So the only aerodynamic surface left to fight the asymmetric yaw is the rudder — Page 379, Lesson 461

Let’s pick this up right where the action is: you’re rolling down the runway, an engine fails, and you’re trying to keep the aeroplane straight. In the air you’d have the ailerons and the rudder to steer with, but on the ground you can’t use the ailerons for yaw control — if you did, you’d bank the wing into the ground. So the only aerodynamic surface left to fight the asymmetric yaw is the rudder. Now, the rudder only works if there’s enough airflow over it to generate the aerodynamic force it needs. That minimum airflow speed over the rudder is called VMCG — the minimum control speed on the ground. If the engine fails below VMCG, there simply isn’t enough airflow over the rudder to counteract the asymmetric yaw, and you cannot continue the take-off. Here’s the key point: the only factor that controls the value of VMCG is thrust. Take-off thrust is more or less constant, so the only variable affecting the amount of take-off thrust generated is air density. Higher air density means more thrust can be generated, which means more yaw when the engine fails — so the airflow over the rudder must be faster to make the rudder effective enough to counteract that yaw. You can see this effect in 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: at low temperatures and low pressure altitudes, where air density is high, VMCG is also high. So the relationship is direct — as density increases, VMCG increases.