CALCULATION OF POINTS OF NO RETURN (PNR) & CRITICAL POINTS (CP)

Disclaimer: 

Retired Air Commodore John Chesterfield AM MRAeS RAAF has kindly given Paradise Air Safaris permission to provide these notes to assist members. 

I highly respect anything John has to say about aviation, however have no idea as to the correctness or accuracy of the content.  Use them for whatever benefit you determine but at your own risk.

1. Point of No Return
   
2. Calculation of PNR When the Alternate is the Departure Field
   
3. Calculation of a PNR When the Alternate is on Track Between the Departure Point and the Destination
   
4. Calculation Of A Critical Point
   
5. Calculation Of Latest Point Of Safe Diversion (LPSD) To An Off-Track Alternate

There may be occasions when a landing at the planned destination is not possible due to weather, and insufficient fuel is available to fly to the destination, attempt an approach and then divert to an alternate.

In this case, pre-flight planning must include calculation of a Point of No Return (PNR). The PNR is also known as the Point of Safe Return (PSR).  This is the furthest point along track that you can fly towards the destination and have sufficient fuel to divert to an alternate, with safe reserves on arrival.  In other words, it is your last chance to assess your prospect of a successful approach and landing at your destination, and decide whether to go on or to divert.  If any doubt exists, divert to the alternate.

There are a number of methods which can be used to calculate a PNR/PSR, but the one most favoured uses what are called Specific Fuel Flows (SFF).

These are calculated by dividing the planned cruise fuel flow by the expected ground speeds towards the destination and towards the alternate field, and the result is the fuel required per nautical mile travelled in each direction.

The general formula used to calculate the distance to the PNR from the Alternate is:

The Flight Fuel Available (FFA) is the Useable Fuel on Board (FOB) minus the Fixed Reserve (FR), any holding fuel and any taxi allowance.

For all IFR flights, and for all extended range flights requiring a PNR, you should allow an additional fuel reserve to provide for winds stronger than forecast or for a higher fuel consumption than that specified in the POH.  Conventionally, this is achieved by reducing the Flight Fuel Available figure by 15%, i.e., dividing the FFA by 1.15.

2. Calculation of PNR When the Alternate is the Departure Field

This is the simplest situation to calculate.

As an example, let’s assume a flight from A to B, with A as the alternate field.  The distance A to B is 500 nms.  Max range cruise power will be used, giving a fuel flow of 80 litres/hr, and this fuel flow will also be used for a Fixed Reserve and any holding.  At this power setting the planned TAS is 160 kts and a 25 kts tailwind is forecast A to B.  Therefore, the ground speed to B is 185 kts, with a return ground speed to A of 135 kts.

The ground specific fuel flow (GSFF) "out" will be 0.43 litres/nm (80/185), and the GSFF "home" will be 0.59 litres/nm (80/135).  The sum of the GSFFs "out" and "home" is 1.02.

The weight of passengers and baggage we want to carry is 480 kg.  We can also carry 390 litres of useable fuel without exceeding the Maximum AUW.

To establish the Flight Fuel Available for the PNR calculation, we must subtract from the Useable Fuel the Fixed Reserve (60 litres), the taxi fuel (10 litres) and the climb allowance (11 litres).  The forecast for a possible return to A does not indicate the need for any holding fuel.

Therefore, the FFA is 390 - (60+10+11):  309 litres.

This figure is now divided by 1.15 to provide a Variable Reserve, giving a final FFA of 269 litres.

The distance to the PNR from A is therefore 269 ÷ 1.02 = 264 nm from A.

The calculation of a PNR for this case is essentially the same as before, except that the "datum" for calculation is over the alternate.

We will use the previous example of a flight from A to B over a distance of 500 nms, but with the possible alternate C 190 nms along track towards B, i.e., the distance from C to B is 310 nms.

The other planning data remains the same as in the previous example , i.e.:

We first determine how much fuel is required to fly from A to overhead C.  This is equal to the distance A to C (190 nms) multiplied by the GSFF "out" (0.43 litres/nm):  82 litres.

This is subtracted from the Flight Fuel Available A to B (269 litres) to give a Flight Fuel Available C to B of 187 litres.

The distance of the PNR from C is therefore 187 ÷ 1.02:  183 nms.  This is 127 nms short of B, and if the aircraft flies beyond this point there will not be sufficient fuel to return to C with the fixed reserve intact.

While the distance to a PNR is dependent on fuel availability and fuel flow, the distance to a Critical Point (CP) is independent of fuel considerations and is based on groundspeeds only.

The CP is also known as the "Equi-time Point" (ETP), because it is the point along track from where it will take the same time to continue to the planned destination as it will to divert/return to an alternate.

The CP/ETP is normally associated with an abnormal flight condition or an emergency where there is a need to minimise the time before landing.  For example, a passenger who falls ill, or an abnormal system operation, eg, an alternator failure in IMC, with a need to minimise the flight time.

The general formula used to calculate the distance of a CP/ETP from an Alternate is:

To illustrate, we will calculate a CP/ETP for the previous example flight.

The required data is:

The distance to the CP from C is therefore (310 x 100) ÷ (150 + 100) = 124 nms, which is 186 nms short of B.  From this point the time on to B is 1.24 hours (186/150), and the time back to C is also 1.24 hours (124/100).

Introduction
1. The calculation of a Latest Point of Safe Diversion (LPSD) to an off-track alternate should be made if there will not be sufficient Fuel On Board at planned fuel consumption rate to fly to a destination and then divert to an alternate with reserves intact.

2. The calculation of a LPSD is slightly more complex than calculating a PNR for an on-track alternate. However, calculation of a LPSD should be a major flight safety consideration for a long flight over water or over other inhospitable terrain with no on-track alternates.

3. As with the calculation of a PNR for an alternate on track, the calculation of a LPSD is dependent on Safe Fuel Endurance.

This is calculated as follows:

4. The Flight Fuel Available (FFA) is equal to the FOB (8) less the Reserves (2 & 4), any Holding Fuel required (5) and taxy fuel (6).

5. The Safe Endurance Available (SEA) for LPSD calculations is determined by dividing the FFA by the planned Fuel Flow, eg, if the FFA is 350 litres and the Planned Fuel Flow (including an allowance for the climb) is 70 LPH, the SEA is 350 ÷ 70 = 5.0 hrs (300 mins).

6. As an example, we will assume a planned flight from A to B on a track of 110°M over a distance of 300 nms. If a landing at B is impossible for some reason, eg, weather, the nearest suitable alternate is C, on a track of 332°M from B at a distance of 117 nms.

7. The planned TAS is 150 kts and the forecast wind is 315 at 20 kts. Therefore, the planned groundspeed from A to B is 168 kts with an ETI of 107 minutes, and the planned groundspeed from B to C is 131 kts with an ETI of 54 minutes. If the aircraft flew from A to B and then had to divert from B to C, a Safe Endurance of 161 (107 + 54) minutes would be required. The weather forecast shows an INTER requirement for the ETA.

8. The fuel calculations for the leg A - B, based on a cruise fuel flow of 80 LPH and a max endurance fuel flow of 60 LPH are as follows:

Cruise Fuel 142 litres (107 mins x 80 LPH)

Climb Allowance 15 litres (from POH)

Variable Reserve (VR) 23 litres (15% of 157 litres)

Flight Fuel Required (FFR) 180 litres (Cruise, Climb and VR)

Fixed Reserve (FR) 45 litres (45 mins @ 60 LPH)

Holding Fuel (HF) 30 litres (30 mins @ 60 LPH)

Taxy Fuel 5 litres (from POH)

Total Fuel Required 260 litres (FFR + VR + FR + HF + taxy)

Fuel On Board (FOB) 280 litres (tank capacity to max AUW)

Margin 20 litres FOB – Total Required)

Maximum Endurance 210 minutes (280 litres ÷ 80 LPH)

10. However, the SEA is the FOB less the VR, FR, Holding and Taxy Fuel, calculated at the Cruise Fuel Flow. Therefore, the SEA in this example is (280 - 23 – 30 – 45 – 5) = 177 litres @ 80 LPH = 133 minutes. However, the SER A > B > C is 161 minutes, so there is insufficient fuel to fly from A to B, hold for 30 minutes and then divert to C with the Reserves intact.

11. In this case, a LPSD along the track A to B needs to be calculated

12. An initial estimate of the LPSD can be made using the formula:

Approx. ETI to LPSD = SEA x ETI to Planned Destination
Safe Endurance Required (SER)

13. This can be solved on the nav computer as follows:

14. Solving for the example flight:

ETI to initial estimate of LPSD = 133 (SEA) x 107 (ETI to B) ÷ 161 (SER) = 88 minutes

15. Therefore, the initial estimated LPSD is 88 minutes from A, ie, 250 nms along track at the planned groundspeed of 170 kts.

16. This initial estimate of the LPSD must be fine-tuned by plotting the estimated LPSD on a chart, eg, the ERC, and measuring the track and distance from the estimated LPSD to the Alternate. The forecast wind and TAS is then applied to this data to determine a revised groundspeed and ETI from the initially estimated LPSD to the Alternate.

17. In the example, the track and distance from the initially estimated LPSD is 353° M and 86 nms. The groundspeed is calculated to be 135 kts, giving a revised ETI from the LPSD > C of 38 minutes.

18. Therefore, the revised SER is 88 minutes (A to Initial LPSD) + 38 minutes (revised ETI from the initial LPSD to C) = 126 minutes. However, the SEA is 133 minutes, so the pre-planned ETI to the initial LPSD can be increased to provide for this 7 minute difference.

19. If the position of the revised LPSD is moved the full 7 minutes further along track towards B (20 nms @ 170 kts GS), the distance from the LPSD to C (and the ETI) will also be increased to some extent, probably increasing the SER beyond the SEA. To counter this effect, the LPSD is moved only approximately half the full amount, eg, 4 minutes / 12 nms.

21. The revised LPSD is therefore 92 minutes from A (262 nms @ the planned GS of 170 kts).

22. The planned LPSD should be revised in-flight to take account of variations in groundspeed (and possibly variations in fuel consumption). This must be done sufficiently in advance of the planned LPSD to allow for slower actual groundspeeds that may significantly increase the required endurance, and enable time for a recalculation of the LPSD before it is passed!!

23. This will require a position fix somewhere before the planned LPSD (using either radio-navaids or GPS) which can be used to determine actual wind/groundspeed. A new ETI to B is then calculated from the fix, together with any estimated changed in ETI from the LPSD to C.

24. In the example, a GPS fix is planned 150 nms along the A > B track. This fix is achieved 60 minutes along track and indicates a new wind of 020°/15 kts, with a revised groundspeed of 150 kts. The distance from the fix to the planned LPSD is 112 nms (262 – 150), which at the new GS of 150 kts will take 45 minutes. The new wind is applied to the LPSD > C track of 348° and 90 nms to give a revised GS on that leg of 138 kts, with a revised ETI of 39 mins. Therefore the SER from the fix is 45 minutes (fix to LPSD) + 39 minutes (LPSD to C) = 84 minutes. The SEA from the fix is 133 – 60 = 73 minutes. Therefore, the SER is now 11 mins more than the SEA and the LPSD must be moved further from B.

25. Intuitively, moving the LPSD towards A about half the 11 minute correction needed, say, 6 mins or 15 nms at the revised GS of 150 kts will also reduce the ETI from the LPSD > C by a similar amount. The in-flight revision now places the LPSD 247 nms from A (262 – 15)

Conclusion

26. The calculation of a LPSD to an off-track alternate is slightly more complex than determining a PNR for an on track alternate, and in-flight revision of the pre-flight calculation takes some time and "number-crunching".

27. However, the procedure becomes easier with practice and, if performing the calculations make the difference between a safe arrival at an alternate or a forced landing/ditching short of the original destination or an alternate, then the effort is certainly worthwhile.

28. Finally, if there is any doubt approaching the LPSD about a safe landing at the planned destination, make a firm decision and divert at, or before, the LPSD.