Shannon (EINN) N5242 W 00855, to Gander (CYQX) N4856 W05434, to Keflavik… — Page 196, Lesson 203

I want to walk you through a worked example that brings together everything we've been building — the Point of Equal Time, or Critical Point, and how we actually calculate it in a real-world North Atlantic scenario. We're using the route from Shannon (EINN) to Gander (CYQX), which we set up in Example 4. The coordinates are: Shannon at N5242 W00855, Gander at N4856 W05434. We also have the other two legs of the triangle — Gander to Keflavik (BIKF) at N6359 W02236, and Keflavik back to Shannon. First, let's look at what Example 4 asks us to do. Part (b) says identify the 120-minute and 180-minute range circles from each airfield. That means on the chart, you draw circles around Shannon, Gander, and Keflavik at distances corresponding to 120 minutes and 180 minutes of flying time — these define your diversion capability boundaries. Part (c) asks for the midpoint line on the Shannon/Gander track. The answer tells us that the midpoint line cuts the track at position N5310 W03248, and that point is 857.5 nautical miles from each airfield. So the midpoint itself is exactly halfway along the great-circle track between Shannon and Gander. Part (d) does the same for the Gander/Keflavik track. The midpoint line cuts that track at N5726 W04142, and it's 683 nautical miles from each airfield. Part (e) gives us the Keflavik/Shannon midpoint: position N5832 W01440, and it's 399.5 nautical miles from each. Now here's the key concept I want you to understand. Any point on that extended midpoint line — either side of the actual midpoint — will be equidistant from either airfield. And that line, in still air with no wind, is where your Point of Equal Time, or Critical Point, lies. We call it the still-air ETP or CP. At 90 degrees to either side of each midpoint line, there's a graticule — a scale or grid — that we use to adjust that still-air ETP/CP for the prevailing wind pattern. You shift it either in the continuing direction, which we call ON, or the returning direction, which we call HOME. Now let's move into Example 5, where we actually calculate the all-engine ETP/CP between Shannon and Gander. We're given our cruise conditions: Flight Level 310, all-engine true airspeed of 426 knots. Our engine-out stabilizing height is Flight Level 240, with an engine-out true airspeed of 370 knots. We have wind components for two altitudes. At FL310, from the midpoint to Gander we have a headwind of minus 80 knots — that's a headwind because it's negative. From the midpoint to Shannon at FL310, we have plus 50 knots — that's a tailwind. At FL240, the engine-out altitude, from midpoint to Gander we have minus 40 knots, and from midpoint to Shannon we have plus 20 knots. Part (a) asks for the equi-time number. The answer is plus 8. That number comes from a calculation or graph we'll see in a moment. Part (b) gives the number of miles from the midpoint: 137 nautical miles. Part (c) tells us the distance to the ETP/CP from Shannon is 994.5 nautical miles. Part (d) gives the time to the ETP/CP as 158.5 minutes. Then we cross-check using the formula. The formula is: distance X to the ETP/CP from EINN equals something over something plus something. The answer for part (e) is 993 nautical miles — very close to our 994.5. And part (f) confirms the time is 158.5 minutes. Now Example 6 is the same route and same conditions, but this time we're calculating the engine-failure ETP/CP — that's the point of equal time assuming one engine has failed, so we're using the engine-out true airspeed of 370 knots and the FL240 wind components. Part (a) gives the equi-time number as plus 4. Part (b) says the number of miles from the midpoint is 68.5 nautical miles — about half the all-engine value, because the engine-out speed is lower and the wind effect is different. Part (c) gives the distance to the engine-failure ETP/CP from Shannon as 926 nautical miles. Part (d) gives the time as 148 minutes. And the cross-check formula in part (e) gives 929 nautical miles, with part (f) confirming 148 minutes. So what you're seeing here is the complete process: you start with the midpoint on the great-circle track, you apply the equi-time number from the ETP graph, that gives you a distance offset from the midpoint, and from that you can calculate the actual distance from your departure airfield and the time to reach that critical point. The all-engine case and the engine-failure case give different answers because the speeds and wind components are different at the two altitudes.