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No this isn't a homework assignment. My last homework assignment was 18 years ago. Then again my last physics class was 21 years ago, hence the post.

The goal is to design a system that works, select a sensor that will provide readings that are within the reasonable range. It isn't and doesn't have to be calibrated. The results will not be converted to engineering units. The impact detector is to help soccer players (kids learning) to kick the properly and accurately for the most power. The result will be 0-999 displayed on a 3 digit 7-segment display. The system will be using a 10-bit ADC and I will drop the last 25 counts to make it fit.

Now for the physics problems.
Problem #1.

Known: Soccer ball, size 4, weight about 0.45 kg.
Known: Free floating target 1 meter square of 3/8" plywood (about 4kg). [Yes free floating let's get the concept down first, then get complicated]
Unknown: Soccer ball velocity
Measurement: Acceleration of target (using Analog Devices ADXLxxxx chip, TBD)

Assume measurement A = 1 = 9.8m/s2

Target: F=mA = 4 * 9.8 = 39.2

Ball: Don't know A, can't use F=mA, assume constant v, use F=1/2*mV2 -> V=sqrt(2*F/m); where F=39.2 = sqrt(2* 39.2 / 0.45) = sqrt(174.2) = 13.2 m/s

According to the internet, this is a reasonable number. Question: Do I have the physics math correct?

Now get complicated:
Known: Soccer ball, size 4, weight about 0.45 kg.
Known: Target 1 meter square of 3/8" plywood (about 4kg), hanging by its top edge.
Unknown: Soccer ball velocity
Measurement: Acceleration of target (using Analog Devices ADXLxxxx chip, TBD)
Assume measurement A = 1 = 9.8m/s2

Target: F= ??
Ball = F=1/2mV2 then use F from the target above.

I'm thinking it needs the moment of inertia or some other factor. (Since I don't know where the force from the ball will be applied, I am going to assume the center).

How do I calculate F for the 1m square 4kg target hanging from the top edge and the force applied to the center?

No this isn't a homework assignment. My last homework assignment was 18 years ago. Then again my last physics class was 21 years ago, hence the post.

The goal is to design a system that works, select a sensor that will provide readings that are within the reasonable range. It isn't and doesn't have to be calibrated. The results will not be converted to engineering units. The impact detector is to help soccer players (kids learning) to kick the properly and accurately for the most power. The result will be 0-999 displayed on a 3 digit 7-segment display. The system will be using a 10-bit ADC and I will drop the last 25 counts to make it fit.

Now for the physics problems.
Problem #1.

Known: Soccer ball, size 4, weight about 0.45 kg.
Known: Free floating target 1 meter square of 3/8" plywood (about 4kg). [Yes free floating let's get the concept down first, then get complicated]
Unknown: Soccer ball velocity
Measurement: Acceleration of target (using Analog Devices ADXLxxxx chip, TBD)

Assume measurement A = 1 = 9.8m/s2

Target: F=mA = 4 * 9.8 = 39.2

Ball: Don't know A, can't use F=mA, assume constant v, use F=1/2*mV2 -> V=sqrt(2*F/m); where F=39.2 = sqrt(2* 39.2 / 0.45) = sqrt(174.2) = 13.2 m/s

According to the internet, this is a reasonable number. Question: Do I have the physics math correct?

Now get complicated:
Known: Soccer ball, size 4, weight about 0.45 kg.
Known: Target 1 meter square of 3/8" plywood (about 4kg), hanging by its top edge.
Unknown: Soccer ball velocity
Measurement: Acceleration of target (using Analog Devices ADXLxxxx chip, TBD)
Assume measurement A = 1 = 9.8m/s2

Target: F= ??
Ball = F=1/2mV2 then use F from the target above.

I'm thinking it needs the moment of inertia or some other factor. (Since I don't know where the force from the ball will be applied, I am going to assume the center).

How do I calculate F for the 1m square 4kg target hanging from the top edge and the force applied to the center?

You will either to hang your target from an "infinitely long" beam to negate "where" on the target the ball hits, or add some IR LED emitter/detector pairs to determine the position the ball hits. Alternatively, some sort of tortion spring system can also be rigged up so the spring(s) deflect the same no matter where the ball hits.

Then, you will need to know how the ball deflects off of the target (drops dead, directly to the ground vs rebounding off of the target. If you have a free-hanging target, the ball will rebound harder if it hits the top and will drop dead if it hits the bottom. Once you decide on the design, the physics become much easier to calculate.

You will either to hang your target from an "infinitely long" beam to negate "where" on the target the ball hits
Sorry, not a clue what this means.

or add some IR LED emitter/detector pairs to determine the position the ball hits.
That's not going to happen as they will get destroyed when the ball hits them.

Alternatively, some sort of tortion spring system can also be rigged up so the spring(s) deflect the same no matter where the ball hits.
No clue here, too.

Then, you will need to know how the ball deflects off of the target (drops dead, directly to the ground vs rebounding off of the target.
Probably not going to happen. Because it would have to be in 2D and in front of the target. Again, kids kicking a soccer ball, likely to get destroyed.
But since the target is not rigid and the recoil of the ball would be due the ball un-deforming (is that a word) from the impact and pressing against the rigid surface. In the theoretical world, the ball would drop having transferred its energy to the movable target and not having anything to press against to change its direction. In the less theoretical world, the ball does not transfer all of its energy instantaneously and instead keeps travelling forward while impacting the target so it hits the ground in the sway-zone of the target, behind the target. The latter is what I experienced today.

If you have a free-hanging target, the ball will rebound harder if it hits the top and will drop dead if it hits the bottom.
The target is the center, the sensor is in the center. Once the equations have been determined for the target, it can be determined how much effect hitting the target will have if the contact is at +0.4m or -0.4m from the center.

Once you decide on the design, the physics become much easier to calculate.
The design of the target is known. 1 meter square of 3/8" plywood (about 4kg), hanging by its top edge.

Just need the physics for the force and acceleration experienced by the target. Even with all of this, the acceleration of the target is what will be measured and requires knowing the force equation for the 1 m2 4kg target hanging by its top edge in order to verify the acceleration is in the range of the sensor and the results are reasonable.

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Just hang your target board on reasonable length ropes or chains, rather than having a rigid hinge.
That way a hit near the top will still give a good deflection.

Then get an accelerometer module, attach to the back of the target and start taking readings. For something like that, it's easier to get data from practical experiments than try to over-think it.

If you want to measure target accuracy as well as impact force you could use three or four accelerometers symmetrically around the back edge, so you can calculate twist due to off-centre impact by the different movement of the target edges.

Just hang your target board on reasonable length ropes or chains, rather than having a rigid hinge.
That way a hit near the top will still give a good deflection.
It is.

Then get an accelerometer module, attach to the back of the target and start taking readings. For something like that, it's easier to get data from practical experiments than try to over-think it.
I did. But how do you determine if the results are reasonable?

According to my results, the peak acceleration detected was 122g. Using F=mA=1/2mv2 results in in the ball travelling at 146m/s. Somehow I don't think I can kick the ball 326 miles per hour.

Personally, I'd measure the ball speed. A rigid frame (with a 1M hole) with a laser diode used to bounce up and down between two strip mirrors - top and bottom would enable you to accurately measure the speed. All sensors would be protected by being behind the board. You'd need to stop the ball bouncing back into the sensors but that shouldn't be too difficult - put a football/soccer net as a back stop.

Mike.

Personally, I'd measure the ball speed. A rigid frame (with a 1M hole) with a laser diode used to bounce up and down between two strip mirrors - top and bottom would enable you to accurately measure the speed. All sensors would be protected by being behind the board. You'd need to stop the ball bouncing back into the sensors but that shouldn't be too difficult - put a football/soccer net as a back stop.

Mike.
That worked well indoors and failed miserably outside in real use (ie., in the sunlight). So back to the accelerometer...

Have you considered something like a punchbag?, when it's struck (or hit by a ball) you could monitor the air forced out of it (for a non-sealed bag), or the internal pressure variation for a sealed bag.

Have you considered something like a punchbag?, when it's struck (or hit by a ball) you could monitor the air forced out of it (for a non-sealed bag), or the internal pressure variation for a sealed bag.
Yes. Both air filled and water filled. The indication on the 'net was water filled only works when laying horizontally as when hanging it becomes tear drop shaped and the water pressure varies. Air filled would work (didn't see that listed on the net) but would it burst when hit? Where would I get a bag large enough, strong enough, and cost effective to present a 1 square meter target and withstand an impact of 140 newtons (units?)?

Thus the accelerometer method.

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Yes. Both air filled and water filled. The indication on the 'net was water filled only works when laying horizontally as when hanging it becomes tear drop shaped and the water pressure varies. Air filled would work (didn't see that listed on the net) but would it burst when hit? Where would I get a bag large enough, strong enough, and cost effective to present a 1 square meter target and withstand an impact of 140 newtons (units?)?

A punchbag takes an awful lot of punishment, although isn't usually 1meter wide (although is more than 1meter high).

A punchbag takes an awful lot of punishment, although isn't usually 1meter wide (although is more than 1meter high).
True. But very heavy and neither water or air filled.

True. But very heavy and neither water or air filled.

If it's filled with foam (to maintain it's shape) it's not heavy, and would work as an air filled bag - it's just another potential option.

If it's filled with foam (to maintain it's shape) it's not heavy, and would work as an air filled bag - it's just another potential option.
But as you mentioned, it is not wide enough.

According to my results, the peak acceleration detected was 122g. Using F=mA=1/2mv2 results in in the ball travelling at 146m/s. Somehow I don't think I can kick the ball 326 miles per hour.

The ball is elastic and will initially deform, then rebound; it's casing part in contact has far lower mass than the target so the peak force will be delayed and is probably about the same time or just before the point the ball reaches maximum distortion. I don't think any straightforward calculation of just peak acceleration will give consistent results.

Using your optical speed measure to calibrate it may allow you to make a lookup table?

Or use the acceleration vs time to calculate displacement of the target?
That's an indication of overall impact energy and should be a better figure than peak acceleration with no duration.

The fact is the acceleration measured is 122g. I can't get the correct answer because I don't have the correct formula for the target. I know the ball is correct, and know the target is not.

How does the mass of an object change by hitting something? The ball drops almost straight down upon hitting the target. Indicating the majority of its forward momentum has been transferred to the target.

Which all circles back around to needing the correct formula for the target.

But as you mentioned, it is not wide enough.

No, and they aren't foam filled either - but you could make a similar bag of the required size, and fill it with foam.

Think I'll stick with the swinging board. K.I.S.S. I'm sure the equation is in my text book, either physics or static & dynamics. Guess I will have to dig the books out tonight.

Why can't you just have someone take some good kicks at it and just use those numbers? No one here has even talked about calculating the numbers for an on-center versus off-center hit which is even trickier. I don't think it's worth the effort when you can just build the system and then kick at it to calibrate some stuff in.

You never did mention if your 0-999 scale was just an arbitrary scoring or the actual ball speed. I can only assume the reason you seem so particular about things is that you want the actual ball speed. On the other hand, I don't see the speed of a soccerball needing to be anywhere 200 of anything, let alone 999 which makes me think you just want an arbitrary scale, because if it is to be an arbitrary rating you definitely do need need any of this. You just have some test kicks and qualitatively classify them arbitrarily for the computer.

rjenkinsgb mentioned this earlier and all you had to respond with was "how do you know the results are reasonable?" Personally, I do not understand this concern because you could flip that question right around to if you had equations. If you had the equations, how do you know those are reasonable? You would have to run out and test them against a bunch of kicks to know.

How do you know the measurement you took with a ruler is reasonable? You take multiple readings and you also eyeball it based on your experience. Same thing here. Take multiple kicks, classify them all and look at their readings to see their median and variance. Then compare that to other types of kicks. If they result in clear groups, it's reasonable. If you want to associate the numbers with a ball speed, then have a speed gun when you perform the tests and punch in the speed for each reading. Then have the processor associate each peak acceleration with the speed and interpolate the curve. Or you could just have the system spit out the peak acceleration measured and write it down along with the measured ball speed and punch it into your PC and interpolate and curve fit it there. Then program that into the system.

TBH, if I were as picky about the accuracy of this as you seem to be, I would only put some accelerometers with simple thresholding behind the wood board to detect an impact (maybe not even accelerometers and just a mechanical shock switch). Then I would mount sonar doppler on the back of the board that looks through the board through a grating to detect the speed. Or doppler radar (affordable modules finally exist now, thank goodness) or infrared rangefinding LEDs. Just put them behind plastic to protect them. Doesn't even have to be visibly transparent plastic, just one that is transparent ti microwaves of IR which is fairly common. Even if they're not you can always recess them so they aren't protruding from the board. for protection. More accurate and no need for this this mathematical gymnastics which isn't even going to be very accurate anyways.

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Why can't you just have someone take some good kicks at it and just use those numbers? The readout scale of 0-999 is arbitrary anyways and no one here has even talked about calculating the numbers for an on-center versus off-center hit which is even trickier. I don't think it's worth the effort when you can just build the system and then kick at it to calibrate some stuff in.

I agree, there's no need for absolute numbers, just relative ones - and even trying to do the maths is going to be wildly inaccurate anyway, as how do you measure most of the values in the first place?.

Why can't you just have someone take some good kicks at it and just use those numbers? No one here has even talked about calculating the numbers for an on-center versus off-center hit which is even trickier. I don't think it's worth the effort when you can just build the system and then kick at it to calibrate some stuff in.

You never did mention if your 0-999 scale was just an arbitrary scoring or the actual ball speed. I can only assume the reason you seem so particular about things is that you want the actual ball speed. On the other hand, I don't see the speed of a soccerball needing to be anywhere 200 of anything, let alone 999 which makes me think you just want an arbitrary scale, because if it is to be an arbitrary rating you definitely do need need any of this. You just have some test kicks and qualitatively classify them arbitrarily for the computer.
I did mention the 999 scale is the digital output of the 10 bit ADC with the last 25 counts dropped. I'm hoping the off-center distance makes little difference to the resulting values, but that can't be know without knowing the force equation for the target.

How do you know the measurement you took with a ruler is reasonable? You take multiple readings and you also eyeball it based on your experience. Same thing here. Take multiple kicks, classify them all and look at their readings to see their median and variance. Then compare that to other types of kicks. If they result in clear groups, it's reasonable. If you want to associate the numbers with a ball speed, then have a speed gun when you perform the tests and punch in the speed for each reading. Then have the processor associate each peak acceleration with the speed and interpolate the curve. Or you could just have the system spit out the peak acceleration measured and write it down along with the measured ball speed and punch it into your PC and interpolate and curve fit it there. Then program that into the system.
How to you plan to get, setup, and power all this sh-stuff in the middle of a soccer field?

All the rest of what you have said is predicated on know the speed of the ball as you seem to be working with the same 1 equation and two unknowns. Having the second equation solves the problem (pun intended and not).

I agree, there's no need for absolute numbers, just relative ones - and even trying to do the maths is going to be wildly inaccurate anyway, as how do you measure most of the values in the first place?.
What values are you interested in measuring? I have the weight, size, and design of the target, and the mass of the soccer ball and can measure the acceleration. Knowing the proper force equation for target will give one of two results.
Either:
1. The actual answer (ie., is the target was actually F=ma=1/2mV2, then I can solve for V knowing everything else)
or
2. A formula based on the distance from the connection (hinge point if you will) to the point of impact. From which, I can then evaluate the value from the impact at the top edge versus the bottom edge to see the magnitude of change due to difference.

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