Computing your CADP: any approach plate is a soup of acronyms and abbreviations. Here's the math behind one you've seen but never spoken.
CADP stands for Constant Angle Descent Point, and is the acronym I've given to the delayed descent point from the FAF to accommodate a Constant Angle Non-Precision Approach (CANPA).
The profile view of the RNAV (GPS) Rwy 30 approach at Clearfield, Penn., (KFIG) shows the delayed de scent point to be 4.9 miles from the threshold or just 0.1 miles beyond the FAF.
The chart shows a Vertical Descent Angle (VDA) of 3.30 degrees and so we have the option to (a) commence a 3.3-degree constant-angle descent from 3300 feet continuously to the MDA starting at 0.1 miles beyond the FAF, (b) begin descent at the FAF using the dive and drive technique, or (c) begin descent at the FAF using the stepped technique, which means descending at each successive intermediate stepdown, and estimating a rate to arrive at each fix at the minimum altitude specified.
Past the Towers
My copy of AIM defines stepdown fix (SF) as a fix permitting additional descent within a segment of an instrument approach procedure by identifying a point at which a controlling obstruction has been safely overflown.
This suggests that for every SF, there corresponds a gradient change. Because we're considering only the final approach segment and the FAF fits the definition of stepdown fix, we could describe the FAF as being the initial stepdown fix.
Maintaining the VDA from the CADP to the runway threshold ensures that you'll clear all obstacles and comply with the minimum altitudes associated with all intermediate SFs. Both NACO and Jeppesen plates publish the VDA, but only Jeppesen shows a CADP. A CADP is shown when there is at least one intermediate stepdown fix and when the steepest gradient along the final approach segment extends from an intermediate stepdown fix to the threshold. Otherwise, if the steepest gradient runs from the FAF to the threshold, there is no need to publish a CADP because it automatically coincides with the FAR Got all that?
Get ready and dust off your mathematics. Assuming we've opted for the CANPA, I'm going to provide some methodology for computing the CADP, VDA, and Rate of Descent (ROD).
Ideally, we'd use Threshold Elevation (THRe) rather than Touchdown Zone Elevation (TDZE) in our equations. Although the TDZE is sometimes equal to or very close to the THRe numerically, it is more appropriate to use the THRe to compute the CADP, VDA, and Visual Descent Point (VDP). That's what TERPS does.
Consequently, it's the sum of THRe and TCH that determines the Threshold Crossing Altitude (THRa) rather than the sum of TDZE and TCH. VDA is the angle associated with that stepdown fix having the steepest descent gradient to the THRa.
If we don't have THRe to work with, though, we can use TDZE and come up with a close approximation. Here are the steps involved:
1. Compute the gradient associated with each stepdown fix (including the FAF) to the runway threshold.
Stepdown Gradient = Stepdown Altitude - (THRe+TCH)/ Stepdown Distance from Threshold
2. Select the maximum stepdown gradient from step 1. You can compute the gradient from each step down if you want to be certain you have the steepest one.
3. Compute the CADP.
CADP = FAF Altitude-(THRe+TCH)/Max Stepdown Gradient
4. Compute the VDA.
VDA = [tan.sup-1] (Max Stepdown Gradient/6076)
5. Compute the required ROD.
ROD = Groundspeed x Gradient/60
Before proceeding further, let me say that cheating is allowed. For example, we'll take advantage of the fact that Jeppesen published the CADP for the approach and, therefore, in accordance with the criteria given above, we can conclude that the intermediate stepdown shown is the fix with the steepest descent gradient and not the FAF.
We'll also assume a final approach groundspeed of 120 knots and compute the CADP, VDA, and ROD for the CANPA as follows:
Stepdown Gradient = 2440-(1516+50)/2.5 nm = 350 feet/nm
CADP = 3300-(1516 + 50)/350 = 4.95 nm
VDA = [tan.sup.1]- (350/6076) = 3.30 degrees
ROD = 120 x 350/60 =700 fpm
What we've managed to do is confirm the numbers depicted on the approach chart and, hopefully, have concluded that this is an excellent learning tool for instrument students. It also serves as a good planning tool allowing stabilized approach fans to use the CANPA descent gradient to compute "check" altitudes at selected points along the CANPA flight path. This image of the CANPA descent profile improves situational awareness.
It's interesting to note as well that as approaches are being rewritten with LPV and LNAV/VNAV minimums, many of these CANPAs are going away, leaving only the LPV VDA published on the plate.
This can create some issues. The old RNAV (GPS) Rwy 18 to Fairfield, Iowa, (KFFL) was LNAV-only and had an MDA of 1180 feet. To go that low, however, you needed to get past a 1090-foot tower 1.5 miles from the runway threshold. A stepdown was published on the plate, as was a CANPA VDA of 3.52 degrees commencing 0.6 miles beyond the FAF and 4.4 miles from the threshold.
The new RNAV (GPS) Rwy 18 at KFFL shows a 3.0-degree VDA from the same FAF right over the same 1090-foot tower. The catch? You must have LPV equipment to fly it. Since there is no longer a stepdown published on the plate, LNAV-only fliers have a new MDA of 1400 feet--220 feet higher than it used to be.
While teaching a trigonometry class, a student asked, "What good is this stuff?" I quickly placed an approach chart transparency on the overhead and got lots of ooohs. I told them that computing the inverse tangent correctly can mean the difference between life and death. The students loved it and so did I.
John Clark teaches mathematics at Cleveland State University. He is a private pilot with a ground instructor certificate.
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|Title Annotation:||APPROACH CLINIC; Constant Angle Descent Point|
|Date:||Jun 1, 2007|
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