I had this Easy Mental Math for Pilots article from Boldmethod in my email this morning.  I’m sure many of you have a few memory items for quick and dirty calculations that you use, but, just in case there are a few new A320 or CJ4 sim pilots out there that have not spent most of their lives in a descent profile or sliding down the ILS in a thunderstorm with a wet behind the ears copilot, I thought I would pass this along.

Easy Mental Math For Pilot

 

 

If you're like us, you probably don't consider yourself a math expert. Here are a few easy tips and tricks you can use to make mental math in the cockpit a little easier...

Descent Planning Mental Math

There are three basic steps to follow when planning your descent:

• Step 1) How much altitude do I need to lose?
• Step 2) How much time to reach the fix?
• Step 3) Altitude to lose / Time = FPM Descent Rate

If you're supposed to answer a mental math question for an interview or test, stick to whole, even rounded, numbers. You're not expected to be a flight computer!

Step 1: How much altitude do I need to lose? When you're doing this, stick to rounded, whole numbers. Do you need to lose 5, 10, 15, or 20 thousand feet? That's the altitude value you'll want to keep in mind.

If you need to lose 3,800 feet, round up to 4,000. In most cases, that will make your mental math a lot easier. More on that in a bit...

Step 2: How much time to reach the fix? This is a two-step process. First, you'll figure out how many miles-per-minute (MPM) you're flying.

Think in multiples of 60

60 knots is 1 mile per minute. 120 knots is 2 MPM. Double that (240 knots), and you're going 4 MPM. If the numbers seem too big to work with, take the zero away and make the values 6, 12, or 24.

For example, let's say you're going 180 knots. 6 goes into 18 three times, so that's 3 MPM.

• 60 knots = 1 MPM
• 90 knots = 1.5 MPM
• 120 knots = 2 MPM
• 150 knots = 2.5 MPM
• 180 knots = 3 MPM

Remember, these speeds are ground speed. When it comes to figuring out your MPM, ground speed is the only speed that matters.

Now that you've got the "miles per minute value", let's look at how far you need to fly.

If you need to fly 20 miles, and you're flying 2 MPM, it'll take you 10 minutes to reach the fix (20 miles / 2 MPM = 10 minutes).

Step 3: Altitude to lose / Time = FPM Descent Rate... Here's an example of a calculated descent rate:

Other Uses For The 60-1 Rule

The basic rule says "at a 1 degree slope (or 1 degree on your attitude indicator or HSI), it's going to be 60 units horizontally for 1 unit vertically." But how else does this apply to your flying?

VOR Courses

If you're flying towards a VOR and you're 1 degree off course at 60 miles, you're 1 mile off track. If you're 2 degrees off track at 60 miles, you'd be 2 miles off track. At 30 miles and 1 degree of deviation, you're 1/2 mile of track. And at 15 miles and 1 degree of deviation, you're only 1/4 mile off track.

DME Arcs

This math can help with flying arcs too. A question you might get during an airline interview is, "how long is this arc segment?"

Let's take a look at this unusual DME arcing approach.

In an arc is 14.7 DME from the VOR, let's call that 15 miles. At 15 miles, every degree flown around the arc takes 1/4 mile. If the arc spans from radial 334 to 060 degrees, that's 86 degrees.

Since every degree of the arc is .25 miles, what's a quarter of 86? Without a calculator, you probably can't work that out in your head.

But, what's a quarter of 80? It'd be 20! (80 / 4 = 20) Since we took 6 off of 86 degrees to make the math easy, let's work on that remaining 6. One-quarter of 6 is 1.5 miles.

So in this quesiton the arc segment is 21.5 miles long (20 + 1.5 = 21.5 miles).

Descent Angles

If you know your flight path angle (FPA), which you'll often find in modern flight decks, the 60-1 rule can make mental math descent planning easy.

For every 1 degree of descent angle, you'll descent 100 feet for every 1 mile you fly.

For example, if you're descending at a 3 degree angle for 3 miles, you'll descend 900 feet.

There just may be a hint or shortcut here that you can use so you don’t have to break your immersion looking for a calculator.

Regards,

Ray

And a few more useful ones from the comments section.

The most common one for me (Cargo Caravan Captain) - jet fuel - pounds to gallons. Always done in a hurry with the fuel truck guy there, and if you're wrong, it is a troublesome mess to fix, especially if overfueled. So, make it easy. Take the pounds required, add a half, drop a digit. Example: need 1000 pounds? Add half - 1000 >> 1500. Drop a digit. 150 gallons. Almost exacfly.  

Similar rule for Avgas at 6# a gallon: Add 2/3 instead of a half and drop a digit. 100# converts to 17 gallons (actually 102# but that's close enough for me)

 

Good applications for the "Rule of 60", but descent planning can be even easier.  Just remember these two things:
1) For a 3° path you should be about 1000' for every 3 miles from the threshold. If you're 30 miles out then you should be at 10,000'. You should cross 3000' when you're 9 nm out.
2) Descent angle is just 5x your ground speed (or half x10). If you're ground speed is 120 kts then your descent rate should be 600 fpm, 180 kts = 900 fpm. Adjust as required to get and stay on the path defined by the first rule.

Ray

 

Some from me:

Determine x-wind component.
Find the difference in runway heading and wind direction. Then apply that to a watchface minutemarkers (1-60) and the see how much of the face your angular difference covers.
Runway bearing: 300 magnetic

Tower winds: 270 / 10kts

Angular difference= 30 degrees. 30  degrees (or minutes...) is 50% of minutemarkers on a watchface. X-wind component is 50% of 10 kts.

(note, everything above 60 degrees is treated as 100% x-wind component in GA flying)

Standard turn estimation:
You've lost your turn/rate gyro and your instructor orders you to fly an NDB hold using standard rate. Simply divide your TAS / 10 and add 7. 
for 120TAS this would be 12+7 =  standard rate for your speed is 19 degree AoB.

Stall speed / Load factor relationship in steep turns
A 60 degree AoB in level flight will put the load factor at 2G. But stall speed is "only" increased by 40%. (100% occurs at roughly LF 4,4/75 degree AoB)

Edited November 20, 20214 yr by SAS443

Great post, thanks for sharing. Mental math is not my strongpoint and I have come to rely on LNM or the Garmins to show me the descent data. Never hurts to get the ol' brain going and doing some calculations! 

3 hours ago, raymar said:

Good applications for the "Rule of 60", but descent planning can be even easier.  Just remember these two things:
1) For a 3° path you should be about 1000' for every 3 miles from the threshold. If you're 30 miles out then you should be at 10,000'. You should cross 3000' when you're 9 nm out.
2) Descent angle is just 5x your ground speed (or half x10). If you're ground speed is 120 kts then your descent rate should be 600 fpm, 180 kts = 900 fpm. Adjust as required to get and stay on the path defined by the first rule.

1. Said another way, for a 3 degree descent, the distance in NM between your Top of Descent and Bottom of Descent will be 3 x (number of 1000s of feet you have to lose). So if you have to lose 15,000 ft you want to start 3x15 = 45NM from the bottom of descent point with a descent RATE in ft/min of 5 x ground speed.

2. Descent rate of 5x ground speed for a 3 degree descent is not only handy for a cruise descent, but also for an approach. A typical ILS Glide Slope or RNAV Glide path is about 3 degs. So 5 x ground speed will give you a good idea on what descent rate will be needed to hold the glide slope/path, e.g., at 90Kts ground speed you will need about 5x90 =  450 ft/min during the approach.  This is particularly useful when no vertical guidance is available such as on a CDFA non-precision approach since again something close to 3 degs is typical  

Al

Edited November 20, 20214 yr by ark

Another convenient way I like to calculate descent rate is Descent rate (ft/min)  = ft/NM to lose x NM/min (ground speed). 

So using the Bold Method example above, if you have to lose 4000ft in 20 miles, that's 200ft/NM assuming a constant rate of descent.  If your ground speed is 120Kts, that's 2NM/min. So the descent rate you need is 200ft/NM x 2NM/min = 400 ft/min.  What I like about this method is there is no need to directly calculate the time for the descent.  This calculation does not assume a particular descent angle (descent angle in this example is about 2 degs)

Al

Edited November 20, 20214 yr by ark

3 hours ago, SAS443 said:

Standard turn estimation:
You've lost your turn/rate gyro and your instructor orders you to fly an NDB hold using standard rate. Simply divide your TAS / 10 and add 7. 
for 120TAS this would be 12+7 =  standard rate for your speed is 19 degree AoB.

Another formula for Standard Rate Turn is 15% of TAS.  So for 120Kts TAS we get 18 degs -- close to the above. 

BTW, a convenient way to calculate 15% is to take 10% and then add half of that value. So 10% of 120 is 12, and half of 12 is 6, 12+6=18. That much I can do in my head when flying, but not much more! 🙂

And since we are talking about TAS,  one way to estimate TAS = indicated airpspeed + 2 percent of your indicated airspeed for every 1000ft of altitude.

TAS = IAS + 2%(IAS) x (ALT/1000).  So if we have an indicated airspeed of 100kts at 15000ft we get

TAS = 100 + 2 x 15 = 130Kts TAS

Al

Edited November 20, 20214 yr by ark