Class A Aircraft - Take-off — Page 395, Lesson 489

Let’s pick this up right where the take-off performance story gets interesting — the brake energy limit. Here’s the physics in one line: for an aircraft of mass M travelling at a true speed V, the kinetic energy is ½ M V². That’s the energy the aircraft carries because it’s moving. Now, if you reject the take-off and brake to a stop from that speed, a large proportion of that energy goes into the brakes as heat. The brakes have a limited energy capacity — they can only absorb so much heat before they degrade or fail. So, for a given mass, there is a limiting speed from which a stop can be made. That speed is called the brake energy limit speed, and its symbol is VMBE. Now, a crucial detail: VMBE is a True Ground Speed. That means the corresponding Indicated Airspeed — the IAS you actually read on the instrument — will vary with altitude, temperature, and wind. Why? Because true speed and indicated speed differ with air density, and ground speed differs with wind. So the IAS that corresponds to VMBE is not a fixed number — it shifts as conditions change. Runway slope also affects the speed, because a change in height involves a change in potential energy. If the runway slopes, part of the aircraft’s energy is gravitational, not just kinetic, and that changes the stopping problem. Here’s the operating rule: the brake energy limit speed VMBE must not be less than the V1 speed. V1, remember, is the decision speed — the speed beyond which you must continue the take-off because you can no longer stop safely on the remaining runway. If VMBE is less than V1, that means you physically cannot stop from V1 without overheating the brakes. So the mass must be reduced until V1 and VMBE are the same. The flight manual will give you the amount of weight to be deducted for each knot that V1 exceeds VMBE — a specific weight-per-knot penalty. Now, practically speaking, for most aircraft VMBE will only be limiting in extremely adverse conditions — high altitude, high temperature, strong wind, or an unfavourable runway slope. In fact, if you look at Figure 14.14, you’ll notice a grey area in the graph on the top left-hand side. If the mass and pressure altitude fall within that grey area, then VMBE will not be limiting — unless you’re operating with a tailwind or using improved climb performance. Those two conditions change the picture and can bring VMBE back into play. The same graph appears in CAP 698, on page 15 of section 4. Now, there’s a second layer to this — brake cooling. The value of VMBE you get from the data assumes the brakes are at ambient temperature before the start of take-off. That’s the baseline assumption. But if a take-off is rejected following a recent landing, or after prolonged taxiing, the brakes will already be at a fairly high temperature. Their ability to absorb further energy is reduced — hot brakes can’t take as much additional heat. So the manual gives data showing the time to be allowed for the brakes to cool before you can rely on the full VMBE again. An example of a brake cooling graph is shown in Figure 14.15, and it can also be found in CAP 698 on page 50 of section 4. So, to tie it together: VMBE is a true ground speed limit set by brake energy capacity, it must never be below V1, you fix a violation by reducing mass at a known weight-per-knot rate, and the whole calculation assumes cold brakes — so after a rejected take-off or long taxi, you must consult the cooling schedule before you can treat VMBE as valid again.