Questions about accelerometer-based alts

A couple of questions for anyone who thinks that an accelerometer will read 0 g at apogee of a rocket flight.

1. Does that mean that the rocket is not accelerating?
2a. If the rocket is not accelerating why does the rocket come back to earth since it has both zero velocity and zero acceleration?
2b. If the rocket is accelerating why doesn't an accelerometer (which measures acceleration) measure this acceleration?




If there is still confusion I will go into a physic 101 discussion to why an accelerometer will measure an acceleration due to gravity equal to 9.8 m/s/s in the direction towards the earth at apogee of a rocket flight, in the vomit comet, and in an low-earth orbiting object (hint: Universal Law of Gravitation), but hopefully these 3 questions will help you decide the same.

P.S. Weightlessness does not equal no acceleration, it equals no opposing force.

Jeff

Correct, and an accelerometer will read 0 gees at apogee. They will also read 0 gees in the vomit comet. Now, to answer your question:

1) Yes, of course it is accelerating in a ballistic trajectory
2) For the same reason that it wouldn't measure an acceleration in orbit. Aside from the slight nuance of tidal forces, which make zero difference in this case, it is IMPOSSIBLE TO TELL from inside a container whether it is in freefall, or whether it is floating in space. An accelerometer cannot measure gravitational acceleration when both it and the container it is in are subject to gravity. An accelerometer can only measure acceleration caused by a force that does not act on the accelerometer directly, but only through its mounting points. Hence, it will measure 1g as it is sitting on the table, and 0g as it is in freefall, and 20g as it is accelerating with a true acceleration of 19g away from the earth's surface. Do I need to go into anything more from basic mechanics (you might say Mechanics 101)?

Originally posted by cjl
Correct, and an accelerometer will read 0 gees at apogee. They will also read 0 gees in the vomit comet. Now, to answer your question:

1) Yes, of course it is accelerating in a ballistic trajectory
2) For the same reason that it wouldn't measure an acceleration in orbit. Aside from the slight nuance of tidal forces, which make zero difference in this case, it is IMPOSSIBLE TO TELL from inside a container whether it is in freefall, or whether it is floating in space. An accelerometer cannot measure gravitational acceleration when both it and the container it is in are subject to gravity. An accelerometer can only measure acceleration caused by a force that does not act on the accelerometer directly, but only through its mounting points. Hence, it will measure 1g as it is sitting on the table, and 0g as it is in freefall, and 20g as it is accelerating with a true acceleration of 19g away from the earth's surface. Do I need to go into anything more from basic mechanics (you might say Mechanics 101)?

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So you are saying that accelerometers measure force, not acceleration?

Originally posted by Henry8minus1
So you are saying that accelerometers measure force, not acceleration?

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they calculate acceleration via force

Exactly, nate said it better than I could have.

On a side note, how else could you calculate acceleration? If you were inside a box freefalling over Jupiter at 25m/s^2, how could you tell that you weren't accelerating at 9.8m/s^2 over earth? You couldn't.

Originally posted by Henry8minus1
A couple of questions for anyone who thinks that an accelerometer will read 0 g at apogee of a rocket flight.

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I don't think it, I know it. Both from first principles (the force of gravity works on all parts of the rocket and accelerometer equally) and from data captured during a rockets flight.

Originally posted by Henry8minus1
A couple of questions for anyone who thinks that an accelerometer will read 0 g at apogee of a rocket flight.

1. Does that mean that the rocket is not accelerating?
2a. If the rocket is not accelerating why does the rocket come back to earth since it has both zero velocity and zero acceleration?
2b. If the rocket is accelerating why doesn't an accelerometer (which measures acceleration) measure this acceleration?




If there is still confusion I will go into a physic 101 discussion to why an accelerometer will measure an acceleration due to gravity equal to 9.8 m/s/s in the direction towards the earth at apogee of a rocket flight, in the vomit comet, and in an low-earth orbiting object (hint: Universal Law of Gravitation), but hopefully these 3 questions will help you decide the same.

P.S. Weightlessness does not equal no acceleration, it equals no opposing force.

Jeff

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The issue is that acceleration is a VECTOR and this discussion is only talking about the magnitude. As a rocket arcs over at apogee the acceleration of the rocket is equal to 1g with a direction that is point down (perpendicular to the rocket airframe).

The acceleration is NOT zero during ballistic flight or else the body would not be able to change direction according to Newton's Law. A body in orbit does NOT have zero acceleration, if it did it would go in a straight line. A body in a circular orbit around the earth experiences a constant acceleration of approx 1g with a direction pointing towards the center of the circle.

A rocket accelerometer will read zero at apogee because it is measuring the magniture of acceleration along the axis of the rocket.

It would still read zero if the rocket were pointed up and down. This is because of the reasons explained about a million times on this thread. This is not to say that the rocket's acceleration is zero, just that it is impossible to distinguish between zero acceleration and a perfect freefall from the altimeter's point of view.

I think I finally get it. I was hung up thinking of the actual acceleration and not the way it is measured and realize now what I was saying was wrong. Thanks everyone for being patient and answering my questions and pointing out I was wrong without calling me an idiot even if I was one.

Jeff

Originally posted by cjl
It would still read zero if the rocket were pointed up and down. This is because of the reasons explained about a million times on this thread. This is not to say that the rocket's acceleration is zero, just that it is impossible to distinguish between zero acceleration and a perfect freefall from the altimeter's point of view.

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Ah yes, BUT if you "ZERO" the accelerometer on the pad when it is reading +1g standing still because of the reasons mentioned a million times in this thread, then during free fall it will read -1g due to this "stationary calibration". Correct?

(Because your calibration effectively subtracts 1g from the absolute reading of the accelerometer).

Originally posted by Henry8minus1
I think I finally get it. I was hung up thinking of the actual acceleration and not the way it is measured and realize now what I was saying was wrong. Thanks everyone for being patient and answering my questions and pointing out I was wrong without calling me an idiot even if I was one.

Jeff

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You were not wrong.

Originally posted by jderimig
A rocket accelerometer will read zero at apogee because it is measuring the magniture of acceleration along the axis of the rocket.

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Wrong. At apogee an accelerometer aligned in any direction you choose will read zero acceleration except for a little bit caused by drag.

Gravity is a force which acts on every bit of the accelerometer equally. The accelerometer works because it has a small lever inside of it that is fixed on one end and free to move on the other. Gravity works on every bit of this lever equally as well as the rest of accelerometer.

When the rocket is at rest before launch there is this big ball of rock applying a force to the base of the rocket keeping it from moving. This upward force gets transferred through the rockets structure to the fixed end of the lever preventing it from moving. There is no force to keep the rest of the lever from moving so it bends slightly from gravity and the accelerometer measures this.

At apogee, or freefall, there is no upward force at the fixed end of the lever as the entire accelerometer experiances a uniform force and accelerates uniformly. Therefore there is no deflection of the lever and no acceleration is sensed.

Yeah, you guys were getting confused because you were thinking about the rocket's acceleration from your point of view instead of what the sensor feels along its axis.

Just think back to Einstein's old guy in an elevator example, which basically demonstrates that it is impossible to tell acceleration apart from gravity.

Originally posted by UhClem
Wrong. At apogee an accelerometer aligned in any direction you choose will read zero acceleration except for a little bit caused by drag.

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edit: you are correct if you are talking about the sensor.

If you are talking about a real device which accounts for the acceleration due to gravity then it can read the true acceleration.

Inertial guidance systems using accelerometers subtracts the acceleration to due gravity from the computed axis of motion.

That is why the military spent a lot of time mapping the gravitational field of the planet, especially the route over the artic. If you know the acceleration due to gravity and the orientation of your accelerometers you can know the acceleration of your body relative to the fixed set of stars.

Of course the sensors are measuring force. An "accelerometer" is the not the sensor but the system that the sensor is part of. If the sensor is reading 0 force and you know where you are pointing, and you know what planet you are on then you know what the true acceleration is.

My accelerometer measures -1g in a free fall. If your's doesn't, I suggest that you replace it with a more intelligent device.

So how would you say using magnetic sensors compares to using electronic gyroscopes for IMUs? I think magnetic sensors would be more accurate since they don't drift, but I'm not sure if they could determine orientation in some situations, like when one of the axes is parallel to the magnetic field, I don't think it could detect itself rotating on that axes. Correct me if I'm wrong, though.

Originally posted by mtwieg
So how would you say using magnetic sensors compares to using electronic gyroscopes for IMUs? I think magnetic sensors would be more accurate since they don't drift, but I'm not sure if they could determine orientation in some situations, like when one of the axes is parallel to the magnetic field, I don't think it could detect itself rotating on that axes. Correct me if I'm wrong, though.

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I think it depends on what you want to do. If you need to hit a target then a gyro system that uses magnetic sensors to correct for drift can work.

If you are simply trying to detect apogee, then just making assumptions on orientation during flight should be good enough, its seemed to work well so far.

Originally posted by jderimig
Ah yes, BUT if you "ZERO" the accelerometer on the pad when it is reading +1g standing still because of the reasons mentioned a million times in this thread, then during free fall it will read -1g due to this "stationary calibration". Correct?

(Because your calibration effectively subtracts 1g from the absolute reading of the accelerometer).

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Now this is true, but only because of the calibration. This is the only way for the accelerometer to measure true acceleration.

After reading the thread, I think the basic question that is being stepped around, however inadvertantly, is how come a single axis accelerometer based altimeter fires the ejection charge even if the rocket doesn't fly straight up or ever experience zero velocity?? The actual answer is scattered throughout the thread....

the velocity does actually integrate back to zero - but why?

The answer lies in the fact the event is not triggered at the actual apogee but sometime afterward in a non-vertical flight.

After burn out the negative G's of deceleration due to gravity and drag subtract from the calculated velocity. If the flight is vertical then apogee is at zero airspeed (in a perfect world.)

Now, if the flight is not vertical then during the upward portion of the flight the calculated velocity reduction after burn out never reaches the increase due to the motor burn (while the rocket is gaining altitude)......The rocket is slowing down however until it is around horizontal (when it was correctly mentioned all forces are pretty much in equilibrium at which point there is zero apparent G's (it isn't at exactly horizontal by the way but is really when the downward acceleration due to gravity exactly matches the deceleration due to drag.)

Now the fun part.....due to the design of the rocket it continues to travel with the nosecone pointed approximately along the velocity vector....as it begins to point downward now gravity is acting in the opposite direction as far as the accelerometer can tell (remember, it's all relative!) and the increasing drag allows the acclerometer to sense the acceleration along it's measurement axis. I.e. it continues to reduce the calculated airspeed until viola.....at zero it fires the apogee charge albiet somewhat after the actual apogee. It's still moving from our point of view but as far as it is concerned it reached zero velocity.

Before anyone starts into the fact the rocket isn't really pointed directly at the ground, remember you can always break the acceleration vector into components and part will be along the measurement axis.

Sorry to be so long winded and hope that answers at least that little bit of the question.

You're awesome Thanks!

Now this question for you; If you had a barometric altimeter and an accelerometer based altimeter and both had live apogee charges wired in, the barometric would blow first, right? Now if you had a barometric only, and an integrating altimeter (like the ARTS) Would the integrated get it sooner or later than the barometric alone?

Originally posted by Nate
You're awesome Thanks!

Now this question for you; If you had a barometric altimeter and an accelerometer based altimeter and both had live apogee charges wired in, the barometric would blow first, right? Now if you had a barometric only, and an integrating altimeter (like the ARTS) Would the integrated get it sooner or later than the barometric alone?

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Not sure I understand the question entirely (the second part of it seems to be the same as the first.)

At apogee, I would expect the accel based one to detect apogee first...

I think most barometric altimeter looks for a measurable decrease in altitude (via a pressure increase) to detect apogee so actually it's firing slightly after in most cases (i.e. it has to fall a bit) and then depending on the size and geometry of the electronics bay it could induce a bit of a delay in the pressure changes (if the holes in the bay are too small the pressure change would lag the actual altitude.)

For a serious non vertical flight I am not sure, I guess it would depend on the flight profile and the apogee detection algorithms involved.....

haha, I guess I was a tad rambly in that question, but you mainly answered it.

Basically my query is this; say you have an RRC2 and a G-Wiz MC2. You rig them both up with an apogee deployment charge, and both are made to be decently energetic charges. Would you program a delay for the MC2 charge, or would you just tell both altimeters to fire at apogee? You wouldn't want them to fire at the same time as it might damage your rocket, but would you rely on the measurement discrepency to offset the charges?

I'd just wire em both up. I'd say it's EXTREMELY unlikely that they'll both go off at precisely the same instant. If you're that worried, set the MC2 for a delay though.

Why not just have one charge with two ematches from separate altimeters?

Then it doesn't matter if they fire at the same time and you still have redundant electronics so one of them is bound to fire the ejection charge.

Only real reason I could ever come up with for two separate charges is a secondary "hail mary" charge considerably bigger than the primary ejection charge......Ground testing should make that really kind of moot.

Just for the record, I did actually have separate charges in my Level III cert flight but that was more from being a nervous nellie and not really thinking it through like I should have. I set my MAWD to have a delay on the charge to eliminate the possibility of simultaneous firing though. (also the Altacc is kind of quirky and would fire the main immediately if the MAWD were to fire it's charge first.....wouldn't hurt the rocket but would result in a loooooong walk and a non-cert on a cert flight due to the flight not going according to plan.)

Smurf, I've read your post about ten times and I still don't get it. Won't the sensor detect 0g before apogee, when the rocket is still slightly pointing up?

Mathematically, I'm looking at it like this:

A(sensed) = sin(angle between rocket and horizontal) + actual acceleration along axis

So for A(sensed) to be 0g, the sin and the acceleration must be opposite. The actual acceleration will be negative due to drag, so sin(angle) must be positive. So the rocket must be pointed above the horizontal.

Originally posted by mtwieg

The actual acceleration will be zero due to drag

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I'm not sure I follow this. The rocket should be accelerating in the negative direction due to drag when it has sufficient velocity, and when the air resistance is negligible, the rocket still has acceleration, just not one detected by the altimeter... Unless I'm confused (which has been known to happen! )

Originally posted by mtwieg
Smurf, I've read your post about ten times and I still don't get it. Won't the sensor detect 0g before apogee, when the rocket is still slightly pointing up?

Mathematically, I'm looking at it like this:

A(sensed) = sin(angle between rocket and horizontal) + actual acceleration along axis

So for A(sensed) to be 0g, the sin and the acceleration must be opposite. The actual acceleration will be zero due to drag, so sin(angle) must be positive. So the rocket must be pointed above the horizontal.

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The measured acceleration is only that due to drag as the rocket is otherwise a freely falling body. The altimeter software assumes that it is operating in a gravitational field and subtracts the measured pre-launch acceleration from the measured acceleration. Thus while the acceleration from drag is rapidly decreasing towards zero (being proportional to the square of air speed) the -1G acceleration from gravity is constant.

Originally posted by Nate
haha, I guess I was a tad rambly in that question, but you mainly
answered it.

Basically my query is this; say you have an RRC2 and a G-Wiz MC2. You
rig them both up with an apogee deployment charge, and both are made to
be decently energetic charges. Would you program a delay for the MC2
charge, or would you just tell both altimeters to fire at apogee? You
wouldn't want them to fire at the same time as it might damage your
rocket, but would you rely on the measurement discrepency to offset the
charges?

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The RRC2 will fire after apogee and the MC2 will fire at some random
time around apogee.

I discussed the reasons for this in my two NAR R&D reports. In
the first one I document a case where an RRC2 fired about 2 seconds past
apogee. As I recall, the manufacturer considered this to be perfectly
acceptable. I didn't, which is why the two R&D reports. Available on my
web site.

Originally posted by UhClem
The measured acceleration is only that due to drag as the rocket is otherwise a freely falling body. The altimeter software assumes that it is operating in a gravitational field and subtracts the measured pre-launch acceleration from the measured acceleration. Thus while the acceleration from drag is rapidly decreasing towards zero (being proportional to the square of air speed) the -1G acceleration from gravity is constant.

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Ah, that clears it up a bit. If I understand correctly, if I were to take the output of the accelerometer, offset it by -1g, then integrate it, the resulting velocity would be zero at apogee?
Is the velocity and acceleration data in that plot in the rocket's vector or in the vertical (I'm assuming the latter)?

Nate, I mistyped. I meant to negative instead of zero (look at the edited post). Still. I'm still sure that the accelerometer will measure 0g before apogee, assuming the rocket reaches the horizontal at apogee. However, I'm not sure if this is a reliable way of determining apogee... I think it's worth thinking on, though.

Originally posted by mtwieg
Ah, that clears it up a bit. Is the velocity and acceleration data in that plot in the rocket's vector or in the vertical?

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The velocity is the output of a Kalman filter which combines the accceleration and barometric altitude data using a dynamic model. The model is one dimensional with that dimension being vertical.

The acceleration, while filtered as well, is that measured along the rockets axis as the data was captured by your basic off the shelf RDAS compact.