Calculating the Mass of a Piston for a Spring-Based Launcher

[InebriatedScientist]

I am trying to teach myself Physics, so I can use it in engineering for my own devices. The project I am working on right now is a very simple spring based launcher. This is frustrating me to no end.

Here is my objective. I want to lunch a golf ball about 10 or so feet.
I know that I need to calculate the springs energy. I also know that the springs energy is approximately equal to kinetic energy. All I am doing is transforming spring energy into kinetic energy.

The equation is like so.. 1/2ks2 approx = 1/2(Mball + Mpiston)V2

The ball is about 0.101lb. In order for me to proceed, I need to know the mass of the piston. I have the other information I can work that out, however...

How the hell would I do that if I have not constructed the piston yet? I looked up how to find the mass. The information I found goes on and on about density and so on. The piston is going to be made out of Metal, more than likely steel. The head is going to be steel and the rod is going to be steel.

Now I am following a tutorial on how to go about constructing this device. Problem is, his measurements are different than mine. Because I have something else in mind for my luncher. For example, my spring is going to be 9.5in long with a maximum weight capacity of 27lb. Obviously, I assume, I am going to overshoot the 10-foot mark. His is half that or so.

I need to know the mass of the piston. How would I find that, if I have not constructed it? Do I just "estmate"

 

[olgerm]

$\frac{k \cdot s^2}{2} \approx \frac{(M_{ball} + M_{piston}) \cdot V^2}{2}$

⇔$M_{piston} \approx \frac{k \cdot s^2}{V^2} - M_{ball}$

$\frac{M_{ball}*V^2}{2}=M_{ball}\cdot h\cdot g$

 

[Nugatory]

I need to know the mass of the piston. How would I find that, if I have not constructed it? Do I just "estmate"

Or you could calculate backwards from what you know of the mass of the ball and the characteristics of the spring to calculate an upper bound on the mass of the piston, then consider whether it is possible to construct a piston that will work with that spring.

 

[sophiecentaur]

It sounds like stating the obvious but, once you have designed the piston, you will know its volume so you can work out its mass. You can easily get a typical value for the density of steel.
There is also some kinetic energy in the moving spring at the point where the ball is launched. I seem to remember that the ke of a spring of mass m when the free end is moving at v is mv²/6. (i.e. 1/3 of a mass m at speed v) Whether this is significant or not will depend on the mass of the spring compared with the rest of the moving parts. If it's a strong spring then it is likely to have mass comparable with the piston ( which will be as light as possible, consistent with being strong enough.)
Does your tutorial mention the ke of the spring?

 

[jrmichler]

You sketch up a piston that looks like it will do the job, then calculate the volume and multiply by density to get the mass. Then you calculate velocity. If it does not work, change something (piston material, piston design, different spring) and try again. It's an iterative problem. The approach of @Nugatory also works.

Also, add half the mass of the spring to the mass of the piston when you do your calculations.

Do you really need a piston? Can the spring push the ball directly?

 

[sophiecentaur]

Also, add half the mass of the spring to the mass of the piston

I am not sure you are right there. If you integrate the ke along the length of the spring, I think you get 1/3.

 

[Nugatory]

The piston is going to be made out of Metal, more than likely steel

If ever there was an application that suggested aluminum...

 

[jrmichler]

I am not sure you are right there. If you integrate the ke along the length of the spring, I think you get 1/3.

You are correct. It's right there in the SMI Handbook of Spring Design.

 

[sophiecentaur]

If ever there was an application that suggested aluminum...

Spoilsport. What's wrong with Titanium?

 

[InebriatedScientist]

Or you could calculate backwards from what you know of the mass of the ball and the characteristics of the spring to calculate an upper bound on the mass of the piston, then consider whether it is possible to construct a piston that will work with that spring.

Right, so, then "estamte"?

 

[InebriatedScientist]

Spoilsport. What's wrong with Titanium?

I actually changed the design. Working with steel would be much harder. I thought I would make this to be mounted on a platform so I would need a longer spring. However, I changed my mind. The budget was supposed to be about 20-30$ but the spring I needed that I estimated for 9 3/5in was too expensive and I am trying to follow constraints that I imposed on myself. At least where I was shopping for it.

So on that note, I am going to just make a "handheld" version and use aluminum. It will be easier to work with anyway.
Maybe when I have more precision tools, I would be able to construct a "turret" size.

 

[InebriatedScientist]

It sounds like stating the obvious but, once you have designed the piston, you will know its volume so you can work out its mass. You can easily get a typical value for the density of steel.
There is also some kinetic energy in the moving spring at the point where the ball is launched. I seem to remember that the ke of a spring of mass m when the free end is moving at v is mv²/6. (i.e. 1/3 of a mass m at speed v) Whether this is significant or not will depend on the mass of the spring compared with the rest of the moving parts. If it's a strong spring then it is likely to have mass comparable with the piston ( which will be as light as possible, consistent with being strong enough.)
Does your tutorial mention the ke of the spring?

Yes, it does, he uses steel compression spring. Well, I am not sure. The equation he uses is 1/2ks2. k= stiffness s= change in length. It makes sense to do that since all we are doing is converting spring energy to kinetic energy. What do I remember is that the lengths of the spring produce more force. That is, the longer it is the father the ball will go.

The problem I had, was...Do I make an estimated piston and then measure the mass or do I just look up the density of a steel and or aluminum piston shaft? I most of the time overthink things. I overthink about things that do not need to be and under think at times for what is important.

Unrelated Rant..sorry.
At one time I decided to just make the spring thinking that I could use any old steel wire. I first thought that this was not possible since I assumed it needed special steel material that is springy. This halted my project. I ask for an advice about my "overthinking" and I was told that I don't need to worry about it, that I should not over think. However when I then directly asked, can I make a spring out of any steel wire and they said no. Obviously, I was annoying since I knew the answer but doubted myself. Only to be told the same exact thing that I knew already. Really sucks, it took up my time. I would rather overthink from now on than underthink.

 

[InebriatedScientist]

⇔$M_{piston} \approx \frac{k \cdot s^2}{V^2} - M_{ball}$

$\frac{M_{ball}*V^2}{2}=M_{ball}\cdot h\cdot g$

huh, interesting, is dividing by 2 the same as using 1/2? Also, I am not sure I understand, it looks like you are solving for the piston mass? I seem to follow this fine. So then I can use mass of the ball and the other variables to actually find the mass of the piston without ever constructing a piston? That is to say, I want to make the piston out of aluminum shaft and wooden or plastic head. However, I don't know the denstiy of any of those object. Can I still find the mass of the piston by working backwards like that?

 

[InebriatedScientist]

If ever there was an application that suggested aluminum...

I replied this to someone else. However I will just make a quick note here. I cam to the same conclusion using aluminum. The reason I used steel in this example is because the device was going to be much larger, about 3x2x2ft.

 

[sophiecentaur]

The equation he uses

The equation for what? That looks like the potential energy stored in the spring. There are three elements with KE in this model and the PE is shared.

I most of the time overthink things.

You have to think all the relevant things. The really important thing is the design of the spring and the energy it can store. You don't seem to have mentioned any maximum for this. If you used a car suspension spring and could manage to compress it, you could send the golf ball the whole length of a football field or further. That would be ridiculous of course so you need to decide on whether you can make one or buy one. Making a 'good' spring is difficult. You can buy a range of springs on eBay etc. Perhaps an airgun spring would suit you. They store around 16J max in the UK (the regs) and they can be compressed by more than 100mm, which requires fairly open coils.
Frankly, the mass of the piston wouldn't be very critical. It only needs to be strong enough to act as a pad between the end or the spring and the actual projectile.

 

[InebriatedScientist]

What I am calculating is KeneticEnergy, Gravitational Potential Energy, and Spring Energy. I personally would start with the Spring I guess. I got a spring, I am still not sure how far this ball will go. It seems what I got was much stronger Maximum Load Capacity. Which I think Max Load 110.74lb rate 49.79lb/in. Don't tell me the answers or anything, I want to calculate this my self. What I will do is update and show you my results for some the equations. Once that happens I would like some input if I am going in the right direction.

By the way, I have not said this yet it seems, but I appreciate this help. Thanks a lot.

 

[gneill]

Golf balls are pretty light and 10 ft or so is not that much range. Forces will not be that large. Why not construct your piston from wood or plastic? You might be able to re-purpose some existing object.

 

[InebriatedScientist]

Golf balls are pretty light and 10 ft or so is not that much range. Forces will not be that large. Why not construct your piston from wood or plastic? You might be able to re-purpose some existing object.

Well, I decided to use an aluminum tubing of 0.049" walls thickness, 1/4' OD, 1/2ft long.

 

[sophiecentaur]

Well, I decided to use an aluminum tubing of 0.049" walls thickness, 1/4' OD, 1/2ft long.

That looks like the cylinder, you're describing.
The piston is what the spring drives forwards and pushes the golf ball. That should be a light as you possible, consistent with being strong enough.

 

[InebriatedScientist]

I give up, this is not helping me. I cannot do the math it seems or Physics. I don't understand any of this. All the problems I am given to solve are hypothetical or they just give you the answers. Then you just copy and paste things like a damn monkey.

I don't understand how ANYONE knows how fast an object moves. For example, I am given a situation. A cheetah is crouched in an ambush 20m to the east of an observer's blind. At time t=0 the cheetah charges an antelope in a clearing of 50m east of the observer. The cheetah runs along a straight line; the observer "ESTIMATES" that during the first 2s of the attack the cheetah's coordinate x varies with time according to the equation x=20m+ (5m*s^-2)t²

This is simple to solve. This is a hypothetical concept. What I don't understand is, how the hell would you ever know you are 20m away? Or it charges in a clearing of 50m? WHERE ARE YOU GETTING THIS INFORMATION?. I mean, HOW would you even COUNT the seconds? How would you know you are counting according to how time passes? What if you are a slower counter or fast counter? <Sentence deleted by mentor>There are so many factors that I don't understand how people are accurate. I feel like I can just eye things and do them that way, by trial and error.

Let me put it this way. Suppose that you saw a dog chasing a ball that was thrown. You don't know how far away you are from the person that is throwing the ball, you "estimate" that you are maybe mid-lengths. You have no idea how far or fast the ball is since you are just observing this. You don't know how fast the dog is. AND NO you did not bring a watch to count out the seconds. YOU KNOW NOTHING! Because this is just a "split second" observation. HOW would you EVER able to calculate this or even began to? I don't understand how people do physics without using a calculator are have a nice classroom environment.
I HATE hypothetical equations. IN real life, you would not know ANY of this information.

Let me give you a second situation. Suppose you were climbing a mountain, and you slipped and landed in a tight hole. HOW would you know how far you fell? Since you had no idea how far up you were? There is just no way you can do any of these calculations. I don't understand how people just come up with the damn numbers.

And yes, this still relates to the ball launcher that I would like to make. Let me make it clear. I CAN MAKE THE BALL LAUNCHER without calculating ANYTHING. I could just eye the damn thing. Do we as humans just guess? The only way I can see myself ever "estimating" the numbers to make a projectile launcher is if I just go and do an assumed walk out "10ft" Then take an assumed mid-size stone and throw it, but as soon as I threw it, I start counting at an assumed rate. The problem with this is that there is so much unreliable info and assumed info. How the hell would you ever be accurate? IF all we do is trial and error, why would anyone spend an hour doing pointless equations when you can just "eye" and "estimate" things, To which we do anyway. I need some help explaining to me, how you approuch problems with no information. Also, I am still trying to calculate the mass of the piston. I looked up the density of aluminum and it said 2.7 grams. I am just going to use that.

 

[berkeman]

I give up, this is not helping me. I cannot do the math it seems or Physics. I don't understand any of this. All the problems I am given to solve are hypothetical or they just give you the answers. Then you just copy and paste things like a damn monkey.

Sounds like you haven't had a very good learning experience so far.

What I don't understand is, how the hell would you ever know you are 20m away? Or it charges in a clearing of 50m?

Lots of ways. Rangefinders are simple technology, radar guns give speeds, you can use landmarks with known distances to help you figure that kind of stuff out...

HOW would you even COUNT the seconds?

Seriously?

I need some help explaining to me, how you approuch problems with no information.

You find the information -- that's part of working on problems. Sometimes the information is easy to figure out, other times it takes more effort and maybe some creativity.

I looked up the density of aluminum and it said 2.7 grams.

No, a density would have units of grams per cubic centimeter, or some other measure of mass per unit volume. Can you post a link to where you looked that up? Thanks.

 

[InebriatedScientist]

Sounds like you haven't had a very good learning experience so far.

Lots of ways. Rangefinders are simple technology, radar guns give speeds, you can use landmarks with known distances to help you figure that kind of stuff out...

Seriously?

You find the information -- that's part of working on problems. Sometimes the information is easy to figure out, other times it takes more effort and maybe some creativity.

No, a density would have units of grams per cubic centimeter, or some other measure of mass per unit volume. Can you post a link to where you looked that up? Thanks.

NONE of what you just typed helped in ANY form what so ever.

I think you missed the point completely. YOU DO NOT HAVE ANY special tech. I made this clear. Are you just going to carry all of that with you? You don't have a phone you just observed this at random. YOU HAVE NOTHING ON YOU..again YOU HAVE NOTHING ON YOU. You are in the woods you have no idea what sort of woods these are. THERE ARE NO KNOWN MARKERS to help you out.

Again how do you not get this? In regards to counting seconds. YES SERIOUSLY. do you just assume that everyone counts at the same rate? Have you ever seen people try to count on 1 2 3? They have to figure out at what rate the person is going to count. it could be 1...2...3...4 or 1234. or 1 2 3 4.

YOU CANNOT FIND THE INFORMATION WHEN YOU HAVE NOTHING WITH YOU. YOU DON"T HAVE A PHONE.
my point is this. Physics is only applicable when you have given information. In reality, you will not have any information that will be useful and even if you do, not at all times and not on the same day. It is completely random.

None of this helps. It is all nice and dandy in a classroom environment when the professor tells you to suppose this and suppose that.

Well, suppose you are in the woods and you came to a cliff. You don't know how high it is. You pick up a mid-size stone and throw it. But wait, you forgot to count how long it took to reach the bottom. You have no equipment to tell you. You don't have a handy device to tell you anything. How would you know at what angle you threw the stone? Or how long it took for it to travel? You would not, you would start assuming things. That means Physics is not precise. It would be better to engineer things and then correct them, rather do physics then engineer and then correct them.

 

[berkeman]

Do you want this moved to the Science Fiction forum? You don't seem to be interested in science.

 

[InebriatedScientist]

Do you want this moved to the Science Fiction forum? You don't seem to be interested in science.

Oof wow, clever, did you have to think about that one?

Way to answer my question. Are you saying you will never be put in a situation that you observed, that would indicate you can use physics but you have no information?
Are you just going to dismiss human history? How do you think bows were made by native american? Did they measure that out? They must have used algebra and physics, oh and calculus.

 

[berkeman]

Oof wow, clever, did you have to think about that one?

Way to answer my question. Are you saying you will never be put in a situation that you observed, that would indicate you can use physics but you have no information?
Are you just going to dismiss human history? How do you think bows were made by native american? Did they measure that out? They must have used algebra and physics, oh and calculus.

Actually, I'm thinking now that maybe we should move this to the medical forums. You seem to be enjoying complaining that you can't figure stuff like this out. Why do you think millions of other young scientists can do this, and you are having trouble doing simple calculations? Is it because you enjoy having trouble doing it, and then complaining about it? I'm pretty sure there is a medical term for that...

(and just between you and me, I had a similar problem in undergrad, but thankfully figured it out and got past it and did well)

Anyway, do you really want to talk about your project? I'm pretty sure I can help if you are willing to do some calculations that I can suggest...

I am trying to teach myself Physics, so I can use it in engineering for my own devices. The project I am working on right now is a very simple spring based launcher. This is frustrating me to no end.

 

[InebriatedScientist]

Actually, I'm thinking now that maybe we should move this to the medical forums. You seem to be enjoying complaining that you can't figure stuff like this out. Why do you think millions of other young scientists can do this, and you are having trouble doing simple calculations? Is it because you enjoy having trouble doing it, and then complaining about it? I'm pretty sure there is a medical term for that...

(and just between you and me, I had a similar problem in undergrad, but thankfully figured it out and got past it and did well)

Anyway, do you really want to talk about your project? I'm pretty sure I can help if you are willing to do some calculations that I can suggest...

sigh...Forget the project, I already made it. The ball flew about 20ft I decided to forgo physics and just use my observational skills.

I also have built lots and lots of circuits WITHOUT having to know any sort of physics. They all worked just fine. I am not arguing math I am arguing how do you find velocity for example, when you don't have any of the information. My question is, DO YOU OR DO YOU NOT assume numbers to a relative of what you think is about right?

Lol, do you think people who play golf know THE EXACT force that they used? Are they also calculating out EVERYTHING to know EXACTLY where the ball will land? Or do they observer and then use trial and error?
How about when they practice? Do they also calculate "well if I use this amount of force and at this angle..."

 

[berkeman]

sigh...Forget the project, I already made it. The ball flew about 20ft I decided to forgo physics and just use my observational skills.

I also have built lots and lots of circuits WITHOUT having to know any sort of physics. They all worked just fine. I am not arguing math I am arguing how do you find velocity for example, when you don't have any of the information. My question is, DO YOU OR DO YOU NOT assume numbers to a relative of what you think is about right?

Lol, do you think people who play golf know THE EXACT force that they used? Are they also calculating out EVERYTHING to know EXACTLY where the ball will land? Or do they observer and then use trial and error?
How about when they practice? Do they also calculate "well if I use this amount of force and at this angle..."

Please stop using all capital letters to yell at me, you already have my attention. Thank you.

When accuracy is important, we find ways to measure the quantities to within the accuracy we need. For example, you can use video capture and analysis to measure motion frame-by-frame (this is done all the time, and is even available now on cell phone apps). For measuring distances, the range finder widgets that I mentioned before have fairly good accuracy, or you can use LIDAR or RADAR ranging. You can also do a pretty good job estimating ranges with some experience and knowing about how tall an object is (I used to use this in hunting all the time to estimate range for ballistics drop).

The bottom line is that there are almost always ways to measure or estimate these things to within the accuracy you need. Start by defining the accuracy you need, and then think about all of the various ways that such quantities can be measured.

Some of the most amazing things in physics are how scientists have figured out how to measure important quantities to very high precision. Some of the tests of cosmological theories have involved measurements to very high precision to prove/disprove new theories. Great stuff.

 

[InebriatedScientist]

Please stop using all capital letters to yell at me, you already have my attention. Thank you.

When accuracy is important, we find ways to measure the quantities to within the accuracy we need. For example, you can use video capture and analysis to measure motion frame-by-frame (this is done all the time, and is even available now on cell phone apps). For measuring distances, the rangefinder widgets that I mentioned before have fairly good accuracy, or you can use LIDAR or RADAR ranging. You can also do a pretty good job estimating ranges with some experience and knowing about how tall an object is (I used to use this in hunting all the time to estimate range for ballistics drop).

The bottom line is that there are almost always ways to measure or estimate these things to within the accuracy you need. Start by defining the accuracy you need, and then think about all of the various ways that such quantities can be measured.

Some of the most amazing things in physics are how scientists have figured out how to measure important quantities to very high precision. Some of the tests of cosmological theories have involved measurements to very high precision to prove/disprove new theories. Great stuff.

I am not using caps to yell at you, I am emphasizing. Jesus Christ, I am going to have a heart attack.

When you play golf, do you also do that? do you pull out the rangefinder pull out your phone? measure everything out? Imagine you are the golfer, you are trying to get a hole in one, obviously, you can't just pull out your gadgets. Let me put you in this situation. You being shot at. It is a hot summer day.
A bullet whizzes by you and makes a hole about half an inch in diameter. Can you calculate on the spot the velocity and at what angle it was shot at or how much force that gun used?

 

[gneill]

In Physics we use established theories to predict and test the outcomes of experiments. In Engineering we use the collective knowledge of physical theory and empirical measurements to design and predict the outcomes of constructed devices or objects.

Information gathered by carefully controlled laboratory experiments, performed by many others, is what engineers use as the basis of design of new creations. There's no "man on the street without any measuring tools" input there. Conflating the fact that the general populous has no readily available test equipment with scientists not knowing what they're doing so that science is useless is just argumentative nonsense.

 

[Capecutterman]

Oh for Heaven's sake!
" the project, I already made it. The ball flew about 20ft.."
OK. You've made a start. Now get a tape measure.
Repeat the experiment lots of times, keeping everything the same each time, and measuring "..about 20ft.." each time.
Take an average, now you actually know something - that with certain parameters your spring/cylinder will propel you ball X ft.
So the X ft is your starting point and you actually have a real (approximate) measure of something.
Now do it with your launcher pointing up at angles of 30/40/50/60/70 and measure x30, x40 etc.
You will have to work the physics backasswards from there with lots of assumptions
until you come out with figures that approximate the real life situation.

It isn't the best way to do physics, but its sort of a way of doing physics.
But you cannot avoid mathematics if you want a meaningful result.

Mac

 

[hmmm27]

I don't know why you'd build a contraption to throw a golf ball 10 feet when you can just walk over and drop it on the ground.

But, if you insist on a mechanical launch...

First you'd want to determine the best method of propulsion : direct spring, direct contact (it's a golf ball, just smack it with the piston), or a hybrid where the spring compresses air which launches the ball (commonly used in air rifles). Those you'd use principles of physics, maybe some rough calcs.

Or use common sense and use the spring to power a small catapult. That one - free of most of the friction that messes up the other ones - you could math away to your heart's content and build it. Once. No wasteage of lumber ; no having to go back to the store and buy a more or less powerful spring.

 

[InebriatedScientist]

In Physics we use established theories to predict and test the outcomes of experiments. In Engineering we use the collective knowledge of physical theory and empirical measurements to design and predict the outcomes of constructed devices or objects.

Information gathered by carefully controlled laboratory experiments, performed by many others, is what engineers use as the basis of the design of new creations. There's no "man on the street without any measuring tools" input there. Conflating the fact that the general populous has no readily available test equipment with scientists not knowing what they're doing so that science is useless is just argumentative nonsense.

THANK YOU.

So then, I would never know at what velocity a mid-size stone that someone threw of a cliff that you have never been to or have seen traveling. Or at what angle and where it will land?

Also, one more thing, if I did observer this, how would I find that angle? Could I use the person's hight?

 

[InebriatedScientist]

I don't know why you'd build a contraption to throw a golf ball 10 feet when you can just walk over and drop it on the ground.

But, if you insist on a mechanical launch...

First you'd want to determine the best method of propulsion : direct spring, direct contact (it's a golf ball, just smack it with the piston), or a hybrid where the spring compresses air which launches the ball (commonly used in air rifles). Those you'd use principles of physics, maybe some rough calcs.

Or use common sense and use the spring to power a small catapult. That one - free of most of the friction that messes up the other ones - you could math away to your heart's content and build it. Once. No wasteage of lumber ; no having to go back to the store and buy a more or less powerful spring.

Yes, all of this would make sense. But like you said it is just common sense. Obviously, if I wanted the ball to fly 30ft I would use a stronger compression spring. I would assume without math that the harder it compresses the further the ball is traveling.

 

[InebriatedScientist]

Oh for Heaven's sake!
" the project, I already made it. The ball flew about 20ft.."
OK. You've made a start. Now get a tape measure.
Repeat the experiment lots of times, keeping everything the same each time, and measuring "..about 20ft.." each time.
Take an average, now you actually know something - that with certain parameters your spring/cylinder will propel you ball X ft.
So the X ft is your starting point and you actually have a real (approximate) measure of something.
Now do it with your launcher pointing up at angles of 30/40/50/60/70 and measure x30, x40 etc.
You will have to work the physics backasswards from there with lots of assumptions
until you come out with figures that approximate the real life situation.

It isn't the best way to do physics, but its sort of a way of doing physics.
But you cannot avoid mathematics if you want a meaningful result.

Mac

Ok good, thank you. That is what I wanted people to tell me. So then YES we do assume stuff until we get it right. That means this is all trial and error. So then, why am I doing math instead of just trial and error with intuitive reasoning?

 

[berkeman]

I am not using caps to yell at you

Thank you. I appreciate that you have stopped using all caps.

When you play golf, do you also do that? do you pull out the rangefinder pull out your phone?

I acually use to play golf when I was younger. Too boring for me now. But back then and even now for professional golfers, you are allowed to use maps of the course that show distances. No cell phone apps allowed or needed.

Hey, PM me if you want to talk about this on a more personal level. Like I said above, I went through something similar early in undergrad, and found a really good way to get through it. Click on my avatar and click on Start a Conversation to start a PM thread with me.