100+ G Accelerometer test

[Adrian A]

Cross-posted.

Today I flew my new 38mm av-bay that has 2 different Parrot altimeters: one with a 70G accelerometer, and one with a 250G accelerometer. They flew in a shortened Thunderbolt 38 that I redecorated and re-christened as der Mad Rex. I put an H999 in there, and the results were pretty spectacular. It left the rail at 150mph, and hit 500 mph in about 0.2 seconds. Best of all, it gave me a great flight to see what the 70G accel does under high Gs:

This 70G accelerometer cut off the output at about 82 Gs. I'm happy to see that the data doesn't do anything too funky when it exceeds the rated output range of 70 Gs. So if a small part of the thrust curve exceeds 70 or even 82 Gs, nothing too bad will happen; the only bad result is that part of the impulse that exceeds 82 Gs won't be taken into account in downstream calculations.

 

[Handeman]

Very interesting data. The only Warp 9 I've flown was the I1299N. That simed to 79.4Gs with my rocket. That 1/3 second burn was like a cannon shot. Very cool. Burnout was at 128 ft and 460 mph. Apogee was 4,028 ft.

What I found interesting was that the same rocket simed on a H999N showed a hair over 100Gs. You would think the I1299N would give you more Gs then the H999N, but it doesn't.

Sounds like the H999N was the perfect motor for your test. It's got a real kick to it.

 

[Adrian A]

The only Warp 9 I've flown was the I1299N. That simed to 79.4Gs with my rocket. That 1/3 second burn was like a cannon shot. Very cool. Burnout was at 128 ft and 460 mph. Apogee was 4,028 ft.

Sounds like a similar flight to the one I had yesterday. I'm an altitude junkie, so normally I like long-burn motors, but I must say it was a thrill to see this substantial rocket go so fast, so quickly.

What I found interesting was that the same rocket simed on a H999N showed a hair over 100Gs. You would think the I1299N would give you more Gs then the H999N, but it doesn't.

Hmm. The H999 thrust curve on thrustcurve.org shows a lot of ringing in the start of the burn, which is most likely just a test artifact. The ringing is enough to make the peak data point for the H999's thrust curve higher than the peak of the I1299's thrust curve. The data I took yesterday shows some ringing in the 250g accel trace, but if the posted thrust curve were true, we would see an acceleration spike at the beginning of about 1.7x the mid-burn value.

 

[bobkrech]

Hmm. The H999 thrust curve on thrustcurve.org shows a lot of ringing in the start of the burn, which is most likely just a test artifact. The ringing is enough to make the peak data point for the H999's thrust curve higher than the peak of the I1299's thrust curve. The data I took yesterday shows some ringing in the 250g accel trace, but if the posted thrust curve were true, we would see an acceleration spike at the beginning of about 1.7x the mid-burn value.

You are correct.

That is a test stand artifact. It looks like the test stand has a resonance at 55 Hz. Either the teststand needs to be stiffened or the thrust curve data needs to be processed with a digital notch notch filter to remove the 55 Hz frequency component which is not real. (A FFT/Inverse FFT processing scheme would also work.) In reality these motors have a nearly constant thrust throughout the burn time which is only 0.3 seconds.

Bob

 

[DMcCauley]

Yep. Think of the warp motor like a hammer to a bell. The hammer strike - the impulse - will excite the bell and cause it resonate at its natural frequency, whatever that may be.

 

[darkhelmet]

That is a test stand artifact. It looks like the test stand has a resonance at 55 Hz. Either the teststand needs to be stiffened or the thrust curve data needs to be processed with a digital notch notch filter to remove the 55 Hz frequency component which is not real. (A FFT/Inverse FFT processing scheme would also work.) In reality these motors have a nearly constant thrust throughout the burn time which is only 0.3 seconds.

Bob

I think you mean the teststand->motor interface needed dampening. Also, any practical digital filter to remove the ringing would cause a significant lagging artifact in the short-burn data. The duration of the burn and the period of the undesired signal are too close.

Without a better test stand, we don't know if there's combustion instability or not. If the oscillations in the accelerometer data have a similar characteristic frequency, it may not be a coincidence. The combustion instability would most likely be at several KHz for that motor, which would mean that the recorded frequency is a sampling alias.

 

[falingtrea]

This 70G accelerometer cut off the output at about 82 Gs. I'm happy to see that the data doesn't do anything too funky when it exceeds the rated output range of 70 Gs. So if a small part of the thrust curve exceeds 70 or even 82 Gs, nothing too bad will happen; the only bad result is that part of the impulse that exceeds 82 Gs won't be taken into account in downstream calculations.

Considering the parts are designed to survive 3000 G I am not surprised that the data does not "go funky". Kinda like Timex,"Takes a lick'en and keeps on tick'en"

 

[bobkrech]

I think you mean the teststand->motor interface needed dampening. Also, any practical digital filter to remove the ringing would cause a significant lagging artifact in the short-burn data. The duration of the burn and the period of the undesired signal are too close.

No, I mean stiffen. Stiffening will raise the resonant frequency, just as tightening a guitar string raises it's frequency. Dampening will simply reduce the frequency response at the resonance frequency and typically at higher frequencies as well.

In any real system, you need to sample at a frequency at least twice the maximum desired response frequency (Nyquest) and IMO a factor of 10 higher to get the proper waveform shapes. The FFT/Inverse FFT method is a post acquisition processing method that does not cause a lagging artifact. If you have a DATAQ data system, you can use the supplied software to do this. All you do is to take an FFT of the data, and remove or reduce the intensity at the resonant frequency, and the perform the inverse FFT to regenerate the original waveform minus the resonance response. Both the high frequency and low frequency response is unaltered.

Without a better test stand, we don't know if there's combustion instability or not. If the oscillations in the accelerometer data have a similar characteristic frequency, it may not be a coincidence. The combustion instability would most likely be at several KHz for that motor, which would mean that the recorded frequency is a sampling alias.

IFAIK most combustion instability measurements in the kilohertz range are done acoustically with microphones or piezoelectric transducers to record the pressure fluctuations in the chamber and/or exhaust plume.

Bob

 

[UhClem]

Without a better test stand, we don't know if there's combustion instability or not. If the oscillations in the accelerometer data have a similar characteristic frequency, it may not be a coincidence. The combustion instability would most likely be at several KHz for that motor, which would mean that the recorded frequency is a sampling alias.

This issue has been dealt with in the past although since there has been a severe loss of data in the rocket forums I suspect the original messages are lost. But if my memory serves someone from Aerotech (probably Gary) said that the data from the Aerotech test stand did not show this oscillation.

The current Aerotech test stand is pretty nice. It has the advantage of being a permanent installation with lots of concrete. Attached is an old photo I grabbed from somewhere.

 

[darkhelmet]

No, I mean stiffen. Stiffening will raise the resonant frequency, just as tightening a guitar string raises it's frequency. Dampening will simply reduce the frequency response at the resonance frequency and typically at higher frequencies as well.

It's not as simple as that. Stiffening is more likely to produce or enhance a resonance. Dampening will reduce the natural frequency and reduce the amplitude of the artifact, or remove it completely. One typical means is to increase the mass of the apparatus. But, this is only affective if structural sources of ringing are isolated and the thrust interface isn't allowed to 'bounce'.

In any real system, you need to sample at a frequency at least twice the maximum desired response frequency (Nyquest) and IMO a factor of 10 higher to get the proper waveform shapes. The FFT/Inverse FFT method is a post acquisition processing method that does not cause a lagging artifact.

There is always an artifact produced by this method. The input is not truly continuous and sinusoidal, but the inverse FFT assumes it is. The result will produce an e^jK(f) that was not in the original signal (ie: a frequency dependent lag in the time domain).

Also, no real-world sampling is noise-free with a perfect anti-aliasing filter. Unless all analog content >fs/2 is less than 1/2 a bit of resolution, there will be artifacting. At 200Hz sampling, a small 101 Hz signal will look like a 1Hz signal, which is impossible to distinguish from real 1Hz information. There is no post-processing digital magic that can remove it.

IFAIK most combustion instability measurements in the kilohertz range are done acoustically with microphones or piezoelectric transducers to record the pressure fluctuations in the chamber and/or exhaust plume.

True. However, it is not uncommon to have combustion resonance show up in professional test stand data. A load cell with a 2-3KHz bandwidth will pick up a significant amplitude if undamped. A data acquisition system may see the actual resonance riding on the thrust data, or record a lower-frequency alias. The transfer of the combustion resonance, even if properly damped and pre-filtered, shows up as a "DC offset" to the thrust or pressure readings due to non-linear phenomena. (ref: Summerfield, et al).

In any case, this is a lot of "amateur rocketry" discussion for a forum that isn't supposed to allow it.

 

[UhClem]

It's not as simple as that. Stiffening is more likely to produce or enhance a resonance. Dampening will reduce the natural frequency and reduce the amplitude of the artifact, or remove it completely. One typical means is to increase the mass of the apparatus. But, this is only affective if structural sources of ringing are isolated and the thrust interface isn't allowed to 'bounce'.

Increasing stiffness will push the resonance to higher frequencies which will then be removed by the pre-sample filter.

Also, no real-world sampling is noise-free with a perfect anti-aliasing filter. Unless all analog content >fs/2 is less than 1/2 a bit of resolution, there will be artifacting. At 200Hz sampling, a small 101 Hz signal will look like a 1Hz signal, which is impossible to distinguish from real 1Hz information. There is no post-processing digital magic that can remove it.

Right idea, wrong frequency. The sampled 101 Hz signal will look exactly
like a 99 Hz signal. A 199 Hz signal will look like a 1Hz signal after sampling.

I dug up a web page with a Java applet that can be used to demonstrate the phenomena.

(ref: Summerfield, et al).

Note exactly a useful reference as it fails to name the title of the book.

 

[Larry Curcio]

Increasing stiffness will push the resonance to higher frequencies which will then be removed by the pre-sample filter.



Right idea, wrong frequency. The sampled 101 Hz signal will look exactly
like a 99 Hz signal. A 199 Hz signal will look like a 1Hz signal after sampling.

I dug up a web page with a Java applet that can be used to demonstrate the phenomena.



Note exactly a useful reference as it fails to name the title of the book.

That is the problem you run into without prior knowledge. Suippose you had some idea of what the thrust curve and drag functions should look like, and you used a rigorous Bayesian estimator like... oh just to pull something out of a hat... like a Kalman filter. Could you get a more accurate rendering?

 

[Larry Curcio]

That is the problem you run into without prior knowledge. Suippose you had some idea of what the thrust curve and drag functions should look like, and you used a rigorous Bayesian estimator like... oh just to pull something out of a hat... like a Kalman filter. Could you get a more accurate rendering?

(Responding to my own post) And while we're at it, what about the effect of harmonic v Gaussian noise with the KF?

Thanks and Regards

 

[Andreas Müller]

... oh just to pull something out of a hat... like a Kalman filter. Could you get a more accurate rendering?

The problem of removing the resonance of the test stand can indeed be solved using a Kalman filter. The attached paper was written some time ago, it shows how the TMT teststand oscillations can be removed. During the preparation of the paper, Fourier transforms were tried as well, but they were not nearly as successful. Their only usefullness was in determining the frequences of the oscillations. The paper also contains another application of interest to rocketeers: removing transients from measurements of opening shocks done by Carmen Müller in a wind tunnel.

Edit: apparently the paper is too large for the forum, probably because of the large number of diagrams. Here is a link to it: Deconvolving oscillatory transients with a Kalman filter

 

[UhClem]

The tricky bit with using a Kalman (or any other model based filter) is figuring out the system model.

But I wouldn't use a Kalman filter on this for a couple of reasons.

The first is that the "noise" is not zero mean Gaussian which is what the Kalman filter assumes. The second is that this is not real time processing and all of the data set is available so non-causal filters can be used. One of the more interesting being the Savitsky-Golay. (I hope I got that right.) For those not wanting to figure it out and code it up, the Dataplot package from NIST can mangle the data for you. It would be nice to have the H999 data set to play with but it isn't available. (The TMT web page doesn't even admit to it being a certified motor.)

There are also variations on the theme of Kalman filters called smoothers that look into the future as well as the past. I have skimmed the section on this in Gelb, et al., but I still wouldn't try to implement one.

As for using a rough profile of the expected thrust curve that would help (it would appear in the equations as a control input) but I wouldn't use it when trying to measure a thrust curve as you could end up in a situation where the tail wags the dog. Adding drag (to a flight model) changes the model to non-linear system requiring the Extended Kalman Filter (EKF).That is for advanced students and I haven't felt the urge to work on it.

 

[jderimig]

Interesting discussion. Here is another 'take'.

Since this is test stand data the value of processing the data in close to real time isn't really that high.

If you can come up with a dynamic model of the test stand (one simple way is banging it with a hammer (impulse) and look at the resulting ringing and decay) then this model can be used to determine the motor thrust curve.

To get the motor thrust curve you would need to simply solve for the required 'forcing function' that would give you the curve you have just recorded. Not a trivial computational exercise but not an impossible one either.

--jd

 

[Andreas Müller]

To get the motor thrust curve you would need to simply solve for the required 'forcing function' that would give you the curve you have just recorded. Not a trivial computational exercise but not an impossible one either.

This is exactly what the paper cited above does. The first approximation for the model of a test stand is always very simple: it's a set of coupled, damped harmonic oscillators. After all, a test stand is always a set of masses held together by things that allow elastic deformation.

 

[Andreas Müller]

The first is that the "noise" is not zero mean Gaussian which is what the Kalman filter assumes.

Depends on what you consider as noise. The ringing of the test stand certainly is not noise, it is completely deterministic. So you simply have to find out what laws govern the ringing. If the origin is mechanical (in contrast to a sensor problem), it most probably is elastic deformation, i.e. coupled damped harmonic oscillators. Unless you have nonelastic deformations in your teststand, that is.

The second is that this is not real time processing and all of the data set is available so non-causal filters can be used.

Yes, but should they be used? After all, we have a phenomenon here that is certainly causal.

 

[UhClem]

Yes, but should they be used? After all, we have a phenomenon here that is certainly causal.

I think you misunderstand. Non-causal simply means that the filter uses information from the future as well as the past. It has nothing to do with the noise.

 

[Andreas Müller]

I think you misunderstand. Non-causal simply means that the filter uses information from the future as well as the past. It has nothing to do with the noise.

I do understand. But why should one consider a non-causal filter? The point is that ringing is completely deterministic, so you should be able to deconvolve it with information from the past only. There are other types of noise in the data, e.g. the measurement noise. To filter that, it doesn't really matter what type of filter you use. Optimal smoothing always uses the standard foward filter solution in some way, so you have to do that first anyway.