 # Descent calculation fundamentals long hand

Today’s lesson is in decent calculations. The long hand way. This is so everyone has a better understand of what is actually taking place, and how to better plan. I figured I’d do this by all the different responses Here. This can also be used for a stepped decent, it just needs to be calculated differently.

Glide path

For this all we are doing is figuring out the sides of a right triangle. H = 30,000 feet
D = ?
GD = 90 NM

1NM = 6076 feet
30,000 feet ÷ 6076 = 4.94 NM

4.94² = 24.40
90² = 8100

8100 - 24.40 = 8075.6
D = √8075.6
D = 89.86 NM

So now how do we find the glide path angle?

So now we take out GD which is 90 ÷ that with our height which is 4.94 then sin¹.
So 4.94 ÷ 90 = .054
sin¹ .054 = 3.14°

So now what if we knew our glide slope, but didn’t know how far out to start our decent?

So for this let’s say we are going into EGLC with a glide slope of 5.5° we are cruising at 30,000 feet again.

So first we need to put our 5.5° back into something we can use.

sin 5.5° = .096

So now we need to figure out what 4.94 ÷ ? = .096
So 4.94 ÷ 51.5 = .096

There for 51.5 is going to be our GD at the same height as before for a 5.5° decent.

Our ground distance for this would be?

4.94² + D² = 51.5²
24.4 + D = 2,652.25
2,652.25 - 24.4 = 2,627.85
√2,627.85 = 51.26
D = 51.26 NM

So the reason I drew this all out is because the basic height X 3 = your distance to descend isn’t always an accurate way of doing it. It works for a 3° glide slope but nothing else.

How fast should my V/S be?

Alright so taking what we learned from above we are also going to apply it here a bit. The question you need to ask prior to asking how fast should my feet per minute be? We need to ask What should my feet per NM be? this is where you will get your true answers. So in RL we figure out our ground speed by timing our known distance then figuring it out. Or if we have a GPS installed it does the work for us.

Since I don’t want to leave you guys short let’s just quickly do a ground speed equation.

So we traveled a 50NM leg in 10:00 what is our ground speed?
50 × 6 = 300
So we where traveling 300 kts per hour.
Easy right?

So now that we know our ground speed, and we know our distance to start decent for a particular glide slope. Now we can figure out our feet to loose per NM.

Let’s say our airport elevation is 1,000 feet. So we are cruising along at 30,000 feet which puts the distance to loose at 29,000 feet.

30,000 − 1,000 = 29,000

We are traveling at 300 Kts per hour, and our distance for the 3.14° glide slope is 90 NM.

We first figure out our feet/NM

29,000 ÷ 90 = 322.2

We need to loose 322.2 feet per NM. Now let’s figure out our FPM. (Feet per minute)

300 ÷ 60 = 5
We took 300 kts divided that by 60 minutes which gave us 5 NM a minute.

322.2 × 5 = 1,611

Then we take our 322.2 feet we need to loose per mile, and times that by how many miles we go in 1 minute which gives us a FPM of 1,611.

As our altitude decreases along with our speed our FPM is going to change as the speed decreases. However our Feet per NM will always remain the same.

So if we do the short cut of GS × 5 =

We get 300 × 5 = 1500

Close but still not 100% right?

So as you can see the short cuts do help in quickly planning. I made this so you can all have an actual understanding of how to come up with the correct answer. By no means am I saying don’t use the short cut. If your going to use the short cut though you might as well know how it’s really calculated.

Aviation shortcuts

How to calculate ToD rule of thumb

If you guys find more shortcuts feel free to post them in the comments, and I’ll add them.

90 Likes

Great tutorial, definitely needed.

7 Likes

Back to school stuff, well maintained; Well done

4 Likes

Off to geometry class we go. @GHamsz would be proud 😂

11 Likes

Nice, this will actually be extremely helpful for all!

1 Like

When global comes around, my descents are going to be based off of STAR charts. But for now, my “shortcut” is just assigning an altitude to a waypoint, and using the time to that waypoint to calculate the descent rate. So if I am 2 minutes away from point a, want to be at 5000 feet when I cross a, and am currently at 8000 feet, I know that I need to descend at a rate of 1500 fpm in order to maintain the descent path I want to follow.

2 Likes

This is why Geometry is easier than Algebra (for me at least). After reading this tutorial, I’m actually really proud of myself for getting an education at school. I’m really proud of myself for loving to go to school so much. This is how you get a good job: go to school!

Yep, this tutorial is great and is needed indeed for your flight! I’ll use this in my next flight :)

7 Likes

Stars don’t give you hard altitudes to follow along the entire approach, so you would still need to calculate your decent to a degree.

This would work if your ground speed remained the same but since it changes as you loose altitude you would also need to adjust that VS. good trick non the less.

6 Likes

I’ve been trying to avoid anything math related for the remainder of my summer vacation, Brandon. Looks like I made a mistake by clicking on this topic.

I don’t want to be the one here to repeat others, but in this case, I will; great topic you have here! This was definitely well thought out and you should be commended for it. A little math definitely does come a long way and it’s good to pass on your advanced knowledge to the community.

I will be sure to use this method for the future. :)

14 Likes

😂 thanks. I figured you need to know the long way to know the errors in the shortcut way.

3 Likes

I was told there would be no math…

This is why I liked to be able to pick up the slope 85 miles out so I can start my descent. lol

5 Likes

Good work! Is this what physics is like?

Nope geometry, physics would be a plane weighs this much, and is traveling this fast. If it stopped moving in a milisececond it would impact with this much force.

5 Likes

This post is amazing. Thanks so much Brandon… Is the title supposed to say “long hand”? ;).

1 Like

Yes that means long / full version

1 Like

Great piece, your info was spot on. May you always find blue skies…

MaxSez: Being a Pilot "Nobody said it was gonna be easy or promised ya a rose garden! @Brandon_Sandstrom, Well done again, pretty soon your gonna need a Flag Locker. 6 Likes

This post reminds me of my school’s Math exam 😂 (Geometry, Algebra are merged into one class in here, Math). But as others said, awesome job for making a great tutorial for users in here 😊. I do hope this tutorial would help many users in here. Once again, thanks alot Brandon! 😆

2 Likes

How do you find the glide distance?

Is there a shorter way to do this?