more on WAAS and its benefits

[olasek]

There was a question about WAAS. I would like to add these graphs contained in the document below. It shows to what degree the positional accuracy is improved by WAAS - as you can see it is improved somewhat but the improvement is not exactly earth shattering. Even without WAAS GPS is amazingly accurate. So what is the main benefit of WAAS - checking integrity of signal and computing the actual worst case error. Without WAAS you would have no idea what this error was.

http://users.erols.com/dlwilson/gpswaas.htm

Also Max Trescott's G1000 book contains some IMHO inaccurate data on WAAS. He lists (horizontal and vertical alarm limits) HAL=40 meters, VAL=50 meters. That did not make much sense to me why vertical limit would be larger than horizontal and also these numbers looked very large to me.. So I started digging and found this very serious paper on WAAS error analysis which lists them as HAL=30 meters, VAL= 15 meters. These values make much more sense. Why are they important? If your WAAS unit calculates the upper bound of your positional error to be above these numbers it will effectively flag you that you no longer have WAAS (there are other reasons too why WAAS may be temporarily unavailable). There are some indications that numbers given by Max were valid at some point in the past but have since been replaced.

http://www.caasd.org/library/documents/mp99w0000060.pdf

 

[flyersfan31]

All that is too much for my primitive caveman brain. Alls I knows is that I don't have to worry about RAIM and I get mins like an ILS.

 

[John Collins]

Also Max Trescott's G1000 book contains some IMHO inaccurate data on WAAS. He lists (horizontal and vertical alarm limits) HAL=40 meters, VAL=50 meters. That did not make much sense to me why vertical limit would be larger than horizontal and also these numbers looked very large to me.. So I started digging and found this very serious paper on WAAS error analysis which lists them as HAL=30 meters, VAL= 15 meters. These values make much more sense. Why are they important? If your WAAS unit calculates the upper bound of your positional error to be above these numbers it will effectively flag you that you no longer have WAAS (there are other reasons too why WAAS may be temporarily unavailable). There are some indications that numbers given by Max were valid at some point in the past but have since been replaced.

http://www.caasd.org/library/documents/mp99w0000060.pdf

Max is sorta right. The HAL for an LPV or a future LP (none exist as of yet) approach is in fact 40 meters. The VAL for approaches with vertical guidance is either 50 meters for those that have a DA equal to or greater than 250 feet or 35 meters for those that have a DA under 250 feet down to 200 ft. The horizontal HAL is determined by how much navigation error is allowed worst case on the approach, it is 40 meters for the LPV/LP and 556 meters for LNAV or LNAV/VNAV. The vertical VAL provides for the worst case vertical navigation, but remember that the DA is based on your baro altitude, not just the vertical GP, so the vertical error has the effect of moving the MAP longitudinally along the final approach course, +/-.

 

[gismo]

The vertical VAL provides for the worst case vertical navigation, but remember that the DA is based on your baro altitude, not just the vertical GP, so the vertical error has the effect of moving the MAP longitudinally along the final approach course, +/-.

The vertical error also has the (more serious) effect of potentially bringing you closer to the obstructions below you on a LPV approach since the underlying clear zone rises (at a smaller angle) with the GS.

 

[John Collins]

The vertical error also has the (more serious) effect of potentially bringing you closer to the obstructions below you on a LPV approach since the underlying clear zone rises (at a smaller angle) with the GS.

This would be true, but as altitude increases the obstruction clearance also increases, so my thinking is that the worst case would be at the DA.

The OCS (Obstacle Clearance Surface), above which no obstacles are permitted on an LPV for a 3 degree glideslope is 34 to 1. A 3 degree glideslope is approximately 19 to 1. So at any point along the final approach course, the minimum obstacle clearance is the difference between the two slopes. At 4750 feet from the threshold close to the point where the DA would nominally be located, the minimum obstruction clearance is is approximately 110 feet, whereas at 12,000 feet (approximately 2 NM from the threshold) this is approximately 280 feet, and so on.

The worst case from an obstacle clearance point of view for a LPV with a 250 foot DA, just considering the vertical error is at the DA where the vertical error is on the low limit of 50 meters or 164 feet. This will push the location of the DA out another 3116 feet. At this point the obstacle clearance is about 202 feet, or using up the 164 feet of GPS vertical error, only 38 feet of clearance, a little scary, but the worst case. Full scale deflection at this point is approximately 50 feet, so you don't want a fly up under these circumstances inside the FAF.

Edit: Looking at the TERPS, there is actually more obstacle clearance then I indicate above. First of all the GP starts at the the point it intersects the ground, not at the threshold. For an approach with a 50 ft TCH (threshold crossing Height), this is 954 feet beyond the threshold. The OCS surface starts 200 feet (or more in some cases) before the threshold. This represents at least 1154 foot offset between the two slopes, or another 61 feet of protection at the DA location. In addition, the two slopes are a straight line in space and don't account for the curvature of the earth which slopes away from the straight lines, so the actual MSL altitude of an obstacle has to be reduced by the curvature of the earth. Close to the DA this effect is small, but grows to over 200 feet further out. So I would revise my estimate of the worst case obstacle clearance to be 38+61 feet, or 99 feet of clearance.

 

[olasek]

Max is sorta right. The HAL for an LPV or a future LP (none exist as of yet) approach is in fact 40 meters. The VAL for approaches with vertical guidance is either 50 meters for those that have a

You are right.

For those that like to read this in-depth analysis of WAAS this is a good (FAA) document:

http://pnt.gov/public/docs/2008/waasps2008.pdf

The vertical alert limit is used to determine whether an aircraft type can avoid penetrating the obstacle clearance surface during vertically guided approaches. The 35 meter VAL was evaluated extensively for all types of aircraft to determine whether the pilot could react adequately to avoid penetrating the Obstacle Clearance Surfaces (OCS) defined by Terminal and En Route Instrument Procedures (TERPS) for LPV approach and missed approach operations. For LPV approach operations, it was determined that this vertical alert limit, in combination with the small WAAS vertical position error distribution, supported a vertically guided approach down to 200’ HAT and missed approach for all categories of aircraft.

One has to realize that VAL/HAL are a bit mathematical constructs - to date no one observed a vertical error exceeding ~15 m.

 

[gismo]

One has to realize that VAL/HAL are a bit mathematical constructs - to date no one observed a vertical error exceeding ~15 m.

I assume you mean that to be true for receivers on the ground. I doubt that's true of GPS navigators in airplanes.

 

[gismo]

This would be true, but as altitude increases the obstruction clearance also increases, so my thinking is that the worst case would be at the DA.

That's what I meant to imply with the "at a smaller angle" comment. But what I was really trying to point out is that:

1) a shift in the "MAP" (intersection of DA and approach path) along the approach path isn't the only effect of a vertical error.

and

2) A vertical error may put you closer to an underlying obstruction than indicated on your chart. While it is indeed true that at DA you would (or is it should) be closest to the obstruction clearance plane, chances are good that this is not the point where the glidepath is closest to an actual obstruction.

 

[tonycondon]

All that is too much for my primitive caveman brain. Alls I knows is that I don't have to worry about RAIM and I get mins like an ILS.

+1...

 

[John Collins]

That's what I meant to imply with the "at a smaller angle" comment. But what I was really trying to point out is that:

1) a shift in the "MAP" (intersection of DA and approach path) along the approach path isn't the only effect of a vertical error.

and

2) A vertical error may put you closer to an underlying obstruction than indicated on your chart. While it is indeed true that at DA you would (or is it should) be closest to the obstruction clearance plane, chances are good that this is not the point where the glidepath is closest to an actual obstruction.

1) What other effects are there for a vertical error at the VAL limit on the low side other than the entire glidepath being lower and therefore closer at each point to the OCS and shifted further out?

2) I can't comment on where an obstruction is more likely to occur, but the protection increases at a rate of 141 ft/NM.

 

[olasek]

I assume you mean that to be true for receivers on the ground. I doubt that's true of GPS navigators in airplanes.

I don't think there is a meaningful difference between the two otherwise all Stanford university publications on WAAS performance/errors would be of little value.

http://waas.stanford.edu/metrics.html

 

[John Collins]

I don't think there is a meaningful difference between the two otherwise all Stanford university publications on WAAS performance/errors would be of little value.

http://waas.stanford.edu/metrics.html

The referenced document is dated 1997 and last updated 1999. The RTCA DO-229C, the specification for GPS WAAS equipment was released in 2001 before there were any aviation WAAS receivers developed and the HAL and VAL values were different than the ones in the 1999 vintage Stanford document. There was an update to RTCA DO-229D in 2006 that updated possible VAL values for LPV with a DA as low as 200 ft. The current values in meters for HAL and VAL are:

LNAV HAL= 556
LNAV/VNAV HAL = 556 , VAL = 50
LPV DA 250 ft or greater, HAL = 40 , VAL = 50
LPV DA Less than 250 ft, HAL = 40, VAL = 35
LP HAL = 40

 

[gismo]

1) What other effects are there for a vertical error at the VAL limit on the low side other than the entire glidepath being lower and therefore closer at each point to the OCS and shifted further out?

Nothing I know of (assuming that the vertical error is consistent as your airplane travels along the glidepath). You had pointed out the effect of shifting the slope along the path and I was adding the (obvious) effect of bringing a plane closer to the closest obstruction which might be located somewhere besides the intersection of the DA and the nominal glidepath.

2) I can't comment on where an obstruction is more likely to occur, but the protection increases at a rate of 141 ft/NM.

Again, the "worst case" loss of obstruction clearance may well be further out. But it is true that as you look further and further away from the runway, the "opportunity" for an obstruction to be closest to the glidepath diminishes (at approximately 140 ft/nm). Consider an approach to a runway elevated a couple hundred feet above the surrounding terrain where there's a tall tower a couple miles from the runway threshold that is the limiting obstruction on the approach. In such a case you would be closer to that tower than anything else underlying the approach prior to reaching DA.

I think we're in complete agreement on the general effects of vertical errors, except that I got the impression that you're thinking the only point in the approach where this matters is at DA and I'm trying to point out that this isn't always true.

 

[John Collins]

I think we're in complete agreement on the general effects of vertical errors, except that I got the impression that you're thinking the only point in the approach where this matters is at DA and I'm trying to point out that this isn't always true.

I am not saying it only matters at the DA, but the DA provides the least vertical protection from a potential obstacle. So if the worst case vertical error still provides protection at the point where the least vertical protection is provided, it will provide more protection at all other points on the approach. Obstacles can be anywhere on the approach course, but the approach protection is premised on no obstacle penetrating the Obstacle Clearance Surface. So my analysis was only done at the location the DA passes thru the worst case glide path due to vertical error.

The VAL represents the 99.99999% probability that the vertical error will not exceed the limit, or 1 in 10 to the 7th power. Even when the VPL is at the VAL limit, there is an extremely remote possibility that the vertical error will be near the worst case, and especially for the two to three minutes that one is on final.