More specifically, "yaw" body rate maps to the left/right accel axis, and "pitch" body rate maps to the up/down accel axis. You don't need to know attitude of the banking turn because we already know that in a 6 DOF IMU, the accel and gyro chips are fixed in orientation relative to each other. "V" is fore/aft body axis airspeed velocity. It all works out very neatly.
Centripetal force, being a "false" force, depends on speed relative to the medium the vehicle is moving through and "pushing against" to generate the forces, with assumption that the vehicle is more or less tracking in that medium without too much slip. If the medium is a racetrack and the vehicle a car, then the proper speed is car relative to the racetrack. If the vehicle is in the air, then it is relative to the air; i.e. airspeed. "Wind" is speed of the air relative to the ground, and has absolutely no bearing on the matter because the vehicle is not in contact with the ground. Thus neither wind speed or ground speed matter for calculating exacting centripetal corrections, only airspeed.
Recall high school physics: centripetal force = V^2/r. Restructure the equation to replace r (radius) with the equivalent body rate (because we can't measure radius of the turn, and already have body rate data form the IMU), then all you need is body speed forward (V, or airspeed) and the body rate in the axis of interest and which accel axis this maps to, and viola you have the centripetal force component affecting that axis. Subtract that force from that raw accel data, and you now have the attitude-only accel component in that axis. Now you can sustain indefinate banking turns without confusing the IMU filter. Of course none of this matters with thermopiles, but for an IMU it is critical. In my opinion, not applying centripetal corrections is a sad ignorance and abuse of an IMU filter. There is no reason to neglect this unless a person was stoned during high school physics and didn't learn anything there. It doesn't take anything more than high school level calculus, physics, and trig to know how to get all the physics correct.
Very interesting that you have connected airspeed via pressure to centripetal correction; I would have figured that windspeeds would have reduced the usefulness of airspeed in centripetal IMU correction. (Of course assuming 0 windspeed, one can easily rely on airspeed, even assuming a fixed windspeed, one could correct for same; but the real world has a broad menagerie of weather types, and one might be forgiven for thinking airspeed via pressure is a nearly optional input.)
P.S. Being a long bearded programmer of uChips, but Spin virgin, I for one am very interested in Dean's random thoughts and reflection on the Propeller chip - if Gary will allow it :)...
... and at these more extreme speeds, you could just ignore "airspeed" because any typical wind is now a small fraction of the airspeed, and just use GPS ground speed divided by Cosine of pitch to get body-speed. Common civilian GPS report speed up to around 500m/s (~ Mach 1.5), thus AttoPilot (as an example) switches over from airspeed sensor at 300 km/h to instead a Cosine-corrected GPS ground speed, which is used all of the way up to GPS max speed (about 1118 mph, 1790 km/h). However, I have never tested AttoPilot above approx. 120 mph (200 km/h) but knowing airspeed is important for accurate centrifugal corrections in the IMU attitude estimate, thus this topic is near and dear to my heart.
The airspeed equation I use has a 7/2 power in it, and thus ram pressure builds rapidly with airspeed. So 7Kpa is not at all unreasonable for measuring airspeed in really fast RC planes or UAVs, for example powered by a turbine. My calcs (with assumptions of 100kPa ambient, and 25C) says 7 kPa is about 385 km/h (240 mph).
37 kPa is > 850 km/h (530 mph) with simple assumptions that ignore real world effects of heating. Of course at this speed, you'd have to use an airspeed equation that accounts for Mach number and other things. The equations are given in Wikipedia. But now we are getting outside of DIY drones, and more towards DIY cruise missiles :)
The Diff P sensor pictured on top right of the Atto board (Freescale MP3V5004G) is describe as "Gauge" type. One port is the nipple as shown, the 2nd port is a vent hole on backside of the package. The 8 leads are structured so that the package backside is approx 0.5 mm elevated from PCB surface.
In any case, a read of a sensor's spec sheet will tell you if it is Differential, or Absolute. I honestly don't recal (or care) why the term "gauge" is used.
New Part on Mouser.
Comments
Centripetal force, being a "false" force, depends on speed relative to the medium the vehicle is moving through and "pushing against" to generate the forces, with assumption that the vehicle is more or less tracking in that medium without too much slip. If the medium is a racetrack and the vehicle a car, then the proper speed is car relative to the racetrack. If the vehicle is in the air, then it is relative to the air; i.e. airspeed. "Wind" is speed of the air relative to the ground, and has absolutely no bearing on the matter because the vehicle is not in contact with the ground. Thus neither wind speed or ground speed matter for calculating exacting centripetal corrections, only airspeed.
Recall high school physics: centripetal force = V^2/r. Restructure the equation to replace r (radius) with the equivalent body rate (because we can't measure radius of the turn, and already have body rate data form the IMU), then all you need is body speed forward (V, or airspeed) and the body rate in the axis of interest and which accel axis this maps to, and viola you have the centripetal force component affecting that axis. Subtract that force from that raw accel data, and you now have the attitude-only accel component in that axis. Now you can sustain indefinate banking turns without confusing the IMU filter. Of course none of this matters with thermopiles, but for an IMU it is critical. In my opinion, not applying centripetal corrections is a sad ignorance and abuse of an IMU filter. There is no reason to neglect this unless a person was stoned during high school physics and didn't learn anything there. It doesn't take anything more than high school level calculus, physics, and trig to know how to get all the physics correct.
@Dean,
Very interesting that you have connected airspeed via pressure to centripetal correction; I would have figured that windspeeds would have reduced the usefulness of airspeed in centripetal IMU correction. (Of course assuming 0 windspeed, one can easily rely on airspeed, even assuming a fixed windspeed, one could correct for same; but the real world has a broad menagerie of weather types, and one might be forgiven for thinking airspeed via pressure is a nearly optional input.)
P.S. Being a long bearded programmer of uChips, but Spin virgin, I for one am very interested in Dean's random thoughts and reflection on the Propeller chip - if Gary will allow it :)...
Your products have done great things recently well done.
Yes I am talking in code people.
The airspeed equation I use has a 7/2 power in it, and thus ram pressure builds rapidly with airspeed. So 7Kpa is not at all unreasonable for measuring airspeed in really fast RC planes or UAVs, for example powered by a turbine. My calcs (with assumptions of 100kPa ambient, and 25C) says 7 kPa is about 385 km/h (240 mph).
37 kPa is > 850 km/h (530 mph) with simple assumptions that ignore real world effects of heating. Of course at this speed, you'd have to use an airspeed equation that accounts for Mach number and other things. The equations are given in Wikipedia. But now we are getting outside of DIY drones, and more towards DIY cruise missiles :)
The Diff P sensor pictured on top right of the Atto board (Freescale MP3V5004G) is describe as "Gauge" type. One port is the nipple as shown, the 2nd port is a vent hole on backside of the package. The 8 leads are structured so that the package backside is approx 0.5 mm elevated from PCB surface.
In any case, a read of a sensor's spec sheet will tell you if it is Differential, or Absolute. I honestly don't recal (or care) why the term "gauge" is used.
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