Couple of questions came up as a result of my post and so after some additional measurements and thoughts, here’s the follow up:
I have measured the output of ADXL193 accelerometer with the Digital Storage Oscilloscope so here’s how it looks through time as read at the sensor location:
As you can see there’s a definite noise caused by the AD conversion which happens 44kSa/s, however this noise should have no effect on the readings as it happens after the AD7680 AD converter latches the input voltage level. Here it is again with Chip Select on the other channel and another wave showing SPI clock. As you can see interference starts way after CS goes down and is actually due to the SPI clock. You can also clearly see 3 transmissions 1 byte each in length:
I am not sure why scope captured CS going down twice, but the second one is the true reading. The spikes at times when CS goes down and up are not there when CS is not measured, so i believe it’s the scope’s impact. There’s definite additional noise at the start of 3rd transmission – it’s source, however, escapes me.
Below is the signal at the AD7680 AD converter input which is worse then at the sensor due to the long cord picking up more interference:
Collected data from results of AD conversion shows a range of 15-25 mV which matches the noise level of 14 mV peak to peak between spikes. If the SPI transmission spikes were getting into AD converter I would expect 40+ mV of noise which isn’t so.
So, after rejecting visible spikes as the source of the noise i started to look at the signal between spikes:
The frequency analysis with FFT (Fast Fourier Transform) shows predominate noise at 3 Mhz and also at 2 Mhz and 1 Mhz. After trying to find the source of this noise i discovered that it is inherent in any circuit including simple probe ground to probe tip loop. With help from the folks at EEVBlog’s Forum i figured out that this is due to the FM radio and that the solution is to use low pass filter to weed these frequencies out. Since i am sampling at 40 kSa/s, i can’t see anything above 40 Mhz, so there’s no harm in putting a 10-40kHz low pas filter. Here is result with such low-pass filter enabled in the scope:
The noise level is reduced to about 2.5 mV which is only 0.3 g. So the lessons learned here are a) beware of radio noise when measuring small signals and b) to avoid that noise do AD conversion very close to input source and put a low-pass filter. The AD193XL breakout that i got from SparkFund did have a 10nF decoupling capacitor but it is connected between VCC and GND filtering power supply rather than output.
Acceleration vs Momentum
After i asked if acceleration is the right measure to use a lot of people responded and suggested that although the Momentum (mass*velocity) is a better measure of energy transfer the peak acceleration is the good indicator of that. Although i agree with that, i figure that the answer depends on the purpose of the punch.
If the goal of the punch is to move opponent then the greater momentum or energy your punch can transfer the faster opponent will move. Momentum is mass of the board * velocity of the board or in terms of acceleration mass * integral of acceleration. Energy is mass * velocity^2 / 2 so it’s also dependent on acceleration integral.
However, if the purpose of the punch is damage (or pain), then compression of soft tissues is your goal. Consider following model for human head:
If a punch force is small but nevertheless applies for very long time the whole head (both masses M and m) will end up moving very fast, however the spring will be compressed very small (F/K where K is spring coefficient) and once the punch force is removed there will be little vibration. Most of the punch energy will go into the kinetic energy of the total system movement rather than oscillation.
if however, the punch force is really large but acts during a very short period of time, the spring will compress significantly and once the force is removed most of the energy will be in the oscillation of tow masses rather then them moving in the same direction away from the punch. If the interaction time is instant then in fact all of the punch energy will be transferred into the movement of mass M which then will cause spring to compress the largest.
So it’s the maximum force we’re looking for which is proportional to board acceleration. It is interesting to note that the two hands having the same energy or momentum but different weights will produce different forces and therefore damage. I would expect the heavier hand moving slower will have greater interaction time and therefore smaller force compared to the smaller faster and more “force full” hand – Bruce Lee’s fans rejoice. This however is provided that both hands have the same energy or momentum, which is usually not the case when comparing lightweight and heavyweight fighters. Again, energy is proportional to force * distance the object moves under the force. Since distance is the same and heavyweight fighters have more muscle mass and therefore can produce greater force will end up with more kinetic energy to transfer to target. Which effect will win: slower speed vs larger energy is beyond me.
Will Robertson from University of Adelaide, Australia sent me an interesting research article comparing full reverse punch against short (3 inch) power punch: A comparison of the reverse and power punches in oriental martial arts. There’s a good discussion of force vs momentum starting on page 16.
I have also had a chance to capture a longer time sequence of readings using the scope, so here’s the chart covering most of the action:
Note: lines have different units and are not plotted to scale.
The plot shows the board acceleration, velocity and position until it reaches maximum deflection. I was surprise that the acceleration has such complex shape rather than simple hill. In my correspondence with Will Robertson, he also explained that after the initial contact with the hand the board can start moving faster than the hand and interrupt the contact. There’s the inverse relationship between the force of the strike and the interaction time – the harder you hit something, the faster it escapes your reach. I think this graph shows that effect in the first dip of the acceleration – board got away from the hand and started to slow down due to tension until the hand reached again and accelerated it even farther. You can also see consecutive vibration where acceleration goes between a positive and negative values and speed fluctuates accordingly until the board comes to rest. I believe this is a different effect from the first two hills and is the vibration of board + completely extended hand as the hand is trying to keep they board flexed. On one of the even longer captures that i have made i could see the actual board release and another set of damping oscillations as the board comes to rest in it’s original position.