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7.4.1 Computations

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Circular Slide Rule

The Circular Slide Rule The circular slide rule found on the reverse of the CRP5, if used effectively, can give reasonably accurate answers to calculations needed for both Flight Planning and General Navigation. The General Navigation examination will have numerous calculations which involve the CRP5. This document is an aide-memoire to help you in solving these questions.

The Slide Rule consists of two scales, an outer fixed scale and an inner moveable scale. Numbers are printed on both scales from 10 to 99.9. When doing any calculation you have to mentally place the decimal point before reading your answer off the slide rule. So 25 can represent any number you wish, for example .0025, .025, .25, 2.5, 25 etc. Note that the scale around the slide rule is not constant but logarithmic.

Multiplication, Division and Ratios

Multiplication

Consider the simple multiplication 8 X 1.5. By mental arithmetic we can easily see that the answer is 12. But we will use simple questions like this to illustrate how the CRP5 is used.

  1. Rotate the inner scale so that the number 10 is under the number 80 (We are using 80 to represent 8 and 10 to represent 1).
  2. On the inner scale go to the number 15 (1.5).
  3. Read off the answer above this number 12.
Division

Division is the exact opposite of multiplication. So using the same numbers for the multiplication let us divide 12 by 1.5. The answer is obviously 8.

  1. Place 15 on the inner scale under 12 on the outer scale.
  2. On the inner scale follow the numbers to 10.
  3. On the outer scale read off the answer 8.
Ratios

Any ratio can be read off the slide rule direct, so for A/B = C/D let us assume that A = 30, B = 15, D = 25 what is C?

  1. Place 15 on the inner scale under 30 on the outer scale.
  2. Follow the inner scale to 25.
  3. Read off the answer on the outer scale 50.
Conversions

Conversions use the same principal as the multiplication, division and ratio calculations.

To ensure accuracy the following rough conversions should be used from the ERSA.

The above datums are printed in red on the outer scale of the slide rule.

Feet – Metres – Yards Convert 3 feet into yards and metres.

  1. Under the feet arrow on the outer scale, place 3 on the inner scale.
  2. On the inner scale opposite the yards and metres datum arrows read off the answers 1 yard .915 metres.

Take-Off and Landing Wind Component

Aircraft are subject to crosswind and tailwind maxima. Both can be calculated using the square scale on the CRP 5.

Runway 31 is in use and the wind velocity reported by ATC is 270/40. Remember that the runway direction is in magnetic and the wind velocity reported by ATC is in magnetic. Find the crosswind and headwind component.

  1. Set the grommet on the zero point of the squared section as shown.
  2. Mark in the wind velocity as normal.
  3. Set the runway direction of 310M against the heading index.
  • The headwind is read from the horizontal zero line 30 knots
  • The crosswind from the vertical centre line 26 knots
Tailwind Component

Suppose that the wind velocity is 210/40 with runway 31 in use. Using the procedure above the answer shows that the wind point is above the zero line. This indicates a tailwind.

Bring the wind point to the zero horizontal line.

  • The grommet will give a tailwind of 7 knots.
Crosswind and Headwind Limits

Runway 21 in use. The wind direction is 180°M. A minimum headwind of 10 knots and maximum crosswind is 16 knots for this runway. What is the minimum and maximum windspeed.

  1. Set the runway direction against the True Heading index and place the grommet on the zero point.
  2. Mark in the maximum crosswind and minimum headwind for the runway as shown. The crosswind is blowing from the left. Wind always blows away from the grommet so the crosswind is drawn on the right.
  3. Set the wind direction against the true heading index.

Read off the maximum and minimum windspeed as shown:

  • Min wind speed 12kt.
  • Max wind speed 32kt.

Speed, Distance and Time

To calculate any of the variables remember that minutes is always on the inner scale. To remind you, the inner scale has minutes written in red between 30 and 35. The calculations work on the factor 60.

All speeds are a distance traveled in 60 minutes so all calculations revolve around this number. To help you with these calculations the number 60 is in white surrounded by a black triangle.

Groundspeed

An aircraft flies 210 nm in 25 minutes, what is the groundspeed

  1. Align the 25 on the inner scale against 210 on the outer scale
  2. Read off the groundspeed against the 60 triangle.
  • 503 knots.
Time

Using the same example. If the groundspeed is 503 knots, how long will it take the aircraft to travel 210 nautical miles.

  1. Align the 60 triangle on the inner scale against 503 on the outer scale
  2. On the outer distance scale go to 210. Read off the time on the inner scale.
  • 25 minutes
Distance Travelled

For a groundspeed of 503 knots, how far will the aircraft travel in 35 minutes.

  1. Align the 60 triangle on the inner scale against 503 on the outer scale
  2. On the inner minutes scale go to 35. Read off the distance traveled on the outer scale.
  • 294 nautical miles

Fuel consumption, fuel and time calculations are done in the same manner.

Calculation of TAS up to 300 Knots

Assume that the Pressure Altitude is 35 000 ft and the Corrected Outside Air temperature (COAT) is – 65°C. What is the TAS if the RAS (CAS) is 160 knots.

  1. Against the COAT of –65° C place the altitude of 35 000 ft as shown in the diagram.
  2. RAS (CAS) is found on the inner scale (To remind you this is written in red between 35 and 40.
  3. Read off the TAS against the RAS (CAS) of 160 knots
  • 275 knots

Triangle of Velocities

Computer Terminology
  1. Grid Ring: The scale around the rotatable protractor.
  2. Computer Face: The transparent plastic of the rotatable protractor.
  3. True or True Course Pointer: The reference mark at the top of the stock, reading against the grid ring.
  4. Drift Scale Scale on the top of the stock to the left and right of the true index. Note that the graduations are equal to those on the grid ring.
  5. The Grommet; The point or circle at the exact centre of the rotatable protractor.
  6. Drift Line: All the drift lines originate from one origin. The numbers on the drift lines indicate the degree of inclination to the centre line.
  7. Heading Line: The central line or zero drift line.
  8. Speed Circles: The arcs of concentric circles around the drift lines are equally spaced and graduated from zero knots up to any required speed. The scale is quite arbitrary. Each side of the sliding scale has a different speed scale, for the CRP5 this is:
    • Side shown: 40 to 350 knots
    • Other side not shown: 300 to 1050 knots

Before you start a flight along a track line you will need to prepare a heading to hold the aircraft on it that will prevent been blown off track by wind and compensate for any headwind or tailwind allowances in time and fuel by using groundspeed.

To help us to prepare a planned flight we calculate the Triangle of Velocities on the back of a Graphical Slide Fight Computer.

The Group of in the Triangle of Velocities are:

  • W / V (Wind Velocity)
  • TR / GS (Track and Groundspeed)
  • HDG / TAS (Heading and True Air Speed)

Use the Triangle of Velocities to find the expected Heading, Drift and Groundspeed with the following data:

Example:

A Track line measured with a protractor from the WAC is 290 degrees relative from true north. A forecast wind is 330T/30kt is relative from true north, and the area has a 10 degrees east magnetic variation. The TAS is 125kt taken from the aircrafts flight manual.

  • W/V 330T 30kt
  • TR 290T
  • TAS 125kt

When using a compass to navigate it always points to the magnetic poles (ignoring errors), so we will need to convert true bearings to magnetic bearings. When given wind directions as True North bearings covert it by adding the magnetic vaiation if it is on the west side of the nil magnetic variation line or subtract it if on the East side (most of Australia is on the east side). The lines of magnetic variation are found on a WAC for your area. Tracks drawn on a WAC are also relative to true north and need to be converted to magnetic bearings.

  • Wind 330T - 10E = 320M
  • TR 290T - 10E = 280M
  • TAS 125kt

Plotting Triangle of Velocities

  1. Start with the Wind Velocity:
    • Rotate the centre disc so the Wind Direction is under the index at the top of the flight computer.
    • From the grommet count UP the centre and draw a line to represent the Wind Speed (You could just put a dot to represent the wind speed).
    • At the top of the line is called the Wind Dot. The wind blows from the Wind Dot to the Grommet, as shown with green arrows.

  2. Rotate the centre disc so the Track is under the True Index at the top of the flight computer:
  3. Sliding the disk down the plate until the TAS is under the Wind Dot (TAS is represented as the arc lines).

You are done. Now it is just a matter of interpreting the numbers.

Read the Drift Angle (Degrees) where it crosses the TAS (Knots) under the Wind Dot. The wind is pushing to the left. The aircraft will have to balance the push by pointing the heading into the wind by 9 degrees right.

  • Drift 9 degrees left

Read the Groundspeed under the centre grommet. There is a headwind slowing the aircraft down relative to the ground.

  • Groundspeed 100kt

To find the Heading add the Drift to the Track if the Wind Dot is on the right of the centre line or subtract the drift to the Track if the Wind Dot is on the left of the centre line.

  • Heading 289 degrees

Wind Velocity Vector Plotting

  1. Start with the wind velocity:
    • Rotate the centre disc so the Wind Direction is under the index at the top of the flight computer.
    • From the grommet count DOWN the centre line and mark the Speed of the Wind. This mark is called the Wind Dot (The wind blows from the Mark to the Grommet).
  2. Rotate the centre disc so the HDG is under the index at the top of the flight computer.
  3. Sliding the TAS (that is written on the plate) under the Grommet.
  4. Read the Ground Speed under the Wind Dot.
  5. Read the Drift Angle (Degrees) where it crosses the GS (Knots) under the Wind Dot.
  6. To find the Track:
    • Add the drift to the HDG if the Wind Dot is on the left of centre line or minus if on right the right of the centre line.

Rates/Gradients of Climb and Descent

Aircraft take-off into wind. This gives the best climb gradient over the shortest distance. As the aircraft gets higher, the wind is stronger. This gives a much better rate of climb over the distance, than an aircraft taking off with a tailwind. In a tailwind take off the distance is increased across the ground.

The surface wind is slowed by friction. On average the surface wind slows by 2/3rd and changes direction by veering right.

Each aircraft has a best climb speed and this should always be used after take-off until a safe height is reached. Pilots of aircraft should read the aircrafts handbook for best climb speeds. Only when at a safe height should you adopt the cruise climb. For pilots the climb gradient must be that shown in the SID charts as a minimum. Noise abatement also comes in to play here. Remember the higher you are the less noise.

Let’s look at two aircraft taking off with the same airspeed and rate of climb. The first one takes off into wind, and the second one with a tailwind.

The aircraft taking off into wind will have travelled a much shorter ground distance to a height 2000ft compared to the aircraft taking off with a tailwind. The climb angle would also be bettered by at least 3 degrees. We will assume the wind to be 20 knots on the ground and at 2000ft it would be double. It is true the faster the aircraft fly’s the more lift it has, but you also have to realize the more ground you will cover before you get to the same height.

Let’s assume the wind is 20 knots and you take off at 140 knots. This means your groundspeed is 140 - headwind speed = 120 knots.

Now let’s assume you take off with a tailwind of 20 knots at a climb out speed of 140 knots, your groundspeed now will be 160 knots 140 +20. Some airfields have minimum climb gradients published for pilots in chart form. This will tell the pilot the minimum climb for the VSI and airspeed allowed for safety at different speeds. Remember a hot day and a high altitude airfield will seriously affect your climb performance.

It is essential that the aircraft manual is checked and the correct speed flown. Also watch your Vertical Speed Indicator.

Convert Climb Gradient to Climb Rate (RoC)


To convert climb gradient to climb rate, multiply the gradient by the airspeed in knots.

Climb rate (fpm) = Climb gradient (%) x Airspeed (kts)

Assumes:

  • 1% climb gradient over a mile = 60 ft (1% of 6000ft=1nm)
  • No wind; groundspeed = airspeed

Example:

Climb gradient = 5.5 %

Airspeed = 220 knots

Climb rate = 5.5 x 220 = 1210 feet per minute

To convert the climb gradient to the climb rate in hundreds of feet, divide your current ground speed by 60 and multiply by climb gradient.

Example:

If you want to gain 200 ft per nm and have a 150 kts ground speed, your rate of climb in hundreds of feet is 500. (150/60 * 200 = 500)

Another way you can do it is to take 500 feet per nm multiplied by your speed in nm per minute. 150kts is 2.5 nm per min.

500ft per nm X 2.5nm per min = 1250ft per min.

Don't forget that for larger climbs, your true airspeed will increase even though your calibrated/indicated speed remains constant.

TOPC and TOPD

An aircraft is cruising at A080 and will arrive 2500ft AGL at an airfield. While adopting the standard rate of decent, find the distance in nautical miles from the airfield which has a 500ft elevation the aircraft will begin its ROD using a 120kt ground speed.

An aircraft is at “X” with an altitude of 3000ft and needs to climb to 9000ft (Refer to Fig 29 of the work booklet). To remain OCTA using a constant ROC of 800fpm at 150kt ground speed find the distance at which the aircraft should commence its ROC from “A”