INSTRUMENT FLIGHT      

60-TO-1 RULE (FORMULAS)

What is the 60-to-1 rule and why should you use ıt ?

 

It's a technique for establishing predictable pitch change and lead point for intercepting courses orarcs. Listed below are three good reasons for using this rule.

It allows the pilot to compute the pitch change necessary when establishing an altitute during the control and performance concept (establish pitch ,trim,and cross-check) of altitute instrument flying .

It reduces the pilot workload and increases efficiency by requiring fewer changes and less guesswork.

 

When Do You Use The 60-to-1 Rule ?

 

Here are examples of the types of pilot problems that can be readily solved by applying the 60-to-1 rules.

You're in level flight and flying 400 ktas airspeed and you want to establish a rate of climb or descent of 1000 feet per minute (feet/minute). What pitch change will give you the desired rate of climb or descent.?

You're 80 DME at DME ,at FL 310 to inbound to YAA VOR ,and you want to cross YAA vor at 5000 feet. When should you start your descent and What pitch change should you make to do that ?

You're climbing at 3000 feet/min at 250 kıas. Wpitch change will be necessary to level your aircraft at FL 350

 

How to Work With the 60-to-1 Rule

 

The 60-to-1 rule gives us a mathematical equation to help you figure out all these questions ,but ıt's almost impossible to turn these calculation and fly at the same time.You need to use these formulas before you fly. Find out what your turn radius is at cruise airspeed up high and at appoach airspeed down lower , find out what a 1° pitch chance will do to your VVI ,and remember those number. Take your appoaches out prior to flıght and write in your lead radial and VVI's right on the IAP .

 

Mathematical Data Supporting the 60-to-1 Rule

 

Let's relate this to a VOR station .We know that the formula for the circumference of circle = 2p r. Therefore ,the circumference of a 60 NM circle around our VOR is

C= ( 2 ) ( 3.14 ) ( 60 )

C= 376.99 NM for a 60 radius circle.

Because there are 360° in a circle ,we can determine the length of a 1° arc

376.99/360 = 1.0472 or approximately 1 NM per degree at 60 NM

Because 1 NM = 6,076 feet or approximately 6000 feet ,we can therefore say

1° = 6000 feet at 60 NM This relationship is true not only in the horizontal plane ,but also in the vertical plane .If wwere make a 1° dive than we would have descended 6000 feet

( 1 NM ) after traveling 60 NM .Though the magic of algebra ,we can break this down to 100 feet per NM for a 1 °dive or picth change.

 

VVI Versus Pitch change .

 

We know now how to calculate the altitute gained or lost for each degree of pitch change over a gıven distance . Throw in a time factor using True airspeed ( TAS ) expressed in NM and we can relate this pitch change to a change in VVI .

Let's convert to speed to NM / MIN ,since the 60-to-1 rule is based on True air speed (TAS ) experssed in NM / MIN.

NM / MİN can be obtained easily from either TAS or the Indicated mach Number

( IMN ) as follows.

*** Directly from TAS :

TAS/60 =NM/MIN

EXAMPLE : 420 TAS/60 =7 NM/MIN

*** From IMN :

IMN x 10 = NM / MIN

Example : 0.7 mach x 10 = 7 NM / MIN

If you don't have a TAS indicator or an IMN , TAS can be compute from indicated airspeed ( IAS ) . TAS increases over IAS at the rate of 2 percent per 1000 feet altitute imcreas . so use the equation :

TAS = IAS + ( 2 %per 1000 feet )x (IAS)

Example : FL 200 ; 270 KIAS

TAS = 270 + ( 2 %. x 20 ) ( 270 ) = 270 + (0.40 ) x (270) = 378 KTAS

Another easy but less accurate formula ( best between 10.000 feet and FL 350)

TAS =FL/2 + IAS

example : FL 200 , 270 KTAS

TAS =200/2 + 270 = 100+ 270 = 370 KTAS

 

NOTE : These basic expression of TAS and NM / MIN will be used often in future discussions.

 

If one degree equals 100 feet per NM ,then our VVI can be calculated by :

VVI = NM / MIN x100 feet

Example : For 0.6 mach and a 1° pitch change :

IMN x 10 = NM / MIN

0.6 x 10 = 6 NM / MIN

VVI for 1° pitch change = NM / MIN x 100 = 6 x 100 = 600 feet / NM

Example 2 : for 420 KTAS and 2 ° pitch change :

TAS/60 = NM/MIN

420 KTAS/60 =7NM/MIN

VVI for 1 ° pitch change = NM / MIN x 100

VVI for 2 ° pitch change = 2 x NM / MIN x 100 = 1400 feet /mın

 

Descent Gradient s for Approach or Enroute Descent

 

Let's look at a real world you on airway VA 16 north east bound to Istanbul and

ATC direct you to cross the YAA VOR at 12.000 feet . According the first calculation you are 25 NM from YAA VOR , and cruısing at FL 270 with mach 0.75 What descent gradient is requıred and what VVI should you expect ?

First you need to know what your descent gradient has to be. You can find the descent gradient by applying the 60-to-1 relatıonship of 100 feet per NM. To lose

15.000 feet in 25 NM you will need a descent gradient of 600 feet/nm or about a 6° pitch change. Here is the math.

descent gradient = 100 of feet / Distance in NM = 150/25 = 6

Now you what descent gradient is required, you can compute what your VVI should be if you make a pitch change of 6° while flying at .75 mach . In thıs case your VVI will be 4500 feet /min to begin with. If you hold 0.75 mach all the way down ,the Vvı will work.

IMN x 10 = NM / MIN

0.75 x 10 = 7.5 NM / MIN

 

VVI = angle ( NM / MIN * 100 ) = 6 ( 7.5 * 100 ) = 4500 feet / min

 

If you maintain an IAS throughout the descent .as many of us do, then your TAS will decrease as you get lower altitute. VVI required to maintain the 6° descent gradient will slowly decrease as you descend. IF you hold 4500 feet / min all the way down to 12.000 feet ,yıu will get down early. The most important part of the quation ( which remains constant no matter what speed you are flying ) is the descent gradient. You must descend at 600 feet / min ( or about 6°) in order to make to altitute restriction at the YAA VOR.

 

Climb Gradient

 

As you might suspect, computing a climb gradient is really no different than the enroute descent calculations, but let's run an example to see how it's done. Let's say you are getting ready to fly a Standard Instrument Departure (SID). You look at the plate and see that you will need a climb gradient of 350 FEET/NM to 10,000 feet. So, we need to climb out at 3.5° angle. Our best climb air speed is 200 KIAS. The airport is 3,000 Feet MSL.

**** First we need to calculate our TAS. In this case, 200 KIAS at 3,000 feet MSL works out to 212 KTAS and 200 KIAS at 10,000 feet MSL is 240 KTAS. Dividing each of these by 60 will give you your speed in NM/MIN at 3,000 and 10,000 feet respectively.

At 3000 feet MSL

TAS = IAS + ( 2% per 1000 feet ) = 200 + ( 3 * .02 * 200 ) =200 + 12 = 212 KTAS

NM / MIN = TAS / 60 = 212 / 60 = 3,5 NM / MIN

At 10.000 feet MSL

TAS = IAS + ( 2% per 1000 feet ) = 200 + ( 10 * .02 * 200 ) =200 + 40 = 240 KTAS

NM / MIN = TAS / 60 = 240 / 60 = 4 NM / MIN

**** Next calculate your VVI. Immediately after takeoff , your VVI will be 1,225 feet / min

As you climb (and your TAS increases ) , your VVI will slowly increases to approximately

1.400 feet /min . There are couple of tecniques to deal with the change in TAS. One tecnique

is to use the higher VVI ( 1,400 feet / min ) throughout the climb. Another way to figure a target VVI is to use an average true airspeed ( for example , using your TAS at 6.500 feet MSL)better yet use groundspeed instead of TAS - using groundspeed accounts for the wind.

At 3.000 feet MSL

VVI = Angle ( NM / MİN * 100 ) = 3.5 ( 3.5 * 100 ) = 1.225 feet / min

At 10.000 feet MSL

VVI = Angle ( NM / MİN * 100 ) = 3.5 ( 4.0 * 100 ) = 1.400 feet / min

Next :

We are going to discuss some formulas about calculating a Visual Descent point (VDP) Precision Glide path , Turn radius ,Lead point (SURF IN SKY magazine August 2000)