What is the TAS, ground distance and Specific Fuel Consumption? — Page 96, Lesson 91

I want to walk you through a worked example that shows exactly how we calculate True Airspeed, ground distance in Nautical Air Miles, and fuel consumption using the Long Range Cruise tables. This is a core skill for flight planning, so let's take it step by step. We have an aircraft at point "A" with a mass of 55 500 kg. The Outside Air Temperature is minus 59°C. Wind is light and variable, meaning effectively zero wind for our calculations. We're cruising using Long Range Cruise, or LRC, at Flight Level 310. The aircraft is to fly for 35 minutes. The question is: what is the fuel consumed from point "A"? Now, before we solve that specific case, the book gives us a fully worked example so we understand the method. Let me walk you through that first. The aircraft is to fly from A to B, a ground distance of 1500 Nautical Ground Miles, or NGM, using Long Range Cruise at Flight Level 330. The aircraft mass at point A is 58 500 kg. The temperature condition is ISA plus 10°C, and there is a 50‑knot tailwind. Step 1 is to find the correct page in the performance manual — in this case, page 31. Step 2 gives us the True Airspeed. For LRC at FL330, the base TAS from the table is 433 knots. Because we are ISA plus 10°C, we add 10 knots, giving a TAS of 443 knots. Step 3 is to convert the 1500 Nautical Ground Miles into Nautical Air Miles, or NAM. This is essential because the cruise tables work in air distance, not ground distance. The formula is: NAM equals NGM multiplied by TAS divided by Ground Speed. Here, TAS is 443 knots, and with a 50‑knot tailwind, the Ground Speed is TAS plus tailwind, so 493 knots. So we calculate: 1500 multiplied by 443 divided by 493, which gives 1348 Nautical Air Miles. Step 4: we enter the cruise table with the aircraft mass at point A, which is 58 500 kg, and extract the cruise NAM. That figure is 4704 Nautical Air Miles. Step 5: we subtract the 1348 NAM we just calculated from the 4704 NAM. That gives us a cruise NAM at point B of 3356 Nautical Air Miles. Step 6: we enter the table again, this time looking for a distance of 3356 NAM. You won't find that exact number, so we take the lower figure — 3354 NAM — and that corresponds to an aircraft mass of 51 000 kg when overhead point B. Step 7: the difference between the starting mass of 58 500 kg and the mass at B of 51 000 kg is 7500 kg. That is the fuel required for the leg. But we then increase that fuel by 0.6%, which is 45 kg, giving a total fuel required of 7545 kg. So the answer for that first example is: TAS is 443 knots, and fuel required is 7545 kg. Now let's look at a second example. The aircraft is to fly from A to B, a distance of 500 Nautical Ground Miles, at Mach 0.74 at Flight Level 290. The aircraft mass at A is 54 400 kg. The temperature is ISA minus 20°C, and there is a 50‑knot headwind. Step 1: find the correct page — page 45. Step 2: TAS. For Mach 0.74 at FL290, the base TAS from the table is 438 knots. Because we are ISA minus 20°C, we subtract 20 knots, giving a TAS of 418 knots. Step 3: convert the 500 NGM into NAM. With a 50‑knot headwind, Ground Speed is TAS minus headwind, so 418 minus 50 equals 368 knots. The calculation is 500 multiplied by 418 divided by 368, which gives 568 Nautical Air Miles. Step 4: enter the table with the aircraft mass at A, 54 400 kg, and extract the cruise NAM. That figure is 3612 Nautical Air Miles. Step 5: subtract the 568 NAM from 3612 NAM, giving a cruise NAM at point B of 3044 Nautical Air Miles. The book stops the worked solution there, but you can see the pattern — you would then continue with steps 6 and 7 to find the mass at B and the fuel required. Now, back to your original question: the aircraft at 55 500 kg, OAT minus 59°C, light and variable wind, LRC at FL310, flying for 35 minutes. The method is the same. You would find the correct page for LRC at FL310, extract the TAS and the cruise NAM for 55 500 kg, then calculate the NAM flown in 35 minutes using TAS and zero wind, subtract that from the starting cruise NAM to find the NAM at the end of the 35 minutes, enter the table to find the corresponding mass, and the difference gives you the fuel consumed. The worked examples I just showed you give you the exact procedure to follow.