X-Virus-Scanned: clean according to Sophos on Logan.com Return-Path: Sender: To: lml@lancaironline.net Date: Wed, 02 Jan 2008 16:55:19 -0500 Message-ID: X-Original-Return-Path: Received: from wind.imbris.com ([216.18.130.7] verified) by logan.com (CommuniGate Pro SMTP 5.2c4) with ESMTPS id 2627247 for lml@lancaironline.net; Tue, 01 Jan 2008 18:28:47 -0500 Received-SPF: none receiver=logan.com; client-ip=216.18.130.7; envelope-from=brent@regandesigns.com Received: from [192.168.1.100] (cbl-238-80.conceptcable.com [207.170.238.80] (may be forged)) (authenticated bits=0) by wind.imbris.com (8.12.11/8.12.11.S) with ESMTP id m01NS6KJ031809 for ; Tue, 1 Jan 2008 15:28:06 -0800 (PST) (envelope-from brent@regandesigns.com) X-Original-Message-ID: <477ACC8B.4060206@regandesigns.com> X-Original-Date: Tue, 01 Jan 2008 15:28:11 -0800 From: Brent Regan User-Agent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.7.2) Gecko/20040804 Netscape/7.2 (ax) X-Accept-Language: en-us, en MIME-Version: 1.0 X-Original-To: Lancair Mailing List Subject: Re: First dumb question of the year.. Content-Type: multipart/alternative; boundary="------------060607010305020205080301" This is a multi-part message in MIME format. --------------060607010305020205080301 Content-Type: text/plain; charset=us-ascii; format=flowed Content-Transfer-Encoding: 7bit "There are no stupid questions, only inquisitive idiots." Gregory House Rick Asks: <> Yes it would if it were not for the fact that most gyroscopic aircraft instruments, including AHRS, have some form of gravity vector aiding. Mechanical attitude gyroscopes have the equivalent of a pendulum that, during level flight, points towards the center of the earth. The coupling of the aiding is weak so that it takes several minutes for the gyroscopic frame of reference to erect normal to the local earth plane. You can see this if you put your plane into a shallow turn for several minutes and then roll level. Your instrument should then have a bank offset that takes several minutes to self correct. What is happening is that the centripetal vector, due to the turn, which is parallel to the earths surface is added to the gravity vector producing a new vector that everything in the airplane feels as gravity. If you are in a 1G (horizontal) turn you would "feel" 1.4 Gs (vector sum) and have a bank angle of approximately 45 degrees. If you held this turn long enough the gyro would erect and show you in level flight. In theory, you could hold a 45 degree indicated bank and "chase" the vector to structural failure or a 90 degree bank, which ever occurs first. Directional Gyroscopes doe not have gravity aiding and DG precession is an example of earth rotation induced error. Remember that at the mid latitudes your velocity while "standing still" is about 700 mph due to earth's rotation and the earth turns "under" you at 15 degrees per hour. In practice the erecting effect is weak enough so that it reasonably averages all flight maneuvers and stays acceptably close to earth normal. Most MEMS AHRS can be upset easier than your typical mechanical artificial horizon and there is usually a flight maneuver, such as a climbing low rate turn, that will cause a MEMS AHRS to lose its reference. This is the major "gotcha" that you can only find out about during flight testing as it is very difficult to replicate in an lab. An AHRS, in theory, could be configured so that once referenced to the earth it would maintain an accurate indication regardless of the duration and rate of the turn. If you know your velocity and yaw rate you can calculate your instantaneous centripetal vector and then subtract that from the measured "gravity" vector. Viola! Sounds easy but in practice there are many secondary effects that conspire to make things difficult. You are fighting sensor accuracy, calibration accuracy, hysteresis, vibration, temperature drift, sensor noise, induced noise, non linearity, rounding errors, aliasing, algorithm approximations, gain drift, sensor aging, mechanical tolerances and production variances to achieve the highest levels of performance. You also need to get your math and algorithms right and implement them in code accurately and efficiently. (Caution: Shameless boasting follows) I know this because these are all the things we had to overcome in order for the Chelton ADAHRS performance to match that of the flight reference system, a Collins AHR-3000, typically used in a Pro Line 21 system. Any idiot can take some cheap sensors and build an AHRS that works fine on the ground. Many have. Take the thing into the air and your problems increase exponentially. The bad news is that flight testing is expensive and the faster your airplane the more AHRS performance you need. An "inexpensive, high performance AHRS" is an oxymoron as engineering and flight testing costs to develop same can run well into 7 figures. Allocate those costs over a few hundred systems and you are into your "cheap AHRS" a couple of grand before you even add in the bill of material costs, assembly costs, overhead and margin. One point of clarification. I do NOT think Rick is an idiot, inquisitive or otherwise. I just couldn't resist the opportunity to include a funny quote. Regards Brent Regan --------------060607010305020205080301 Content-Type: text/html; charset=us-ascii Content-Transfer-Encoding: 7bit "There are no stupid questions, only inquisitive idiots." Gregory House

Rick Asks:
<<over time,shouldn't the rotation of the earth cause the gyro to indicate a change
(error) relative to earth's horizon. >>

Yes it would if it were not for the fact that most gyroscopic aircraft instruments, including AHRS, have some form of gravity vector aiding. Mechanical attitude gyroscopes have the equivalent of a pendulum that, during level flight, points towards the center of the earth. The coupling of the aiding is weak so that  it takes several minutes for the gyroscopic frame of reference to erect  normal to the local earth plane. You can see this if you put your plane into a shallow turn for several minutes and then roll level. Your instrument should then have a bank offset that takes several minutes to self correct. What is happening is that the centripetal vector, due to the turn, which is parallel to the earths surface is added to the gravity vector producing a new vector that everything in the airplane feels as gravity. If you are in a 1G (horizontal)  turn you would "feel" 1.4 Gs (vector sum) and have a bank angle of approximately 45 degrees. If you held this turn long enough the gyro would erect and show you in  level flight.  In theory, you could hold a 45 degree indicated bank and "chase" the vector to structural failure or a 90 degree bank, which ever occurs first.

Directional Gyroscopes doe not have gravity aiding and DG precession is an example of earth rotation induced error.  Remember that at the mid latitudes your velocity while "standing still" is about 700 mph due to earth's rotation and the earth turns "under" you at 15 degrees per hour.

In practice the erecting effect is weak enough so that it reasonably averages all flight maneuvers and stays acceptably close to earth normal. Most MEMS AHRS can be upset easier than your typical mechanical artificial horizon and there is usually a flight maneuver, such as a climbing low rate turn, that will cause a MEMS AHRS to lose its reference. This is the major "gotcha" that you can only find out about during flight testing as it is very difficult to replicate in an lab.

An AHRS, in theory, could be configured so that  once referenced to the earth it would maintain an accurate indication regardless of the duration and rate of the turn. If you know your velocity and yaw rate you can calculate your instantaneous centripetal vector and then subtract that from the measured "gravity" vector. Viola! Sounds easy but  in practice there are many secondary effects that conspire to make things difficult. You are fighting sensor accuracy, calibration accuracy, hysteresis, vibration, temperature drift, sensor noise, induced noise, non linearity, rounding errors, aliasing, algorithm approximations,  gain drift, sensor aging, mechanical tolerances and production variances to achieve the highest levels of performance. You also need to get your math and algorithms right and implement them in code  accurately and efficiently. (Caution: Shameless boasting follows) I know this because these are all the things we had to overcome in order for the Chelton ADAHRS performance to match that of the flight reference system, a Collins AHR-3000, typically used in a Pro Line 21 system. 

Any idiot can take some cheap sensors and build an AHRS that works fine on the ground. Many have. Take the thing into the air and your problems increase exponentially. The bad news is that flight testing is expensive and the faster your airplane the more AHRS performance you need. An "inexpensive, high performance AHRS" is an oxymoron as engineering and flight testing costs to develop same can run well into 7 figures. Allocate those costs over a few hundred systems and you are into your "cheap AHRS" a couple of grand before you even add in the bill of material costs, assembly costs, overhead and margin.

One point of clarification. I do NOT think Rick is an idiot, inquisitive or otherwise. I just couldn't resist the opportunity to include a funny quote.

Regards
Brent Regan


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