# How to quantify martial arts strikes?

Subtitled: Ah, strong am I with the Force, but how do I measure it?

With all due apologies for paraphrasing Yoda, I am trying to measure a force. Fortunately, it's an easier force to measure than midi-chlorians.

When I tutor others in karate, one of the things I emphasize is a focus on the technique behind the basic strikes. Experience has shown that the proper technique can yield a lot more force behind any strike. The problem I run into is that even though a student claims they can "feel" the difference in a strike being more powerful, they often revert back to their incorrect technique because they haven't convinced themselves that the difference is truly there.

I would like to design a system that measures the force behind a strike. In particular, I need to identify some sensor at the point of impact that can be used. National Geographic has done something very similar, but the equipment they use, such as crash test dummies, is prohibitively expensive. Likewise, I don't need the resolution or accuracy provided by that equipment. Whether someone hit with 100 or 101 lbf of force is immaterial. I want to demonstrate when then go from 100 to 200.

What sensor or system could I use in order to measure the force at impact from various karate strikes? Ideally, I could mount the device in a focus mitt, or similar, and be able to attach the pad to an adjustable system so various strikes could be measured.

My principle design constraints are:

• low(er) cost
• repeatable measurements
• range of 0–2,000 lbf

I'm not looking for a complete system design, which would include all the monitoring electronics. I'm just trying to focus on a sensor that can provide a measurable output of some sort, such as voltage.

Also note that I plan on running wires to the device, so I already have an easy way to power the system. I may go wireless at some point, but I would use a battery then and I want this question to remain focused on the sensor itself.

• So you want to measure force, not energy or power? – HDE 226868 Feb 20 '15 at 1:52
• @HDE226868 What I have commonly seen measured from a strike is force, so I think that's what my students would also expect to see. That said, if you're thinking of a system that would measure a related dimension then that's a fair answer. It will work so long as I can show the student measurable progress by using the correct striking technique. – user16 Feb 20 '15 at 12:28
• @InstructedA - Thought you might be interested to see this question: engineering.stackexchange.com/q/1788/16 I welcome your answer to it. – user16 Feb 22 '15 at 21:23
• I don't think force is a good measure of a strike. Energy, or power would be a better metric. The problem with measuring impact simply as a force is that you're neglecting time. A relatively low energy impact between two inelastic bodies (think two marbles) can create a high peak force, but that force will have a very short duration. A higher energy impact between cushioned bodies can have a much lower peak force since the impact energy is dissipated over a much longer time. – DLS3141 Aug 12 '15 at 17:30
• @DLS3141 - have a look at this question then – user16 Aug 12 '15 at 17:35

You could just hit a pendulum and measure the angle to which it swings. I have found that three liter soda bottles filled with water and hanging from a rope are good for hitting. Knowing the weight of the bottle, a little trig will give the energy, from which you can get the force.

Edit: If the transfer of energy from fist to target happens through a short enough time span, then the acceleration of the bottle forward will be approximately the centripetal acceleration through the bottom of the arc. The potential energy at the top of the swing is equal to the kinetic energy at the bottom.

$$F=ma \to \text{with substitutions} \to F=\frac{m\left(2\left(\frac{mgh}{m}\right)\right)}{r} = \frac{2mgh}{r} = 2mg(1-\cos(\theta))$$

$$a=v^2/r$$

$a$ = centripetal acceleration

$v$ = speed along the arc

$r$ = radius (rope length)

$$PE=mgh$$

$PE$=potential energy

$m$ = mass

$g$ = acceleration due to gravity (about 9.80665 m/s2 or 32.1740 ft/s2)

$h$ = height

$$KE=0.5mv^2 \text {or } v^2=2KE/m$$

$KE$ = kinetic energy

$m$ = mass

$v$ = speed along the arc

$$h=r-r(\cos(\theta))$$

$h$ = height $r$ = rope length $\theta$ = the greatest angle of the rope from vertical

• +1 for simplicity. I agree with HDE though, you should add the mathematics to make it a more complete answer. – Chris Mueller Feb 20 '15 at 17:41
• Not sure converting the swing into a force number is that meaningful. Swings higher pendulum does when harder hit it is (Yoda). If you are talking to kids (or even advanced students) that is all they need to know (don't think an advanced physics class is going to help a karatee student). – Martin York Feb 22 '15 at 3:03
• Hopefully the hit is not that hard that the bottle breaks. – Paŭlo Ebermann Feb 22 '15 at 9:00

I think that an impact force sensor is what you're looking for. I'm not sure how expensive the linked sensors are so you could also use an acceleration sensor and do a little math. The second option is likely to be less accurate but I suspect that it will also be significantly less expensive!

I know you said that you didn't want the complete system design but I figured I'd go for the extra credit in the second link. ;)

I think what you want is a piezoelectric pressure sensor. You might be able to steal one from an old bathroom scale, but the sensors in a scale may only be good up to ~100 lbs of force. These piezoelectric transducers convert applied pressure to a small voltage across the two leads. This pressure can be converted to force by measuring the surface area of the sensor.

In order to read it out you will need to build an amplification stage, probably consisting of a low noise preamp stage and a more robust amplification stage. The second part is a circuit which holds the maximum value since you are probably most interested in the maximum force applied. You can probably do both the second stage of amplification and any data processing with an Arduino.

You need to be careful how you mount the piezoelectric transducer to the focus mitt. You want to make it something that people can punch without transferring too much of the pressure past the sensor. Once you have it built, you can calibrate it by placing known weights on top of it.

• A modified electric scale (maybe kitchen rather than bathroom) is exactly what I was thinking of! – AndyT Feb 20 '15 at 13:39
• Anything piezzo is fragile against impact type force; the piezzo crystals are - well, crystals. – SF. Feb 21 '15 at 8:16
• @SF Excellent point. – Chris Mueller Feb 21 '15 at 20:26
• @SF Then how do you explain the use of peizo sensors in impact testing? I and many others use PE accelerometers, force sensors and the like for shock testing, drop testing and other impact test and have done so for many years. The piezo crystal is a quartz crystal and is more akin to a rock, not glass. – DLS3141 Aug 12 '15 at 16:56

I'm going to offer a slightly less helpful answer by poking holes in the answers of others to explain why they aren't ideal, then offering an incomplete, poorly thought through answer of my own.

The majority of answers here suffer from one of three stumbling blocks:

1. they require unnecessarily large jigs to be feasible with complexities which make them undesirable (pendulum, I'm looking at you here)
2. they ignore Newton's Laws of reactionary forces in their implication.
3. the solution is absurdly complex for the task at hand.

Ok, so starting with the pendulum, first of all, very novel solution, in theory a very good one, but there are two issues here: how do you mount the pendulum? Does the instructor hold the end of the string high above their head and hope they don't get hit? Or do you use a swing-like A-frame that you might find at a playground? If so, you may as well just go to a playground, stand on a swing and have them hit you/a pad, it's a free solution. If you want something more technical and you do figure out how to suspend the pendulum, how do you guarantee that they hit it squarely, in the plane in which you measure height, without wasting a bucket of energy spinning the milk carton? If you ever used a tyre swing as a kid you'll know that swinging it in a plane of your choosing, and without spinning, is tricky. The lighter the mass of the carton the more you are going to see instantaneous force only, which could be what you want, I don't fight so I don't know, but I do know that the heaviest blow will be backed up a heap of energy, not a very brief impulse of intense momentum. Standardising between blows will also be a challenge as the amount of contact time with the carton will greatly affect the height it rises to (energy = force x distance).

Anything which you hold in your hands is going to require you to not move; unless you are Superman you are going to move a bit, especially as your students improve, so the force which is registered is going to tail off as you provide less resistance to the blows, which means your students are going to see deminishing returns on improving their technique. Hardly ideal. The only fix to this is to mount this to something rigid and have them hit that. I would suggest a wall or similar if you can.

Conductive foam? How complex is this getting? It's a nice theoretical solution but I can't imagine that being the simplest installation.

So, the solution - any solution must meet three criteria: it's got to be cheap and cheerful, it's got to have repeatable results, and it has to be calibrated somehow.

Building on a variant of @ToyB's solution, a leaf spring is the simplest fix here, mounted on a board to something like a wall. At each end the spring should have a slot cut with a bolt through it to attach the spring to the board whilst allowing the spring to deflect. Attach a strain gauge to the back and connect it up to a simple voltmeter. You could buy all of the necessary components for \$10. Calibrate by placing a range of weights on the spring (just place the spring, on its board, on a table to do this) and measure the voltages. To add a step to the complexity but improve the solution, swap the simple voltmeter for a simple datalogger and record the voltage curve that you get as you hit the spring, then use Excel or similar and a lookup table with your voltage-force relationship to give your students a complete force curve of their hits. You could even have a few spring options for people/blows of different hits to improve your accuracy. I'd imagine you could achieve all of this for less than \$50.

• The pendulum idea is not so original - check out the ballistic pendulum, which has been around since it was first published in 1742. Regarding the positioning of the pendulum, if I may use some crude ASCII art: V___V Two ropes form an inverted A-frame on either end, with a log/cylindrical pendulum in the middle. The V shape minimizes lateral motion, support on both ends minimize yawing motion. – Chuck Oct 4 '15 at 0:49

Conductive foam will change it resistance when compressed, so it makes a good, cheap force sensor, as long as you have a system to make many measurements in quick succession and remember the one with the least resistance.

Depending on the force you want to measure, you can use several layers above each other, and because you can cut it into any shape, you're not restricted to the (small) surface of a specific sensor.

• Will that foam return back to it's original form? – user16 Feb 20 '15 at 14:50
• From my experience, yes, but there are several kinds of foam. It's often used to protect ICs, that type is harder, but won't decompress much after you compress it the first time. Other foams are quite soft though, and they decompressed at least several dozen times. Instructables has a project to build a sensor, and they say there's different types of foam as well. Maybe you should contact a manufacturer/vendor to find out which foam meets your needs best. – Guntram Blohm Feb 20 '15 at 15:02
• I believe that this is the approach used in electronic drum triggers - devices that record the impact of a drumstick on the membrane to convert them to digital signals - MIDI notes/events. They use a kind of a foam cone that touches the drumskin and measures the impact. – Peteris Feb 21 '15 at 13:56

I agree 100% with Jeff, the advantage of this is that you could build it for cheap, very, very solid. The height it swings to will give you the energy with the formula $E=mgh$ where

E=energy in Joules,

m=mass in kg,

g=9.81m/s^2,

h=height difference in m

This will be the total amount of energy transferred to the target. Unfortunately, this amount of energy is not necessarily representative of how destructive/fight-ending a strike is, as pushing it to that height slowly will require the same energy.

Knock-out power is also represented by the acceleration of the head in the few split-seconds directly after impact, this is what causes a concussion. This could be measured with a circuit that measures the time taken for it to pass two closely spaced points, the first of which should be very close to the initial position of the pendulum. The strike should go through such that the fist/foot goes further than the last of these sensors. If these points are very closely spaced relative to the arc length of the pendulum, you can use $a=2s/t^2$ where

a=acceleration in m/s^2

s=distance between sensors in m

t=time in s

You would have two aims, arguably in order of importance:

1.) make it accelerate as fast as possible 2.) get it as high as possible

If you achieve aim 1 you may cause a concussion/broken rib, assuming you have enough of 2, meaning you would also need to push through the strike! If you achieve aim 2 with a poor aim 1, you will push away your opponent without causing any real damage. I guess I don't really need to expand on this as you are a karate instructor, apologies for going over things you probably already know, it's just best to be precise and complete. Caution, these values will not be "real" in the sense that due to the distribution of the mass through the moving pendulum you will have a more complicated formula to calculate the real values. However, you will get numerical values that you can have higher or lower, and you could "calibrate" it by giving it a kick yourself, setting targets for your students. Also, you could try for example a snapping side kick and a thrusting front kick to show what values you need for the two numbers for different goals, ie (cracked rib/flash knockout) vs (create distance/cause them to fall down)

A strain guage attached to a target would be helpful.

Unlike piezzo, they are very durable against impact type force (piezzo crystals tend to shatter when the pressure is applied rapidly).

They can be attached to pretty much arbitrary "board" which yields very little, so unlike pendulum types they will not falsify the results with force applied slower, or sink the energy into the pendulum's own flexibility. If you use a water bottle, as suggested in a different answer, "stirring the water" with the impact will sink a major part of the energy, only part of it going into propelling the bottle itself.

And by changing the material you attach them to, you can tune them in to pretty much any force - they measure the stress in the material and basing on the material's Young's Modulus, they can be adapted to sensing anything from sub-Newton forces, to loads on bridges and freight ship hulls.

How to approach using them practically? You pick some kind of plank, bar, or other surface that will serve as the hit target and will bend somewhat upon the impact, but strong enough that it won't snap, attached firmly with both ends. You glue the guage to the "safe" side, somewhere around the point of impact. Then you use some simple microcontroller (PSoC4 comes to mind, easy to program and with all the remaining hardware needed on-board) and measure peak resistance changes. A simple program that picks peak resistance over certain threshold within given time frame and sends it over RS232 to the PC should be simple enough.

How to calibrate it? Place the contraption horizontally, put a known static weight at the point of impact, measure the difference between the resistance unencumbered and with the weight. 1kg weight will exert 9.806 newtons force, and unless you went very fancy with the material, linear approximation of the Young's Modulus is pretty good; your readouts will be linearly proportional to the force, so a simple proportion will suffice to get the measurement in Newtons.

• This week I was fortune enough to attend a PSoC4+BLE training session. I have not used PSoC before but looks like it is a great product – Mahendra Gunawardena Feb 21 '15 at 12:14
• @MahendraGunawardena: While PSoC has many interesting advantages, CY8CKIT-049 in particular adds puny price to that. – SF. Feb 21 '15 at 13:53

These are few suggestions to develop the system

I suggest using a polymeric bladder type approach used in Passage Occupancy Detection Systems in automotive industry. This patent describes the automotive application. The bladder system would be part of the focus mitt, which include a MEMS base differential pressure sensor. When impact force will be detected by the pressure sensor, the data will be processed by the simple microprocessor like a Atmel tiny, MSP430 or a PIC. In case analog pressure sensor is chosen then an Analog Front End (AFE) stage is required, but I2C or SPI options are available too.

Another approach will be to use an inertial measurement unit (IMU) which provides two to six degrees of freedom (DOF) couple with a microprocessor like the MSP430 or PIC. These IMU have Gyroscopes and accelerometers. This approach will give more data that can be used for later analysis. Also the communication is done via I2C or SPI to the microprocessor

The system will require simple power system like a simple rechargeable button battery. USB power charging system might be your best choice. The USB charging system will enable the data download option. Also some type of energy harvesting mechanism such as vibration could be used to generate energy required to power the system, similar to some of the new gym machines such as treadmills, elliptical bikes etc. This can be a great low power application.

Another option would be to connect a wearable such as a fit bit that will not only provide the power source but also data storage, review and analysis. Fit bit will also give the ability connect to a Smart phone of real time analysis and feedback to the student.

Going directly from focus mitt to Smart might be a great value added proposition. This can be achieve in many ways. Using Cortex ARM M0 micro with an on-chip BLE might be the best currently available option. Many vendors such as NXP, Freescale, and Cypress offer this option. It is even better is a Cortex ARM M0/M4 + Bluetooth Low Energy/Bluetooth Smart in a module. Below is an example of such device.

All of these vendors offer small form factor affordable development kit.

Finally to address the VOC the students, providing real-time measurable feedback between correct and incorrect techniques will drive the students desire to attain perfection.

References:

Here is a really cheap and cheerful way of showing the size of an impact. Take 2 boards of plywood, put a large compression spring between one and the other board so the spring is sandwiched but removable by at least one of the boards like an "H". Bolt this to a wall."H|" Get set size balls of playdo (kids putty) place on of these inside the spring (probably in a plastic bag or similar to save on mess), refit 2nd board and hit the board hard. The impact on the playdo will cause different deformation depending on how hard it was hit.

If you make the board which is fixed to the wall have sides around it like a box, place 5 (shorter than the sides) compression springs (four corners and the middle holding the putty) you could probably have a piece of string to pull out the second board for ease of getting to the playdo.

Is this too simplistic? it really depends how scientific you want the result and how good you are with a soldering iron as opposed to 6 bits of wood and 5 compression springs

The problem with quantifying impact force is the short duration of what is usually a 'peaky' pulse. Bathroom scales are usually damped to give a steady reading of a static force and won't capture transient peaks. Ballistic pendulums also have problems - some of which have been discussed. However, for training young fighters, I'd suggest that you don't really need to quantify the force but, rather, compare their performance over time and let them compare themselves with other students. To do this, all you need do is fill an open box (about 30 cm square) with a thick layer of modelling clay and fix the box to the wall. When the student throws a punch, the clay will act as a witness material and deform plastically. Just measure the maximum depth of the depression and record this on the student's personal record.

The clay is, of course, resusable but you might have to experiment to get the right modelling clay: Roma Plastilina was the preferred material for firearms ballistics but Plasticine or Play-Doh might be less painful to young karate-ka.