Point of Safe Return (PSR) — Page 264, Lesson 265

I want to walk you through the Point of Safe Return, or PSR. This is a critical fuel-planning concept for any long-range flight, especially over water or remote terrain where you cannot simply land at an alternate. Let's start with the definition. The Point of Safe Return, previously called the Point of No Return, is the last point on a route from which the aircraft can still return to its departure aerodrome using the fuel that remains, given the prevailing wind conditions. If you go beyond that point, you no longer have enough fuel to get back to where you started — you must continue to the destination or a suitable alternate. Now, let's look at how the formula is derived. I want you to picture a single leg out from your departure point, and then the same leg back home. The key idea is that the fuel you burn going out to the PSR, plus the fuel you burn coming back from the PSR, must equal your total usable fuel — or more precisely, your safe endurance, which is total endurance minus any reserves you are required to hold. The derivation starts with the simple relationship: the distance out to the PSR is the same as the distance back from the PSR. That distance, let's call it D, is equal to the ground speed out multiplied by the time out, and also equal to the ground speed home multiplied by the time home. So we have: D = GS_out × T_out = GS_home × T_home The total time available, which is the safe endurance E, is the sum of the time out and the time home: E = T_out + T_home If we rearrange the first equation, we get T_home = (GS_out / GS_home) × T_out. Substitute that into the endurance equation, and after a bit of algebra, we arrive at the standard PSR formula: T_out = (E × GS_home) / (GS_out + GS_home) That gives you the time to fly from departure to the PSR. Multiply that time by your ground speed out, and you get the distance to the PSR. Now, let's look at how we transpose that formula onto a navigation computer. On a circular slide rule, you typically set up the ratio of ground speeds and read the time directly. The exact method depends on the computer model, but the principle is the same: you are solving that proportion. Let's talk about the effect of wind on the location of the PSR. I have a worked example here. Assume a total endurance E of 10 hours, and a true airspeed of 300 knots. First, in still air, your ground speed out and home are both 300 knots. Plugging into the formula: T_out = (10 × 300) / (300 + 300) = 3000 / 600 = 5 hours Distance = 5 hours × 300 knots = 1500 nautical miles. Now, add a 50-knot headwind on the outward leg. Your ground speed out is 300 minus 50, so 250 knots. Your ground speed home, with the wind now as a tailwind, is 300 plus 50, so 350 knots. T_out = (10 × 350) / (250 + 350) = 3500 / 600 = 5.833 hours, which is 5 hours and 50 minutes. Distance = 5.833 hours × 250 knots = 1458 nautical miles. Now, reverse it: a 50-knot tailwind on the outward leg. Ground speed out is 350 knots, ground speed home is 250 knots. T_out = (10 × 250) / (350 + 250) = 2500 / 600 = 4.167 hours, which is 4 hours and 10 minutes. Distance = 4.167 hours × 350 knots = 1458 nautical miles. Notice the pattern. In still air, the distance to the PSR is the greatest. Any wind component — headwind or tailwind — reduces the distance to the PSR. And interestingly, the distance is the same for a headwind or a tailwind of the same value. The greater the wind component, the greater the reduction in distance to the PSR. Now let's work through a single-leg PSR example. Study Figure 14.4 in your materials. The aircraft is flying towards its destination at a true airspeed of 220 knots, with a wind component of plus 45 knots. That means a tailwind on the outward leg, so ground speed out is 220 plus 45, which is 265 knots. Ground speed home, against the wind, is 220 minus 45, which is 175 knots. Total endurance is 7 hours 40 minutes, but safe endurance is 6 hours. That means we have 1 hour 40 minutes of reserve fuel that we are not allowed to use for the PSR calculation. We use safe endurance, which is 6 hours. Plug into the formula: T_out = (6 × 175) / (265 + 175) = 1050 / 440 = 2.386 hours Convert 0.386 hours to minutes: 0.386 × 60 = 23 minutes. So T_out is 2 hours 23 minutes. Distance = 2.383 hours × 265 knots = 632 nautical miles. So the PSR is 2 hours 23 minutes and 632 nautical miles from departure. Now, the excerpt ends with some practice questions. These are the book's practice questions — let's try them one at a time.