Class A Aircraft - Take-off — Page 383, Lesson 476

Let's pick up with the rotation speed, \(V_R\). We've already dealt with \(V_1\) and \(V_{MCG}\), so now we're looking at what actually makes the aeroplane rotate on take-off. The good news is that the factors affecting \(V_R\) are exactly the same family as those affecting \(V_1\). And the source for all of this is the CAP 698 document — specifically, pages 18 and 19 of section 4. On those pages you'll find a table, the second one from the top, that lists the three V speeds — \(V_1\), \(V_R\), and \(V_2\) — against the aeroplane mass. That table is our tool for seeing how each factor changes \(V_R\). Let's start with mass. Take a mass of 50,000 kg. Under density column A, \(V_R\) is 131 knots. Now increase the mass to 65,000 kg, and \(V_R\) rises to 155 knots. So the relationship is direct: increasing mass increases \(V_R\). That makes sense physically — a heavier aeroplane needs more speed to generate the lift required to rotate. Next, configuration — specifically flap angle. Page 18 gives the V speeds for 5 degrees of flap, and page 19 gives them for 15 degrees. Compare the same mass on both pages. At 55,000 kg with 5 degrees of flap, \(V_R\) is 139 knots. With 15 degrees of flap, same mass, \(V_R\) drops to 131 knots. So increasing flap angle decreases \(V_R\). More flap means more lift at a given speed, so you can rotate earlier. Now density. On page 17 of section 4 there's a density graph. Band A is high density; band F is lower density. Back on page 18, take 50,000 kg in band A — high density — and \(V_R\) is 131 knots. Move through bands B, C, D, and E, and \(V_R\) increases progressively. So as density decreases, \(V_R\) increases. Lower density air gives less lift per unit of speed, so you need more speed to rotate. Now, in modern airliners, you don't actually sit there reading speed tables. \(V_R\) is computed by the aeroplane itself. Once the relevant data is entered into the flight management computer — or the multipurpose computer display unit — the system calculates \(V_1\) and \(V_R\). The pilots then enter those values into the Flight Management System, and they're displayed on the speed scale on the left-hand side of the Primary Flight Display, or PFD — also known as the Electronic Attitude Director Indicator, the EADI. So to summarise the three factors: mass up means \(V_R\) up; flap up means \(V_R\) down; density down means \(V_R\) up. And the actual computation in the cockpit is done by the flight management computer, with the result shown on the PFD speed scale.