## catapult project ( raspberry pi ) - physics - need help

danjperron
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### Re: catapult project ( raspberry pi ) - physics - need help

Why not using webcams which follow the target.Then it is just a question of calibrating them and do a simple triangulation!

davidcoton
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### Re: catapult project ( raspberry pi ) - physics - need help

Heater wrote:davidcoton,

We should not get confused by "acceleration".

Does that mean actual physical movement at an increasing velocity through space? Like taking distance/speed measurements of a rock falling from a tower. Or measuring the 0 to 60mph acceleration of my Ferrari?

Or does it mean the measurement you get out of an accelerometer stuck to that rock or Ferrari?

Recall that an accelerometer sitting on your desk will record 1g of acceleration due to gravity. Whilst it is permanently stationary!

This is why I mentioned Einstein. He observed that a falling object experiences no effects of acceleration itself whilst falling, despite accelerating at 9.81m/s/s as far as we the observer are concerned.

The thought experiment with a spring and a weight I mentioned above should help make this clear.
I think there is some confusion between acceleration and force, the two being related by the equation F=ma. Acceleration is the rate of change of velocity, hence the reason it can be integrated over time (from a known starting condition) to determine velocity, and integrated again to determine position. Force is the influence causing a mass to accelerate. A body in orbit is accelerating, otherwise it would travel in a straight line, not a circle or ellipse. A body in free fall is (air resistance excluded) accelerating, the force is not felt but it is still there. The force of gravity works equally on all parts of the body, when it reaches a solid object the equal but opposite contact force (opposing gravity) is felt. See http://www.physicsclassroom.com/class/n ... g-of-Force

It's a pretty useless accelerometer that claims an object is accelerating when it isn't (part of the problem is that it's all relative ). It is experiencing a force of gravity -- if we could measure that directly (and ignore the equal but opposite contact force) then that force would be present. Unbalanced force causes acceleration, acceleration does not cause a force between masses in free fall (though there is a small gravitational attraction between any two masses, caused by the masses and in turn causing acceleration towards each other, unless opposed).
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Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

davidcoton,
It's a pretty useless accelerometer that claims an object is accelerating when it isn't...
And yet, that is exactly what all accelerometers do!

Try it yourself, get a three axis gyro and sit it on your desk, stationary as it is it will report 1g of acceleration in the appropriate direction.
Acceleration is the rate of change of velocity...
Except when it isn't.

As you say, F = ma.

OK, when I stand on my bathroom scales it reports that I have a mass of 80Kg, that is "m". It knows that because it responds to the force my body applies to it when I stand on it, that is "F". What about that "a"? I'm certainly not accelerating. I'm standing still. But Newton insists there is an "a", it's 9.81m/s/s. The acceleration due to gravity at the Earth's surface.

So there is Einstein's equivalence principle. The effects of gravity are are indistinguishable from those of actual acceleration.

The classic example of this is to imagine standing in an elevator. Whilst the elevator is stationary you feel your weight on your feet. That's gravity. Now take the Earth away, have the elvator in free space but actually accelerated, by a rocket say, at 9.81m/s/s. You feel exactly the same weight on your feet.

That is why our accelerometer reports an acceleration when it is totally stationary. Poor thing has no way to tell movement from gravity.

End result: Accelerometers on a projectile in free fall read zero.
A body in orbit is accelerating
From our point of view on the ground. As far as the body is concerned it is travelling in a straight line. Any passengers in that body feel no acceleration and can't tell if they are travelling in a straight line or following a curved orbit.
...the problem is that it's all relative...
Yep
Last edited by Heater on Thu Dec 24, 2015 12:31 pm, edited 1 time in total.
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davidcoton
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### Re: catapult project ( raspberry pi ) - physics - need help

Heater wrote:davidcoton,

OK, when I stand on my bathroom scales it reports that I have a mass of 80Kg, that is "m". It knows that because it responds to the force my body applies to it when I stand on it, that is "F". What about that "a"? I'm certainly not accelerating. I'm standing still. But Newton insists there is an "a", it's 9.81m/s/s. The acceleration due to gravity at the Earth's surface.
There is no acceleration, because there is no net force acting on you. The force of gravity is opposed by the scales pushing up on you -- Newton's third law. You know that is true, you can feel it. So no net force, no acceleration.
The classic example of this is to imagine standing in an elevator. Whilst the elevator is stationary you feel your weight on your feet. That's gravity. Now take the Earth away, have the elevator in free space but actually accelerated, by a rocket say, at 9.81m/s/s. You feel exactly the same weight on your feet.
When the elevator is stationary you feel the equal and opposite force of the elevator on you. You cannot feel the force of gravity because it acts on every part of you (and the elevator) with the same force per unit mass. That's why you are weightless in freefall.
And yet, that is exactly what all accelerometers do!

Try it yourself, get a three axis gyro and sit it on your desk, stationary as it is it will report 1g of acceleration in the appropriate direction.
Actually, I agree about your accelerometer -- almost. I don't have an accelerometer to hand to check, but I think it can't actually detect acceleration. All it can detect is a force acting directly on its casing, but not on the sprung mass (or whatever). So it can detect acceleration from the catapult, but not from gravity, which affects its measurement element and its reference equally. The answer is to compensate the readings -- let it sit at rest, and remove the phantom acceleration (which will actually indicate that it is accelerating upwards). As long as the context has acceptably constant gravity, this works. If you go high enough to change the value of g, it fails.

Don't believe an instrument that tells you it is accelerating, when common sense (and the definition of acceleration) tells you it is not. Apply the appropriate correction, or at least understand that it is not measuring acceleration, but force -- and then only one of two equal and opposite forces acting on it.
A body in orbit is accelerating
From our point of view on the ground. As far as the body is concerned it is travelling in a straight line. Any passengers in that body feel no acceleration and can't tell if they are travelling in a straight line or following a curved orbit.
Of course they can tell. They are not moving away from the planet. They may not feel the gravitational force directly, but simple observation tells them they are accelerating and therefore maintaining orbit.

CAVEAT: I wrote this during a sleepless might at some silly time in the morning. Please forgive any errors on my part!
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gregeric
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### Re: catapult project ( raspberry pi ) - physics - need help

davidcoton wrote:
Heater wrote:
And yet, that is exactly what all accelerometers do!

Try it yourself, get a three axis gyro and sit it on your desk, stationary as it is it will report 1g of acceleration in the appropriate direction.
Actually, I agree about your accelerometer -- almost. I don't have an accelerometer to hand to check, but I think it can't actually detect acceleration. All it can detect is a force acting directly on its casing, but not on the sprung mass (or whatever).
Accelerometers behave exactly as Heater describes. Put it on its side & (x,y,z) now reads (9.8,0,0). Turn it upside down and you get (0,0,9.8) etc Picture the sagging springs the sprung mass is suspended from, it reports the compression/stretch on those. Similar to the analogy I gave of passengers in flight - in level flight you can feel g through your buttocks, in a parabolic flight you're floating.

Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

davidcoton,

My simple assertion was that accelerometers on a free falling body will read zero in all directions. Where "free falling" is an object falling straight down, or following a parabolic trajectory after being thrown, or following an elliptical orbit under the influence of gravity. Or even following some complex path among a number of sources of gravity.

It's going to get very long and confusing if I reply to each of your points. So I'd like to make an appeal to experiment and observation:

Accelerometers measure acceleration. It says so on the packet. They cannot measure force as they don't know their own mass, they certainly don't know the mass of anything they are attached to, and hence can't arrive at F which m * a. As you pointed out above.

Now my appeals to thought experiments involving bathroom scales and masses on springs have not convinced you so I have to leave it to you to do the experiment yourself and see.

It seems that the problem for you is the concept that an object can have acceleration whilst not actually moving at all. Which is natural. I guess that stems from the school book definition of acceleration which goes something like:

"Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity."

Which is fair enough as far as it goes. Good old Newtonian mechanics. Unfortunately such a definition says nothing about that 9.81m/s/s my accelerometer is reading whilst totally stationary on my desk. If I were in school today being taught that I'd be sticking my hand up and asking: What's up with that?

The problem of course is that that definition says nothing about gravity. Luckily Einstein does in his equivalence principle:

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system."

In short acceleration and gravity are indistinguishable. If you are standing stationary on the ground you feel you own weight on your feet. If you are in free space being accelerated "upwards" you feel the same weight on your feet.

Even if we don't pursue that principle into relativity theory it immediately accounts for why my accelerometer is showing acceleration whilst not actually moving anywhere.

Aside:

I forgot to mention, my passengers in my orbiting craft cannot see outside of their ship. There is no experiment they can do to determine if they are stationary, moving in a straight line in free space, orbiting a planet, or free falling directly downwards to one, etc etc. There is no acceleration for them. Despite what we on the ground think about it.

As you said, "it's all relative".
Last edited by Heater on Thu Dec 24, 2015 12:24 pm, edited 1 time in total.
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jahboater
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### Re: catapult project ( raspberry pi ) - physics - need help

If we ignore air resistance, and the catapult launches the projectile at an angle and not vertically, then I presume, knowing the value of g, we could calculate all (maximum height, launch velocity) from the distance the projectile lands from the catapult?

Since air drag is extremely difficult to calculate for an irregularly shaped object, perhaps fire an object with known drag (say a shiny round ball) and measure the distance, then repeat with the real projectile - can we not then compute the actual drag from the difference?
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karrika
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### Re: catapult project ( raspberry pi ) - physics - need help

jahboater, you are correct. Forget all I wrote.

The ultimate solution is to measure the flight time. The height can be calculated from there!

So just some simple impact sensor. Perhaps two spheres inside each other that make contact on impact. And 2 GPIO wires.

davidcoton
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### Re: catapult project ( raspberry pi ) - physics - need help

Please, Heater, if you quote me, get my name right.

I'll make one more attempt to show that Einstein's equivalence of acceleration and force is not required to understand what is happening.
Heater wrote:davidcoton,

My simple assertion was that accelerometers on a free falling body will read zero in all directions. Where "free falling" is an object falling straight down, or following a parabolic trajectory after being thrown, or following an elliptical orbit under the influence of gravity. Or even following some complex path among a number of sources of gravity.
Agreed. I explained why -- the difference between forces acting equally on all parts of the accelerometer (as with gravity), and one acting on the outer casing only.
It's going to get very long and confusing if I reply to each of your points. So I'd like to make an appeal to experiment and observation:

Accelerometers measure acceleration. It says so on the packet. They cannot measure force as they don't know their own mass, they certainly don't know the mass of anything they are attached to, and hence can't arrive at F which m * a. As you pointed out above.
How does an accelerometer work? By suspending a mass between springs, and measuring the compression or extension of the springs? Spring compression is proportional to force, not acceleration. Ergo it is measuring the force on the mass relative to the housing, which is proportional to acceleration. As long as that acceleration is not due to gravity. Incidentally, the mass of the moving bit of the accelerometer does not need to be known -- calibration of the system takes care of that. The important point is that the relationship between spring compression and acceleration is linear. But the compression excludes any component due to gravity, so the acceleration given by a device sitting on a desk does not reflect the net force (and therefore acceleration), which for almost all practical purposes is zero (relative to the desk. Lets not get into what happens when the desk accelerates relative to the earth ).
Now my appeals to thought experiments involving bathroom scales and masses on springs have not convinced you so I have to leave it to you to do the experiment yourself and see.
They convince me completely. I just interpret the evidence in a different, simpler, way.
It seems that the problem for you is the concept that an object can have acceleration whilst not actually moving at all. Which is natural. I guess that stems from the school book definition of acceleration which goes something like:

"Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity. An object is accelerating if it is changing its velocity."

Which is fair enough as far as it goes. Good old Newtonian mechanics. Unfortunately such a definition says nothing about that 9.81m/s/s my accelerometer is reading whilst totally stationary on my desk. If I were in school today being taught that I'd be sticking my hand up and asking: What's up with that?

The problem of course is that that definition says nothing about gravity. Luckily Einstein does in his equivalence principle:

"we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system."

In short acceleration and gravity are indistinguishable. If you are standing stationary on the ground you feel you own weight on your feet. If you are in free space being accelerated "upwards" you feel the same weight on your feet.
Gravity and acceleration are different physical measurements (technically, they have different dimensions). They are linearly related by the mass of the object. In that sense they are equivalent. They are NOT the same, even in an Einsteinian world. In your example you are , in each case, feeling the non-gravitational force acting on you. You cannot feel the force of gravity.

Even if we don't pursue that principle into relativity theory it immediately accounts for why my accelerometer is showing acceleration whilst not actually moving anywhere.
No. The fact that the force of gravity has not been accounted for immediately explains the result. So you have a nonsensical result. Either your premise is wrong, or you have made an error in your chain of reasoning.
Aside:

I forgot to mention, my passengers in my orbiting craft cannot see outside of their ship. There is no experiment they can do to determine if they are stationary, moving in a straight line in free space, orbiting a planet, or free falling directly downwards to one, etc etc. There is no acceleration for them. Despite what we on the ground think about it.
If you set up an unrealistically limited scenario, you get a limited result. Perform the experiment properly and the truth is revealed.
As you said, "it's all relative".
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davidcoton
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### Re: catapult project ( raspberry pi ) - physics - need help

gregeric wrote: Accelerometers behave exactly as Heater describes. Put it on its side & (x,y,z) now reads (9.8,0,0). Turn it upside down and you get (0,0,9.8) etc Picture the sagging springs the sprung mass is suspended from, it reports the compression/stretch on those. Similar to the analogy I gave of passengers in flight - in level flight you can feel g through your buttocks, in a parabolic flight you're floating.
Turning an accelerometer upside down should change the reading on the vertical axis from positive to negative (or vice versa). It should not shift the discrepancy to a different axis. I am interested to know if the polarity of the reading "at rest" corresponds to and upward or downward acceleration. Place the accelerometer so that it gives a positive reading at rest. Apply an upward force. The reading should (by my explanation) increase. If it were reading the phantom "acceleration due to gravity", it would decrease, because its movement towards the mass of earth is lessened. A simple experiment which will show whether my explanation or Heater's is correct. (Whatever the result, there remains the possibility that we are both wrong...)
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karrika
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### Re: catapult project ( raspberry pi ) - physics - need help

We really need to try this acceleration thing with a real catapult.

--
Catapultam habeo. Nisi pecuniam omnem mihi dabis, ad caput tuum saxum immane mittam.

davidcoton
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### Re: catapult project ( raspberry pi ) - physics - need help

@karrika

Mea culpa.
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gregeric
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### Re: catapult project ( raspberry pi ) - physics - need help

I think you need to get one & play with it David. The right way up (that's arbitrary for a start), while sat on my bench it reads (0,0,-g). Turn it upside down, (0,0,g). On it side, it might read (g,0,0) or (0,-g,0) etc depending on which side you put down.

I think what we really want to know is did the RPi/Sense HAT in space record its launch into orbit!

karrika
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### Re: catapult project ( raspberry pi ) - physics - need help

gregeric wrote:I think you need to get one & play with it David. The right way up (that's arbitrary for a start), while sat on my bench it reads (0,0,-g). Turn it upside down, (0,0,g). On it side, it might read (g,0,0) or (0,-g,0) etc depending on which side you put down.

I think what we really want to know is did the RPi/Sense HAT in space record its launch into orbit!
If it did I would love to have access to the data. Anyone knows?

Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

davidcoton,

Ooops, sorry. I went back and correct all (I hope) misspellings of your name.

OK now I'm confused. Previously you were outright disagreeing with me. As in "I don't think you are right" and "It's a pretty useless accelerometer that claims an object is accelerating when it isn't"

Now we seem to agree on the accelerometer measurements we expect to see and only have a little different way of looking at or describing what goes on.

My preference is to try look at it in the same way my measurements tell me it is. If my accelerometer says there is 9.81m/s/s of acceleration then I will accept the fact that there is actually an acceleration of 9.81m/s/s. Even if it is not moving.

Your preference, if I understand you correctly, is to insist that acceleration does not exist with out actual changes in actual velocity, i.e movement. That is why you refer to the "phantom acceleration due to gravity" that is reported by the resting accelerometer.

I feel that disagreeing with your instruments and introducing "phantoms" is a more complex way of looking at it than to just simply say that acceleration and gravity are equivalent.
Gravity and acceleration are different physical measurements (technically, they have different dimensions)
Not around here they are not. My accelerometer and bathroom scales are disagreeing with you as we speak

I could present it like this:

Newton gives us a relation for the force involved in accelerating a mass (real actual movement type acceleration that is):

Code: Select all

``````F = m * a                       1)
``````
He also gives us a relation force between two masses due to gravity:

Code: Select all

``````F = m * M * G / (r * r)         2)
``````
At the surface of the Earth M is the mass of the Earth, r is the radius of the Earth, G is just a constant. All of these are constant so we can wrap them up into a single constant, call it g:

Code: Select all

``````g = M * G / (r * r)
``````
Putting that g into eqn. 2) we have:

Code: Select all

``````F = m * g                       3)
``````
Well, what do we see here? Eqn. 1) and eqn 3) have exactly the same form. "a" and "g" have exactly the same dimensions. "a" is our good old fashioned movement type acceleration, "g" is gravity.

Ergo, acceleration and gravity are equivalent. There is no "phantom". My accelerometer does not lie to me.

This equivalence principle goes back to Galileo and Kepler. It's not such a radical idea.

Edit: One might want to throw in a minus sign somewhere in my above working to get the force to go the right way.
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Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

karrika,
We really need to try this acceleration thing with a real catapult.
Oh yeah. I could get into that.
Memory in C++ is a leaky abstraction .

danjperron
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### Re: catapult project ( raspberry pi ) - physics - need help

Remember my egg dropper . I still have it!
I just need a small change to trigger the capture.
viewtopic.php?p=387822#p387822
If I could get some spare time on holydays I will build
a small catapult and get video and accelerometer data.

I'm gona do Rhett Allain ( from wired.com) of myself

B.T.W. My accelerometer is 16G max. You will need to investigate for an accelerometer with more G.

karrika
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### Re: catapult project ( raspberry pi ) - physics - need help

Heater wrote:karrika,
We really need to try this acceleration thing with a real catapult.
Oh yeah. I could get into that.
Great! I remember seeing a real catapult in one of the medieval villages. Have to ask my brother. He has medieval things as a hobby.

Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

Memory in C++ is a leaky abstraction .

gregeric
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### Re: catapult project ( raspberry pi ) - physics - need help

If anyone here needs the mother of all 100% latex elastic bands or cord to create your catapult, then PM me, supplied gratis. You trebochet guys have no need of my warez.

Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

Do you have a specs on that, length, diameter, spring constant (or whatever they call it in latex band land?) Max force/extension? Any pictures?

Certainly be interested.
Memory in C++ is a leaky abstraction .

gregeric
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### Re: catapult project ( raspberry pi ) - physics - need help

No specs other than 100% latex rubber, heat-sensitized dip moulded, in various sizes. May have some old extruded cord stock. All you need to know is it's very elastic, stretchy (500% elongation), as BIG as you want, & if NASA had this stuff they wouldn't bother with those rocket things they favour. Let me know your preferred size.

Heater
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### Re: catapult project ( raspberry pi ) - physics - need help

Size and weight is an issue. I'm in Finland, postage might get huge! I'd be willing stump up for postage though.

I can't really visualized it with out width/thickness/diameter and breaking strain.
Memory in C++ is a leaky abstraction .

gregeric
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### Re: catapult project ( raspberry pi ) - physics - need help

I challenge you to break it. I'll happily send you all manner of sizes/thicknesses. It can be doubled or tripled-up for extra stored energy. What mass do you envisage catapulting, maybe I can check here (empirically) what might work?

karrika
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### Re: catapult project ( raspberry pi ) - physics - need help

The obvious payload is a Raspberry Pi and sense HAT. There is one Pi that has the same form factor as the HAT. The weight is around 250g of the complete capsule. Perhaps we could paint it orange and shoot it out to the sea. It then needs to float.

I wonder how long range a catapult has for a 250g target?