General Navigation Problems — Page 514, Lesson 519

Let’s work through this timing-to-a-beacon problem together, because it’s a classic trap that catches a lot of pilots. The core idea is simple: to time your arrival at a beacon, you need the right ground speed. But here’s the catch — ground speed is a combination of your true airspeed and the wind component, and what you actually control in the cockpit is the Mach number or CAS, which is directly proportional to TAS, not to ground speed. So let’s set up the scenario. You’re flying at a True Mach Number of 0.77, in a static air temperature of minus 55 degrees Celsius. At 1000 hours, you are 150 nautical miles from a DME, with an ETA of 1017. ATC asks you to slow down so you arrive at 1021 instead. The question is: what new True Mach Number do you need, if you reduce speed with 150 NM still to go? First, let’s find your current ground speed. You have 150 NM to cover in 17 minutes — from 1000 to 1017. That gives you 530 knots ground speed. Now, you need to cover that same 150 NM in 21 minutes — from 1000 to 1021. That requires a new ground speed of 429 knots. Here’s the trap. A lot of people would just take the ratio of the new ground speed to the old ground speed, multiply it by the old Mach number, and call it done. That would give you 0.77 times 429 over 530, which comes out to about Mach 0.62. But that’s wrong, because it ignores the wind. You have to take the wind into consideration. Let’s break it down. Your old ground speed is 530 knots. Your TAS at Mach 0.77 and minus 55°C is 442 knots. So the wind component is the difference — 530 minus 442, which is plus 88 knots. That means you have an 88-knot tailwind. Now, your new required ground speed is 429 knots. But the wind component doesn’t change — it’s still 88 knots, except now you have to reverse the sign. Since you’re still flying the same direction, that tailwind is still helping you, so to get a ground speed of 429 knots, your TAS must be 429 minus 88, which is 341 knots. Now you can apply the Mach number ratio properly. Your new Mach number is the old Mach number times the ratio of new TAS to old TAS. That’s 0.77 times 341 over 442, which gives you Mach 0.59. So the correct answer is d — Mach 0.59. The key lesson here is: never convert ground speed ratios directly into Mach number ratios. Always strip out the wind component first, work in TAS, then convert back to Mach. That’s the professional way to handle it, and it’s exactly what the examiner wants to see.