Opensource MicroGravity Laboratory

Nanotube 3d accelerometer

        This technology was invented by Carsten Koenig in 1999, and it is based on a technology to measure mass of virus-sized objects using nanotubes published in AIP's Physics News Update 417 .

        Because the expected effects of the fundamental physics experiments conducted in the container can be tiny - with some setups only aprox. 10-9 times the acceleration of Earth (G) -, we need a system, able of measuring such small accelerations. Not only to measure the values of the experiment, but also for the measurement of the external, disturbing gravitational field. This is needed, because we have to subtract the external accelerations and remaining gravitational field from our recordings, to get the bare effects of the experiments – this is the purpose the Gravity Monitoring Box is designed for.

        There are some restrictions we have to keep in mind:

• The measurement of the accelerations within the container must not interfere with the experiment.

• The accelerations need to be measured very exactly at a high frequency.

How can we do it?

        First of all we need a system capable of measuring nano-accelerations or even below. This can be done by „Vibrating Carbon Nanotubes“, which are even able to get down to the range of femto-accelerations. As described in the Article of the AIP [Physics News Update 417, American Institute of Physics], they might be used for the weight measurement of viruses. Exactly speaking, they were developed for mass measurement in general. But when you know the mass, you can derive the acceleration [...]. But how do they work?

Image 1:  When applying an alternating current to a carbon nanotube, it will vibrate with it’s characteristic frequency. When a sample is attached to the nanotube, it’s characteristic frequency will change. From this change, you can derive the weight of the sample. On the other hand, when the weight of the sample is well known, you can derive the acceleration applied to the nanotube-weight system - and therefore the gravitational field. With this in mind, you’ve got a nano-accelerometer. These nano-accelerometers can be used in two different ways: first as single accelerometers to measure the acceleration at one specific point within the experiment, or second – as intended by the Monitoring Box – as a grid of several nano-accelerometers to monitor the influence from the surrounding environment to the experiment. Both maps are needed: you have to subtract the external (disturbing) accelerations (monitored by the Monitoring Box) from the accelerations measured within the box (monitored by the experimental setup) to get the bare effects of the observed experiment.

Image 2: To monitor the accelerations within the experiment, there needs to be done a gravity mapping of the experimental setup down on Earth before launch, like the “centre of gravity test” conducted for the Space Shuttle before each flight. With this you will get a gravity map of all fixed items in the experimental container. Every dynamic activity of the experiment should be monitored by special, additional accelerometers (e.g. those nano-accelerometers). These might be part of every fixed item, but it must be ensured that the exact positions of these accelerometers are well known. But if you want to get a map of the disturbing, external gravitational field and other accelerations, you need to build an array of those accelerometers. So think of a square consisting of 3 x 3 nano-accelerometers. Because you do not have the accelerations between the different accelerometers, you have to interpolate it. Horizontally, this will be done easily by the following equation: g=(a*l1)+(b*l2) Where g is the acceleration at the point interpolated, a and b is the acceleration measured by two accelerometers next to each other and l1+l2=1 is the relative position between the two accelerometers. When interpolating 4 squared, planar arranged accelerometers (e.g. a, b, d, e in the picture below), you will get the following equation:  g = ½ * (g0,1+g0,2) + (g1,0+g2,0) g = ½ * {[(r*l0,1)+(s*l0,2)] + [(t*l1,0)+(u*l2,0)]} g = ½ * {[{(a*l0,1)+(b*l0,2)}*l0,1] + [{(d*l0,1)+(e*l0,2)} *l0,2] + [{(a*l1,0)+(d*2,0)}*l1,0] +          [{(b*l1,0)+(e*2,0)}*l2,0]   } So to use one wall of nano-accelerometers you will need a system looking something like the following: The nano-accelerometers continuously send the measured accelerations to the registers of their level, in a way, that these registers build a matrix containing the measured acceleration values. The CPU catches those values to feed the Gravity Interpolation Program with data. The program calculates the accelerations between the accelerometers with the equation mentioned above in steps defined by the experimentator. A resolution of x=0,5 means one step horizontally between the accelerometers, where 0,1 means 10 steps from accelerometer a to accelerometer b. The interpolated accelerations are calculated the way shown in the figure: column after column. All these interpolated accelerations are written to a memory, with an array, consisting of several matrices (called R above; as many as times of measurement) containing the accelerations of one specific time of measurement (stored at the positions 1,1 to v,h above).

Image 3: To interpolate the gravity distribution caused by the surrounding environment to the experiment, you need to monitor it in three dimensions – therefore you can build a cube around the experiment consisting of those nano-accelerometer walls described above. With this container you can measure the disturbance of external accelerations (e.g. vibrations, active vibration dampers, shock waves...) and the still remaining small gravitational field to the experiment being conducted within the walls. But with this cube it gets quiet a little more difficult, because you don’t have only the edges of the cube, but acceleration-information from within the walls of that cube. Also, you have to look for the direction of the applied acceleration. When the acceleration is only measured 90° against the wall, you have information to compare like: g= [  (g1,0,0 +  g2,0,0)²  +  (g0,1,0 +  g0,2,0)²  +  (g0,0,1 +  g0,0,2)²  ]½   Where g(x,y,z) is the acceleration measured at the walls of the gravitation measurement container - like described above -, but already corrected by their relative position to the point between two opposite walls. g= [ (I1,0,0 *  g1,0,0  +  I2,0,0 *  g2,0,0)  +  (I0,1,0 * g0,1,0  +  I0,2,0 *  g0,2,0)  +  (I0,0,1 *  g0,0,1  +    +  I0,0,2   *  g0,0,2) ]  When you want to do so for accelerometers capable of measuring the direction of the acceleration (actually you will need this to be more accurate), you will have to do this equation by using vectors, so you will get the final equation: Every vector represents the acceleration on one side of the wall (with 1 and 2 indicating opposite walls). These vectors are corrected by their relative position using e.g. I1,0,0+I2,0,0=1 as a relative intensity indicator. The vectors themselves are build by adding the accelerations measured by the nano-accelerometers and interpolated to the wall as described above.