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CALCULATION OF POINTS OF NO RETURN (PNR) = & CRITICAL=20 POINTS (CP)
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There may be occasions when a landing at the = planned=20 destination is not possible due to weather, and insufficient fuel = is=20 available to fly to the destination, attempt an approach and then = divert=20 to an alternate. In this case, pre-flight planning must include=20 calculation of a Point of No Return (PNR). The PNR is also known = as the=20 Point of Safe Return (PSR). This is the furthest point = along=20 track that you can fly towards the destination and have sufficient = fuel to=20 divert to an alternate, with safe reserves on = arrival. In other=20 words, it is your last chance to assess your prospect of a = successful=20 approach and landing at your destination, and decide whether to go = on or=20 to divert. If any doubt exists, divert to the=20 alternate. 1. Point of No Return (AKA point of safe = return) There are a number of methods which can be used = to=20 calculate a PNR/PSR, but the one most favoured uses what are = called=20 Specific Fuel Flows (SFF). These are calculated by dividing the planned = cruise fuel=20 flow by the expected ground speeds towards the destination and = towards the=20 alternate field, and the result is the fuel required per nautical = mile=20 travelled in each direction. The general formula used to calculate the = distance to the=20 PNR from the Alternate is: Distance to PNR =3D Flight Fuel Available = (Alternate to=20 Destination) =F7 (SFF (To Destination) + SFF (To Alternate))=20 The Flight Fuel Available (FFA) is the Useable = Fuel on=20 Board (FOB) minus the Fixed Reserve (FR), any holding fuel = and any=20 taxi allowance. Variable Reserve For all IFR flights, and for all extended range = flights=20 requiring a PNR, you should allow an additional fuel reserve to = provide=20 for winds stronger than forecast or for a higher fuel consumption = than=20 that specified in the POH. Conventionally, this is = achieved by=20 reducing the Flight Fuel Available figure by 15%, i.e., dividing = the FFA=20 by 1.15. 2. Calculation of PNR When the Alternate is = the=20 Departure Field This is the simplest situation to = calculate. As an example, let=92s assume a flight from A = to B, with A=20 as the alternate field. The distance A to B is 500=20 nms. Max range cruise power will be used, giving a fuel = flow of=20 80 litres/hr, and this fuel flow will also be used for a Fixed = Reserve and=20 any holding. At this power setting the planned TAS is = 160 kts=20 and a 25 kts tailwind is forecast A to B. Therefore, = the ground=20 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=20 litres/nm (80/185), and the GSFF "home" will be 0.59 litres/nm=20 (80/135). The sum of the GSFFs "out" and "home" is = 1.02. The weight of passengers and baggage we want to = carry is=20 480 kg. We can also carry 390 litres of useable fuel = without=20 exceeding the Maximum AUW. To establish the Flight Fuel Available for the = PNR=20 calculation, we must subtract from the Useable Fuel the Fixed = Reserve (60=20 litres), the taxi fuel (10 litres) and the climb allowance (11=20 litres). The forecast for a possible return to A does = not=20 indicate the need for any holding fuel. Therefore, the FFA is 390 - = (60+10+11): 309=20 litres. This figure is now divided by 1.15 to provide a = Variable=20 Reserve, giving a final FFA of 269 litres. The distance to the PNR from A is therefore 269 = =F7 1.02 =3D=20 264 nm from A. 3. Calculation of a PNR When the Alternate is on = Track=20 Between the Departure Point and the Destination The calculation of a PNR for this case is = essentially the=20 same as before, except that the "datum" for calculation is over = the=20 alternate. We will use the previous example of a flight = from A to B=20 over a distance of 500 nms, but with the possible alternate C 190 = nms=20 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=20 previous example , i.e.: a. Flight Fuel Available at A =3D 269 litres =
(after=20
allowing for a Variable Reserve) We first determine how much fuel is required to = fly from=20 A to overhead C. This is equal to the distance A to C = (190 nms)=20 multiplied by the GSFF "out" (0.43 litres/nm): 82 = litres. This is subtracted from the Flight Fuel = Available A to B=20 (269 litres) to give a Flight Fuel Available C to B of 187 = litres. The distance of the PNR from C is therefore 187 = =F7=20 1.02: 183 nms. This is 127 nms short = of B,=20 and if the aircraft flies beyond this point there will not be = sufficient=20 fuel to return to C with the fixed reserve intact.
4. CALCULATION OF A CRITICAL POINT While the distance to a PNR is dependent on = fuel=20 availability and fuel flow, the distance to a Critical Point (CP) = is=20 independent of fuel considerations and is based on groundspeeds = only. The CP is also known as the "Equi-time Point" = (ETP),=20 because it is the point along track from where it will take the = same=20 time to continue to the planned destination as it will to=20 divert/return to an alternate. The CP/ETP is normally associated with an = abnormal flight=20 condition or an emergency where there is a need to minimise the = time=20 before landing. For example, a passenger who falls ill, = or an=20 abnormal system operation, eg, an alternator failure in IMC, with = a need=20 to minimise the flight time. The general formula used to calculate the = distance of a=20 CP/ETP from an Alternate is: Distance to CP =3D Distance (Alt to Dest) x Groundspeed to Alt = =F7=20 (Groundspeed to Dest + Groundspeed to=20 = Alternate) To illustrate, we will calculate a CP/ETP for = the=20 previous example flight. The required data is: =95 Distance Alternate (C) to Destination (B) =
=3D 310=20
nms The distance to the CP from C is therefore (310 = x 100) =F7=20 (150 + 100) =3D 124 nms, which is 186 nms short of = B. From=20 this point the time on to B is 1.24 hours (186/150), and the time = back to=20 C is also 1.24 hours (124/100).
5. Calculation of a latest point of safe = diversion (LPSD)=20 to an Off-track alternate Introduction 2. The calculation of a LPSD is slightly more = complex=20 than calculating a PNR for an on-track alternate. However, = calculation of=20 a LPSD should be a major flight safety consideration for a long = flight=20 over water or over other inhospitable terrain with no on-track=20 alternates. 3. As with the calculation of a PNR for an = alternate on=20 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=20 (8) less the Reserves (2 & 4), any Holding Fuel required (5) = and taxy=20 fuel (6). 5. The Safe Endurance Available (SEA) for LPSD=20 calculations is determined by dividing the FFA by the planned Fuel = Flow,=20 eg, if the FFA is 350 litres and the Planned Fuel Flow (including = an=20 allowance for the climb) is 70 LPH, the SEA is 350 =F7 70 =3D 5.0 = hrs (300=20 mins). Pre-flight Planning for a LPSD 6. As an example, we will assume a planned = flight from A=20 to B on a track of 110=B0M over a distance of 300 nms. If a = landing at B is=20 impossible for some reason, eg, weather, the nearest suitable = alternate is=20 C, on a track of 332=B0M from B at a distance of 117 nms. 7. The planned TAS is 150 kts and the forecast = wind is=20 315 at 20 kts. Therefore, the planned groundspeed from A to B is = 168 kts=20 with an ETI of 107 minutes, and the planned groundspeed from B to = C is 131=20 kts with an ETI of 54 minutes. If the aircraft flew from A to B = and then=20 had to divert from B to C, a Safe Endurance of 161 (107 + 54) = minutes=20 would be required. The weather forecast shows an INTER requirement = for the=20 ETA. 8. The fuel calculations for the leg A - B, = based on a=20 cruise fuel flow of 80 LPH and a max endurance fuel flow of 60 LPH = are as=20 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=20 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 +=20 taxy) Fuel On Board (FOB) 280 litres (tank capacity to = max=20 AUW) Margin 20 litres FOB =96 Total Required) Maximum Endurance 210 minutes (280 litres =F7 80 = LPH) 10. However, the SEA is the FOB less the VR, = FR, Holding=20 and Taxy Fuel, calculated at the Cruise Fuel Flow. Therefore, the = SEA in=20 this example is (280 - 23 =96 30 =96 45 =96 5) =3D 177 litres @ 80 = LPH =3D 133=20 minutes. However, the SER A > B > C is 161 minutes, so = there is=20 insufficient fuel to fly from A to B, hold for 30 minutes and then = divert=20 to C with the Reserves intact. 11. In this case, a LPSD along the track A to B = needs to=20 be calculated 12. An initial estimate of the LPSD can = be made=20 using the formula: Approx. ETI to LPSD =3D SEA x ETI to Planned =
Destination 13. This can be solved on the nav computer as=20 follows:
14. Solving for the example flight: ETI to initial estimate of LPSD =3D 133 (SEA) x = 107 (ETI to=20 B) =F7 161 (SER) =3D 88 minutes 15. Therefore, the initial estimated = LPSD is 88=20 minutes from A, ie, 250 nms along track at the planned groundspeed = of 170=20 kts.
Fine-Tuning of LPSD 16. This initial estimate of the LPSD = must be=20 fine-tuned by plotting the estimated LPSD on a chart, eg, the ERC, = and=20 measuring the track and distance from the estimated LPSD to the = Alternate.=20 The forecast wind and TAS is then applied to this data to = determine a=20 revised groundspeed and ETI from the initially estimated LPSD to = the=20 Alternate. 17. In the example, the track and distance from = the=20 initially estimated LPSD is 353=B0 M and 86 nms. The groundspeed = is=20 calculated to be 135 kts, giving a revised ETI from the LPSD > = C of 38=20 minutes. 18. Therefore, the revised SER is 88 minutes (A = to=20 Initial LPSD) + 38 minutes (revised ETI from the initial LPSD to = C) =3D 126=20 minutes. However, the SEA is 133 minutes, so the pre-planned ETI = to the=20 initial LPSD can be increased to provide for this 7 minute = difference. 19. If the position of the revised LPSD is = moved the full=20 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=20 extent, probably increasing the SER beyond the SEA. To counter = this=20 effect, the LPSD is moved only approximately half the full amount, = eg, 4=20 minutes / 12 nms. 21. The revised LPSD is therefore 92 minutes = from A (262=20 nms @ the planned GS of 170 kts). Inflight Revision of LPSD 22. The planned LPSD should be revised = in-flight to take=20 account of variations in groundspeed (and possibly variations in = fuel=20 consumption). This must be done sufficiently in advance of the = planned=20 LPSD to allow for slower actual groundspeeds that may = significantly=20 increase the required endurance, and enable time for a = recalculation of=20 the LPSD before it is passed!! 23. This will require a position fix somewhere = before the=20 planned LPSD (using either radio-navaids or GPS) which can be used = to=20 determine actual wind/groundspeed. A new ETI to B is then = calculated from=20 the fix, together with any estimated changed in ETI from the LPSD = to=20 C. 24. In the example, a GPS fix is planned 150 = nms along=20 the A > B track. This fix is achieved 60 minutes along track = and=20 indicates a new wind of 020=B0/15 kts, with a revised groundspeed = of 150=20 kts. The distance from the fix to the planned LPSD is 112 nms (262 = =96 150),=20 which at the new GS of 150 kts will take 45 minutes. The = new wind=20 is applied to the LPSD > C track of 348=B0 and 90 nms to give a = revised=20 GS on that leg of 138 kts, with a revised ETI of 39 mins. = Therefore=20 the SER from the fix is 45 minutes (fix to LPSD) + 39 minutes = (LPSD to C)=20 =3D 84 minutes. The SEA from the fix is 133 =96 60 =3D 73 minutes. = Therefore,=20 the SER is now 11 mins more than the SEA and the LPSD must be = moved=20 further from B. 25. Intuitively, moving the LPSD towards A = about half the=20 11 minute correction needed, say, 6 mins or 15 nms at the revised = GS of=20 150 kts will also reduce the ETI from the LPSD > C by a similar = amount.=20 The in-flight revision now places the LPSD 247 nms from A (262 =96 = 15) Conclusion 26. The calculation of a LPSD to an off-track = alternate=20 is slightly more complex than determining a PNR for an on track = alternate,=20 and in-flight revision of the pre-flight calculation takes some = time and=20 "number-crunching". 27. However, the procedure becomes easier with = practice=20 and, if performing the calculations make the difference between a = safe=20 arrival at an alternate or a forced landing/ditching short of the = original=20 destination or an alternate, then the effort is certainly = worthwhile. 28. Finally, if there is any doubt approaching = the LPSD=20 about a safe landing at the planned destination, make a firm = decision and=20 divert at, or before, the=20 LPSD. |