## Tuesday, May 27, 2014

### New Pitot flange family: Front Mounting Flange for 8mm Pitot

We're into the hardware test phase of our new BasicAirData pitot flange.
Have a look to the work in progress forum topic
http://basicairdata.freeforums.org/front-mounting-flange-for-8mm-pitot-t24.html

Figure 1 Front Mounting Flange for 8mm Pitot

Pinpoints of this design are, directly from the designer Graziano mouth:

1) This solution doesn't require to glue the Pitot to the flange, and neither to drill the assembled Pitot. It only requires a small additional drill on external chamber;
2) You can easily remove the Pitot element for substitution of for cleaning, without disconnecting any pipe inside the plane, only acting on the 4 front screws.
3) It has relatively small size;
4) Eventual possible condensation on Pitot is stopped by that flange. We must empty it before it is completely full of water;
5) We could provide an easy way to empty flange from water by adding two additional exits, that normally are kept closed;

During early stage development new features were added

1) Holes that link Pitot with Connectors on rear flange are now Ø4 mm, to allow a better ease of cleaning after the 3D Printing process (Thank'you JLJ  ;) );
2) All threaded holes, as previously seen, are now placed on middle element. Screws are placed on front and on back;
3) All screws are M4. I removed M3 threads because (especially if on plastic) a bigger pitch is to be preferred;
4) O-Ring seatings are normalized ISO3601/01 and DIN3771. I think these O-RINGS are a good solution for sealings, but any suggestion are welcome!
5) Taper on frontal fixing elements is now based on Bikon Commercial Taper Bushes;
6) Connectors are for Ø4 pipes;

You can find the most recent information on the new forum
http://basicairdata.freeforums.org/

## Monday, May 19, 2014

### Inertial Measurement Unit Placement

In this post I will expose a numerical compensation technique for the acceleration measurements of an airframe, this kind of compensation require the knowledge of airframe angular rates. The measurements are usually available from an Inertial Measurement Unit. Gyroscopes measurements don't need to be compensated.

Figure P45.1 Commercial Eagle tree telemetry system and BasicAirData Air Data Boom

Accelerometers measurements are affected by the position of the IMU respect to the center of gravity. In an ideal layout the measurements don't need to be compensated and the accelerometers are placed exactly over the center of gravity C.G., although that will rarely happen.
On many airframes the center of gravity is located over or near the main spar that fact makes nearly impossible to put the sensor over the C.G. Even on a middle wing or a low wing plane this location is often crowded by standard RC equipment. As general rule the closer is the IMU to the C.G the better; is to bear in mind that compensation for position offset reduces overall accuracy.

The C.G. position should be evaluated in the three dimensions; if the weight, typically affected by fuel consumption, or the aerodynamic configuration of the airframe changes during the fly then also the C.G. position should be tracked. This kind of procedures will not be treated here.

The C.G. is the point of rotation of the entire airframe. Let's use a body-fixed reference system; the origin is set to be coincident with C.G .On a conventional plane $$x$$ coordinate is  defined along the airframe from aft to fore, $$y$$ is orientate along the right wing and $$z$$ points toward the ground. Angular rates respect $$x,y,z$$ axes are $$p,q,r$$. Often $$p$$ is called roll rate, $$q$$ pitch rate and $$r$$ yaw rate. $$p$$ is positive rolling to right, $$q$$ is positive pitching up and $$r$$ is positive yawing right.
The IMU is installed, in the body reference frame, at $$[x_a y_a z_a]^T$$ coordinates. The IMU output is denoted as $$g[a_xIMU a_yIMU a_zIMU]^T$$

Refer to the following figure. Let's examine a planar case.  We consider airplane symmetry plane $$(x,z)$$ and set to zero all the angular rates outside this plane;we suppose also small rotation misalignment between body and instrument reference frames [1][2]. The variables for our problem are reduced to$$x,z,q,\dot{q},x_a,z_a$$. If the IMU is placed at a certain distance from C.G. centripetal and tangential acceleration terms affect the measured acceleration.

Figure P45.2 Reduced dimensions problem definition
By figure inspection we can write.
$$d cos(\alpha)=x_a$$
$$d sin(\alpha)=z_a$$
It is possible to write the transformation matrix from body reference frame to IMU reference frame, than by inversion we get the following acceleration expression [2]. Originally the expression have seven terms, many of them are set to zero by our assumptions.
$$ga_{xC.G.}=ga_{xIMU} + q^2 x_a- \dot{q}z_a$$
That is the explicit relation between measured acceleration and acceleration at C.G.
Suppose we've taken an acceleration measurement along x IMU axis of 3g; the IMU position is $$[0.25 \ 0\ 0]^T$$, $$q=2.6 1/s$$ that is equivalent to a pitch rate of 150° per second.
Calculated acceleration along $$x$$ at C.G. $$a_x$$ is 4.7g, we have 36% of offset error in the acceleration measurement. With this simple example is evident the magnitude of the error impact of a casual or undetermined placement of the IMU.

Extending this approach to the three dimensions we can write [1]
Equation 45.1
$$g\begin{bmatrix}a_x\\a_y\\a_z\end{bmatrix}=g\begin{bmatrix}a_xIMU\\a_yIMU\\a_zIMU\\\end{bmatrix}+ \begin{bmatrix}(q^2+r^2)&-(pq-\dot{r})&-(pr+\dot{q})\\–(pq+\dot{r})& (p^2+r^2)&-(qr-\dot{p})\\–(pr-\dot{q})&-(qr+\dot{p})&(p^2+q^2)\\ \end{bmatrix} \begin{bmatrix} x_a\\y_a\\z_a \end{bmatrix}$$

The last equation confirms our result for the reduced dimensions case previously presented.
Installation position can cause a relevant measurement error, that error is systematic and can be removed from the measurements using equation 45.1.

[1] Valdislav Klein and Eugene A. Morelli (2006), Aircraft System Idenification,AIAA
See Chapter 10. Equation 10.12

[2] Gainer, T.G., and Hoffman, S.(1972), Summary of Transformation Equations and Equation of motion Used in Free-Flight and Wind-Tunnel Data Reduction Analysis, NASA
Page 69 Case II, Formula A11-A12-A13
[3] Explicit calculation by ja72 in this link
I quote here in behalf of the reader
"
Starting from the well known acceleration transformation formula between an arbitrary point _A_ and the center of mass _C_ with $\vec{c} = \vec{AC}$.

$$\vec{a}_C = \vec{a}_A + \dot{\vec{\omega}} \times \vec{c} + \vec{\omega} \times \vec{\omega} \times \vec{c}$$

one can you the 3×3 [cross product operator](https://en.wikipedia.org/wiki/Cross_product#Conversion_to_matrix_multiplication) to transform the above into

$$\vec{a}_C = \vec{a}_A + \begin{vmatrix} 0 & -\dot{\omega}_z & \dot{\omega}_y \\ \dot{\omega}_z & 0 & -\dot{\omega}_x \\ -\dot{\omega}_y & \dot{\omega}_x & 0 \end{vmatrix} \vec{c} + \begin{vmatrix} 0 & -\omega_z & \omega_y \\ \omega_z & 0 & -\omega_x \\ -\omega_y & \omega_x & 0 \end{vmatrix} \begin{vmatrix} 0 & -\omega_z & \omega_y \\ \omega_z & 0 & -\omega_x \\ -\omega_y & \omega_x & 0 \end{vmatrix} \vec{c}$$

or in the form seen the linked post

$$\vec{a}_C = \vec{a}_A + \begin{vmatrix} -\omega_y^2-\omega_z^2 & \omega_x \omega_y - \dot{\omega}_z & \omega_x \omega_z + \dot{\omega}_y \\ \omega_x \omega_y + \dot{\omega}_z & -\omega_x^2-\omega_z^2 & \omega_y \omega_z + \dot{\omega}_x \\ \omega_x \omega_z - \dot{\omega}_y & \omega_y \omega_z + \dot{\omega}_x & -\omega_x^2 - \omega_y^2 \end{vmatrix} \vec{c}$$
"

## Sunday, May 11, 2014

### BasicAirData 8mmESP Series Probe manual

After a concentration of information from the last months experiences and articles the Pitot manual is online. Definitely a milestone for BasicAirData.

Into the manual you find indications about sizing and recommended installation positions.

Enjoy Open Basic Air Data Instruments

## Monday, May 5, 2014

### Air data computer open project starts

Every Basic Air Data instrument needs some electronic part to be fully functional. Implementations for stand alone instruments have been shown on the BAD main web site. When all the electronics needed for the operation of different sensors is collected into a single unit we name it Air Data Computer

This time we're facing the design of an Air Data Computer or ADC. The development process will take place on the brand new BasicAirData forum, this post introduces the preliminary requirements for ADC. Some work has been already done, have a look to the following figure.

Figure P44. Some preliminary virtual prototype and an example commercial air data computer

Within this project we will develop an Air Data Computer that can manage one Pitot-static probe, one barometer and one temperature sensor; the following measurements will be available.

-Static pressure, Pa
-Differential pressure, Pa
-Outside air temperature, Degree Kelvin
After sensor data fusion the unit will provide the followings data through a serial link.
-Indicated airspeed IAS, m/s
-True airspeed TAS, m/s
-Outside air temperature, °K/°C

The separate implementation of every function is more expensive than monolithic approach. Main advantage is that since all the necessary electronics is located in the same place it is easier to remove or install the equipment. As standard pneumatic and data link connection are provided then also placement on different airframes is fast and somewhat standardized.

-Reduced dimensions and weight, so the unit can be fitted into middle/smalls UAS. Let's say about 50x20x20mm and 20g.
-Able to withstand high G-loads, more than 8
-3.3V Hardware with on board voltage regulator
-Standard pneumatic connection
-Standard serial connection
-On board sensor data processing
-Static pressure accuracy better than "0,5 meter". Maximum IAS airspeed below 300 km/h; accuracy at full scale 1% or better.