Many of us are familiar with the rule that your vertical speed on a 3-degree glideslope should be GS*5, e.g. at 100 knots you need 500 FPM. Captain Eddie has a good explanation of why it works. The only problem is that this doesn't work for other glide path angles that we increasingly see on some of the newer RNAV approaches, so we need a more flexible rule. As with the turn-in rule, we can lean on the fact that at small angles, the change in angle and the change of the tangent of that angle are fairly proportional (any engineers please take a deep breath), at least to the precision required to fly well. Let's take an example and use that as a basis. One approach that catches some people off guard on the descent is the RNAV 16Z into Renton. It's got a 4.2 degree glide path, so any time someone's coming in and pulls power to where they'd want it for a 3-degree path, they're going to end up high, and then sometimes chase the diamond to get back on glide. With that steep approach, that can mean exceeding 1000 FPM in the descent. If we use the equation VS=tan(GPA)*GS, we can figure out what our VS should be, and then make a rule. We need to convert from knots to FPM, which means multiplying by 6076 (ft/nm) and dividing by 60 (hr/min), so with GS in knots, we get VS=tan(GPA)*101*GS. Taking our example at Renton and assuming a GS of 90 kts, this gives us VS=tan(4.2)*101.3*90=670 FPM. Ultimately we need a rule that uses GS and GPA as inputs, and spits out a decent approximation of VS. Dividing a set of common values yields VS=k*GPA*GS, where k reliably ends up around 1.76 or 1.77. That's a bit hard to remember, so let's genericize it a bit: Rule: VS=1.8*GPA*GSFor common examples, that gets us within 10-20 FPM, which is less error than our instruments show anyway. Any time I see a plate with non-standard glide paths, I annotate the target VS (rounded to the nearest 10 FPM) based on some ground speed inputs (to account for headwinds) and call attention to the non-standard glide path: Knowing what the target descent rate should be also helps smooth out corrections better than chasing the glide path diamond. If you're a bit high and you know you should be at 600 FPM, maybe try 650-700 until you start to bring it back in, then re-intercept the target value. This practice is also good for flying CDFA approaches more precisely if there's no vertical guidance.
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The first time I flew an arc approach in the simulator during my instrument training, we tried the VOR-A into Paine Field, and my approach ground track looked something like this: I told myself, and my amused CFII, that I wouldn't do that again, and that there must be a better way to turn inbound on that arc, and set about figuring out what that would look like. I sketched it out a bit to look like this: The goal is to find the leadoff angle (LA), and from that derive the turning radial to roll out right on center. We already know about the relationship between our ground speed and the turn-in arc flown and the radius of that arc, so we can use that go get started. Looking at that little box on the left, we have a nice right triangle of base DME and height AR. Thus, the tangent of LA is AR/DME, or LA=atan(AR/DME). All we now need to do is whip out our calculator when we're in the soup and punch in LA=atan[(GS/188)/DME], no pressure. Don't forget to make sure it's not in radians mode. Maybe a bit of turbulence will help you fat-finger it and send you off course, just make sure cumulus granitus isn't nearby when losing situational awareness.
We obviously don't want to be fiddling with calculators in flight, so let's make up a rule that will work to approximate this. Because AR scales linearly with GS, and DME affects LA, I figured it had to be some function of GS/DME. I tried a few combinations and came up with the following: Rule: LA=GS/3*DMEThis works when the angles are fairly small, which they usually are. Applying this to the example of the Paine VOR-A approach flown at 100 kts: Trig: LA=atan[(100/188)/9]=3.38 degrees Rule: LA=100/(3*9)=3.7 degrees The rule gives you an answer that's about 10% too aggressive which is mostly trivial in a world where our instruments only go to full degrees. If you're on a small arc like 5 DME and you're doing 150 knots, it'll be a full degree early, but you can roll out a tad slowly and nobody would be any the wiser. The next time I flew the VOR-A with my instructor, I told him about the rule and set the CDI to 156 degrees. As soon as we crossed the radial I started the turn, then adjusted the CDI to the 160 inbound, and rolled out right on the needle. Now that I've started teaching it myself, I tell learners to pre-calculate the turn-in radials and scribble them on the plate to make life easier for themselves: When flying DME arc approaches, we need to turn on or off the arc, often at 90-degree angles. To do this precisely, it's good to have a simple rule to get it right, so that we can either be right on the target DME value, or roll out right on the inbound course. Fortunately, the way we're supposed to fly makes it relatively straightforward to compute when to turn. If we make standard-rate turns of 3 degrees per second, then a 90-degree turn will take 30 seconds. Over that time, we'll fly an arc A with radius AR. Because we always fly 30-second (half-minute) turns, the length of A will simply be our speed divided by that half minute. In a no-wind scenario, we'd use TAS as our metric, but then we might get pushed long or short if we have a headwind or tailwind. Thus, if our goal is to roll out on the 90-degree course, we're better off starting with GS, although in quartering crosswind scenarios that might put us slightly off. To get from knots to nautical miles, we just divide by 120, because there are 120 half minutes in an hour. Thus, A=GS/120. To get AR, we look at some more basic geometry, namely the relationship of circumference to radius, 2πr. In our case, we're flying a quarter circle, so A=(2πAR/4). If we approximate π to 3.14, then that gives us A=1.57AR. If we're after AR, we can invert that to get AR=.64A. That in turn means that AR=GS/(1.57*120)=188. Fortunately, 188 is within 6% of a nice big round number, namely 200, so we can use the following approximation:
Rule: AR=GS/200So if we're flying along at 100 knots, we turn in half a mile short of the perpendicular course. |
## AuthorMerlin is a pilot, cyclist, environmentalist, and product manager. ## Archives
May 2022
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