Measuring Engine Performance DURING Actual Flight

jderimig said:

Using your example, if I have a motor that produces a thrust that 2x the weight of the rocket, the accelerometer will read 2g as you say. Assuming drag is negliable this will be a direct calculation of motor thrust , T=ma, where m=mass of the rocket, a=acceleration recorded by the accelerometer with the 1g offset applied.

In this case, thrust = 2x weight of rocket, you will get this same 2g accelerometer reading if the rocket is going vertically up, totally horizontal (perpendicular to the gravity vector) or straight down. Gravity is not affecting the raw accelerometer reading in each of these three cases because the readings will all be identical.

Click to expand...

jderimig said:

Using your example, if I have a motor that produces a thrust that 2x the weight of the rocket, the accelerometer will read 2g as you say. Assuming drag is negliable this will be a direct calculation of motor thrust , T=ma, where m=mass of the rocket, a=acceleration recorded by the accelerometer with the 1g offset applied.

In this case, thrust = 2x weight of rocket, you will get this same 2g accelerometer reading if the rocket is going vertically up, totally horizontal (perpendicular to the gravity vector) or straight down. Gravity is not affecting the raw accelerometer reading in each of these three cases because the readings will all be identical.

Click to expand...

Here's what the accelerometers in your situations will read:

If up, reads +2g in direction of rocket [up] (2mg thrust - mg = 1g up + 1g gravity = 2g)
Even though rocket accelerates 1g in direction of rocket (up)

If upside down, reads +2g in direction of rocket [down] (2mg thrust + mg = 3g down - 1g gravity = 2g)
Even though rocket accelerates 3g in direction of rocket (down)

If sideways to the left, reads +2.236g, 30 degrees up from sideways (2g to the left, 1g gravity up, sqrt(2g^2 + 1g^2)=sqrt(5g)=2.236g),
Even though the rocket accelerates straight to the side at 2g

In none of these cases can you read the accelerometer reading and infer the correct rocket motion relative to the earth unless you properly "back out" the gravity that was measured in the proper direction.

I think you are saying that because the accelerometer in both the up/down cases reads 2g, that it can't sense gravity. Not true. Because in neither case is the rocket accelerating at 2g. To get to true earth-referenced motion, you need to back out the 1g of gravity that the accelerometer sensed. In the up case, you subtract it (gravity acts in opposite direction of rocket), in the down case you add it (gravity acts in the same sense as the rocket). If you don't properly compensate for the gravity that the accelerometer DID MEASURE, you can't get the proper motions of 1g and 3g (in the direction of the rocket) that were actually occurring.

At any angle other than vertical (where gravity and the motion of the rocket are aligned) it starts to get hard to "back out" the 1g part of the reading (always pointing up) caused by gravity.

If you think that a rocket accelerating sideways at 2g only reads 2g on a 3D accelerometer, you are mistaken. There will be a 1g reading on what is now the vertical axis as well. The total magnitude will be 2.236g, at the combined angle of 30 above horizontal. 2g sideways + 1g vertical.

Here's the drill:
1. Get the accelerometer reading
2. "Back out" gravity effect in the vertical direction

That gives you the true rocket motion. No other way to do it.

John & John -
Interesting discussion. I am actually processing the data from my flights to "measure gravity" in a way - but not along the way you guys are talking.
Actually during my flights I make the bold assumption that gravity is staying at exactly 1g. Recall though, that I am flying a 3-axis accelerometer.
So far in this thread the discussion has been about measuring the acceleration in the UP/DOWN axis of the rocket, which starts out aligned with the standard launch pad
reference frame "UP" direction (ie towards the clouds). I have a second accelerometer which starts out pointing in the EAST/WEST direction and a third accelerometer
pointing in the NORTH/SOUTH direction. Prior to launch the second and third accelerations are zero and the UP/DOWN acceleration is 1g.

In most flights there ends up being some amount of tipping of the rocket at least a (hopefully) little bit and often some amount of roll. I am trying to detect this during my flights by looking
for small non-zero acceleration in the second and third axes. For example, if there is a small tip of the rocket towards the east then the EAST/WEST accelerometer starts
to report a small amount of g's proportional to the amount of tip (actually to the cosine of the angle of tip). Likewise for tip in the North/South direction, and roll about the rocket
axis looks like a sinewave variation of the second and third accelerometers at the same rate.

I *think* I have seen this in my flights so far, but the g's I am measuring are very small, there is a lot of noise in the data, and my sample rate has been relatively slow. If
I believe my current data, my Big Daddy rocket is rolling at a rate of 5 revolutions per second by the time it reaches apogee. While this is possible, I don't actually believe it
and have not observed this from the ground or in the smoke track. In order to better understand what I am seeing I am next going to add a magnetometer so I can pick up
magnetic north. (I could add a gyro, but I don't think that is as good of a reference frame as the magnetometer).

I need to fly a few more flights like this and then I will come back and post my data here on RocketryForum.

-Kerry

PS - I was inspired to do a lot of this accelerometer flying by a presentation on the Jolly Altimeter that John gave at a NARCON in Massachusetts several years ago. Pretty neat that we'd be
having this discussion here on RF after all that time. I still remember the part where John described how to gain additional accelerometer range by flying 2 off-axis accelerometers at 45 degrees....

John Beans said:

Here's what the accelerometers in your situations will read:

If up, reads +2g in direction of rocket [up] (2mg thrust - mg = 1g up + 1g gravity = 2g)
Even though rocket accelerates 1g in direction of rocket (up)

If upside down, reads +2g in direction of rocket [down] (2mg thrust + mg = 3g down - 1g gravity = 2g)
Even though rocket accelerates 3g in direction of rocket (down)

If sideways to the left, reads +2.236g, 30 degrees up from sideways (2g to the left, 1g gravity up, sqrt(2g^2 + 1g^2)=sqrt(5g)=2.236g),
Even though the rocket accelerates straight to the side at 2g

Click to expand...

Edit: My analysis is for a single-axis accelerometer aligned with the axis of flight (parallel to the thrust and drag forces). That is the axis that is pertinent to the OP's topic of motor and drag characterization. Maybe that is the source of the confusion.

The last case is incorrect. See the FBD's of the accelerometer sensing element that is attached. Assume a rocket with a motor thrust equal to 2 Mg of the rocket, neglect drag. In all cases, in all orientations with respect to ground and the gravity vector the accelerometer reading will always be 2.

It will be 2 if this rocket and motor is flown in the depth of space (no gravity).
It will be 2 if this rocket and motor is flown on the moon,
It will be 2 if this rocket and motor is flown on Jupiter.
It will be 2 if this rocket and motor is flown on a black hole (maybe).

The only factors that affect the accelerometer reading during flight is the motor thrust and the rocket mass. That's it. The gravity field if any that the rocket flys in does not affect the accelerometer reading at all. If the gravity field has no affect on the accelerometer reading (just the motor thrust and rocket mass does), then the accelerometer is incapable of measuring gravity effects during flight.

Therefore the raw accelerometer reading (before adding any assumed offsets) can be directly used to calculate the applied external forces on the rocket. You do not have to account for the body force, you do not have to add offsets, and you do not need to consider the acceleration wrt earth.

John Beans said:

Here's what the accelerometers in your situations will read:

That gives you the true rocket motion. No other way to do it.

Click to expand...

Agreed, this is the only way to know the rocket motion wrt earth. But this knowledge is not required to use accelerometer data to characterize the thrust and drag forces on a rocket during flight, which is the OP's post subject.

Edit: I added the accelerometer analysis for this same flight on the moon. (last slide). Same result; Accelerometer reading = 2.

Look at Case 4, the 45 degree angle example.
You started doing a free body diagram, then you just declared that "Fs=2mg," rather than calculating it.
Here's what you get when you solve for Fs:.


This makes intuitive sense: the force of the spring has to be high enough to not only accelerated the body at 2g, but also to fight against the component of gravity in that direction.
So it's higher than 2mg.

John Beans said:

Look at Case 4, the 45 degree angle example.
You started doing a free body diagram, then you just declared that "Fs=2mg," rather than calculating it.
Here's what you get when you solve for Fs:.

This makes intuitive sense: the force of the spring has to be high enough to not only accelerated the body at 2g, but also to fight against the component of gravity in that direction.
So it's higher than 2mg.

Click to expand...

.

Almost.... A motor with a thrust of 2Mg will result in a rocket acceleration of 1.293g that is flying 45 degrees off horizontal.

Sum Fx = 1.293*mg
Fs - mg cos45 = 1.293*mg
Fs = mg(1.293 + cos45) = 2mg
Fs = 2g accelerometer reads 2g

Oops, you're right: I changed the starting assumption to be that resulting acceleration was 2g, not that thrust was 2mg. Sorry about that.
Both calculations are correct, but I shouldn't have changed the problem assumptions.

Your original: thrust 2mg, acceleration 1.293g, reading 2g
Mine: thrust 2.707mg, acceleration 2g, reading 2.707g

But notice that no matter how you set up the problem, the accelerometer reading and the actual acceleration aren't the same.

I think this is a rhetorical issue, which comes down to this:

A. Accelerometers can't detect gravity in flight, so you have to add it in later to calculate true motion.
-or-
B. Accelerometer readings are always affected by gravity, so you have to back it out later to calculate true motion.

And I'm rhetorically in Camp B. To me, accelerometers are affected by gravity in the same manner whether they are on the pad and in the air. They read 1g on the ground when they are not moving, and you have to back that out. They read 2g at an angle even when the rocket is accelerating at 1.293g. You have to back out the vertical gravity component of 0.707g. Same approach whether on the ground or on the pad.

John Beans said:

Oops, you're right: I changed the starting assumption to be that resulting acceleration was 2g, not that thrust was 2mg. Sorry about that.
Both calculations are correct, but I shouldn't have changed the problem assumptions.

Your original: thrust 2mg, acceleration 1.293g, reading 2g
Mine: thrust 2.707mg, acceleration 2g, reading 2.707g

But notice that no matter how you set up the problem, the accelerometer reading and the actual acceleration aren't the same.

Click to expand...

Yes! In flight the on-board accelerometer only "feels" the external forces applied in the axis of the accelerometer, it does not "feel" the body force (mg) in that axis. The net force on the sensing spring element (which is what the accelerometer "feels") is exactly proportional to the net external force on the rocket (Thrust - Drag). The FBD math proves that. No thrust nor drag, no spring mass deflection = feels nothing.

John Beans said:

I think this is a rhetorical issue, which comes down to this:

A. Accelerometers can't detect gravity in flight, so you have to add it in later to calculate true motion.
-or-
B. Accelerometer readings are always affected by gravity, so you have to back it out later to calculate true motion.

Click to expand...

-or-
C. The rocket motion is always affected by gravity but the accelerometer does not feel gravity in flight (in the ballistic axis) . So you need to add in the mg term to the accelerometer output to get the rocket motion.

John Beans said:

And I'm rhetorically in Camp B. To me, accelerometers are affected by gravity in the same manner whether they are on the pad and in the air. They read 1g on the ground when they are not moving, and you have to back that out. They read 2g at an angle even when the rocket is accelerating at 1.293g. You have to back out the vertical gravity component of 0.707g. Same approach whether on the ground or on the pad.

Click to expand...

I think we starting to converging but maybe with one small difference.

[Agree] You need to account for the gravity body force and direction to determine the rocket motion. However there is always error in this correction because the true exact direction of the gravity vector wrt rocket is unknowable.

[Not sure if concurred yet] You do NOT have to account for gravity body force AT ALL to determine the net applied external force on the rocket. The uncompensated raw accelerometer reading is a one-to-one direct measurement of Thrust-Drag. In this calculation there is no error (other than accelerometer error) because we do not have make a gravity offset assumption (which always has error)

A given rocket and motor combination will give the exact same accelerometer reading in a flight through a vacuum ANYWHERE in the universe regardless of the gravity field it is flying in. You do not need to know what the gravity is or what the vector direction is to determine the forces on a rocket. All you need is the raw accelerometer data.

PS. John, What I am saying in summary is: We can write a closed form equation for Thrust = F(x) based on flight data that doesn't need a "g" or "mg" term in it. All we need are the raw (uncompensated, un-offsetted) accelerometer reading. Agree?

What would you say the accelerometer would read in this situation:

The rocket is traveling straight up, but the drag forces have risen to balance the thrust, so the speed of the rocket is a constant 200 MPH.

John Beans said:

Accelerometers can DEFINITELY measure gravity during a flight.

Click to expand...

I'm sorry. This statement is objectively incorrect.

The only gravitational force that an accelerometer reacts to is tidal force - which is negligible near the earth's surface. When you subtract 1g from the accelerometer reading you are not subtracting out the acceleration of gravity; you are actually adding it in. That is, you are adding -1g, which is the acceleration of gravity - the component that is missing from the reading.

The 1g reading you get on the pad is actually the force from the pad underneath. This is the force (a kind of thrust) that is balancing gravity,which is not registered. When you add in the gravitational acceleration of -1g, you get the true acceleration before launch: 0g.

If you take the pad away, the force from beneath stops, and the reading goes to zero, but gravity still pertains. Again, it's not measured. If you add in the (missing) gravitational acceleration of -1g, you get the true acceleration.

In the absence of wind (and neglecting buoyancy), the reading during flight is the sum of thrust and drag acceleration - given that the angle of attack is zero (or, in practice, sensibly near zero). A traditional accelerometer analysis program is nothing more than a simple vertical (1-dimensional) altitude simulation program in which accelerometer reading is substituted for the sum of thrust and drag acceleration. The same substitution can be done in a 2-dimensional simulation to represent off-vertical trajectories.

A vertical trajectory is assumed in the 1-dimensional analysis; a ballistic trajectory is assumed in the 2-dimensional analysis. This is true even for the 3-dimensional accelerometer in your instrument precisely because it doesn't measure gravity and doesn't know where the gravity is coming from. That is, gravity must still be simulated in the analysis according to one of these assumptions, even if the instrument measures all other accelerations in three dimensions according to an internal coordinate set, the rotations of which are not tracked.

Inertial altitude and speed aren't wholly empirical statistics; they're semi-empirical. The accelerometer readings are empirical, but the gravitational parts of those figures are simulated. That is why accelerometer deployment can be inaccurate. If a rocket takes a sharp left turn in mid flight, the accelerometer will not know.

For more information, see my NARAM 49 report, _Analysis of Flight Computer Data From Off-Vertical Trajectories_. I'll be happy to send it to anyone who wants it.

Best Regards and Sorry to be Disagreeable,
-Larry Curcio

As I said, I truly think this is just a rhetorical argument, Larry. The math is all entirely the same.

An accelerometer reads 1g as it sits there because gravity pulls the sensing mass down and makes the flexing member deform even when the entire thing is not accelerating, just like a person standing on a dock with a fishing pole bent by the weight of a lure on the end of it.

You (and I would assume John D) would say,

"The fishing pole is bent NOT because the weight on the end of the pole is affected by gravity, but because the person is standing on a dock, which pushes up on the person. And since the 'reading' of the pole is 'bent' (1g), you have to 'add in' the effect of gravity that it can't sense to get back to the true value of acceleration, which should be 'not bent.' (zero)"

And I would say,

"The fishing pole is bent because gravity pulls the weight down. He's not moving up and down, so it's just reacting to gravity. To use the pole to accurately reflect acceleration, you would have to subtract this effect of gravity."

If the fisherman was on an elevator that was going upward at 1g, the pole would bend twice as far.

You would say:

"The fishing pole is bent twice as far because the elevator is pushing up on the fisherman at 2mg."

I would say:

"The fishing pole is bent twice as far because the elevator is accelerating at 1g and gravity always affects the weight 1g, and that effect has to be removed to get to the true acceleration."

John Beans said:

As I said, I truly think this is just a rhetorical argument, Larry. The math is all entirely the same.

An accelerometer reads 1g as it sits there because gravity pulls the sensing mass down and makes the flexing member deform even when the entire thing is not accelerating, just like a person standing on a dock with a fishing pole bent by the weight of a lure on the end of it.

You (and I would assume John D) would say,

"The fishing pole is bent NOT because the weight on the end of the pole is affected by gravity, but because the person is standing on a dock, which pushes up on the person. And since the 'reading' of the pole is 'bent' (1g), you have to 'add in' the effect of gravity that it can't sense to get back to the true value of acceleration, which should be 'not bent.' (zero)"

And I would say,

"The fishing pole is bent because gravity pulls the weight down. He's not moving up and down, so it's just reacting to gravity. To use the pole to accurately reflect acceleration, you would have to subtract this effect of gravity."

If the fisherman was on an elevator that was going upward at 1g, the pole would bend twice as far.

You would say:

"The fishing pole is bent twice as far because the elevator is pushing up on the fisherman at 2mg."

I would say:

"The fishing pole is bent twice as far because the elevator is accelerating at 1g and gravity always affects the weight 1g, and that effect has to be removed to get to the true acceleration."

Click to expand...

Well, it's true that there is a perfect reflection of gravity by the launch pad, while the rocket sits there before launch. Then the fishing pole example pertains nicely. Let's, now, substitute a rocket engine for the launch pad. The engine thrusts upward with the same thrust as the weight of the rocket. The rocket (in our little fantasy) is perfectly balanced, just as it was on the pad. The accelerometer is registering 1g, as it did before. According to my way of accounting, the instrument, not sensing gravity, thinks it is in free space, where this thrust would be accelerating it at 1g. Now it's clearly registering thrust, but your fishing pole example still pertains.

NOW. Suppose we were to take the rocket assembly above, and turn the rocket 90 degrees. The accelerometer STILL registers 1g, because it's STILL registering thrust. It will register 1g in ANY orientation, because it doesn't sense gravity. That is the difference.

In the coast phase, there is no thrust. ALL of the accelerometer's reading is drag there - in ANY orientation of the rocket with respect to gravity. If there were no air, there would be no accelerometer reading at all, and the entire analysis would be simulation thenceforth.

THERE IS A HUGE DIFFERENCE.

Your example rests on a perfect reflection of gravity, which is a property of things like tables and launch pads and anchored fishing poles. If you push down on a launch pad, it happens to push up with exactly the same force. If that force is gravity, it pushes back with an equivalent acceleration of 1g, and there is no difference. Rocket motors are not like that.

Suppose you reduce the thrust of a vertically oriented rocket system as described above so that the thrust is 3/4 of the weight of the rocket. The accelerometer now registers 3/4g, and the rocket falls at 1/4 g. If you point the rocket sideways, it STILL registers 3/4 g - and it falls downward. This will be true until drag intervenes and changes the acceleration, even if the rocket reorients and points downward. The difference in orientations WRT gravity is NOT in the accelerometer reading, it is in the motion of the rocket.

But... I've been wrong many times in the past (as people on this forum well know :blush . Can you tell me how gravity is being measured in these examples?

Regards
-LarryC

The math shows that the accelerometer will give the exact same reading for a given rocket-motor combination in flight regardless of the gravity envirornment it is flying in.

It then follows that the 'g' term is not in the equation that predicts the accelerometer reading of a rocket in flight, the only terms are rocket thrust and aerodynamic drag. If flying in a vacuum then the only term that predicts the accelerometer reading is motor thrust.

If the above is not the case then please show me the math. Accelerometer reading = F ( ).

Since the g term is not in the accelerometer reading function then it follows that the accelerometer is incapable of responding to or measuring g in flight.

So John, Here is my challenge.

Find the accelerometer reading from a FBD analysis of:
1. A 1kg rocket with a 5N thrust motor flying at 45 degrees on Earth (g = 9.8m/s2)
2. A 1kg rocket with a 5N thrust motor flying at 45 degrees on the Moon (g = 1.622 m/s2)

From the results tell me how you can tell from the accelerometer reading alone whether the rocket was flying on the moon or the Earth?

John Beans said:

What would you say the accelerometer would read in this situation:

The rocket is traveling straight up, but the drag forces have risen to balance the thrust, so the speed of the rocket is a constant 200 MPH.

Click to expand...

In this case the motor will producing 2Mg, drag will be 1Mg and body force 1Mg. Thrust - Drag = 1Mg. Accelerometer reads 1. Again accelerometer exactly measures Thrust - Drag.

No g term needed. g does not affect accelerometer reading only the net external force on the rocket (Thrust, Drag) determines the accelerometer reading.

"

John Beans said:

An accelerometer reads 1g as it sits there because gravity pulls the sensing mass down and makes the flexing member deform even when the entire thing is not accelerating, just like a person standing on a dock with a fishing pole bent by the weight of a lure on the end of it.

Click to expand...

Gravity is pulling on all particles with mass in the accelerometer equally. If it were in orbit (aka free fall) then there would be no deflection in the sensing mass because while it is being accelerated, so is the rest of the sensor so there is no net force.

But when it is at rest on the ground, the ground provides an upward force. This is what a rocket accelerometer sees on the pad.

Then there is that Einsteinian equivalence thing where you cannot distinguish between acceleration from an applied force and a field. https://www.einstein-online.info/spotlights/equivalence_principle

"This meeting of the Thrust Society is now in session. Thank you for coming. I understand we have a guest today?"


"Yes, I brought my friend Michael to the meeting today."


"Welcome, Michael. How did you get interested in our little group?"


"Hi. Well, I posted a question on a forum and Jake here thought I should join and learn more."


"That's cool. What did you post?"


"Oh, I just built an Arduino flight computer for my drone, and the data was weird, so I posted to see if anyone else had the same issue."


"What was the issue?"


"Okay. So I got most of the sensors working fine, but the accelerometer data was weird."


"The what?"


"The accelerometer?"


"Oh, you mean 'thrust meter.' It's called a thrust meter."


"No, I'm pretty sure the data sheet calls it an accelerometer..."


"That's a common misconception. Those chips sense net thrust. You can USE them to gauge acceleration, but they only indicate net thrust. Calling them accelerometers is an unfortunate accident of history."


"Uh, okay. Anyhow... my issue was that even when my drone was just sitting there on the ground, the data value was 1365, which the data sheet says is equivalent to 1 earth g of acceleration. But the drone wasn't moving!"


"Right. See, your thrust meter was actually working perfectly. The ground was thrusting your drone up at 1g, right? Otherwise it would have been falling. It was working perfectly!"


"Oh. And so when I was flying around at constant speed, it kept reading 1g, always pointing straight down, even when I flew up at angle, it still pointed straight down to the earth. My question on the forum was 'Is this gravity?'"


"Well, it's good you came today. Your thrust meter was measuring how much upward thrust it took to stay level or climb at a constant speed like that."


"Oh, thanks."


"You're welcome. Okay, next order of business: we've been invited to help the local high school with their lunar payload. As you know, the head of NASA made some space available on the next lunar probe for school kids, and our local school was chosen. Yes, Anne, you have a question?"


"Yes. Did they accept our name change for the project?"


"Well, we're still working on that. I'm confident they will come around. Oh, to fill you in, Michael--the original name of the project was Lunar Gravitational Measurement. Of course we told them they need to change it to Lunar Ground Thrust Measurement."


"Is there a big design change for that?"


"Oh, no, that's the cool thing! They can use the same thrust meter they chose originally. Obviously, they're not breaking any new ground here. If it works right, the thrust meter will record 0.1655 of the thrust sitting in the crater that it would sitting here on earth, like you'd expect. But getting them to stop saying the thrust meter is measuring gravity would be a huge win for our cause. Michael, you have a question?”


“I’m still new to the group, so can you forgive a little ignorance? [Group nods all around] Well, how do you take the thrust reading and compute the acceleration from it? You can, right? I was promised my acc… thrust meter could measure acceleration.”


“Oh, that’s simple. You just have to realize that the accelerometer is always blind to gravity. You just add in its effect when you’re calculating acceleration.”


“So when it’s sitting on the ground measuring ground thrust, we correct its inability to measure gravity by 1g, so that converts the 1g reading to actual zero acceleration?”


“Yes!!! You’ve got it. That’s why it’s a thrust meter, not an accelerometer. It always accurately measures net thrust, not acceleration. Because it’s blind to gravity!”


“Ah. So that’s why you want to change the name of the kids project—because they are trying to use a thrust meter to measure gravity, and in reality the thrust meter is BLIND to gravity, right?”


“You are going to fit right in here, my friend.”


“I think I’m starting to get it. So why was the kids’ teacher not teaching them this? And how did their project get accepted with all of their misconceptions?”


“Well, it’s a sad story. Like a lot of the medical stuff you see on TV, there’s also a lot of bad science floating around. And physics is just, like, beyond most people. The teacher was taking advantage of the fact that they came to the same answer, even though they were thinking of it in a muddle-headed way.”


“How so?”


“It’s not worth really spending time on. Sigh. But okay, here’s how it was explained to the kids. The little sensing mass in the ’accelerometer’ is always pulled toward the ground by the force of gravity anytime it’s in a gravity field, like near the earth or the moon. So to calculate acceleration, you need to subtract this effect from the reading. So (in their erroneous way of thinking) when it’s sitting on the ground reading 1g, it’s really just ‘reading gravity’ [giggles from audience]. You are then supposed to subtract out this 1g to get the true acceleration, zero. And you do the same thing when it’s flying: you always back out this 1g of gravity-induced reading that always points down to get true acceleration.” [crowd now openly laughs]


“So how did all of this get past NASA? They used that language in their proposal?”


“Well, they’re kids, first off, and they’re still learning. You have to cut them some slack. Also, they got lucky in that the math works out exactly the same.”

This forum doesn't supply enough 'like' buttons for this.

I'm sorry if I hurt anyone's feelings with the humor piece.
People who know me personally know that I'm not a mean person.
But I can be sarcastic, and that post, in an attempt to make a point, was perhaps a little heavy-handed given the audience and the forum.

If it offended anyone, I'm truly sorry.

For a humor post, it was actually pretty informative!

John Beans said:

I'm sorry if I hurt anyone's feelings with the humor piece.
People who know me personally know that I'm not a mean person.
But I can be sarcastic, and that post, in an attempt to make a point, was perhaps a little heavy-handed given the audience and the forum.

If it offended anyone, I'm truly sorry.

Click to expand...

I enjoyed it greatly, thank you for that!

John Beans said:

I'm sorry if I hurt anyone's feelings with the humor piece.
People who know me personally know that I'm not a mean person.
But I can be sarcastic, and that post, in an attempt to make a point, was perhaps a little heavy-handed given the audience and the forum.

If it offended anyone, I'm truly sorry.

Click to expand...

Not at all. The humor was good.

As for accelerometers, they either respond to gravity or they don't. Our discussion doesn't determine the state of nature, but our arguments are not equivalent.


-LarryC

P.S.
I look forward to your dual deploy system.

I love the humor in John B's post - even if I think he's mixing up some terminology.

The source of all mis-information says accelerometers measure 'proper acceleration'. So yes, they really are 'thrust meters'. They read 0 in free fall. (The deciding case for me.) They read drag/air resistance when falling in air. They read net force along the measuring axis when flying at at angle (remember - free falling toward the center of the earth at the same time).
https://en.wikipedia.org/wiki/Accelerometer
https://en.wikipedia.org/wiki/Proper_acceleration

I think John D. had it right here.

jderimig said:

C. The rocket motion is always affected by gravity but the accelerometer does not feel gravity in flight (in the ballistic axis) . So you need to add in the mg term to the accelerometer output to get the rocket motion.

Click to expand...

And I think that both John's are right in saying that when translating proper acceleration to geometric acceleration, you have to add in your local geodesic acceleration - due to the local gravity field (not an external force, mind you). And I think John B might be right in the sense that the math collapses back to the same - in the situations that most fliers will encounter.

And John D, I think you're right. The raw (proper) accelerometer reading should be able to yield the net of a = Thrust-Drag. And you only have to account for gravity if trying to translate that back to a velocity or seperation.

OK, I have FBDs swimming in my head after all these posts. I want to get to the bottom line for my application. If I have a MARSA or Raven accelerometer altimeter, and want to back out Cd during coast phase, the fundamental equation is (assuming 1D flight):

-Drag = ma

Correct? Or did I just start the argument all over again?

Buckeye said:

OK, I have FBDs swimming in my head after all these posts. I want to get to the bottom line for my application. If I have a MARSA or Raven accelerometer altimeter, and want to back out Cd during coast phase, the fundamental equation is (assuming 1D flight):

-Drag = ma

Correct? Or did I just start the argument all over again?

Click to expand...

If you have a Marsa then you just have to use the motor and drag characterization feature in the MarsaConnect program.

If you want to do the calculation yourself then you need to know whether the acceleration reported by the altimeter includes the 1g offset (reporting earth framed acceleration). The Marsa does. So you would need to add 1g to the data and then perform the calculation. Drag = m(a+1). I think Raven is the same.

Internally the MarsaConnect program just uses the raw accelerometer value to characterize Drag and compute the motor thrust curve.

Charles_McG said:

And I think John B might be right in the sense that the math collapses back to the same - in the situations that most fliers will encounter.

Click to expand...

If the rocket is pointed downward, the accelerometer still registers thrust+drag (drag is negative) accelerations - same as if it is pointed upward. Same with any angle in between. Any influence of gravity changes that result, no?

Perhaps, in qualifying this assertion, you mean that we use accelerometers in only vertical launches? Off-vertical launches can be analyzed if you just leave gravity out of your accelerometer readings, and then we may encounter more situations.

Maybe I'm wrong. Please explain.

Regards,
-LarryC

I think looking at the edge cases is helpful.
Assuming 1 accelerometer, aligned with the flight axis of the rocket, and a raw reading, not with an intercept applied by the display system.

On the pad, a_sub_T(thrust)=0, a_sub_d(rag) = 0, a_sub_g(gravity) = -1g, v = 0, dv/dt = 0. There is a reaction force from the ground holding the rocket up. Otherwise dv/dt wouldn't be 0. The accelerometer reads that.

At apogee, a_sub_T(thrust)=0, a_sub_d(rag) = 0, a_sub_g(gravity) = -1g, v = 0, dv/dt = -9.8m/s^2. The rocket is momentarily motionless with respect to the ground. There's no thrust or drag. dv/dt is 9.8m/s^2 downward. It's accelerating in the ground frame of reference, but not in it's own interial frame. Free fall. Accelerometer reads 0.

Thrusting straight down at 1 g - launched from a balloon
a_sub_T(thrust)=-1g, a_sub_d(rag) = f(v), a_sub_g(gravity) = -1g, v = f(aT+ad+ag, t), dv/dt = a*t where a is sum of accelerations, or 2g less drag) The accelerometer reads 1g down.

Cruise missle mode:
a_sub_T(thrust)= 1g on a vector in line with the rocket, a_sub_d(rag) = f(v) in a vector in line with the rocket, a_sub_g(gravity) = -1g, v = f(aT+ad+ag), on a vector diagonally down, dv/dt = a*t - also a vector diagonally down. In the rockets frame of reference, it is in free fall toward the ground. so dv/dt in the vertical axis is -9.8m/s^2 (ignoring air resistance for the moment). The accelerometer reads the thrust+ (-) drag along its flight-aligned axis. The net vector is a diagonal down. If you had a 2nd accelerometer mounted to align vertically with the ground, it would still read 0 - it's in free fall in that direction. (Actually it would read the drag, up to terminal velocity, where it would be 1g)

I'm convinced that accelerometers read net applied force, but don't read gravity (they read zero in free fall, even in a gravity field). But that to get the geometric (or coordinate) motion, you have to account for gravity (and convert everything to vectors) - and the math looks the same where Mr. Newton rules. Which isn't everywhere - but is pretty close for the surface of the Earth.

I -think- (but am not positive) that John B is arguing that they read dv/dt, with an intercept to account for the resting on ground case. And John D is arguing that they read net a in an intertial reference frame (which the Earth's surface is not - but you can correct for the local gravity field).

What most rocketeers are interested in most of the time is the acceleration in the earth-frame. Unfortunately this quantity is unknowable from accelerometer data alone because you need rockets attitude during flight in order to apply the correct gravity offset. This can only come from an external observation or another independent measurement from a gyro for example.

The acceleration from the rocket frame is knowable (within instrument error). And thus (Thrust + Drag) is knowable provided there is no rotation or w x r term. This term can be nulled by placing the accelerometer at the center of rotation (r=0) of the rocket, or neglected if this term is small compared to (Thrust+Drag).

Charles_McG said:

I'm convinced that accelerometers read net applied force, but don't read gravity (they read zero in free fall, even in a gravity field). But that to get the geometric (or coordinate) motion, you have to account for gravity (and convert everything to vectors) - and the math looks the same where Mr. Newton rules. Which isn't everywhere - but is pretty close for the surface of the Earth.

Click to expand...

Yes. Yes yes.

-LarryC

jderimig said:

. And thus (Thrust + Drag) is knowable provided there is no rotation or w x r term. This term can be nulled by placing the accelerometer at the center of rotation (r=0) of the rocket, or neglected if this term is small compared to (Thrust+Drag).

Click to expand...

This brings to my mind Niven's story 'Neutron Star', where Beowulf is frantically figuring out the safest place on the ship - the center of gravity. 'Where did the Puppeteers put the accelerometer? they're sticklers for 10 significant figures.'