Reality check

Meeting friends for lunch at an out-of-the-way airport, perhaps featuring a short grass strip with an interesting approach, tops my list of fun day trips. But summer also brings hotter temperatures and, accordingly, longer landing distances and takeoff runs. So, it’s not unusual to say goodbye to friends and depart a short runway surrounded by tall trees and high terrain during the worst heat of the afternoon.

While we should consult the aircraft operating handbook to ensure the runway length is sufficient, given the current atmospheric and weight conditions, it’s imperative to know how to make a go/no-go call during the takeoff run if things just don’t seem right. Early in my aviation career, I heard advice to ensure safety with such a departure: If the airplane has not reached 70 percent of its rotation speed by the time 50 percent of the runway has been used, abort the takeoff.

The 70-50 rule seems universally touted by many organizations that promote aviation safety. For years I wondered how this rule of thumb was generated but have never been able to trace its source. I surmised that it must emanate from a mathematical model constructed using the important forces during the takeoff roll and decided to explore potential models that might culminate in such a rule.

The modeling process often starts with the most basic assumptions and generates a rule that is then tested to see how well it represents what we observe. If it falls short, we add just enough assumptions (and therefore complexity to the model) until it represents the physical situation well. Ideally the model is realistic but simple enough to extract rules of thumb we can use.

Even if this model were correct, performance that barely results in a "'go" decision means the wheels would lift off in the last foot of runway. Any way you slice it, the 70-50 rule is just plain dangerous.For example, we can set up a model that describes the growth of rabbit populations. Assume that when two rabbits mate they produce six kits (baby rabbits), three of each gender. After four months, each of the three pairs breeds again and produces another six kits. In the short term, this model may seem reasonable. But, if this process continues, it will take less than 60 years for the number of kits born in a cycle to surpass the number of atoms in the universe and that’s just silly. We would then update the model to include a mechanism by which procreation dwindles as access to food supply wanes. The new model will feature a population carrying capacity—an upper limit to the number of rabbits that can exist given the ability of the ecosystem to support them.

In an analogous way, we can construct a model that represents Niky beginning the takeoff roll on the runway. The most basic one involves the assumption that the engine produces constant thrust and ignores any other forces that might be at play. In this case, we find the velocity will be a linear function of time: if the aircraft is traveling at 10 knots, five seconds into the takeoff roll, it will be at 20 knots after 10 seconds. Taking it further reveals the inadequacies of the model: After one minute, Niky is at 120 knots and in a few more the airplane will approach and pass the speed of sound—a preposterous idea.

It’s clear that introducing drag caused by air resistance is an important feature for the model. The faster Niky moves, the higher the penalty air resistance will exact. Updating the model accordingly produces a new one with a terminal velocity, the analog of a carrying capacity for rabbit populations. This terminal velocity—the top speed given a specific set of atmospheric conditions—is consistent with that found in the pilot’s operating handbook. This second model is far more realistic and can shed light on takeoff performance.

Let’s get back to the rule of thumb for takeoffs. What really matters here is not how the Bonanza develops speed with respect to time but how its speed increases as a function of distance along the runway. Returning to the more basic of the two models, it’s not hard to show that it implies that speed is proportional to the square root of the distance traveled along the runway. That means in order to reach the rotation speed by the end of the runway, you should have about 70 percent of the rotation speed when the aircraft reaches the 50-percent mark along the runway.

It seems that 70-50 rule is extracted from the most basic and unrealistic model for aircraft takeoffs that ignores air resistance. The same model that predicts my Bonanza goes supersonic is the one that pilots use to make the go/no-go decision along the runway.

Exploring the updated model that incorporates air resistance shows that achieving rotation speed by the end of the runway can require significantly more than 70 percent of rotation speed at the halfway point.

Is there an X-Y rule that can be salvaged using the updated model? This model incorporates air resistance and an engine that produces constant thrust during the takeoff roll. But propeller-driven aircraft produce less thrust as speed increases and you likely know this from your own experience: When you first apply takeoff manifold pressure, your back is pressed into your seat as the aircraft accelerates, but by the time you rotate you don’t feel such pressure anymore. Therefore, it turns out that even the updated model would produce a rule of thumb that is overly optimistic.

Even if you find this modeling discussion less than compelling, there are other arguments for ditching the rule. For example, if I attempt a takeoff from a 10,000-foot-long runway the rule says that as long as I have 70 percent of my 70-knot rotation speed, or 49 knots, I should develop enough speed to rotate by the end. But if Niky has only reached 49 knots after 5,000 feet of runway, something is seriously wrong with her. Furthermore, even if this model were correct, performance that barely results in a “go” decision at the halfway point means the wheels would lift off in the last foot of runway with no margin for error. Any way you slice it, the 70-50 rule is just plain dangerous.

What should we do to ensure safety in such a takeoff scenario? The only X-Y thumb rule that makes any sense is when X=100. Use your takeoff performance chart to determine your anticipated takeoff distance and pad it with a value that represents degraded performance, varying pilot technique, and an engine that isn’t new. Find a point along the runway—maybe a taxiway, windsock, or similar landmark—and use this as the abort point. And don’t even attempt the takeoff if the runway isn’t longer than your computed distance plus additional necessary to safely bring the airplane to a stop.

Perhaps the 70-50 rule conveys a sense of legitimacy because it sounds rooted in science. But piercing that thin veneer reveals a rule generated from an overly simplistic model that falls well short of reality. Rules of thumb can be helpful but it’s important that pilots view them critically to ensure they are safe.