Descent formulas

[HalinTexas]

It's ground speed.

Recalculate once or twice on the way down. Winds change, so airspeed changes. If your vertical descent speed doesn't match your calculations then you'll need to adjust it. Most turbine aircraft can descend at the required speed, but recalculate anyway.

 

[CX880]

• If you are 200 miles out @ 310, ATC wants 110 @ 40 DME, when do you descent ( I WAS THINKING 80 MILES BEFORE THE 40 DME, ANY INSIGHT ? )
• At 2000 feet on localizer, 5 miles back, where do you expect glideslope to be (This one is confusing 5 miles back from where ? Typical 3:1 here however )

1. You need to loose 20,000 feets. That's 60 miles. So that means you need to descend 100 miles out. Gspeed times 5 for rate of descent

2. Your high

 

[JustaNumber]

Dividing numbers that large in my head makes me feel ill.

It's not as hard as it first looks. Here's how to do it easily (and impress your captain/fo at the same time):

Everyone knows that certain numbers are easily divisible by 3 (3,6,9,12,15,18,21,24,27,30,etc.). If you have to lose 18,000', it's 60 miles; if you have to lose 21,000', it's 70 miles. But what if your altitude is in-between those numbers? Notice that there are always only two choices (in this case 19,000' and 20,000'). The lower of the two choices will be 63.333 (call it 63); the higher of the two will be 66.667 (call it 67). The lower number will always end in 3, the higher will always end in 7.

Try another example: 13,000'--it's closest to 12,000', so the distance will be 43 miles. 14,000'--it's closest to 15,000', so the distance will be 47 miles. This always works, and with a little practice you can look at a number and tell instantly what the correct distance is.

This method is especially useful for the precision necessary for approach descent planning, particularly the op's original question about being at 2000' and 5 miles out--where is the G/S? At 2000', that's closer to 2100' (which would be 7 miles) than 1800' (which would be 6 miles), so you need to start down 6.7 miles out. If you indeed are at 2000' at 5 miles, you're WAY high! (You should be at 1500' at 5 miles). If you're still confused, just ask the guy sitting next to you.

 

[Clutch]

2. Your high

So... I'm on vacation.. Eff you!

 

[RJLoser]

It's not as hard as it first looks. Here's how to do it easily (and impress your captain/fo at the same time):

Everyone knows that certain numbers are easily divisible by 3 (3,6,9,12,15,18,21,24,27,30,etc.). If you have to lose 18,000', it's 60 miles; if you have to lose 21,000', it's 70 miles. But what if your altitude is in-between those numbers? Notice that there are always only two choices (in this case 19,000' and 20,000'). The lower of the two choices will be 63.333 (call it 63); the higher of the two will be 66.667 (call it 67). The lower number will always end in 3, the higher will always end in 7.

Try another example: 13,000'--it's closest to 12,000', so the distance will be 43 miles. 14,000'--it's closest to 15,000', so the distance will be 47 miles. This always works, and with a little practice you can look at a number and tell instantly what the correct distance is.

This method is especially useful for the precision necessary for approach descent planning, particularly the op's original question about being at 2000' and 5 miles out--where is the G/S? At 2000', that's closer to 2100' (which would be 7 miles) than 1800' (which would be 6 miles), so you need to start down 6.7 miles out. If you indeed are at 2000' at 5 miles, you're WAY high! (You should be at 1500' at 5 miles). If you're still confused, just ask the guy sitting next to you.

Last Transmission was broken and stupid.

 

[JustaNumber]

Last Transmission was broken and stupid.

That's okay. Some pilots like to improve their mental abilities with age. Others prefer to be RJLosers their entire life. Take your pick.

 

[RJLoser]

That's okay. Some pilots like to improve their mental abilities with age. Others prefer to be RJLosers their entire life. Take your pick.

I don't see the positive outcome of over complicating things. If you want to whip out your math camp skills go ahead. My way worked in fast planes with no vnav as well.

 

[FO 4 Life]

It's not as hard as it first looks. Here's how to do it easily (and impress your captain/fo at the same time):

Everyone knows that certain numbers are easily divisible by 3 (3,6,9,12,15,18,21,24,27,30,etc.). If you have to lose 18,000', it's 60 miles; if you have to lose 21,000', it's 70 miles. But what if your altitude is in-between those numbers? Notice that there are always only two choices (in this case 19,000' and 20,000'). The lower of the two choices will be 63.333 (call it 63); the higher of the two will be 66.667 (call it 67). The lower number will always end in 3, the higher will always end in 7.

Try another example: 13,000'--it's closest to 12,000', so the distance will be 43 miles. 14,000'--it's closest to 15,000', so the distance will be 47 miles. This always works, and with a little practice you can look at a number and tell instantly what the correct distance is.

3 X the altitude = distance.
18k=54 miles
21k= 63 miles
1 mile for 10 knots airspeed to lose.

You are making stuff way too hard and simply wrong.

 

[JustaNumber]

3 X the altitude = distance.
18k=54 miles
21k= 63 miles
1 mile for 10 knots airspeed to lose.

You are making stuff way too hard and simply wrong.

Okay, rather than arguing, "you're simply wrong" back and forth, let's do the math and put this question to bed. I had always been told that you descend 300' per nautical mile in a 3 degree descent. If this is true, then my way would be the most precise, and your way would be "close enough." But let's see.

So let's break out the trigonometry: we're looking at a right triangle with the base being 1 nautical mile, and the height being the altitude to lose (we'll call it "x"). We would use:

tangent (angle)=opposite/adjacent
tan 3=x/(1 NM)
tan 3=x/6000'
x=6000(tan 3)
x=314.4
Therefore, in a true 3 degree descent, you descend 314.4 feet per nautical mile.

Given your example of a descent of 18,000',
your method = start down 54 miles out (18x3)
my method = start down 60 miles out (18/3)
actual answer = start down 57.25 miles out (18,000/314.4)

You're under by 3.25 miles; I'm over by 2.75 miles. Therefore, my method is a tiny bit more precise (and a little more conservative for those who don't want to bust an altitude), but it's not "simply wrong." Bottom line, use whichever method you want; there's nothing wrong with discussing why each method works, though. I'd suggest that doing the mental math for multiplying by 3 is often just as "making stuff way too hard" as dividing by 3.

Also, the poster who mentioned the need to recalculate descent rate as you descend due to changing winds made an excellent point. This is sometimes a factor, but the change in groundspeed due to the slowing of true airspeed as you descend is always a factor.

 

[wrxpilot]

You're under by 3.25 miles; I'm over by 2.75 miles. Therefore, my method is a tiny bit more precise (and a little more conservative for those who don't want to bust an altitude), but it's not "simply wrong." Bottom line, use whichever method you want; there's nothing wrong with discussing why each method works, though.

I know what you're saying, and technically you are of course correct. But in reality you aren't just going to make one mental calc and call it good for 60 miles, and just hope for the best. Things change along the way... Winds, TAS, temp, etc. So of course a good pilot is going to monitor his/her progress along the way for the crossing restriction. In the example given by the OP I would use 3:1 and begin my descent 60 miles out from the restriction. At about 30, I'd check again. I should roughly be around FL210. If no, then I'd adjust my descent rate accordingly. I'd check again at 20, and again at around 10.

VNAV or not, it's a very good idea to keep yourself in the loop. I used to fly an airplane that had more VNAV bells and whistles than most airliners out there (ProLine 21), but we still kept a check on things with a little bit of mental math.

It's pretty easy to get complacent with this stuff using VNAV and ATC in the USA, but even then there are times that you'll be left WAY too high if you're not used to quickly calculating a TOD in your head. Outside of the US, you'll definitely need to do this.

 

[JustaNumber]

I know what you're saying, and technically you are of course correct. But in reality you aren't just going to make one mental calc and call it good for 60 miles, and just hope for the best. Things change along the way... Winds, TAS, temp, etc. So of course a good pilot is going to monitor his/her progress along the way for the crossing restriction. In the example given by the OP I would use 3:1 and begin my descent 60 miles out from the restriction. At about 30, I'd check again. I should roughly be around FL210. If no, then I'd adjust my descent rate accordingly. I'd check again at 20, and again at around 10.

VNAV or not, it's a very good idea to keep yourself in the loop. I used to fly an airplane that had more VNAV bells and whistles than most airliners out there (ProLine 21), but we still kept a check on things with a little bit of mental math.

It's pretty easy to get complacent with this stuff using VNAV and ATC in the USA, but even then there are times that you'll be left WAY too high if you're not used to quickly calculating a TOD in your head. Outside of the US, you'll definitely need to do this.

Definitely great points, and you're right about how easy it is to get complacent.

 

[BoilerUP]

The mental math for cross-check starts getting a bit complicated when you're flying into a 50kt headwind and program a 4.5° descent to a crossing restriction...but in the end, 3:1 combined with a little of that "pilot sh!t" will get ya where you need to be.

...just don't forget 1 mile for every 10kts you need to slow...

 

[platinum750]

you guys r so gay

 

[CRJ puppy]

My eyes are bleeding...

 

[Flyer1015]

How much wood could a woodchuck chuck if a woodchuck could chuck wood?

 

[JustaNumber]

Dividing numbers that large in my head makes me feel ill.

Last Transmission was broken and stupid.

you guys r so gay

My eyes are bleeding...

How much wood could a woodchuck chuck if a woodchuck could chuck wood?

It's kind of sad that when you want to talk about pilot stuff on a pilot forum, particularly math formulas in a thread clearly titled, "Descent FORMULAS", that some of the responses would be so imbecilic. Whatever happened to intellectual curiosity, or even a vague desire to learn something new or become a more-informed pilot? Trying to be cool about being a moron surprises me most, though.

 

[CX880]

It's gone

 

[wrxpilot]

It's kind of sad that when you want to talk about pilot stuff on a pilot forum, particularly math formulas in a thread clearly titled, "Descent FORMULAS", that some of the responses would be so imbecilic. Whatever happened to intellectual curiosity, or even a vague desire to learn something new or become a more-informed pilot? Trying to be cool about being a moron surprises me most, though.

I was going to refrain from further comment on this thread, but you're absolutely right. I was actually fairly impressed that we were having such a discussion on Flightinfo, then the B-team had to pipe in. It's sad really, but not surprising I guess.

Those that have been proclaiming the downfall of our profession certainly do have all the proof they need here... Aviation is starting to attract some real winners.

 

[RJLoser]

It's kind of sad that when you want to talk about pilot stuff on a pilot forum, particularly math formulas in a thread clearly titled, "Descent FORMULAS", that some of the responses would be so imbecilic. Whatever happened to intellectual curiosity, or even a vague desire to learn something new or become a more-informed pilot? Trying to be cool about being a moron surprises me most, though.

Well..... my first post was correct (not moron) and on topic. The poking took place after you came to the table with smarty pants info. Relax a little.

 

[Clutch]

It's kind of sad that when you want to talk about pilot stuff on a pilot forum, particularly math formulas in a thread clearly titled, "Descent FORMULAS", that some of the responses would be so imbecilic. Whatever happened to intellectual curiosity, or even a vague desire to learn something new or become a more-informed pilot? Trying to be cool about being a moron surprises me most, though.

Personally, this stuff is private pilot garbage. But dont let me stop you guys from impressing yourselves.