so to speak. I looked at another lock today, it was 160 dollars, which seems like a lot, since my new bike was only 300. That was probably because it was made of expensive materials. I mean i could surround the lock with some kind of material like used in the protective chainsaw chaps pants that loggers use which catch in the chainsaws blade and tangle it up and stop it very quickly when blade hits pants so that the cutting disc attack is negated. You could make it so that it pulse sprays bear spray in all directions when the lock metal temp exceeds the 700 degrees during friction cutting but keeping it closer to reality, I'm just trying to see how with any given material the design can be improved in a provable way to have a better chance of surviving. If a lock gets so capable that it can fend of most forms of attack they will just cut the frame and leave the lock. taking the bike away and repair the frame it or strip it for bits.

anyway I know this is kind of floating away from the subject of math, so feel free to comment on it. I will find it interesting to hear a mathmatical perspective but I wont clutter your forum up with off topic stuff. I know that can be annoying to some.

 

[Deleted member 4993]

they will just cut the frame and leave the lock. taking the bike away

You could use electronics to stop that. If the lock is detached from the bike - there could be piercing alarm to chase away any nefarious person....

 

[lev888]

Thanks for you reply,
I just meant to add that yes I know there are several other ways to break a lock with grinders etc. There is not a lock made that can not be broken somehow. I was really just trying to build a better mousetrap so to speak. I looked at another lock today, it was 160 dollars, which seems like a lot, since my new bike was only 300. That was probably because it was made of expensive materials. I mean i could surround the lock with some kind of material like used in the protective chainsaw chaps pants that loggers use which catch in the chainsaws blade and tangle it up and stop it very quickly when blade hits pants so that the cutting disc attack is negated. You could make it so that it pulse sprays bear spray in all directions when the lock metal temp exceeds the 700 degrees during friction cutting but keeping it closer to reality, I'm just trying to see how with any given material the design can be improved in a provable way to have a better chance of surviving. If a lock gets so capable that it can fend of most forms of attack they will just cut the frame and leave the lock. taking the bike away and repair the frame it or strip it for bits.

anyway I know this is kind of floating away from the subject of math, so feel free to comment on it. I will find it interesting to hear a mathmatical perspective but I wont clutter your forum up with off topic stuff. I know that can be annoying to some.

For mathematical perspective you should provide some parameters/constraints. E.g. We have a cable of length L and thickness T. On it we have spheres of radius R. Between every 2 sphere we have a nut-like shape with dimensions X, Y, Z. Math lets you calculate other quantities in addition to given dimensions, e.g. minimum thickness of the whole thing (between spheres and the hex shapes). Given all that info you can then use physics to calculate forces required to break the lock.

 

[ARHOTEEHAROWER]

You could use electronics to stop that. If the lock is detached from the bike - there could be piercing alarm to chase away any nefarious person....

My first thought from a thiefs perspective would be if i was going to chop the bike to steal it, id just chop out the bit that the lock was attached to so it wouldnt be activated although In reality i think a thief just wants easy targets that yeild them something of value. Chopping the soft lightweight aluminium frame to steal itsnt hard at all but it certainly reduces its value. All the component gear on a flash bike is worth bomb though if you can be bothered going to that trouble of selling it. Well it is from my perspective as a buyer of such stuff (from bike shops of course, not thieves).

 

[ARHOTEEHAROWER]

For mathematical perspective you should provide some parameters/constraints. E.g. We have a cable of length L and thickness T. On it we have spheres of radius R. Between every 2 sphere we have a nut-like shape with dimensions X, Y, Z. Math lets you calculate other quantities in addition to given dimensions, e.g. minimum thickness of the whole thing (between spheres and the hex shapes). Given all that info you can then use physics to calculate forces required to break the lock.

You are right. I know there needs to be some point from which this analysis can begin. it is not possible to make calculations on what does not currently exist. The point is that If i start down the path of prototyping my physical ideas into a model it seems like Im getting dragged back to my usual ways of doing it then just using math to refine and test it later on. Since I havnt even made a physical model yet I don't have any measurements to go off but I know a lot of which I will base it on. I was kind of hoping to somehow use math to gain a different form of insight and send me down a path I would not normally take to solve these kinds of problems.

The spherical shapes i described were for the sake of easy explanation of my idea. A system using them may be the best but my hunch was that there may be better modified versions. This is where my iterative manual process comes in. I really need to do some drawings so you can better see what I'm having a hard time describing, and this in addition to setting up some approximate shapes in a jig might help me eliminate some ideas early on (or maybe elimate all of them !)

I thought an oblate spheroid m&m kind of shape might be good for its sharper curves at the extremes making it harder for the cutters to get a grip when trying to cut it through its longer axis. but a further variation of this is that the m&m shape is twisted in such a way that it never allows the cutters to be able to position stably enough to apply pressure vertically, it always tries to push the cutters sideways somewhat but when they are positioned at that sideways point they get pushed out of the cutters because the shape has changed at that point to put the jaws a very much less grippy angle.

Kind of like a constantly changing shape that is never stable enough between the jaws to allow pressure to be applied without either wanting to either shift sideways or out of the jaws. A bit like the "modified reuleaux tetrahedron" that the makers muse youtube channel features in his solids of constant width video. Like that shape in as much as from any angle it has very little suface area touching the two plane surfaces that border it in his video for the demonstration. If i could make this twisted m&m in such a way that is constantly offering only the least surface area for cutter grip at an angle that is constantly at the worst combination of angle for a rigidly inline set of cutter jaws to exert pressure. This will involve a bit of experimentation on my part but there may be a mathmatical form that describes what im talkng about. Maybe a toridal reuleaux tetradron lol. Well i know thats impossible since its not a shape but a a shape that combines the features i need from each of them but in a constantly evolving loop to serve as a lock chain..

Its too difficult to describe really. I need some actual shapes and photos. Maybe the shape that works in the way i want with the attributes i want is possibly not even possible.

Imagine its like when you go to the chinese restaurant and try to eat with chopsticks. You get most of down but at the end there is always a couple of odd shaped bits of slippery sausage meat or whatever thats pretty much impossible to pic up from any angle with the chopsticks. Model that !

ok. im out here now for now. It's late were I come from.