How do we turn our high altitude, high speed projectile into a graceful bird ready for approach at a lower altitude and reduced airspeed?
Yes, math is involved, but it is math you can do.
Figure: Descent options, from Eddie's notes.
We can sometimes be the master of our fates and start descent at our own discretion. Chances are your FMS has a "TOD" function, where it depicts a top of descent and maybe even gives you a count down. There can be a few problems:
For those days you are told to start down "at your discretion," give the FMS a vote, but you have the final decision. There are two good start down points depending on your airplane and your arrival expectations.
Figure: 3° Top of Descent, from Eddie's notes.
Air Traffic Control used to be designed around the idea most airplanes are most efficient flying a three degree descent and there are still parts of the world where you can do this. Figuring it is easy. The rule for descents is that your gradient equals flight levels divided by nautical miles to go. If you throw in a 3.33 degree descent, the math becomes easy . . .
We can hardly detect 0.33 degrees so we'll call it 3.
Rule of Thumb: Start descent at three times your altitude (in thousands of feet) to achieve a 3 degree descent.
If you are at 45,000 feet, for example, round the altitude up to 50, just to make things easy, and start down at 3 x 50 = 150 miles out. If you are descending to a high altitude airport, you may want to adjust for the field's elevation.
Figure: 2.5° Top of Descent, from Eddie's notes.
Not all aircraft can manage a 3 degree descent. The G450, for example, cannot do 3 degrees at high altitudes without picking up speed. It can, however, manage half a degree less. The math for a 2.5 degree descent is just as easy for 3.0 . . .
The actual math comes to 2.4°, which is close enough to 2.5°.
Rule of Thumb: Start descent at four times your altitude (in thousands of feet) to achieve a 2.5 degree descent.
If you are at 45,000 feet, for example, round the altitude up to 50, just to make things easy, and start down at 4 x 50 = 200 miles out. If you are descending to a high altitude airport, you may want to adjust for the field's elevation.
Figure:Gradient required, from Eddie's notes.
What happens if you don't have a choice and are told to get down within a fixed distance? You could program that into your FMS and chances are it will make it happen. But sometimes it doesn't. You should always come up with your own answer to check the FMS or to have a Plan B for the days the FMS throws up its hands and says, "I don't know, you do it."
You can compute a required descent gradient by dividing the flight levels to lose by the nautical miles to go. (See 60 to 1 for an explanation of why.) Once you have that, you can compute a desired VVI. (More on that after an example.)
Rule of Thumb: Required descent gradient = flight levels to lose divided by nautical miles to go.
So there you are:
Photos: from Eddie's aircraft.
You are at FL410 and they gave you direct ALB with 435 nm to go and you have absolutely nothing to do for the next 48 minutes. But then they throw in a curve ball: "Cross 100 miles west of Albany at 10,000 feet." No problem, says you, just enter ALB//100/10000 in the line above ALB in the FMS and the box does everything for you. But then, for some reason, the airplane flies right through TOD. Maybe you never hit the VNAV key, maybe the PM put one fewer slash on the FMS command line than Mister Honeywell expected, or maybe there is a gremlin in the system. But you are behind in the game now.
How could you have detected this earlier? Well, once you typed in all that data you could have taken one more step. Figure a start descent point on your own. For a three degree descent you would have to start down no later than:
At this point I would brief the PM, "If the box doesn't start us down 193 miles from ALB, I will.
But that is water under the bridge. You are now at FL410 at 180 DME, you only have 80 miles to go. The flustered PM can't seem to get the FMS to communicate and you need to get down. You can hit Flight Level Change, pull out the boards, and end up droning for a few miles, red-faced. Or you can start the nose down and do some quick mental math.
Figure: Gradient example, from Eddie's notes.
We know the descent gradient is equal to the flight levels to lose divided by the nautical miles to go, but the math
isn't so straight forward.
We want to do this without a calculator, slide rule, or Stephen Hawking in the jump seat. Well, 8 is a factor of 32 — it divides easily — and if we can make the gradient with 320 flight levels to lose we can certainly do it with only 310 flight levels. And that makes life for us as pilots easier:
If we achieve a 4° descent gradient, we will make it to our restriction with room to spare. So leave the boards stowed for now and see what kind of VVI we've got with the power levers at idle.
60 to 1 tells us that nautical miles per minute times the descent gradient times 100 gives us our required VVI. But we don't have a meter that tells us our nautical miles per minute, do we? Most modern cockpit do have a ground speed readout, however, and that is easily converted.
Rule of Thumb: Required VVI = Required Descent Gradient times (nautical miles per minute) times 100.
It is easier if you break this down into steps. Take your ground speed and divide by sixty and round that to the nearest number. Back to our example:
In our Boston example we see our ground speed is 542 nm/hour so:
So we are looking for 3,600 fpm. If idle and clean gives us that, we are good to go. Not enough? Sneak just enough boards out to get it.
Once we've started down we should make occasional progress checks to make sure our initial math was okay and that the winds aren't changing the conditions on us. As we descend, picking the right altitude or distance can simply for math. For example . . .
Figure: Progress check, from Eddie's notes.
Let's say in our example we started down a bit aggressively, trying to take care of the steepest part of the descent early. We should pick easy altitudes to give ourselves a progress check. Perhaps crossing FL250 we find ourselves at 150 DME:
So we've caught up on the descent and now have a nice, normal, three degree gradient in front of us. Our ground speed will have decreased with altitude, of course, and now reads 350. We can round that up to 360 so we have 6 nm/min, which makes the required VVI easy:
Most airplanes are happiest when descending on a 3 degree glide path all the way from altitude to touchdown. Some, like my G450, can't quite manage the 3 degrees at high altitude without accelerating, but generally speaking 3 degrees is the magic number.
Is this number magic or is it related to the 60 to 1 cult many of us belong to? Neither. It is simply math: if you multiply the distance to go (in feet) by the tangent of 3 degrees you get the height at that point (in feet). For a 3 degree glide path that comes to 318 feet every nautical mile. Or you can round that to 320 feet per nautical mile, or even 300 feet per nautical mile.
More about this: Trigonometry.
What if the math just doesn't work in your head? I can offer three solutions:
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