Let's pick this up right where the asymmetric yaw problem leaves us — Page 379, Lesson 461

Let's pick this up right where the asymmetric yaw problem leaves us. We've got an engine failure on take-off, and the aeroplane wants to swing. In the air, you'd use the ailerons and the rudder together to steer. But on the ground, that's a different story. Here's the critical point: when the aeroplane is on the ground, you cannot use the ailerons to control the yaw. Why? Because if you deflect the ailerons, you might bank the wing into the ground. So the only aerodynamic surface left to control that asymmetric yaw is the rudder. Now, for the rudder to actually be effective at controlling the yaw, there must be sufficient airflow over it to generate the required aerodynamic force. This minimum airflow speed over the rudder is called VMCG — that's the minimum control speed on the ground. If the engine were to fail below this speed, there is insufficient flow over the rudder to counteract the asymmetric yaw, and therefore it is not possible to continue the take-off. That's the whole point of VMCG — it's the speed below which you simply cannot keep the aeroplane straight on the ground with the rudder alone. Now, what controls the value of VMCG? The only factor is thrust. And since take-off thrust is more or less constant, the only variable on the amount of take-off thrust generated is air density. Let me walk you through that chain of cause and effect. The higher the air density, the more thrust that can be generated. More thrust means more yaw is generated when the engine fails. Therefore, the airflow over the rudder must be faster to make the rudder effective enough to counteract that yaw. So higher density pushes VMCG up. You can see this effect of air density on VMCG by looking at the second table from the bottom on pages 18 and 19 of section 4 in CAP 698. That table has temperature on one side and pressure altitude on the other. Look at the VMCG values in the table and you'll notice that at low temperatures and low pressure altitudes — where the air density would be high — the value of VMCG is also high. So the rule is simple: as density increases, VMCG increases. That's the relationship you need to hold onto. VMCG is the minimum control speed on the ground, it's governed by thrust, and thrust is governed by air density. Dense air means more thrust, more yaw, and a higher VMCG.