Using Accelerometers for stability of aircraft.

[Onemorechance]

Can anybody prove me wrong or right when I claim the following statement:

Accelerometers can be useful in measuring rotational accelerations, but it is absolutely impossible to measure translational accelerations because of the unknown direction of the gravitational field.

Onemorechance

 

[IRstuff]

The proof is that the MX ICBM has a less than 1 mi CEP using its inertial navigation system, consisting of gyros and accelerometers.

TTFN

 

[IRstuff]

Ditto for the B-52, B-1 and B-2. They all have inertial navigation systems comparable to the MX and Minuteman.

TTFN

 

[Onemorechance]

I was not complete in my statement. Again.

Using only accelerometers can be useful in measuring rotational accelerations, but with only accelerometers it is absolutely impossible to measure translational accelerations because of the unknown direction of the gravitational field.

Onemorechance

 

[Tads]

Hmmm... not sure what your real question is.

All modern navigation systems utilise gyros to measure 3-axis angles and rate of change (turn rates). This flows into most Automatic Heading Reference Systems (AHRS). Once this is known, simple vector mathematics can translate the linear accelerations (from the accelerometers) for the Intertial Navigation System (INS).

All the examples mentioned, as well as the aircraft I have worked on have similar systems.

 

[IRstuff]

Your question does not make sense. Linear accelerometers are used in every aircraft to measure translational accelerations. What does gravity have to do with it; it's an acceleration just like any other.

TTFN

 

[navigate87]

Since gravity is a known force, the INS, IRU, AHARS mathmatically compensates for the force of gravity. Gyro/accel based systems use various geodetic models of the earth as correction for gravity

 

[Onemorechance]

Linear accelerometers are used in every aircraft to measure translational accelerations.

OK. Assume you have an accelerometer mounted on the Z-axis of an axes system pointing down, X and Y in a horizontal plane. Adding a force in negative Z-direction equaling the weight of the accelerometer will result in the accelerometer just hanging there. What does it measure? It measures an acceleration of –1g. We know that the thing is just hanging there. The accelerometer doesn’t know it, it may think (if it could think) it is accelerating with 1g in negative Z-direction.
Now, give the XYZ axes system a rotational speed about say the Y-axis. If the changing angle of the Z-axis with the vertical is theta, the gravitational acceleration makes this angle with the Z-axis, and so what is left in Z-direction due to gravity is –g cos(theta).
My question is, what measures the accelerometer now?

Onemorechance

 

[IRstuff]

Suggest you go find a good textbook.

The Germans successfully used these principles to bomb England with the V-2.



TTFN

 

[Onemorechance]

Is there really nobody thinking out there? Did I ever mention the word gyro?

Anybody can tell me what the accelerometer measures?

Onemorechance.

 

[IRstuff]

That's because your statements make no sense:

"Using only accelerometers can be useful in measuring rotational accelerations, but with only accelerometers it is absolutely impossible to measure translational accelerations because of the unknown direction of the gravitational field."



Accelerometers CANNOT be used to measure rotation, that's what gyros are for.
Accelerations CAN measure translational accelerations, including gravity. Your previous posting shows that you even agree with that.

TTFN

 

[Onemorechance]

IRstuff,

You seem to be irritated with my question, well that was not my intention. This question is not so senseless as you might think.
Continuing from my previous post…
…
Now, give the XYZ axes system a rotational speed about say the Y-axis. If the changing angle of the Z-axis with the vertical is theta, the gravitational acceleration makes this angle with the Z-axis, and so what is left in Z-direction due to gravity is –g cos(theta).
My question is, what measures the accelerometer now?

It still measures –1g !

Why? Remember the XYZ axes system (to which the accelerometer is attached) has a force in negative Z-direction equaling the weight of the accelerometer. Because the Z-axis now makes an angle theta with the vertical, there is no force equilibrium in Z-direction any more. The XYZ axes system is accelerating with

- (1-cos(theta))*g

in Z-direction. This creates an extra mass force in Z direction:

accelerometermass*(1-cos(theta))*g

this adds on to the mass force

accelerometermass*cos(theta)*g

which comes from gravity.

Resulting in a total mass force of

accelerometer-mass * g,

And thus the accelerometer measures a 1g acceleration in negative Z-direction while the real motion has an acceleration in Z-direction of -(1-cos(theta))*g.

In other words only accelerometers are useless in measuring motion translational acceleration. You need more than that. You need a gyro to provide the direction of the gravitational field. Now you can solve the problem. The gyro provides theta, the accelerometer provides the acceleration of the total measured mass force, ... with theta gravity terms are filtered out from motion terms.


Accelerometers CANNOT be used to measure rotation.
I don’ t agree!
Yes , they can not be used to measure an angle of rotation, but they could perfectly be used to measure rotational acceleration. You can use 4 accelerometers in the XY-plane of the above mentioned XYZ-system to measure rotational acceleration about the Z-axis.
Say you have 2 of them mounted on the X-axis, one at –L, one at +L, both directed in +Y-direction. The other 2 are mounted on the Y-axis, also one at –L , one at +L, both directed in +X-direction.
The average of the sum of the average measured differences in X and Y accelerations gives you L * Z-rotational acceleration.


See, gyros are expensive and relatively high weight for certain applications, is it possible to only use accelerometers for stabilizing, maybe in combination with other lightweight devices? I am thinking of accelerometers + accelerometers on pendulum or so? Please don’t get irritated again, think about it, if you have a decent answer I would be glad to read it.


Ps: Is it a coincidence that you mentioned the V-2 bomb? Just happens to be that my grandfather was forced to work on the damn thing.

 

[IRstuff]

It is neither cheaper nor lighter. You've constructed a 4 sensor + associated electronics system to measure what a single gyro can do.

Given that there are very few applications that only require rotation measurement in one axis, you'll actually need 6 accelerometers to do a real task.

At that point, you've got three extra accelerometers, which might as well be replaced by gyros that can measure the rotation directly and more accurately.



TTFN

 

[astroclone]

I agree with onemorechance.
Not in the z-axis accellerometer bit, but with the idea of using accellerometers as rotation sensors.

I've thought about it and I think you can get all the measurements you need with 4. Possibly 3, but I'm pretty sure 4.

The thing is if you are using the accellerometers to measure rotation, subtract the signals from each other and then solve for the rotation rates and accellerations.

The rotation rate will be the same for all fixed accellerometers. The relative speed will be zero.
R1-R2 is known, R1dot-R2dot = 0 as do the relative accellerations.

What you are left with is the rotation terms.

R(doubledot) = r(doubledot) + 2 * w cross(r(dot)) + w(dot) cross(r) + w cross(w cross(r))
dot being the time derivative.

When you subtract 2 accellerometer measurements you get:
w(dot) cross(r) + w cross(w cross(r))

r is known. w and w(dot) are not. But by strategically placing the accellerometers or solving by matrices and such you can get the unknown values.
Those values plugged back into the original equation give you linear accelleration that won't be affected by rotations and so on.
Just my thoughts.
T

If you have the z accellerometer and tilt it to 90 deg it will measure nothing at 90 deg. It will measure transients and rotation forces along the way. But steady state at 90 deg will be 0.

 

[IRstuff]

You are not the first to think this, nor the last. Given over 50 years of trying, no one has successfully fielded such a system.


You're welcome to dream on. I'll simply refer you to page 38 of "Modern Inertial Technology" by Anthony Lawrence, Springer-Verlag 1998. It discusses the fact that even angular accelerometers are not up to the task.



TTFN

 

[navigate87]

In addition to "Modern Inertial Technology" check out "Fundamentals of High Accuracy Inertial Navigation" by Averil B. Chatfield.

 

[birdstruck]

I believe that IRStuff may be correct in saying:

You are not the first to think this, nor the last. Given over 50 years of trying, no one has successfully fielded such a system.


However, I have seen a physical working prototype in the labratory of a relatively less known university in which the application was for control of space-based vehicles. The entire system was less than 2 lbs and about the size of a can of soda. An aluminum tuning fork was mounted vertically upon a base. Three orthagonal accelerometers were mounted upon one tine of the fork. A piezoelectric driver was situated between the tines, resonating it by means of sound pressure. I am not that familiar with the mathamatics, however, in the presence of rotation within one axis, the signals from the transducers in the other two directions were cancelled out. Through some small electronic device, they were able to filter out the carrier signal and measure extremely small rotations. By the way, the entire package was hermetically sealed in a small glass cylinder. The year was 1992 when I saw the system and I SPECULATE that the military may be using them on specialized space applications.

For what it is worth.

Birdstruck

 

[Onemorechance]

Thanks Irstuff, Navigate87 and Astroclone for your opinions.
I am convinced that looking at textbook wisdom is really a must (especially for me).
But I also want to comment that thinking and dreaming is still necessary and a good thing to do. Remember that it has always been through people thinking and dreaming that progress was achieved.

Onemorechance

Ps: Astroclone; in the z-axis accelerometer bit I was right too. Another way of understanding it is:
Say you hold an accelerometer vertically. It measures 1g upwards. Now you let it fall. From that moment on it measures 0g. Why? Because the accelerometer measures mass forces and both the gravity and the motion acceleration produce mass forces. Only the gravitational force can be seen as an external force ‘F’ acting on the accelerometer causing it to accelerate ‘a’ (law of Newton F=mass*a). The mass force – mass*a is pointing the other way (see Newtons law), so the accelerometer don’t measure anything. Thus in order to know the motion acceleration you need to know the direction of the gravitational field. And of course I know that this can be provided by gyros or by hooking up integrating electronics onto accelerometers etc..

 

[navigate87]

Birdstruck,
What you refer to has been perfected to a point and is now called the "wineglass" gyro. It works best in a vacum so space applications are ideal.